TSTP Solution File: SWW337+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW337+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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 12:25:59 EDT 2023

% Result   : Theorem 45.81s 45.06s
% Output   : Proof 45.81s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW337+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 22:40:59 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 45.81/45.06  
% 45.81/45.06  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 45.81/45.06  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.81/45.06  %-----------------------------------------------------
% 45.81/45.06  ncf(matrix, plain, [(52833 ^ _2095419) ^ [_2095436] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), _2095436), v_G)), -(c_Hoare__Mirabelle_Otriple__valid(t_a, 52831 ^ [], _2095436))], (52842 ^ _2095419) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(t_a, 52831 ^ [], 52838 ^ [])], (52840 ^ _2095419) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), 52838 ^ []), v_ts)))], !, (2172 ^ _781404) ^ [_812900, _812902, _812904, _812906, _812908, _812910, _812912, _812914] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_812914, _812910, _812906, _812902) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_812912, _812908, _812904, _812900)), _812914 = _812912, _812910 = _812908, _812906 = _812904, _812902 = _812900], (23607 ^ _781404) ^ [_1205398, _1205400] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205398), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205400)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1205398, _1205400)))], (37396 ^ _781404) ^ [_1484830, _1484832, _1484834, _1484836, _1484838, _1484840] : [-(hAPP(c_Relation_OImage(_1484830, _1484832, _1484834), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484836, tc_fun(_1484830, tc_HOL_Obool)), _1484838), _1484840)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484836, tc_fun(_1484832, tc_HOL_Obool)), _1484838), hAPP(hAPP(c_COMBB(tc_fun(_1484830, tc_HOL_Obool), tc_fun(_1484832, tc_HOL_Obool), _1484836), c_Relation_OImage(_1484830, _1484832, _1484834)), _1484840)))], (12945 ^ _781404) ^ [_1006034, _1006036, _1006038, _1006040, _1006042, _1006044] : [-(_1006034 = _1006036), -(hAPP(c_Fun_Ofun__upd(_1006038, _1006040, _1006042, _1006036, _1006044), _1006034) = hAPP(_1006042, _1006034))], (22899 ^ _781404) ^ [_1190826, _1190828] : [-(_1190826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1190828), _1190826) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1190828), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1190828), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1190826), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (12716 ^ _781404) ^ [_1001411, _1001413, _1001415, _1001417, _1001419] : [-(hBOOL(hAPP(hAPP(c_member(_1001411), _1001413), c_SetInterval_Oord_OatLeastAtMost(_1001411, _1001415, _1001417, _1001419)))), hBOOL(hAPP(hAPP(_1001415, _1001417), _1001413)), hBOOL(hAPP(hAPP(_1001415, _1001413), _1001419))], (12708 ^ _781404) ^ [_1001262, _1001264, _1001266, _1001268, _1001270] : [hBOOL(hAPP(hAPP(c_member(_1001262), _1001264), c_SetInterval_Oord_OatLeastAtMost(_1001262, _1001266, _1001268, _1001270))), 12711 ^ _781404 : [(12714 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1001266, _1001264), _1001270)))], (12712 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1001266, _1001268), _1001264)))]]], (39061 ^ _781404) ^ [_1527930, _1527932, _1527934, _1527936] : [hBOOL(hAPP(hAPP(c_member(_1527930), _1527932), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1527930, tc_HOL_Obool)), _1527934), hAPP(c_Set_OCollect(_1527930), _1527936)))), 39064 ^ _781404 : [(39067 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1527936, _1527932)))], (39065 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527930), _1527932), _1527934)))]]], (14520 ^ _781404) ^ [_1035786, _1035788] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035786), _1035788) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035788), _1035786))], (51738 ^ _781404) ^ [_1828998, _1829000, _1829002] : [class_Divides_Osemiring__div(_1828998), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828998), _1829000), _1829002)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828998), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1828998), _1829002), _1829000)), _1829000) = _1829002)], (39081 ^ _781404) ^ [_1528405, _1528407, _1528409] : [hBOOL(hAPP(_1528405, _1528407)), -(hAPP(c_Set_OCollect(_1528409), hAPP(hAPP(c_COMBS(_1528409, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1528409), c_fconj), hAPP(hAPP(c_COMBC(_1528409, _1528409, tc_HOL_Obool), c_fequal), _1528407))), _1528405)) = hAPP(hAPP(c_Set_Oinsert(_1528409), _1528407), c_Orderings_Obot__class_Obot(tc_fun(_1528409, tc_HOL_Obool))))], (47479 ^ _781404) ^ [_1735897, _1735899] : [-(hAPP(c_List_Orev(_1735897), c_List_Oconcat(_1735897, _1735899)) = c_List_Oconcat(_1735897, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1735897), tc_List_Olist(_1735897)), c_List_Orev(_1735897)), hAPP(c_List_Orev(tc_List_Olist(_1735897)), _1735899))))], (17381 ^ _781404) ^ [] : [-(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))))], (46131 ^ _781404) ^ [_1707061, _1707063] : [hBOOL(hAPP(c_List_Odistinct(_1707061), _1707063)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1707061, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707061), tc_fun(_1707061, tc_HOL_Obool)), c_List_Oset(_1707061)), c_Enum_Osublists(_1707061, _1707063)))))], (36292 ^ _781404) ^ [_1458953, _1458955, _1458957, _1458959, _1458961, _1458963] : [c_Finite__Set_Ofolding(_1458953, _1458955, _1458957, _1458959), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458953), _1458961)), hBOOL(hAPP(hAPP(c_member(_1458953), _1458963), _1458961)), -(hAPP(_1458959, _1458961) = hAPP(c_Fun_Ocomp(_1458955, _1458955, _1458955, hAPP(_1458959, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1458953, tc_HOL_Obool)), _1458961), hAPP(hAPP(c_Set_Oinsert(_1458953), _1458963), c_Orderings_Obot__class_Obot(tc_fun(_1458953, tc_HOL_Obool)))))), hAPP(_1458957, _1458963)))], (21611 ^ _781404) ^ [_1165631, _1165633, _1165635, _1165637] : [class_Rings_Olinordered__ring__strict(_1165631), 21614 ^ _781404 : [(21629 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165631), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165631), _1165633), _1165635)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165631), _1165637), _1165635)))), 21630 ^ _781404 : [(21637 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165631), _1165635), c_Groups_Ozero__class_Ozero(_1165631))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165631), _1165637), _1165633))], (21631 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165631), c_Groups_Ozero__class_Ozero(_1165631)), _1165635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165631), _1165633), _1165637))]]], (21615 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165631), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165631), _1165633), _1165635)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165631), _1165637), _1165635))), 21620 ^ _781404 : [(21623 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165631), _1165633), _1165637)))], (21621 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165631), c_Groups_Ozero__class_Ozero(_1165631)), _1165635)))]], 21624 ^ _781404 : [(21627 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165631), _1165637), _1165633)))], (21625 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165631), _1165635), c_Groups_Ozero__class_Ozero(_1165631))))]]]]], (40966 ^ _781404) ^ [_1581302, _1581304, _1581306, _1581308] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1581302, _1581304, _1581306, tc_prod(_1581304, _1581306)), _1581308), c_Product__Type_OPair(_1581304, _1581306)) = _1581308)], (14550 ^ _781404) ^ [_1036369, _1036371, _1036373, _1036375] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1036369), _1036371)), 14553 ^ _781404 : [(14554 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1036373), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1036369, tc_fun(_1036373, tc_HOL_Obool)), _1036371), _1036375))), 14557 ^ _781404 : [(14558 ^ _781404) ^ [_1036553] : [hBOOL(hAPP(hAPP(c_member(_1036369), _1036553), _1036371)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1036373), hAPP(_1036375, _1036553))))]]], (14564 ^ _781404) ^ [] : [14566 ^ _781404 : [(14569 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1036373), hAPP(_1036375, 14565 ^ [_1036369, _1036371, _1036373, _1036375])))], (14567 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1036369), 14565 ^ [_1036369, _1036371, _1036373, _1036375]), _1036371)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1036373), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1036369, tc_fun(_1036373, tc_HOL_Obool)), _1036371), _1036375))))]]], (27787 ^ _781404) ^ [_1278468, _1278470] : [class_Rings_Odivision__ring(_1278468), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278468), _1278470), c_Groups_Oone__class_Oone(_1278468)) = _1278470)], (50227 ^ _781404) ^ [_1796490, _1796492, _1796494] : [c_Relation_Osym(_1796490, _1796492), c_Relation_Osym(_1796490, _1796494), -(c_Relation_Osym(_1796490, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1796490, _1796490), tc_HOL_Obool)), _1796492), _1796494)))], (47105 ^ _781404) ^ [_1728318, _1728320, _1728322, _1728324] : [class_Orderings_Olinorder(_1728318), -(c_List_Olinorder__class_Osorted(_1728318, hAPP(hAPP(c_List_Omap(_1728320, _1728318), _1728322), c_List_Olinorder__class_Osort__key(_1728320, _1728318, _1728322, _1728324))))], (29739 ^ _781404) ^ [_1314108, _1314110, _1314112, _1314114] : [class_Fields_Olinordered__field(_1314108), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314108), _1314110), c_Groups_Ozero__class_Ozero(_1314108))), 29746 ^ _781404 : [(29753 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314108), _1314114), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1314108), _1314112), _1314110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314108), _1314112), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314108), _1314114), _1314110))))], (29747 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314108), _1314112), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314108), _1314114), _1314110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314108), _1314114), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1314108), _1314112), _1314110))))]]], (10491 ^ _781404) ^ [_960006, _960008, _960010] : [10492 ^ _781404 : [(10495 ^ _781404) ^ [] : [_960008 = _960010], (10493 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960006, tc_HOL_Obool)), _960008), _960010))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960006, tc_HOL_Obool)), _960008), _960010)))], (39754 ^ _781404) ^ [_1554206, _1554208, _1554210, _1554212, _1554214, _1554216, _1554218, _1554220] : [hBOOL(hAPP(hAPP(_1554206, _1554208), _1554210)), hBOOL(hAPP(hAPP(_1554212, _1554210), _1554214)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1554216, _1554218, _1554220, _1554206, _1554212), _1554208), _1554214)))], (25281 ^ _781404) ^ [_1233665] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233665))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27781 ^ _781404) ^ [_1278339, _1278341, _1278343] : [class_Rings_Odivision__ring(_1278339), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1278339), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278339), _1278341), _1278343)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278339), hAPP(c_Groups_Ouminus__class_Ouminus(_1278339), _1278341)), _1278343))], (51373 ^ _781404) ^ [_1821560, _1821562, _1821564, _1821566] : [51376 ^ _781404 : [(51379 ^ _781404) ^ [] : [hAPP(_1821564, 51374 ^ [_1821560, _1821562, _1821564, _1821566]) = hAPP(_1821564, 51375 ^ [_1821560, _1821562, _1821564, _1821566])], (51377 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1821560, _1821560)), hAPP(hAPP(c_Product__Type_OPair(_1821560, _1821560), 51374 ^ [_1821560, _1821562, _1821564, _1821566]), 51375 ^ [_1821560, _1821562, _1821564, _1821566])), _1821562)))]], -(c_Equiv__Relations_Ocongruent(_1821560, _1821566, _1821562, _1821564))], (44343 ^ _781404) ^ [_1667689, _1667691] : [hBOOL(hAPP(c_List_Odistinct(_1667689), _1667691)), -(hBOOL(hAPP(c_List_Odistinct(_1667689), hAPP(c_List_Orotate1(_1667689), _1667691))))], (33550 ^ _781404) ^ [_1392232, _1392234, _1392236, _1392238, _1392240, _1392242] : [-(hAPP(c_Set_Ovimage(_1392232, _1392234, _1392236), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392238, tc_fun(_1392234, tc_HOL_Obool)), _1392240), _1392242)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392238, tc_fun(_1392232, tc_HOL_Obool)), _1392240), hAPP(hAPP(c_COMBB(tc_fun(_1392234, tc_HOL_Obool), tc_fun(_1392232, tc_HOL_Obool), _1392238), c_Set_Ovimage(_1392232, _1392234, _1392236)), _1392242)))], (17941 ^ _781404) ^ [_1101382] : [-(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)), _1101382))))], (45349 ^ _781404) ^ [_1689638, _1689640, _1689642, _1689644, _1689646] : [c_Fun_Oinj__on(_1689638, _1689640, _1689642, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1689638, tc_HOL_Obool)), hAPP(c_List_Oset(_1689638), _1689644)), hAPP(c_List_Oset(_1689638), _1689646))), 45352 ^ _781404 : [(45359 ^ _781404) ^ [] : [_1689644 = _1689646, -(hAPP(hAPP(c_List_Omap(_1689638, _1689640), _1689642), _1689644) = hAPP(hAPP(c_List_Omap(_1689638, _1689640), _1689642), _1689646))], (45353 ^ _781404) ^ [] : [hAPP(hAPP(c_List_Omap(_1689638, _1689640), _1689642), _1689644) = hAPP(hAPP(c_List_Omap(_1689638, _1689640), _1689642), _1689646), -(_1689644 = _1689646)]]], (25559 ^ _781404) ^ [_1238068, _1238070] : [25560 ^ _781404 : [(25563 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238070))], (25561 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238068))]], 25564 ^ _781404 : [(25571 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1238068), _1238070)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1238068)), hAPP(c_Int_Onat, _1238070))))], (25565 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1238068)), hAPP(c_Int_Onat, _1238070))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1238068), _1238070)))]]], (45325 ^ _781404) ^ [_1689011] : [-(hAPP(c_List_Omap(_1689011, _1689011), c_COMBI(_1689011)) = c_Fun_Oid(tc_List_Olist(_1689011)))], (40154 ^ _781404) ^ [_1563110, _1563112, _1563114, _1563116] : [hBOOL(hAPP(hAPP(c_member(_1563110), _1563112), hAPP(c_Relation_ODomain(_1563110, _1563114), _1563116))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563110, _1563114)), hAPP(hAPP(c_Product__Type_OPair(_1563110, _1563114), _1563112), 40157 ^ [_1563110, _1563112, _1563114, _1563116])), _1563116)))], (34817 ^ _781404) ^ [_1428540, _1428542] : [hAPP(c_Nat_OSuc, _1428540) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428542), -(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(_1428542))), 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)), _1428540))))))], (36116 ^ _781404) ^ [_1455382, _1455384, _1455386] : [36118 ^ _781404 : [(36121 ^ _781404) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1455386, 36117 ^ [_1455382, _1455384, _1455386]))], (36119 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1455382), 36117 ^ [_1455382, _1455384, _1455386]), _1455384)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1455382, tc_Int_Oint), _1455386), _1455384) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1455382, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1455382), c_Int_Onat), _1455386)), _1455384)))], (45483 ^ _781404) ^ [_1692672, _1692674] : [hAPP(c_Code__Numeral_Oof__nat, _1692672) = hAPP(c_Code__Numeral_Oof__nat, _1692674), -(_1692672 = _1692674)], (50332 ^ _781404) ^ [_1798108, _1798110] : [50333 ^ _781404 : [(50334 ^ _781404) ^ [_1798164] : [hBOOL(hAPP(hAPP(_1798108, _1798164), _1798164))]], c_Predicate_Osymp(_1798110, _1798108), c_Predicate_Otransp(_1798110, _1798108), -(c_Equiv__Relations_Opart__equivp(_1798110, _1798108))], (39317 ^ _781404) ^ [_1536924, _1536926, _1536928] : [class_Groups_Olinordered__ab__semigroup__add(_1536924), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536924), _1536926)), -(_1536926 = c_Orderings_Obot__class_Obot(tc_fun(_1536924, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1536924), _1536928), c_Big__Operators_Olinorder__class_OMax(_1536924, _1536926)) = c_Big__Operators_Olinorder__class_OMax(_1536924, hAPP(c_Set_OCollect(_1536924), hAPP(hAPP(c_COMBB(tc_fun(_1536924, tc_HOL_Obool), tc_HOL_Obool, _1536924), c_HOL_OEx(_1536924)), hAPP(hAPP(c_COMBC(_1536924, tc_fun(_1536924, tc_HOL_Obool), tc_fun(_1536924, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536924, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1536924, tc_HOL_Obool), tc_fun(_1536924, tc_HOL_Obool)), _1536924), c_COMBS(_1536924, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536924, tc_HOL_Obool), tc_fun(_1536924, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1536924), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536924), c_fconj)), hAPP(hAPP(c_COMBC(_1536924, tc_fun(_1536924, _1536924), tc_fun(_1536924, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536924, tc_HOL_Obool), tc_fun(tc_fun(_1536924, _1536924), tc_fun(_1536924, tc_HOL_Obool)), _1536924), c_COMBB(_1536924, tc_HOL_Obool, _1536924)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1536924), _1536928))))), hAPP(hAPP(c_COMBC(_1536924, tc_fun(_1536924, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536924)), _1536926))))))], (41177 ^ _781404) ^ [_1587324, _1587326] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587324, _1587324), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1587324, _1587326)), c_Relation_OId(_1587324)) = c_Transitive__Closure_Ortrancl(_1587324, _1587326))], (21213 ^ _781404) ^ [_1158410, _1158412] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1158410)), _1158412) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158410), _1158412)))], (38002 ^ _781404) ^ [_1499910, _1499912, _1499914, _1499916] : [38004 ^ _781404 : [(38007 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1499910, _1499910, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1499910, tc_fun(_1499910, _1499912), tc_fun(_1499910, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499912, tc_HOL_Obool), tc_fun(tc_fun(_1499910, _1499912), tc_fun(_1499910, tc_HOL_Obool)), _1499910), c_COMBB(_1499912, tc_HOL_Obool, _1499910)), hAPP(hAPP(c_COMBB(_1499912, tc_fun(_1499912, tc_HOL_Obool), _1499910), c_fequal), _1499916))), _1499916)), 38003 ^ [_1499910, _1499912, _1499914, _1499916]))], (38005 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1499910, _1499910)), 38003 ^ [_1499910, _1499912, _1499914, _1499916]), _1499914)))]], -(c_Equiv__Relations_Ocongruent(_1499910, _1499912, _1499914, _1499916))], (33305 ^ _781404) ^ [_1384016, _1384018, _1384020, _1384022, _1384024] : [_1384016 = c_Orderings_Obot__class_Obot(tc_fun(_1384018, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384020, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384018, tc_fun(_1384020, tc_HOL_Obool)), _1384016), _1384022)), _1384024) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384020, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1384020, tc_HOL_Obool))), _1384024))], (46892 ^ _781404) ^ [_1724724, _1724726, _1724728] : [46893 ^ _781404 : [(46896 ^ _781404) ^ [] : [_1724728 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46894 ^ _781404) ^ [] : [-(_1724724 = c_List_Olist_ONil(tc_List_Olist(_1724726)))]], 46900 ^ _781404 : [(46903 ^ _781404) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724726)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1724726)), _1724724), 46899 ^ [_1724724, _1724726, _1724728])) = _1724728], (46901 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46899 ^ [_1724724, _1724726, _1724728]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1724726))), _1724724))))]], -(c_List_Otranspose(_1724726, _1724724) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1724726)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1724726)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1724726), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1724726)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1724726)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1724726), hAPP(hAPP(c_COMBB(tc_List_Olist(_1724726), tc_fun(tc_Nat_Onat, _1724726), tc_Nat_Onat), c_List_Onth(_1724726)), hAPP(c_List_Onth(tc_List_Olist(_1724726)), _1724724))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1724726))), _1724724)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1724728)))], (1436 ^ _781404) ^ [_802394, _802396] : [-(class_Lattices_Obounded__lattice__top(_802394)), _802396 = _802394, class_Lattices_Obounded__lattice__top(_802396)], (11001 ^ _781404) ^ [_968231, _968233] : [class_Groups_Oordered__ab__group__add(_968231), 11004 ^ _781404 : [(11011 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968231), _968233), c_Groups_Ozero__class_Ozero(_968231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968231), c_Groups_Ozero__class_Ozero(_968231)), hAPP(c_Groups_Ouminus__class_Ouminus(_968231), _968233))))], (11005 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968231), c_Groups_Ozero__class_Ozero(_968231)), hAPP(c_Groups_Ouminus__class_Ouminus(_968231), _968233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968231), _968233), c_Groups_Ozero__class_Ozero(_968231))))]]], (37914 ^ _781404) ^ [_1498122] : [-(c_Equiv__Relations_Oequivp(_1498122, c_fequal))], (16798 ^ _781404) ^ [_1080580, _1080582, _1080584, _1080586, _1080588] : [class_Groups_Ocomm__monoid__add(_1080580), class_Groups_Oordered__cancel__ab__semigroup__add(_1080580), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080582), _1080584)), -(_1080584 = c_Orderings_Obot__class_Obot(tc_fun(_1080582, tc_HOL_Obool))), 16816 ^ _781404 : [(16819 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080580), hAPP(_1080586, 16815 ^ [_1080580, _1080582, _1080584, _1080586, _1080588])), hAPP(_1080588, 16815 ^ [_1080580, _1080582, _1080584, _1080586, _1080588])))], (16817 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1080582), 16815 ^ [_1080580, _1080582, _1080584, _1080586, _1080588]), _1080584)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080580), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080582, _1080580), _1080586), _1080584)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080582, _1080580), _1080588), _1080584))))], (47169 ^ _781404) ^ [_1729567, _1729569, _1729571] : [class_Orderings_Olinorder(_1729567), 47172 ^ _781404 : [(47185 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1729567, hAPP(hAPP(c_List_Olist_OCons(_1729567), _1729569), _1729571))), c_List_Olinorder__class_Osorted(_1729567, _1729571), 47191 ^ _781404 : [(47194 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1729567), _1729569), 47190 ^ [_1729567, _1729569, _1729571]))], (47192 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1729567), 47190 ^ [_1729567, _1729569, _1729571]), hAPP(c_List_Oset(_1729567), _1729571))))]]], (47173 ^ _781404) ^ [] : [c_List_Olinorder__class_Osorted(_1729567, hAPP(hAPP(c_List_Olist_OCons(_1729567), _1729569), _1729571)), 47176 ^ _781404 : [(47179 ^ _781404) ^ [_1729753] : [hBOOL(hAPP(hAPP(c_member(_1729567), _1729753), hAPP(c_List_Oset(_1729567), _1729571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1729567), _1729569), _1729753)))], (47177 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1729567, _1729571))]]]]], (19247 ^ _781404) ^ [_1123669] : [-(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), _1123669))))], (34437 ^ _781404) ^ [_1419430, _1419432, _1419434, _1419436] : [-(hAPP(c_Set_Oimage(_1419430, _1419432, _1419434), _1419436) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419430, tc_fun(_1419432, tc_HOL_Obool)), _1419436), hAPP(hAPP(c_COMBC(_1419430, tc_fun(_1419432, tc_HOL_Obool), tc_fun(_1419432, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1419432, tc_fun(tc_fun(_1419432, tc_HOL_Obool), tc_fun(_1419432, tc_HOL_Obool)), _1419430), c_Set_Oinsert(_1419432)), _1419434)), c_Orderings_Obot__class_Obot(tc_fun(_1419432, tc_HOL_Obool)))))], (30910 ^ _781404) ^ [_1337037, _1337039, _1337041] : [class_Int_Onumber(_1337037), class_Orderings_Oord(_1337037), 30917 ^ _781404 : [(30924 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337037), hAPP(c_Int_Onumber__class_Onumber__of(_1337037), _1337039)), hAPP(c_Int_Onumber__class_Onumber__of(_1337037), _1337041)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1337037), hAPP(c_Int_Onumber__class_Onumber__of(_1337037), _1337039)), hAPP(c_Int_Onumber__class_Onumber__of(_1337037), _1337041)) = hAPP(c_Int_Onumber__class_Onumber__of(_1337037), _1337041))], (30918 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337037), hAPP(c_Int_Onumber__class_Onumber__of(_1337037), _1337039)), hAPP(c_Int_Onumber__class_Onumber__of(_1337037), _1337041))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1337037), hAPP(c_Int_Onumber__class_Onumber__of(_1337037), _1337039)), hAPP(c_Int_Onumber__class_Onumber__of(_1337037), _1337041)) = hAPP(c_Int_Onumber__class_Onumber__of(_1337037), _1337039))]]], (32464 ^ _781404) ^ [_1366155, _1366157, _1366159] : [class_Orderings_Olinorder(_1366155), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366155), _1366157)), -(c_Big__Operators_Olinorder__class_OMax(_1366155, hAPP(hAPP(c_Set_Oinsert(_1366155), _1366159), _1366157)) = hAPP(hAPP(c_Finite__Set_Ofold(_1366155, _1366155, c_Orderings_Oord__class_Omax(_1366155)), _1366159), _1366157))], (46217 ^ _781404) ^ [_1709032, _1709034] : [hBOOL(hAPP(c_List_Odistinct(_1709032), _1709034)), -(c_List_Oremdups(_1709032, _1709034) = _1709034)], (52460 ^ _781404) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (33827 ^ _781404) ^ [_1399983, _1399985, _1399987] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399983, tc_Nat_Onat), _1399985), _1399987)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399983, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1399983), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1399985)), _1399987))], (34953 ^ _781404) ^ [_1431691, _1431693] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431691)), hAPP(c_Nat_OSuc, _1431693)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1431691))), 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, _1431693))), 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)), _1431693)))))], (9134 ^ _781404) ^ [_936494, _936496, _936498, _936500] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936494, tc_HOL_Obool)), _936496), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936494, tc_HOL_Obool)), _936498), _936500)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936494, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936494, tc_HOL_Obool)), _936496), _936498)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936494, tc_HOL_Obool)), _936496), _936500)))], (34175 ^ _781404) ^ [_1410303, _1410305, _1410307, _1410309, _1410311, _1410313] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1410303, _1410305)), hAPP(hAPP(c_Product__Type_OPair(_1410303, _1410305), _1410311), _1410313)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool)), _1410307), _1410309))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410303, tc_fun(_1410305, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1410303, tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_fun(_1410305, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410305, tc_fun(tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_fun(_1410305, tc_HOL_Obool)), _1410303), c_COMBC(_1410305, tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410305, tc_prod(_1410303, _1410305)), tc_fun(_1410305, tc_fun(tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_HOL_Obool)), _1410303), hAPP(c_COMBB(tc_prod(_1410303, _1410305), tc_fun(tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_HOL_Obool), _1410305), c_member(tc_prod(_1410303, _1410305)))), c_Product__Type_OPair(_1410303, _1410305)))), _1410307)), hAPP(hAPP(c_COMBC(_1410303, tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_fun(_1410305, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410305, tc_fun(tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_fun(_1410305, tc_HOL_Obool)), _1410303), c_COMBC(_1410305, tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410305, tc_prod(_1410303, _1410305)), tc_fun(_1410305, tc_fun(tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_HOL_Obool)), _1410303), hAPP(c_COMBB(tc_prod(_1410303, _1410305), tc_fun(tc_fun(tc_prod(_1410303, _1410305), tc_HOL_Obool), tc_HOL_Obool), _1410305), c_member(tc_prod(_1410303, _1410305)))), c_Product__Type_OPair(_1410303, _1410305)))), _1410309)), _1410311), _1410313)))], (50151 ^ _781404) ^ [_1795113, _1795115] : [c_Relation_Osym(_1795113, _1795115), 50154 ^ _781404 : [(50155 ^ _781404) ^ [_1795219, _1795221] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1795113, _1795113)), hAPP(hAPP(c_Product__Type_OPair(_1795113, _1795113), _1795221), _1795219)), _1795115)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1795113, _1795113)), hAPP(hAPP(c_Product__Type_OPair(_1795113, _1795113), _1795219), _1795221)), _1795115)))]]], (14717 ^ _781404) ^ [_1039482, _1039484] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1039482, tc_HOL_Obool)), hAPP(c_Set_OPow(_1039482), _1039484))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039482), _1039484)))], (32224 ^ _781404) ^ [_1361372, _1361374, _1361376, _1361378] : [class_Orderings_Olinorder(_1361372), 32227 ^ _781404 : [(32236 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361372), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361372), _1361374), _1361376)), _1361378))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361372), _1361374), _1361378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361372), _1361376), _1361378))], (32228 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361372), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361372), _1361374), _1361376)), _1361378)), 32231 ^ _781404 : [(32234 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361372), _1361376), _1361378)))], (32232 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361372), _1361374), _1361378)))]]]]], (38562 ^ _781404) ^ [_1514229, _1514231, _1514233, _1514235, _1514237] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1514229, _1514231), _1514233), hAPP(hAPP(c_COMBS(_1514229, tc_fun(_1514231, tc_HOL_Obool), tc_fun(_1514231, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514231, tc_HOL_Obool), tc_fun(tc_fun(_1514231, tc_HOL_Obool), tc_fun(_1514231, tc_HOL_Obool)), _1514229), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1514231, tc_HOL_Obool))), _1514235)), _1514237)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1514229, _1514231), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1514229, _1514231), _1514233), _1514235)), hAPP(hAPP(c_Product__Type_OSigma(_1514229, _1514231), _1514233), _1514237)))], (7755 ^ _781404) ^ [_908991, _908993, _908995, _908997] : [class_Lattices_Osemilattice__inf(_908991), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908991), _908993), _908995)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908991), _908993), _908997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908991), _908993), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_908991), _908995), _908997))))], (12162 ^ _781404) ^ [_990466, _990468, _990470, _990472, _990474, _990476] : [c_Fun_Oinj__on(_990466, _990468, _990470, _990472), -(_990474 = _990476), hBOOL(hAPP(hAPP(c_member(_990466), _990474), _990472)), hBOOL(hAPP(hAPP(c_member(_990466), _990476), _990472)), hAPP(_990470, _990474) = hAPP(_990470, _990476)], (16708 ^ _781404) ^ [_1078695, _1078697, _1078699] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1078695), _1078697)), hBOOL(hAPP(_1078699, _1078697)), 16719 ^ _781404 : [(16722 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1078695), 16717 ^ [_1078695, _1078697, _1078699]), 16718 ^ [_1078695, _1078697, _1078699])))], (16724 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1078699, 16718 ^ [_1078695, _1078697, _1078699])))], (16726 ^ _781404) ^ [] : [hBOOL(hAPP(_1078699, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078695, tc_HOL_Obool)), 16718 ^ [_1078695, _1078697, _1078699]), hAPP(hAPP(c_Set_Oinsert(_1078695), 16717 ^ [_1078695, _1078697, _1078699]), c_Orderings_Obot__class_Obot(tc_fun(_1078695, tc_HOL_Obool))))))], (16720 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1078695), 16718 ^ [_1078695, _1078697, _1078699])))]], -(hBOOL(hAPP(_1078699, c_Orderings_Obot__class_Obot(tc_fun(_1078695, tc_HOL_Obool)))))], (1366 ^ _781404) ^ [_801519, _801521] : [-(class_Groups_Oabs__if(_801519)), _801521 = _801519, class_Groups_Oabs__if(_801521)], (45505 ^ _781404) ^ [_1693004, _1693006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1693004), _1693006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1693004)), hAPP(c_Code__Numeral_Oof__nat, _1693006))))], (17058 ^ _781404) ^ [_1085189] : [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), _1085189))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085189) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085189)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (34859 ^ _781404) ^ [_1429462] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429462))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1429462)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43811 ^ _781404) ^ [_1654904, _1654906, _1654908, _1654910, _1654912] : [_1654904 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1654906, _1654908, _1654910), _1654904), _1654912) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654908), _1654906), c_List_Olist_ONil(_1654908)), _1654912))], (39779 ^ _781404) ^ [_1554726, _1554728, _1554730, _1554732, _1554734, _1554736, _1554738] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1554726, _1554728, _1554730, _1554732, _1554734), _1554736), _1554738))), 39780 ^ _781404 : [(39781 ^ _781404) ^ [_1554797] : [hBOOL(hAPP(hAPP(_1554732, _1554736), _1554797)), hBOOL(hAPP(hAPP(_1554734, _1554797), _1554738))]]], (11263 ^ _781404) ^ [_972563, _972565, _972567, _972569, _972571] : [c_Fun_Oinj__on(_972563, _972565, _972567, c_Orderings_Otop__class_Otop(tc_fun(_972563, tc_HOL_Obool))), 11266 ^ _781404 : [(11273 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972563, tc_HOL_Obool)), _972569), _972571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972565, tc_HOL_Obool)), hAPP(c_Set_Oimage(_972563, _972565, _972567), _972569)), hAPP(c_Set_Oimage(_972563, _972565, _972567), _972571))))], (11267 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972565, tc_HOL_Obool)), hAPP(c_Set_Oimage(_972563, _972565, _972567), _972569)), hAPP(c_Set_Oimage(_972563, _972565, _972567), _972571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972563, tc_HOL_Obool)), _972569), _972571)))]]], (20293 ^ _781404) ^ [_1141559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141559), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1141559)))], (5841 ^ _781404) ^ [_874043, _874045, _874047, _874049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874043, tc_HOL_Obool)), _874045), _874047)), hBOOL(hAPP(_874045, _874049)), -(hBOOL(hAPP(_874047, _874049)))], (19709 ^ _781404) ^ [] : [-(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)))))], (41714 ^ _781404) ^ [_1600244, _1600246] : [-(c_Relation_Osingle__valued(_1600244, _1600244, c_Relation_OId__on(_1600244, _1600246)))], (50827 ^ _781404) ^ [_1808992, _1808994, _1808996, _1808998, _1809000, _1809002, _1809004, _1809006] : [c_Fun_Obij__betw(_1808992, _1808994, _1808996, _1808998, _1809000), c_Fun_Obij__betw(_1808994, _1809002, _1809004, _1809000, _1809006), -(c_Fun_Obij__betw(_1808992, _1809002, hAPP(c_Fun_Ocomp(_1808994, _1809002, _1808992, _1809004), _1808996), _1808998, _1809006))], (1276 ^ _781404) ^ [_800394, _800396] : [-(class_Groups_Oab__group__add(_800394)), _800396 = _800394, class_Groups_Oab__group__add(_800396)], (9913 ^ _781404) ^ [_950734, _950736, _950738, _950740, _950742] : [c_Fun_Oinj__on(_950734, _950736, _950738, _950740), -(c_Fun_Oinj__on(_950734, _950736, _950738, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950734, tc_HOL_Obool)), _950740), _950742)))], (37116 ^ _781404) ^ [_1477627, _1477629, _1477631, _1477633, _1477635, _1477637] : [hAPP(c_Product__Type_Oapfst(_1477627, _1477629, _1477631, _1477633), _1477635) = hAPP(c_Product__Type_Oapfst(_1477627, _1477629, _1477631, _1477637), _1477635), -(hAPP(_1477633, hAPP(c_Product__Type_Ofst(_1477627, _1477631), _1477635)) = hAPP(_1477637, hAPP(c_Product__Type_Ofst(_1477627, _1477631), _1477635)))], (46718 ^ _781404) ^ [_1721336, _1721338, _1721340, _1721342] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1721336, tc_Nat_Onat), _1721336), c_Product__Type_Ofst(_1721336, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1721336, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1721336, 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(_1721336, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1721336, tc_Nat_Onat))), _1721338)), hAPP(hAPP(c_List_Ozip(_1721336, tc_Nat_Onat), _1721340), c_List_Oupt(_1721342, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1721342), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721336)), _1721340)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1721336, tc_Nat_Onat), _1721336), c_Product__Type_Ofst(_1721336, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1721336, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1721336, 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(_1721336, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1721336, 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(_1721336, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1721336, tc_Nat_Onat))), _1721342))), _1721338)), hAPP(hAPP(c_List_Ozip(_1721336, tc_Nat_Onat), _1721340), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721336)), _1721340))))))], (44046 ^ _781404) ^ [_1660361, _1660363, _1660365] : [_1660365 = c_List_Olist_ONil(_1660361), -(hAPP(hAPP(c_List_Oappend(_1660361), _1660363), _1660365) = _1660363)], (51183 ^ _781404) ^ [_1816066, _1816068, _1816070, _1816072, _1816074] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1816066, _1816068, tc_HOL_Obool, _1816070), _1816072), _1816074)), -(hBOOL(hAPP(_1816070, hAPP(hAPP(c_Product__Type_OPair(_1816066, _1816068), _1816072), _1816074))))], (2574 ^ _781404) ^ [_819305, _819307, _819309, _819311] : [-(c_Set_Othe__elem(_819311, _819307) = c_Set_Othe__elem(_819309, _819305)), _819311 = _819309, _819307 = _819305], (26001 ^ _781404) ^ [_1245991, _1245993] : [-(c_Int_Onat__aux(_1245991, _1245993) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1245991)), _1245993))], (46395 ^ _781404) ^ [_1712330, _1712332] : [46397 ^ _781404 : [(46400 ^ _781404) ^ [] : [46396 ^ [_1712330, _1712332] = c_List_Olist_ONil(_1712330)], (46398 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712330)), 46396 ^ [_1712330, _1712332]), hAPP(c_List_Oset(tc_List_Olist(_1712330)), _1712332))))]], -(c_List_Olist_ONil(_1712330) = c_List_Oconcat(_1712330, _1712332))], (34123 ^ _781404) ^ [_1408074, _1408076, _1408078, _1408080, _1408082] : [_1408074 = c_Orderings_Obot__class_Obot(tc_fun(_1408076, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408078, tc_HOL_Obool)), _1408080), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408076, tc_fun(_1408078, tc_HOL_Obool)), _1408074), _1408082)) = _1408080)], (7940 ^ _781404) ^ [_913481, _913483] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913481, tc_HOL_Obool)), _913483), c_Orderings_Otop__class_Otop(tc_fun(_913481, tc_HOL_Obool)))))], (24586 ^ _781404) ^ [_1222428, _1222430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222428)), -(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)))), _1222430))), 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)))), _1222428)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222430), _1222428))], (43986 ^ _781404) ^ [_1659040, _1659042, _1659044, _1659046] : [_1659042 = _1659046, -(hAPP(hAPP(c_List_Oappend(_1659040), _1659042), _1659044) = hAPP(hAPP(c_List_Oappend(_1659040), _1659046), _1659044))], (2652 ^ _781404) ^ [_820532, _820534, _820536, _820538] : [-(c_Nitpick_Onorm__frac(_820538, _820534) = c_Nitpick_Onorm__frac(_820536, _820532)), _820538 = _820536, _820534 = _820532], (48202 ^ _781404) ^ [_1751785, _1751787] : [class_Enum_Oenum(_1751785), 48205 ^ _781404 : [(48212 ^ _781404) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1751785), _1751787)), -(hBOOL(hAPP(_1751787, 48215 ^ [_1751785, _1751787])))], (48206 ^ _781404) ^ [] : [48207 ^ _781404 : [(48208 ^ _781404) ^ [_1751887] : [hBOOL(hAPP(_1751787, _1751887))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1751785), _1751787)))]]], (20669 ^ _781404) ^ [_1147787] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147787))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147787)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27582 ^ _781404) ^ [_1274018, _1274020, _1274022] : [class_Groups_Oab__semigroup__mult(_1274018), -(_1274020 = c_Orderings_Obot__class_Obot(tc_fun(_1274018, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274018), _1274020)), -(hBOOL(hAPP(hAPP(c_member(_1274018), _1274022), _1274020))), -(hAPP(c_Finite__Set_Ofold1(_1274018, c_Groups_Otimes__class_Otimes(_1274018)), hAPP(hAPP(c_Set_Oinsert(_1274018), _1274022), _1274020)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274018), _1274022), hAPP(c_Finite__Set_Ofold1(_1274018, c_Groups_Otimes__class_Otimes(_1274018)), _1274020)))], (9284 ^ _781404) ^ [_940123, _940125, _940127, _940129] : [class_Orderings_Olinorder(_940123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940123), _940125), _940127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940123), _940127), _940129)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940123, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_940123, _940125, _940127)), c_SetInterval_Oord__class_OgreaterThanLessThan(_940123, _940127, _940129)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_940123, _940125), _940129))], (1546 ^ _781404) ^ [_803769, _803771] : [-(class_Finite__Set_Ofinite(_803769)), _803771 = _803769, class_Finite__Set_Ofinite(_803771)], (49814 ^ _781404) ^ [_1787097, _1787099, _1787101] : [c_List_Olist__ex(_1787097, _1787099, _1787101), 49818 ^ _781404 : [(49821 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1787099, 49817 ^ [_1787097, _1787099, _1787101])))], (49819 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1787097), 49817 ^ [_1787097, _1787099, _1787101]), hAPP(c_List_Oset(_1787097), _1787101))))]]], (35674 ^ _781404) ^ [_1447137, _1447139] : [_1447137 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1447139, _1447137) = 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), _1447139)))], (20851 ^ _781404) ^ [_1151722, _1151724] : [class_Rings_Omult__zero(_1151722), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151722), _1151724), c_Groups_Ozero__class_Ozero(_1151722)) = c_Groups_Ozero__class_Ozero(_1151722))], (49237 ^ _781404) ^ [_1773785, _1773787, _1773789] : [-(_1773785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1773787), c_List_Oreplicate(_1773787, _1773785, _1773789)) = hAPP(hAPP(c_Set_Oinsert(_1773787), _1773789), c_Orderings_Obot__class_Obot(tc_fun(_1773787, tc_HOL_Obool))))], (46121 ^ _781404) ^ [_1706707, _1706709, _1706711, _1706713] : [-(hAPP(c_List_Oset(tc_prod(_1706707, _1706709)), c_Enum_Oproduct(_1706707, _1706709, _1706711, _1706713)) = hAPP(hAPP(c_Product__Type_OSigma(_1706707, _1706709), hAPP(c_List_Oset(_1706707), _1706711)), hAPP(c_COMBK(tc_fun(_1706709, tc_HOL_Obool), _1706707), hAPP(c_List_Oset(_1706709), _1706713))))], (14739 ^ _781404) ^ [_1039910, _1039912, _1039914, _1039916] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039910), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1039910, tc_HOL_Obool)), _1039912), hAPP(hAPP(c_Set_Oinsert(_1039910), _1039914), _1039916)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039910), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1039910, tc_HOL_Obool)), _1039912), _1039916))))], (8453 ^ _781404) ^ [_923981] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _923981)], (11879 ^ _781404) ^ [_984757, _984759, _984761, _984763, _984765, _984767] : [c_Fun_Oinj__on(_984757, _984759, _984761, _984763), hAPP(_984761, _984765) = _984767, hBOOL(hAPP(hAPP(c_member(_984757), _984765), _984763)), -(hAPP(c_Fun_Othe__inv__into(_984757, _984759, _984763, _984761), _984767) = _984765)], (52514 ^ _781404) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (26045 ^ _781404) ^ [_1246758, _1246760] : [c_Nat__Transfer_Onat__set(_1246758), c_Nat__Transfer_Onat__set(_1246760), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1246758), _1246760) = 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), _1246758)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1246760))))], (48855 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43915 ^ _781404) ^ [_1657361, _1657363, _1657365, _1657367] : [-(hAPP(hAPP(c_List_Oappend(_1657361), hAPP(hAPP(c_List_Olist_OCons(_1657361), _1657363), _1657365)), _1657367) = hAPP(hAPP(c_List_Olist_OCons(_1657361), _1657363), hAPP(hAPP(c_List_Oappend(_1657361), _1657365), _1657367)))], (8317 ^ _781404) ^ [_921681, _921683, _921685, _921687] : [_921687 = c_Orderings_Obot__class_Obot(tc_fun(_921683, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_921681, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_921683, _921681, _921685), _921687))], (19677 ^ _781404) ^ [_1131116, _1131118, _1131120] : [class_Rings_Osemiring__1(_1131116), hBOOL(hAPP(hAPP(c_member(_1131116), _1131118), c_Nat_Osemiring__1__class_ONats(_1131116))), hBOOL(hAPP(hAPP(c_member(_1131116), _1131120), c_Nat_Osemiring__1__class_ONats(_1131116))), -(hBOOL(hAPP(hAPP(c_member(_1131116), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131116), _1131118), _1131120)), c_Nat_Osemiring__1__class_ONats(_1131116))))], (17931 ^ _781404) ^ [_1101230, _1101232] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1101230, _1101232))))], (10239 ^ _781404) ^ [_955587, _955589, _955591] : [class_Orderings_Olinorder(_955587), 10242 ^ _781404 : [(10249 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955587), _955591), _955589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955587), _955589), _955591))], (10243 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955587), _955589), _955591))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955587), _955591), _955589)))]]], (32382 ^ _781404) ^ [_1364782, _1364784, _1364786, _1364788] : [class_Orderings_Olinorder(_1364782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364782), _1364784)), hBOOL(hAPP(hAPP(c_member(_1364782), _1364786), _1364784)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364782), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364782), _1364786), _1364788)), hAPP(hAPP(c_Finite__Set_Ofold(_1364782, _1364782, c_Orderings_Oord__class_Omax(_1364782)), _1364788), _1364784))))], (9132 ^ _781404) ^ [_936410, _936412, _936414, _936416] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936410, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_936410, tc_HOL_Obool)), _936412), _936414)), _936416) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_936410, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936410, tc_HOL_Obool)), _936412), _936416)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936410, tc_HOL_Obool)), _936414), _936416)))], (43591 ^ _781404) ^ [_1650198, _1650200] : [_1650200 = c_List_Olist_ONil(_1650198), -(c_Orderings_Obot__class_Obot(tc_fun(_1650198, tc_HOL_Obool)) = hAPP(c_List_Oset(_1650198), _1650200))], (12951 ^ _781404) ^ [_1006090, _1006092, _1006094, _1006096, _1006098] : [hAPP(_1006090, _1006092) = _1006094, -(c_Fun_Ofun__upd(_1006096, _1006098, _1006090, _1006092, _1006094) = _1006090)], (2140 ^ _781404) ^ [_812432, _812434, _812436, _812438] : [-(c_Int_Onat__aux(_812438, _812434) = c_Int_Onat__aux(_812436, _812432)), _812438 = _812436, _812434 = _812432], (52278 ^ _781404) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (8491 ^ _781404) ^ [_924604] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_924604, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_924604, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_924604, tc_HOL_Obool)))], (18301 ^ _781404) ^ [_1107469, _1107471] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107469), _1107471))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1107471, _1107469) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1107471), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1107471), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1107469)))], (34789 ^ _781404) ^ [_1427778, _1427780, _1427782] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1427778), _1427780)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1427778, tc_HOL_Obool)), _1427782), _1427780) = hAPP(hAPP(c_Finite__Set_Ofold(_1427778, tc_fun(_1427778, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1427778, tc_HOL_Obool), tc_fun(tc_fun(_1427778, tc_HOL_Obool), tc_fun(_1427778, tc_HOL_Obool)), _1427778), hAPP(c_COMBC(tc_fun(_1427778, tc_HOL_Obool), tc_fun(_1427778, tc_HOL_Obool), tc_fun(_1427778, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1427778, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1427778, tc_fun(_1427778, tc_HOL_Obool), tc_fun(_1427778, tc_HOL_Obool)), c_Set_Oinsert(_1427778)), c_Orderings_Obot__class_Obot(tc_fun(_1427778, tc_HOL_Obool))))), _1427782), _1427780))], (19999 ^ _781404) ^ [_1136686, _1136688] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136686) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136688), -(_1136686 = _1136688)], (12672 ^ _781404) ^ [_1000524, _1000526, _1000528, _1000530] : [hBOOL(hAPP(hAPP(c_member(_1000524), _1000526), c_SetInterval_Oord_OatLeast(_1000524, _1000528, _1000530))), -(hBOOL(hAPP(hAPP(_1000528, _1000530), _1000526)))], (41055 ^ _781404) ^ [_1583515] : [-(c_Transitive__Closure_Otrancl(_1583515, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583515, _1583515), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583515, _1583515), tc_HOL_Obool)))], (11683 ^ _781404) ^ [_981452, _981454, _981456, _981458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_981452, tc_HOL_Obool)), _981454), _981456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_981452, tc_HOL_Obool)), _981456), _981458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_981452, tc_HOL_Obool)), _981454), _981458)))], (14526 ^ _781404) ^ [_1035943, _1035945, _1035947] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035943), _1035945) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035943), _1035947), -(_1035945 = _1035947)], (6596 ^ _781404) ^ [_886862, _886864, _886866, _886868, _886870] : [class_Orderings_Oorder(_886862), class_Orderings_Oorder(_886864), c_Orderings_Oorder__class_Omono(_886864, _886862, _886866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886864), _886868), _886870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886862), hAPP(_886866, _886868)), hAPP(_886866, _886870))))], (15555 ^ _781404) ^ [_1056734, _1056736] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1056734, _1056736)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1056736)), _1056734))], (14324 ^ _781404) ^ [_1031701, _1031703, _1031705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031701), _1031703)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031703), _1031701))), _1031705) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1031703)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031701), _1031705)))], (52302 ^ _781404) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (41183 ^ _781404) ^ [_1587439, _1587441] : [-(hAPP(c_Relation_ODomain(_1587439, _1587439), c_Transitive__Closure_Ortrancl(_1587439, _1587441)) = c_Orderings_Otop__class_Otop(tc_fun(_1587439, tc_HOL_Obool)))], (42348 ^ _781404) ^ [_1618123, _1618125, _1618127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1618123, _1618123), tc_HOL_Obool)), _1618125), _1618127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1618123), tc_List_Olist(_1618123)), tc_HOL_Obool)), c_List_Olistrel1(_1618123, _1618125)), c_List_Olistrel1(_1618123, _1618127))))], (39053 ^ _781404) ^ [_1527601, _1527603] : [-(hAPP(c_Set_OCollect(_1527601), hAPP(hAPP(c_COMBC(_1527601, tc_fun(_1527601, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527601)), _1527603)) = _1527603)], (25499 ^ _781404) ^ [_1237221, _1237223] : [_1237221 = hAPP(c_Int_Onat, _1237223), 25502 ^ _781404 : [(25509 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237223))), -(_1237221 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25503 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237223)), -(_1237223 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1237221))]]], (15176 ^ _781404) ^ [_1049107, _1049109, _1049111, _1049113, _1049115] : [c_Finite__Set_Ofolding__one(_1049107, _1049109, _1049111), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049107), _1049113)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049107), _1049115)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1049107, tc_HOL_Obool)), _1049113), _1049115) = c_Orderings_Obot__class_Obot(tc_fun(_1049107, tc_HOL_Obool))), -(hAPP(hAPP(_1049109, hAPP(_1049111, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1049107, tc_HOL_Obool)), _1049113), _1049115))), hAPP(_1049111, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1049107, tc_HOL_Obool)), _1049113), _1049115))) = hAPP(hAPP(_1049109, hAPP(_1049111, _1049113)), hAPP(_1049111, _1049115)))], (31436 ^ _781404) ^ [_1346800, _1346802, _1346804] : [class_Orderings_Olinorder(_1346800), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346800), _1346802)), -(c_Big__Operators_Olinorder__class_OMin(_1346800, hAPP(hAPP(c_Set_Oinsert(_1346800), _1346804), _1346802)) = hAPP(hAPP(c_Finite__Set_Ofold(_1346800, _1346800, c_Orderings_Oord__class_Omin(_1346800)), _1346804), _1346802))], (10787 ^ _781404) ^ [_964584, _964586, _964588] : [class_Complete__Lattice_Ocomplete__lattice(_964584), class_Orderings_Olinorder(_964584), 10794 ^ _781404 : [(10804 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964584), _964586), c_Complete__Lattice_OSup__class_OSup(_964584, _964588)))), 10805 ^ _781404 : [(10806 ^ _781404) ^ [_964890] : [hBOOL(hAPP(hAPP(c_member(_964584), _964890), _964588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964584), _964586), _964890))]]], (10795 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964584), _964586), c_Complete__Lattice_OSup__class_OSup(_964584, _964588))), 10799 ^ _781404 : [(10802 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964584), _964586), 10798 ^ [_964584, _964586, _964588])))], (10800 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_964584), 10798 ^ [_964584, _964586, _964588]), _964588)))]]]]], (42356 ^ _781404) ^ [_1618321, _1618323] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1618321), tc_List_Olist(_1618321)), tc_HOL_Obool)), c_List_Olistrel1(_1618321, c_Transitive__Closure_Ortrancl(_1618321, _1618323))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1618321), c_List_Olistrel1(_1618321, _1618323)))))], (10703 ^ _781404) ^ [_963242, _963244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963242), _963244)), -(_963242 = _963244), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963242), _963244)))], (4818 ^ _781404) ^ [_854765, _854767] : [_854767 = _854765, -(c_Wellfounded_Ofinite__psubset(_854767) = c_Wellfounded_Ofinite__psubset(_854765))], (12062 ^ _781404) ^ [_988333, _988335, _988337, _988339, _988341, _988343] : [hBOOL(hAPP(hAPP(c_member(_988333), _988335), _988337)), _988339 = hAPP(_988341, _988335), -(hBOOL(hAPP(hAPP(c_member(_988343), _988339), hAPP(c_Set_Oimage(_988333, _988343, _988341), _988337))))], (26055 ^ _781404) ^ [_1246925, _1246927] : [c_Nat__Transfer_Onat__set(_1246925), c_Nat__Transfer_Onat__set(_1246927), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1246925), _1246927) = 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), _1246925)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1246927))))], (11431 ^ _781404) ^ [_976422, _976424, _976426, _976428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976422, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976422, tc_HOL_Obool)), _976424), hAPP(hAPP(c_Set_Oinsert(_976422), _976426), c_Orderings_Obot__class_Obot(tc_fun(_976422, tc_HOL_Obool))))), _976428)), hBOOL(hAPP(hAPP(c_member(_976422), _976426), _976424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976422, tc_HOL_Obool)), _976424), hAPP(hAPP(c_Set_Oinsert(_976422), _976426), _976428))))], (24854 ^ _781404) ^ [_1226930, _1226932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226932)), 24861 ^ _781404 : [(24868 ^ _781404) ^ [] : [_1226930 = _1226932, -(hAPP(c_Int_Onat, _1226930) = hAPP(c_Int_Onat, _1226932))], (24862 ^ _781404) ^ [] : [hAPP(c_Int_Onat, _1226930) = hAPP(c_Int_Onat, _1226932), -(_1226930 = _1226932)]]], (46137 ^ _781404) ^ [_1707198, _1707200, _1707202] : [-(hAPP(c_List_Oset(tc_List_Olist(_1707198)), c_Enum_On__lists(_1707198, _1707200, _1707202)) = hAPP(c_Set_OCollect(tc_List_Olist(_1707198)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1707198), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1707198)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1707198), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1707198)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1707198)))), _1707200))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1707198), tc_fun(_1707198, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1707198, tc_HOL_Obool), tc_fun(tc_fun(_1707198, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1707198)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1707198, tc_HOL_Obool))), c_List_Oset(_1707198))), hAPP(c_List_Oset(_1707198), _1707202)))))], (48182 ^ _781404) ^ [_1751346, _1751348, _1751350] : [class_Enum_Oenum(_1751346), class_Enum_Oenum(_1751348), 48189 ^ _781404 : [(48196 ^ _781404) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1751348), hAPP(hAPP(c_COMBB(tc_fun(_1751346, tc_HOL_Obool), tc_HOL_Obool, _1751348), c_Enum_Oenum__class_Oenum__ex(_1751346)), hAPP(hAPP(c_COMBB(tc_fun(_1751346, tc_prod(_1751348, _1751346)), tc_fun(_1751346, tc_HOL_Obool), _1751348), hAPP(c_COMBB(tc_prod(_1751348, _1751346), tc_HOL_Obool, _1751346), _1751350)), c_Product__Type_OPair(_1751348, _1751346))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1751348, _1751346)), _1751350)))], (48190 ^ _781404) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1751348, _1751346)), _1751350)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1751348), hAPP(hAPP(c_COMBB(tc_fun(_1751346, tc_HOL_Obool), tc_HOL_Obool, _1751348), c_Enum_Oenum__class_Oenum__ex(_1751346)), hAPP(hAPP(c_COMBB(tc_fun(_1751346, tc_prod(_1751348, _1751346)), tc_fun(_1751346, tc_HOL_Obool), _1751348), hAPP(c_COMBB(tc_prod(_1751348, _1751346), tc_HOL_Obool, _1751346), _1751350)), c_Product__Type_OPair(_1751348, _1751346))))))]]], (43168 ^ _781404) ^ [_1641355, _1641357, _1641359, _1641361, _1641363] : [-(hAPP(hAPP(c_List_Olist__update(_1641355, hAPP(hAPP(c_List_Olist_OCons(_1641355), _1641357), _1641359)), hAPP(c_Nat_OSuc, _1641361)), _1641363) = hAPP(hAPP(c_List_Olist_OCons(_1641355), _1641357), hAPP(hAPP(c_List_Olist__update(_1641355, _1641359), _1641361), _1641363)))], (3828 ^ _781404) ^ [_838854, _838856, _838858, _838860, _838862, _838864, _838866, _838868] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_838868, _838864, _838860, _838856) = c_New__Random__Sequence_Opos__not__random__dseq(_838866, _838862, _838858, _838854)), _838868 = _838866, _838864 = _838862, _838860 = _838858, _838856 = _838854], (44589 ^ _781404) ^ [_1673466, _1673468] : [-(_1673466 = c_List_Olist_ONil(_1673468)), -(hAPP(c_List_Ohd(_1673468), _1673466) = hAPP(hAPP(c_List_Onth(_1673468), _1673466), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4526 ^ _781404) ^ [_850163, _850165] : [_850165 = _850163, -(c_Lazy__Sequence_Oyield(_850165) = c_Lazy__Sequence_Oyield(_850163))], (51403 ^ _781404) ^ [_1822503, _1822505, _1822507, _1822509, _1822511, _1822513, _1822515, _1822517] : [c_Finite__Set_Ofolding__image(_1822503, _1822505, _1822507, _1822509, _1822511), hBOOL(hAPP(c_Finite__Set_Ofinite(_1822505), _1822513)), 51413 ^ _781404 : [(51416 ^ _781404) ^ [] : [hAPP(_1822515, 51412 ^ [_1822503, _1822505, _1822507, _1822509, _1822511, _1822513, _1822515, _1822517]) = hAPP(_1822517, 51412 ^ [_1822503, _1822505, _1822507, _1822509, _1822511, _1822513, _1822515, _1822517])], (51414 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1822505), 51412 ^ [_1822503, _1822505, _1822507, _1822509, _1822511, _1822513, _1822515, _1822517]), _1822513)))]], -(hAPP(hAPP(_1822511, _1822515), _1822513) = hAPP(hAPP(_1822511, _1822517), _1822513))], (26843 ^ _781404) ^ [_1260427, _1260429, _1260431] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1260427, _1260429, _1260431, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1260429)], (31510 ^ _781404) ^ [_1348217, _1348219, _1348221] : [class_Orderings_Olinorder(_1348217), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348217), _1348219)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348217), _1348221)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348217, tc_HOL_Obool)), _1348219), _1348221) = c_Orderings_Obot__class_Obot(tc_fun(_1348217, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348217), c_Big__Operators_Olattice_OInf__fin(_1348217, c_Orderings_Oord__class_Omin(_1348217), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1348217, tc_HOL_Obool)), _1348219), _1348221))), c_Big__Operators_Olattice_OInf__fin(_1348217, c_Orderings_Oord__class_Omin(_1348217), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348217, tc_HOL_Obool)), _1348219), _1348221))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348217), c_Big__Operators_Olattice_OInf__fin(_1348217, c_Orderings_Oord__class_Omin(_1348217), _1348219)), c_Big__Operators_Olattice_OInf__fin(_1348217, c_Orderings_Oord__class_Omin(_1348217), _1348221)))], (35450 ^ _781404) ^ [_1442662, _1442664, _1442666, _1442668, _1442670] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1442662, _1442664)), hAPP(hAPP(c_Product__Type_OPair(_1442662, _1442664), _1442668), _1442670)), _1442666)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1442662, _1442664, _1442666), _1442668), _1442670)))], (26690 ^ _781404) ^ [_1257121, _1257123, _1257125] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1257121, tc_HOL_Obool)), _1257123)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257121), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1257121, tc_HOL_Obool), _1257123))), 26700 ^ _781404 : [(26703 ^ _781404) ^ [] : [hAPP(c_Finite__Set_Ocard(_1257121), 26699 ^ [_1257121, _1257123, _1257125]) = _1257125], (26701 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1257121, tc_HOL_Obool)), 26699 ^ [_1257121, _1257123, _1257125]), _1257123)))]], 26707 ^ _781404 : [(26711 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1257121, tc_HOL_Obool)), 26709 ^ [_1257121, _1257123, _1257125]), _1257123)))], (26713 ^ _781404) ^ [] : [26706 ^ [_1257121, _1257123, _1257125] = 26709 ^ [_1257121, _1257123, _1257125]], (26715 ^ _781404) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1257121, tc_HOL_Obool)), 26706 ^ [_1257121, _1257123, _1257125]), 26709 ^ [_1257121, _1257123, _1257125]) = c_Orderings_Obot__class_Obot(tc_fun(_1257121, tc_HOL_Obool))], (26708 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1257121, tc_HOL_Obool)), 26706 ^ [_1257121, _1257123, _1257125]), _1257123)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1257125), hAPP(c_Finite__Set_Ocard(tc_fun(_1257121, tc_HOL_Obool)), _1257123)) = hAPP(c_Finite__Set_Ocard(_1257121), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1257121, tc_HOL_Obool), _1257123)))], (34101 ^ _781404) ^ [_1407612, _1407614, _1407616, _1407618, _1407620, _1407622] : [c_Nitpick_Opair__box_OPairBox(_1407612, _1407614, _1407616, _1407618) = c_Nitpick_Opair__box_OPairBox(_1407612, _1407614, _1407620, _1407622), 34104 ^ _781404 : [(34107 ^ _781404) ^ [] : [-(_1407618 = _1407622)], (34105 ^ _781404) ^ [] : [-(_1407616 = _1407620)]]], (38011 ^ _781404) ^ [_1500285, _1500287, _1500289, _1500291, _1500293, _1500295, _1500297, _1500299, _1500301, _1500303] : [c_Equiv__Relations_Ocongruent2(_1500285, _1500287, _1500289, _1500291, _1500293, _1500295), hBOOL(hAPP(hAPP(c_member(tc_prod(_1500285, _1500285)), hAPP(hAPP(c_Product__Type_OPair(_1500285, _1500285), _1500297), _1500299)), _1500291)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1500287, _1500287)), hAPP(hAPP(c_Product__Type_OPair(_1500287, _1500287), _1500301), _1500303)), _1500293)), -(hAPP(hAPP(_1500295, _1500297), _1500301) = hAPP(hAPP(_1500295, _1500299), _1500303))], (35165 ^ _781404) ^ [_1436493, _1436495] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436493), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 35168 ^ _781404 : [(35177 ^ _781404) ^ [] : [-(c_Nitpick_Onorm__frac(_1436495, _1436493) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1436495), _1436493)), 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), _1436495))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1436493)))), -(_1436495 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1436493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35169 ^ _781404) ^ [] : [35170 ^ _781404 : [(35173 ^ _781404) ^ [] : [_1436493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (35171 ^ _781404) ^ [] : [_1436495 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1436495, _1436493) = 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)))]]], (20505 ^ _781404) ^ [] : [-(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))))], (32975 ^ _781404) ^ [_1375825, _1375827, _1375829, _1375831, _1375833, _1375835, _1375837] : [class_Groups_Oab__semigroup__mult(_1375825), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375827), _1375829)), c_Fun_Oinj__on(_1375827, _1375831, _1375833, _1375829), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1375825, _1375831, c_Groups_Otimes__class_Otimes(_1375825)), _1375835), _1375837), hAPP(c_Set_Oimage(_1375827, _1375831, _1375833), _1375829)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1375825, _1375827, c_Groups_Otimes__class_Otimes(_1375825)), hAPP(c_Fun_Ocomp(_1375831, _1375825, _1375827, _1375835), _1375833)), _1375837), _1375829))], (46163 ^ _781404) ^ [_1707751, _1707753, _1707755, _1707757] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1707751)), _1707753), hAPP(c_List_Oset(tc_List_Olist(_1707751)), c_Enum_On__lists(_1707751, _1707755, _1707757)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707751)), _1707753) = _1707755)], (49733 ^ _781404) ^ [_1785276, _1785278] : [c_Relation_Otrans(_1785276, hAPP(c_Relation_Oconverse(_1785276, _1785276), _1785278)), -(c_Relation_Otrans(_1785276, _1785278))], (17389 ^ _781404) ^ [_1091608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1091608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1091608)))], (9200 ^ _781404) ^ [_938201, _938203, _938205, _938207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938201, tc_HOL_Obool)), _938203), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938201, tc_HOL_Obool)), _938205), _938207))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938201, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938201, tc_HOL_Obool)), _938203), _938205)), _938207)))], (37453 ^ _781404) ^ [_1486441] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1486441)) = _1486441)], (52112 ^ _781404) ^ [_1835467, _1835469, _1835471, _1835473] : [class_Divides_Osemiring__div(_1835467), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835467), _1835469), _1835471)), -(c_Divides_Odiv__class_Omod(_1835467, c_Divides_Odiv__class_Omod(_1835467, _1835473, _1835471), _1835469) = c_Divides_Odiv__class_Omod(_1835467, _1835473, _1835469))], (20965 ^ _781404) ^ [_1153797, _1153799, _1153801, _1153803] : [class_Rings_Ocomm__semiring__1(_1153797), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153797), _1153799), _1153801)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153797), _1153803), _1153801)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153797), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153797), _1153799), _1153803)), _1153801))], (364 ^ _781404) ^ [_786972, _786974, _786976, _786978, _786980, _786982, _786984, _786986] : [-(c_Finite__Set_Ofolding(_786984, _786980, _786976, _786972)), c_Finite__Set_Ofolding(_786986, _786982, _786978, _786974), _786986 = _786984, _786982 = _786980, _786978 = _786976, _786974 = _786972], (46279 ^ _781404) ^ [_1710112, _1710114, _1710116, _1710118] : [_1710112 = _1710114, -(hAPP(c_List_OremoveAll(_1710116, _1710112), hAPP(hAPP(c_List_Olist_OCons(_1710116), _1710114), _1710118)) = hAPP(c_List_OremoveAll(_1710116, _1710112), _1710118))], (2904 ^ _781404) ^ [_824474, _824476] : [_824476 = _824474, -(c_Nat_Ofunpow(_824476) = c_Nat_Ofunpow(_824474))], (52752 ^ _781404) ^ [_1842543] : [hBOOL(hAPP(c_fNot, _1842543)), hBOOL(_1842543)], (1716 ^ _781404) ^ [_805894, _805896] : [-(class_Groups_Oab__semigroup__add(_805894)), _805896 = _805894, class_Groups_Oab__semigroup__add(_805896)], (22735 ^ _781404) ^ [_1187828, _1187830] : [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), _1187828), _1187830))), 22738 ^ _781404 : [(22741 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1187830)))], (22739 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1187828)))]]], (45646 ^ _781404) ^ [_1696056] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1696056)) = _1696056)], (17699 ^ _781404) ^ [_1096932, _1096934, _1096936, _1096938, _1096940] : [c_Finite__Set_Ofolding__one__idem(_1096932, _1096934, _1096936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096932), _1096938)), -(hAPP(_1096936, hAPP(hAPP(c_Set_Oinsert(_1096932), _1096940), _1096938)) = hAPP(hAPP(c_Finite__Set_Ofold(_1096932, _1096932, _1096934), _1096940), _1096938))], (49843 ^ _781404) ^ [_1787655, _1787657, _1787659] : [c_List_Olist__ex(_1787655, _1787659, _1787657), 49847 ^ _781404 : [(49850 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1787659, 49846 ^ [_1787655, _1787657, _1787659])))], (49848 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1787655), 49846 ^ [_1787655, _1787657, _1787659]), hAPP(c_List_Oset(_1787655), _1787657))))]]], (52714 ^ _781404) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (9425 ^ _781404) ^ [_942980, _942982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942982), _942980)), -(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), _942980), _942982))))], (42175 ^ _781404) ^ [_1612282, _1612284, _1612286, _1612288, _1612290, _1612292] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1612282, _1612284, _1612286), _1612288), hAPP(hAPP(c_Product__Type_OPair(_1612282, _1612284), _1612290), _1612292)) = hAPP(hAPP(_1612288, _1612290), _1612292))], (36312 ^ _781404) ^ [_1459447, _1459449, _1459451, _1459453, _1459455, _1459457] : [c_Finite__Set_Ofolding(_1459447, _1459449, _1459451, _1459453), -(hAPP(c_Fun_Ocomp(_1459449, _1459449, _1459449, hAPP(_1459451, _1459455)), hAPP(_1459451, _1459457)) = hAPP(c_Fun_Ocomp(_1459449, _1459449, _1459449, hAPP(_1459451, _1459457)), hAPP(_1459451, _1459455)))], (35494 ^ _781404) ^ [_1443690, _1443692, _1443694, _1443696, _1443698, _1443700] : [hAPP(hAPP(c_Product__Type_OPair(_1443690, _1443692), _1443694), _1443696) = hAPP(hAPP(c_Product__Type_OPair(_1443690, _1443692), _1443698), _1443700), 35497 ^ _781404 : [(35500 ^ _781404) ^ [] : [-(_1443696 = _1443700)], (35498 ^ _781404) ^ [] : [-(_1443694 = _1443698)]]], (13468 ^ _781404) ^ [_1015701, _1015703] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015701), _1015703)), _1015703) = _1015701)], (21017 ^ _781404) ^ [_1154748, _1154750] : [class_Groups_Ocomm__monoid__mult(_1154748), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154748), c_Groups_Oone__class_Oone(_1154748)), _1154750) = _1154750)], (44082 ^ _781404) ^ [_1661004, _1661006, _1661008] : [_1661004 = hAPP(hAPP(c_List_Oappend(_1661006), _1661004), _1661008), -(_1661008 = c_List_Olist_ONil(_1661006))], (24803 ^ _781404) ^ [_1226103] : [-(hBOOL(hAPP(_1226103, 24810 ^ [_1226103]))), 24804 ^ _781404 : [(24805 ^ _781404) ^ [_1226155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226155)), hBOOL(hAPP(_1226103, hAPP(c_Int_Onat, _1226155)))]]], (45776 ^ _781404) ^ [_1699024, _1699026] : [-(hBOOL(hAPP(c_List_Olistsp(_1699024, _1699026), c_List_Olist_ONil(_1699024))))], (34001 ^ _781404) ^ [_1405483, _1405485, _1405487, _1405489, _1405491] : [class_Groups_Ocomm__monoid__add(_1405483), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405485, _1405483), hAPP(hAPP(c_COMBS(_1405485, _1405483, _1405483), hAPP(hAPP(c_COMBB(_1405483, tc_fun(_1405483, _1405483), _1405485), c_Groups_Oplus__class_Oplus(_1405483)), _1405487)), _1405489)), _1405491) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1405483), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405485, _1405483), _1405487), _1405491)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405485, _1405483), _1405489), _1405491)))], (45537 ^ _781404) ^ [_1693569, _1693571, _1693573, _1693575] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693569)), _1693571) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693573)), _1693575), -(hAPP(hAPP(c_List_Omap(tc_prod(_1693569, _1693573), _1693573), c_Product__Type_Osnd(_1693569, _1693573)), hAPP(hAPP(c_List_Ozip(_1693569, _1693573), _1693571), _1693575)) = _1693575)], (34993 ^ _781404) ^ [_1432857, _1432859, _1432861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1432857), _1432859)), -(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)), _1432857)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1432861), _1432859)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1432861), _1432857)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1432859), _1432857)))], (13509 ^ _781404) ^ [_1016505] : [13511 ^ _781404 : [(13514 ^ _781404) ^ [_1016615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 13510 ^ [_1016505, _1016615]), _1016615))], (13512 ^ _781404) ^ [_1016581] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 13510 ^ [_1016505, _1016581]), _1016505)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1016505)))], (23661 ^ _781404) ^ [_1206445, _1206447] : [class_Divides_Osemiring__div(_1206445), -(c_Divides_Odiv__class_Omod(_1206445, _1206447, c_Groups_Oone__class_Oone(_1206445)) = c_Groups_Ozero__class_Ozero(_1206445))], (13476 ^ _781404) ^ [_1015877, _1015879, _1015881] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015877), _1015879)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015881), _1015879)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015877), _1015881))], (52370 ^ _781404) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (35079 ^ _781404) ^ [_1434611, _1434613] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434611)), hAPP(c_Nat_OSuc, _1434613)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1434611))), 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)), _1434613)))))], (10481 ^ _781404) ^ [_959878, _959880, _959882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959878, tc_HOL_Obool)), _959880), _959882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_959878, tc_HOL_Obool)), _959880), _959882))), -(_959880 = _959882)], (43103 ^ _781404) ^ [_1639814, _1639816, _1639818, _1639820] : [43105 ^ _781404 : [(43108 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1639818, 43104 ^ [_1639814, _1639816, _1639818, _1639820])), hAPP(_1639820, 43104 ^ [_1639814, _1639816, _1639818, _1639820])))], (43106 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1639814), 43104 ^ [_1639814, _1639816, _1639818, _1639820]), hAPP(c_List_Oset(_1639814), _1639816))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1639814, _1639818, _1639816)), c_List_Olist_Olist__size(_1639814, _1639820, _1639816))))], (5072 ^ _781404) ^ [_858768, _858770] : [_858770 = _858768, -(c_Fun_Oid(_858770) = c_Fun_Oid(_858768))], (31382 ^ _781404) ^ [_1345929, _1345931, _1345933] : [class_Orderings_Olinorder(_1345929), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345929), _1345931)), -(_1345931 = c_Orderings_Obot__class_Obot(tc_fun(_1345929, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1345929, hAPP(hAPP(c_Set_Oinsert(_1345929), _1345933), _1345931)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345929), _1345933), c_Big__Operators_Olinorder__class_OMin(_1345929, _1345931)))], (33807 ^ _781404) ^ [_1399546, _1399548, _1399550, _1399552, _1399554] : [-(hBOOL(hAPP(hAPP(c_member(_1399546), _1399548), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399550, tc_fun(_1399546, tc_HOL_Obool)), _1399552), _1399554)))), 33808 ^ _781404 : [(33809 ^ _781404) ^ [_1399628] : [hBOOL(hAPP(hAPP(c_member(_1399550), _1399628), _1399552)), hBOOL(hAPP(hAPP(c_member(_1399546), _1399548), hAPP(_1399554, _1399628)))]]], (52498 ^ _781404) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (28813 ^ _781404) ^ [_1297198, _1297200, _1297202] : [class_Fields_Ofield__inverse__zero(_1297198), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297198), hAPP(c_Groups_Ouminus__class_Ouminus(_1297198), _1297200)), hAPP(c_Groups_Ouminus__class_Ouminus(_1297198), _1297202)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297198), _1297200), _1297202))], (41658 ^ _781404) ^ [_1599081, _1599083] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1599081, _1599081)), _1599083)), c_Wellfounded_Oacyclic(_1599081, _1599083), -(c_Wellfounded_Owf(_1599081, hAPP(c_Relation_Oconverse(_1599081, _1599081), _1599083)))], (46792 ^ _781404) ^ [_1722720, _1722722, _1722724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1722720), _1722722)), _1722724)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1722722), c_List_Oupt(_1722720, _1722724)) = c_List_Oupt(_1722720, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1722720), _1722722)))], (2496 ^ _781404) ^ [_818008, _818010, _818012, _818014, _818016, _818018, _818020, _818022, _818024, _818026] : [-(c_Product__Type_Oprod_Oprod__size(_818026, _818022, _818018, _818014, _818010) = c_Product__Type_Oprod_Oprod__size(_818024, _818020, _818016, _818012, _818008)), _818026 = _818024, _818022 = _818020, _818018 = _818016, _818014 = _818012, _818010 = _818008], (19147 ^ _781404) ^ [] : [-(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)))))], (50580 ^ _781404) ^ [_1803314, _1803316, _1803318, _1803320] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1803314, _1803316, c_Orderings_Otop__class_Otop(tc_fun(_1803314, tc_HOL_Obool)), _1803318), _1803320) = c_Hilbert__Choice_OEps(_1803314, hAPP(hAPP(c_COMBC(_1803314, _1803316, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1803316, tc_fun(_1803316, tc_HOL_Obool), _1803314), c_fequal), _1803318)), _1803320)))], (17991 ^ _781404) ^ [_1102235, _1102237, _1102239] : [class_Rings_Olinordered__semidom(_1102235), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102235), c_Groups_Ozero__class_Ozero(_1102235)), _1102237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102235), c_Groups_Ozero__class_Ozero(_1102235)), hAPP(hAPP(c_Power_Opower__class_Opower(_1102235), _1102237), _1102239))))], (19436 ^ _781404) ^ [] : [-(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))], (48540 ^ _781404) ^ [_1759463, _1759465] : [c_List_Olist__ex(_1759463, _1759465, c_List_Olist_ONil(_1759463))], (46265 ^ _781404) ^ [_1709867, _1709869] : [-(hAPP(c_List_OremoveAll(_1709867, _1709869), c_List_Olist_ONil(_1709867)) = c_List_Olist_ONil(_1709867))], (38898 ^ _781404) ^ [_1523952, _1523954, _1523956, _1523958, _1523960, _1523962, _1523964, _1523966, _1523968, _1523970] : [hAPP(c_Set_Oimage(_1523952, _1523954, _1523956), _1523958) = _1523960, hAPP(c_Set_Oimage(_1523962, _1523964, _1523966), _1523968) = _1523970, -(hAPP(c_Set_Oimage(tc_prod(_1523952, _1523962), tc_prod(_1523954, _1523964), c_Product__Type_Omap__pair(_1523952, _1523954, _1523962, _1523964, _1523956, _1523966)), hAPP(hAPP(c_Product__Type_OSigma(_1523952, _1523962), _1523958), hAPP(c_COMBK(tc_fun(_1523962, tc_HOL_Obool), _1523952), _1523968))) = hAPP(hAPP(c_Product__Type_OSigma(_1523954, _1523964), _1523960), hAPP(c_COMBK(tc_fun(_1523964, tc_HOL_Obool), _1523954), _1523970)))], (1296 ^ _781404) ^ [_800644, _800646] : [-(class_Rings_Ocomm__ring__1(_800644)), _800646 = _800644, class_Rings_Ocomm__ring__1(_800646)], (10697 ^ _781404) ^ [_963145, _963147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963145), _963147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963145), _963147)))], (25209 ^ _781404) ^ [_1232515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232515)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1232515)) = _1232515)], (41367 ^ _781404) ^ [_1591984, _1591986, _1591988, _1591990] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591984, _1591984)), hAPP(hAPP(c_Product__Type_OPair(_1591984, _1591984), _1591986), _1591988)), c_Transitive__Closure_Ortrancl(_1591984, _1591990)))), 41368 ^ _781404 : [(41371 ^ _781404) ^ [] : [-(_1591986 = _1591988), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591984, _1591984)), hAPP(hAPP(c_Product__Type_OPair(_1591984, _1591984), _1591986), _1591988)), c_Transitive__Closure_Otrancl(_1591984, _1591990)))], (41369 ^ _781404) ^ [] : [_1591986 = _1591988]]], (36135 ^ _781404) ^ [_1455816, _1455818, _1455820] : [36137 ^ _781404 : [(36140 ^ _781404) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1455816, _1455818), 36136 ^ [_1455816, _1455818, _1455820]))], (36138 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1455818, 36136 ^ [_1455816, _1455818, _1455820]), _1455820)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1455816, _1455818), _1455820)))], (48696 ^ _781404) ^ [_1762448] : [class_Nat_Osize(_1762448), -(c_FunDef_Ois__measure(_1762448, c_Nat_Osize__class_Osize(_1762448)))], (4992 ^ _781404) ^ [_857458, _857460, _857462, _857464, _857466, _857468, _857470, _857472, _857474, _857476] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_857476, _857472, _857468, _857464, _857460) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_857474, _857470, _857466, _857462, _857458)), _857476 = _857474, _857472 = _857470, _857468 = _857466, _857464 = _857462, _857460 = _857458], (46209 ^ _781404) ^ [_1708883, _1708885] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708883)), c_List_Oremdups(_1708883, _1708885))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708883)), _1708885))))], (35370 ^ _781404) ^ [_1440672, _1440674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1440672)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1440674)), -(c_Divides_OposDivAlg(_1440672, _1440674) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1440672), _1440674)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1440672, _1440674)))], (33365 ^ _781404) ^ [_1385612, _1385614, _1385616] : [33367 ^ _781404 : [(33370 ^ _781404) ^ [] : [hBOOL(hAPP(_1385614, 33366 ^ [_1385612, _1385614, _1385616]))], (33368 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1385612), 33366 ^ [_1385612, _1385614, _1385616]), _1385616)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1385612, _1385614), _1385616)))], (43054 ^ _781404) ^ [_1638945, _1638947] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1638945, _1638947) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1638945, _1638947)))], (9651 ^ _781404) ^ [_946538, _946540, _946542] : [class_Orderings_Olinorder(_946538), -(_946540 = _946542), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946538), _946540), _946542))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946538), _946542), _946540)))], (386 ^ _781404) ^ [_787325, _787327, _787329, _787331] : [-(c_FunDef_Oreduction__pair(_787329, _787325)), c_FunDef_Oreduction__pair(_787331, _787327), _787331 = _787329, _787327 = _787325], (49115 ^ _781404) ^ [_1771630, _1771632, _1771634, _1771636] : [49116 ^ _781404 : [(49119 ^ _781404) ^ [] : [_1771632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49117 ^ _781404) ^ [] : [hBOOL(hAPP(_1771636, _1771634))]], 49120 ^ _781404 : [(49121 ^ _781404) ^ [_1771755] : [hBOOL(hAPP(hAPP(c_member(_1771630), _1771755), hAPP(c_List_Oset(_1771630), c_List_Oreplicate(_1771630, _1771632, _1771634)))), -(hBOOL(hAPP(_1771636, _1771755)))]]], (43843 ^ _781404) ^ [_1655848, _1655850, _1655852, _1655854, _1655856] : [hAPP(hAPP(c_List_Olist_OCons(_1655848), _1655850), _1655852) = hAPP(hAPP(c_List_Oappend(_1655848), _1655854), _1655856), 43848 ^ _781404 : [(43851 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1655848), _1655850), _1655852) = _1655856)], (43849 ^ _781404) ^ [] : [-(_1655854 = c_List_Olist_ONil(_1655848))]], 43853 ^ _781404 : [(43856 ^ _781404) ^ [] : [-(_1655852 = hAPP(hAPP(c_List_Oappend(_1655848), 43852 ^ [_1655848, _1655850, _1655852, _1655854, _1655856]), _1655856))], (43854 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1655848), _1655850), 43852 ^ [_1655848, _1655850, _1655852, _1655854, _1655856]) = _1655854)]]], (33756 ^ _781404) ^ [_1397881, _1397883, _1397885, _1397887] : [_1397885 = _1397887, -(hAPP(hAPP(c_COMBC(_1397881, tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_fun(_1397883, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1397883, tc_fun(tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_fun(_1397883, tc_HOL_Obool)), _1397881), c_COMBC(_1397883, tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1397883, tc_prod(_1397881, _1397883)), tc_fun(_1397883, tc_fun(tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_HOL_Obool)), _1397881), hAPP(c_COMBB(tc_prod(_1397881, _1397883), tc_fun(tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_HOL_Obool), _1397883), c_member(tc_prod(_1397881, _1397883)))), c_Product__Type_OPair(_1397881, _1397883)))), _1397885) = hAPP(hAPP(c_COMBC(_1397881, tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_fun(_1397883, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1397883, tc_fun(tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_fun(_1397883, tc_HOL_Obool)), _1397881), c_COMBC(_1397883, tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1397883, tc_prod(_1397881, _1397883)), tc_fun(_1397883, tc_fun(tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_HOL_Obool)), _1397881), hAPP(c_COMBB(tc_prod(_1397881, _1397883), tc_fun(tc_fun(tc_prod(_1397881, _1397883), tc_HOL_Obool), tc_HOL_Obool), _1397883), c_member(tc_prod(_1397881, _1397883)))), c_Product__Type_OPair(_1397881, _1397883)))), _1397887))], (778 ^ _781404) ^ [_793125, _793127, _793129, _793131, _793133, _793135] : [-(c_List_Olist__all(_793133, _793129, _793125)), c_List_Olist__all(_793135, _793131, _793127), _793135 = _793133, _793131 = _793129, _793127 = _793125], (2788 ^ _781404) ^ [_822680, _822682, _822684, _822686, _822688, _822690] : [-(c_FunDef_Oin__rel(_822690, _822686, _822682) = c_FunDef_Oin__rel(_822688, _822684, _822680)), _822690 = _822688, _822686 = _822684, _822682 = _822680], (6353 ^ _781404) ^ [_882420, _882422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882420), _882422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _882420)), hAPP(c_Nat_OSuc, _882422))))], (36806 ^ _781404) ^ [_1470229, _1470231] : [class_Orderings_Owellorder(_1470229), 36811 ^ _781404 : [(36812 ^ _781404) ^ [_1470323] : [hBOOL(hAPP(_1470231, _1470323))]], -(hBOOL(hAPP(_1470231, c_Orderings_Oord__class_OLeast(_1470229, _1470231))))], (19653 ^ _781404) ^ [_1130708, _1130710, _1130712] : [class_Rings_Oring__1(_1130708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130710), _1130712)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130712), _1130710)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130708), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130708), _1130712)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130708), _1130710)))], (19249 ^ _781404) ^ [_1123706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123706)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33750 ^ _781404) ^ [_1397332, _1397334, _1397336, _1397338] : [hAPP(hAPP(c_COMBC(_1397332, tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_fun(_1397334, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1397334, tc_fun(tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_fun(_1397334, tc_HOL_Obool)), _1397332), c_COMBC(_1397334, tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1397334, tc_prod(_1397332, _1397334)), tc_fun(_1397334, tc_fun(tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_HOL_Obool)), _1397332), hAPP(c_COMBB(tc_prod(_1397332, _1397334), tc_fun(tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_HOL_Obool), _1397334), c_member(tc_prod(_1397332, _1397334)))), c_Product__Type_OPair(_1397332, _1397334)))), _1397336) = hAPP(hAPP(c_COMBC(_1397332, tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_fun(_1397334, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1397334, tc_fun(tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_fun(_1397334, tc_HOL_Obool)), _1397332), c_COMBC(_1397334, tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1397334, tc_prod(_1397332, _1397334)), tc_fun(_1397334, tc_fun(tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_HOL_Obool)), _1397332), hAPP(c_COMBB(tc_prod(_1397332, _1397334), tc_fun(tc_fun(tc_prod(_1397332, _1397334), tc_HOL_Obool), tc_HOL_Obool), _1397334), c_member(tc_prod(_1397332, _1397334)))), c_Product__Type_OPair(_1397332, _1397334)))), _1397338), -(_1397336 = _1397338)], (3148 ^ _781404) ^ [_828234, _828236, _828238, _828240, _828242, _828244, _828246, _828248] : [-(c_Nat_Onat_Onat__case(_828248, _828244, _828240, _828236) = c_Nat_Onat_Onat__case(_828246, _828242, _828238, _828234)), _828248 = _828246, _828244 = _828242, _828240 = _828238, _828236 = _828234], (1176 ^ _781404) ^ [_799144, _799146] : [-(class_Groups_Oordered__ab__group__add__abs(_799144)), _799146 = _799144, class_Groups_Oordered__ab__group__add__abs(_799146)], (42965 ^ _781404) ^ [_1636525, _1636527, _1636529, _1636531, _1636533] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1636525, _1636527)), _1636529), hAPP(hAPP(c_List_Ozip(_1636525, _1636527), _1636531), _1636533)) = hAPP(hAPP(c_List_Ozip(_1636525, _1636527), hAPP(hAPP(c_List_Otake(_1636525), _1636529), _1636531)), hAPP(hAPP(c_List_Otake(_1636527), _1636529), _1636533)))], (50057 ^ _781404) ^ [_1793026] : [-(c_Relation_Oantisym(_1793026, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1793026, _1793026), tc_HOL_Obool))))], (29927 ^ _781404) ^ [_1317898, _1317900, _1317902, _1317904] : [class_Groups_Ocomm__monoid__mult(_1317898), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1317900), _1317902))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317900, _1317898), _1317904), _1317902) = c_Groups_Oone__class_Oone(_1317898))], (47447 ^ _781404) ^ [_1735194, _1735196] : [_1735196 = c_List_Olist_ONil(_1735194), -(hAPP(c_List_Orev(_1735194), _1735196) = c_List_Olist_ONil(_1735194))], (43292 ^ _781404) ^ [_1644233, _1644235, _1644237, _1644239] : [hBOOL(hAPP(c_List_Odistinct(_1644233), _1644235)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1644237, _1644233)), hAPP(hAPP(c_List_Ozip(_1644237, _1644233), _1644239), _1644235))))], (12562 ^ _781404) ^ [_998308, _998310, _998312, _998314, _998316] : [-(hAPP(c_Set_Ovimage(_998308, _998310, _998312), hAPP(hAPP(c_Set_Oinsert(_998310), _998314), _998316)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998308, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_998308, _998310, _998312), hAPP(hAPP(c_Set_Oinsert(_998310), _998314), c_Orderings_Obot__class_Obot(tc_fun(_998310, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_998308, _998310, _998312), _998316)))], (2584 ^ _781404) ^ [_819454, _819456, _819458, _819460, _819462, _819464] : [-(c_Partial__Function_Oflat__lub(_819464, _819460, _819456) = c_Partial__Function_Oflat__lub(_819462, _819458, _819454)), _819464 = _819462, _819460 = _819458, _819456 = _819454], (11913 ^ _781404) ^ [_985505, _985507, _985509] : [-(hAPP(c_Set_Ovimage(_985505, _985507, _985509), c_Orderings_Otop__class_Otop(tc_fun(_985507, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_985505, tc_HOL_Obool)))], (19263 ^ _781404) ^ [_1123983, _1123985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123983)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123983), _1123985)))], (21183 ^ _781404) ^ [_1157755, _1157757, _1157759, _1157761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157755), _1157757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157759), _1157761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157755), _1157759)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157757), _1157761))))], (24564 ^ _781404) ^ [_1222029, _1222031] : [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), _1222029))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1222031))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1222029))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222031)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222029)))], (41514 ^ _781404) ^ [_1595369, _1595371] : [c_Wellfounded_Oacyclic(_1595369, _1595371), -(c_Wellfounded_Oacyclic(_1595369, hAPP(c_Relation_Oconverse(_1595369, _1595369), _1595371)))], (21237 ^ _781404) ^ [_1158903, _1158905] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158903), _1158905) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1158903 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1158905 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (49537 ^ _781404) ^ [_1780715, _1780717] : [-(c_Lazy__Sequence_Oappend(_1780715, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1780715), _1780717) = _1780717)], (13878 ^ _781404) ^ [_1023464, _1023466, _1023468] : [class_Groups_Ogroup__add(_1023464), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1023464), _1023466), _1023468) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023464), _1023466), hAPP(c_Groups_Ouminus__class_Ouminus(_1023464), _1023468)))], (23878 ^ _781404) ^ [_1209868, _1209870, _1209872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209868), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23881 ^ _781404 : [(23882 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1209870, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1209872), _1209868)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1209872, _1209868))), 23885 ^ _781404 : [(23886 ^ _781404) ^ [_1210078, _1210080] : [-(hBOOL(hAPP(hAPP(_1209870, _1210080), _1210078))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209868), _1210078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210078), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1209872 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1209868), _1210080)), _1210078)]]], (23900 ^ _781404) ^ [] : [23903 ^ _781404 : [(23906 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23902 ^ [_1209868, _1209870, _1209872]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23908 ^ _781404) ^ [] : [-(_1209872 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1209868), 23901 ^ [_1209868, _1209870, _1209872])), 23902 ^ [_1209868, _1209870, _1209872]))], (23910 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1209870, 23901 ^ [_1209868, _1209870, _1209872]), 23902 ^ [_1209868, _1209870, _1209872]))], (23904 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209868), 23902 ^ [_1209868, _1209870, _1209872])))]], -(hBOOL(hAPP(hAPP(_1209870, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1209872), _1209868)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1209872, _1209868))))]]], (39516 ^ _781404) ^ [_1545965, _1545967, _1545969] : [-(hAPP(c_Fun_Ocomp(_1545965, _1545965, _1545967, c_Fun_Oid(_1545965)), _1545969) = _1545969)], (45797 ^ _781404) ^ [_1699483, _1699485, _1699487, _1699489] : [hBOOL(hAPP(c_List_Olistsp(_1699483, hAPP(hAPP(c_COMBS(_1699483, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1699483), c_fconj), _1699485)), _1699487)), _1699489)), 45800 ^ _781404 : [(45803 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1699483, _1699487), _1699489)))], (45801 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1699483, _1699485), _1699489)))]]], (47591 ^ _781404) ^ [_1738300, _1738302, _1738304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738300), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738302)), _1738304))), -(hAPP(hAPP(c_List_Onth(_1738302), hAPP(c_List_Orev(_1738302), _1738304)), _1738300) = hAPP(hAPP(c_List_Onth(_1738302), _1738304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738302)), _1738304)), hAPP(c_Nat_OSuc, _1738300))))], (11797 ^ _781404) ^ [_983250, _983252, _983254, _983256, _983258] : [hBOOL(hAPP(hAPP(c_member(_983254), hAPP(_983256, _983252)), _983258)), -(hBOOL(hAPP(hAPP(c_member(_983250), _983252), hAPP(c_Set_Ovimage(_983250, _983254, _983256), _983258))))], (29639 ^ _781404) ^ [_1312131, _1312133, _1312135, _1312137, _1312139] : [class_Fields_Ofield(_1312131), -(_1312133 = c_Groups_Ozero__class_Ozero(_1312131)), -(_1312135 = c_Groups_Ozero__class_Ozero(_1312131)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1312131), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312131), _1312137), _1312133)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312131), _1312139), _1312135)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312131), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1312131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312131), _1312137), _1312135)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312131), _1312139), _1312133))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312131), _1312133), _1312135)))], (4474 ^ _781404) ^ [_849319, _849321, _849323, _849325] : [-(c_Wellfounded_Oaccp(_849325, _849321) = c_Wellfounded_Oaccp(_849323, _849319)), _849325 = _849323, _849321 = _849319], (19420 ^ _781404) ^ [_1126774, _1126776, _1126778] : [class_Rings_Olinordered__semidom(_1126774), 19423 ^ _781404 : [(19430 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126776), _1126778)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126774), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1126774), _1126776)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1126774), _1126778))))], (19424 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126774), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1126774), _1126776)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1126774), _1126778))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126776), _1126778)))]]], (20081 ^ _781404) ^ [_1138093, _1138095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138093), _1138095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1138093)), c_Int_OBit0(_1138095))))], (52262 ^ _781404) ^ [_1837572, _1837574] : [-(class_Enum_Oenum(tc_fun(_1837572, _1837574))), class_Enum_Oenum(_1837572), class_Enum_Oenum(_1837574)], (27345 ^ _781404) ^ [_1269804] : [_1269804 = 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), _1269804)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (39954 ^ _781404) ^ [_1557948, _1557950] : [c_Wellfounded_Owf(_1557948, _1557950), 39957 ^ _781404 : [(39958 ^ _781404) ^ [_1558017] : [-(hBOOL(hAPP(hAPP(c_member(_1557948), _1558017), c_Wellfounded_Oacc(_1557948, _1557950))))]]], (37443 ^ _781404) ^ [_1486139, _1486141, _1486143] : [class_Rings_Oring__1(_1486139), -(hAPP(c_Int_Oring__1__class_Oof__int(_1486139), 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), _1486141), _1486143)), 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(_1486139), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1486139), _1486141)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1486139), _1486143)))], (39141 ^ _781404) ^ [_1529998, _1530000, _1530002, _1530004, _1530006, _1530008, _1530010] : [class_Groups_Ocomm__monoid__add(_1529998), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530000), _1530002)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530004), _1530006)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1530000, _1529998), hAPP(hAPP(c_COMBS(_1530000, tc_fun(_1530004, tc_HOL_Obool), _1529998), hAPP(hAPP(c_COMBB(tc_fun(_1530004, _1529998), tc_fun(tc_fun(_1530004, tc_HOL_Obool), _1529998), _1530000), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1530004, _1529998)), _1530008)), hAPP(hAPP(c_COMBB(tc_fun(_1530004, tc_HOL_Obool), tc_fun(_1530004, tc_HOL_Obool), _1530000), c_Set_OCollect(_1530004)), hAPP(hAPP(c_COMBB(tc_fun(_1530004, tc_HOL_Obool), tc_fun(_1530004, tc_HOL_Obool), _1530000), hAPP(c_COMBS(_1530004, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1530004), c_fconj), hAPP(hAPP(c_COMBC(_1530004, tc_fun(_1530004, tc_HOL_Obool), tc_HOL_Obool), c_member(_1530004)), _1530006)))), _1530010)))), _1530002) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1530004, _1529998), hAPP(hAPP(c_COMBS(_1530004, tc_fun(_1530000, tc_HOL_Obool), _1529998), hAPP(hAPP(c_COMBB(tc_fun(_1530000, _1529998), tc_fun(tc_fun(_1530000, tc_HOL_Obool), _1529998), _1530004), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1530000, _1529998)), hAPP(c_COMBC(_1530000, _1530004, _1529998), _1530008))), hAPP(hAPP(c_COMBB(tc_fun(_1530000, tc_HOL_Obool), tc_fun(_1530000, tc_HOL_Obool), _1530004), c_Set_OCollect(_1530000)), hAPP(hAPP(c_COMBB(tc_fun(_1530000, tc_HOL_Obool), tc_fun(_1530000, tc_HOL_Obool), _1530004), hAPP(c_COMBS(_1530000, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1530000), c_fconj), hAPP(hAPP(c_COMBC(_1530000, tc_fun(_1530000, tc_HOL_Obool), tc_HOL_Obool), c_member(_1530000)), _1530002)))), hAPP(c_COMBC(_1530000, _1530004, tc_HOL_Obool), _1530010))))), _1530006))], (8750 ^ _781404) ^ [_928854, _928856, _928858, _928860] : [class_Orderings_Oorder(_928854), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928854, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_928854, _928856), _928858)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_928854, _928858), _928860)) = c_Orderings_Obot__class_Obot(tc_fun(_928854, tc_HOL_Obool)))], (10075 ^ _781404) ^ [_953184, _953186, _953188] : [class_Orderings_Opreorder(_953184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953184), _953186), _953188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953184), _953186), _953188)))], (52708 ^ _781404) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (27572 ^ _781404) ^ [_1273763, _1273765, _1273767, _1273769, _1273771, _1273773, _1273775] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1273763, _1273765, _1273767, _1273769, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273763, tc_HOL_Obool)), _1273771), hAPP(hAPP(c_Set_Oinsert(_1273763), _1273773), c_Orderings_Obot__class_Obot(tc_fun(_1273763, tc_HOL_Obool))))), _1273775)), hBOOL(hAPP(hAPP(c_member(_1273763), _1273773), _1273771)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1273763, _1273765, _1273767, _1273769, _1273771), hAPP(hAPP(_1273767, _1273773), _1273775))))], (52356 ^ _781404) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (28709 ^ _781404) ^ [_1295177, _1295179, _1295181, _1295183] : [class_Fields_Olinordered__field__inverse__zero(_1295177), 28712 ^ _781404 : [(28713 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295177), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295177), _1295179), _1295181)), _1295183)), 28716 ^ _781404 : [(28723 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295177), c_Groups_Ozero__class_Ozero(_1295177)), _1295181))), 28726 ^ _781404 : [(28733 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295177), _1295181), c_Groups_Ozero__class_Ozero(_1295177)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295177), c_Groups_Ozero__class_Ozero(_1295177)), _1295183)))], (28727 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295177), _1295181), c_Groups_Ozero__class_Ozero(_1295177))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295177), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295177), _1295183), _1295181)), _1295179)))]]], (28717 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295177), c_Groups_Ozero__class_Ozero(_1295177)), _1295181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295177), _1295179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295177), _1295183), _1295181))))]]], (28739 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295177), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295177), _1295179), _1295181)), _1295183))), 28742 ^ _781404 : [(28745 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295177), _1295179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295177), _1295183), _1295181)))], (28743 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295177), c_Groups_Ozero__class_Ozero(_1295177)), _1295181)))]], 28746 ^ _781404 : [(28749 ^ _781404) ^ [] : [28750 ^ _781404 : [(28753 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295177), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295177), _1295183), _1295181)), _1295179))], (28751 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295177), _1295181), c_Groups_Ozero__class_Ozero(_1295177))))]], 28754 ^ _781404 : [(28757 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295177), c_Groups_Ozero__class_Ozero(_1295177)), _1295183))], (28755 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295177), _1295181), c_Groups_Ozero__class_Ozero(_1295177)))]]], (28747 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295177), c_Groups_Ozero__class_Ozero(_1295177)), _1295181))]]]]], (6417 ^ _781404) ^ [_883368, _883370, _883372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883368), _883370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883370), _883372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883368), _883372)))], (1196 ^ _781404) ^ [_799394, _799396] : [-(class_Rings_Oring__1__no__zero__divisors(_799394)), _799396 = _799394, class_Rings_Oring__1__no__zero__divisors(_799396)], (14631 ^ _781404) ^ [_1037852, _1037854] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1037852, _1037854)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1037852, _1037854), tc_HOL_Obool)))), 14634 ^ _781404 : [(14637 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1037854), c_Orderings_Otop__class_Otop(tc_fun(_1037854, tc_HOL_Obool)))))], (14635 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1037852), c_Orderings_Otop__class_Otop(tc_fun(_1037852, tc_HOL_Obool)))))]]], (32492 ^ _781404) ^ [_1366577, _1366579, _1366581] : [class_Orderings_Olinorder(_1366577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366577), _1366579)), 32499 ^ _781404 : [(32506 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366577, tc_HOL_Obool)), _1366579), hAPP(hAPP(c_Set_Oinsert(_1366577), _1366581), c_Orderings_Obot__class_Obot(tc_fun(_1366577, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1366577, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1366577, hAPP(hAPP(c_Set_Oinsert(_1366577), _1366581), _1366579)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366577), _1366581), c_Big__Operators_Olinorder__class_OMax(_1366577, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366577, tc_HOL_Obool)), _1366579), hAPP(hAPP(c_Set_Oinsert(_1366577), _1366581), c_Orderings_Obot__class_Obot(tc_fun(_1366577, tc_HOL_Obool)))))))], (32500 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366577, tc_HOL_Obool)), _1366579), hAPP(hAPP(c_Set_Oinsert(_1366577), _1366581), c_Orderings_Obot__class_Obot(tc_fun(_1366577, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1366577, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1366577, hAPP(hAPP(c_Set_Oinsert(_1366577), _1366581), _1366579)) = _1366581)]]], (13518 ^ _781404) ^ [_1016684, _1016686, _1016688, _1016690, _1016692] : [class_Groups_Ocomm__monoid__add(_1016684), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016686), _1016688)), -(hBOOL(hAPP(hAPP(c_member(_1016686), _1016690), _1016688))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1016686, _1016684), _1016692), hAPP(hAPP(c_Set_Oinsert(_1016686), _1016690), _1016688)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016684), hAPP(_1016692, _1016690)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1016686, _1016684), _1016692), _1016688)))], (48941 ^ _781404) ^ [_1767487, _1767489, _1767491, _1767493] : [-(c_New__Random__Sequence_Opos__map(_1767487, _1767489, _1767491, _1767493) = c_New__Random__Sequence_Opos__bind(_1767487, _1767489, _1767493, hAPP(c_Fun_Ocomp(_1767489, 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(_1767489))))), _1767487, c_New__Random__Sequence_Opos__single(_1767489)), _1767491)))], (26479 ^ _781404) ^ [_1253452, _1253454, _1253456] : [class_Rings_Oring__1(_1253452), -(hAPP(c_Int_Oring__1__class_Oof__int(_1253452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1253454), _1253456)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1253452), hAPP(c_Int_Oring__1__class_Oof__int(_1253452), _1253454)), hAPP(c_Int_Oring__1__class_Oof__int(_1253452), _1253456)))], (51758 ^ _781404) ^ [_1829388, _1829390, _1829392] : [class_Divides_Osemiring__div(_1829388), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829388), _1829390), _1829392)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829388), _1829390), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1829388), _1829392), _1829390)) = _1829392)], (40908 ^ _781404) ^ [_1579816, _1579818, _1579820, _1579822] : [hBOOL(hAPP(hAPP(c_member(_1579816), _1579818), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1579816, tc_HOL_Obool), _1579820))), c_Orderings_Oorder__class_Omono(tc_fun(_1579816, tc_HOL_Obool), tc_fun(_1579816, tc_HOL_Obool), _1579820), 40918 ^ _781404 : [(40921 ^ _781404) ^ [] : [hBOOL(hAPP(_1579822, 40917 ^ [_1579816, _1579818, _1579820, _1579822]))], (40919 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1579816), 40917 ^ [_1579816, _1579818, _1579820, _1579822]), hAPP(_1579820, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1579816, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1579816, tc_HOL_Obool), _1579820)), hAPP(c_Set_OCollect(_1579816), _1579822))))))]], -(hBOOL(hAPP(_1579822, _1579818)))], (34805 ^ _781404) ^ [_1428273, _1428275] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428273) = hAPP(c_Nat_OSuc, _1428275), -(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(_1428273))), 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)), _1428275))))))], (49127 ^ _781404) ^ [_1771906, _1771908, _1771910, _1771912, _1771914] : [c_List_Oreplicate(_1771906, _1771908, _1771910) = c_List_Oreplicate(_1771906, _1771912, _1771914), 49130 ^ _781404 : [(49133 ^ _781404) ^ [] : [-(_1771908 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1771910 = _1771914)], (49131 ^ _781404) ^ [] : [-(_1771908 = _1771912)]]], (6283 ^ _781404) ^ [_881338] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _881338)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _881338))], (33910 ^ _781404) ^ [_1403175, _1403177, _1403179, _1403181, _1403183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403175, tc_HOL_Obool)), _1403177), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1403179, tc_fun(_1403175, tc_HOL_Obool)), _1403181), _1403183))), 33913 ^ _781404 : [(33914 ^ _781404) ^ [_1403308] : [hBOOL(hAPP(hAPP(c_member(_1403179), _1403308), _1403181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403175, tc_HOL_Obool)), _1403177), hAPP(_1403183, _1403308))))]]], (5723 ^ _781404) ^ [_871697, _871699] : [class_Orderings_Opreorder(_871697), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871697), _871699), _871699)))], (10507 ^ _781404) ^ [_960332, _960334, _960336] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960332, tc_HOL_Obool)), _960334), _960336))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960332, tc_HOL_Obool)), _960334), _960336)), -(_960334 = _960336)], (43089 ^ _781404) ^ [_1639609, _1639611] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1639609, _1639611) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1639609), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1639611)))], (26107 ^ _781404) ^ [_1247748, _1247750] : [c_Code__Numeral_OSuc__code__numeral(_1247748) = c_Code__Numeral_OSuc__code__numeral(_1247750), -(_1247748 = _1247750)], (35081 ^ _781404) ^ [_1434668, _1434670] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1434668)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434670)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1434670))), 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), _1434668)), c_Int_Onat)))))], (52018 ^ _781404) ^ [_1833837, _1833839, _1833841] : [class_Rings_Olinordered__idom(_1833837), 52021 ^ _781404 : [(52028 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833837), _1833839), _1833841)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833837), _1833839), hAPP(c_Groups_Oabs__class_Oabs(_1833837), _1833841))))], (52022 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833837), _1833839), hAPP(c_Groups_Oabs__class_Oabs(_1833837), _1833841))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833837), _1833839), _1833841)))]]], (43663 ^ _781404) ^ [_1651504, _1651506, _1651508] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651504), tc_List_Olist(_1651504))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651504), tc_List_Olist(_1651504)), _1651506), c_List_Olist_ONil(_1651504))), c_List_Olistrel1(_1651504, _1651508)))], (34149 ^ _781404) ^ [_1408714, _1408716, _1408718, _1408720, _1408722] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408714, tc_fun(_1408716, tc_HOL_Obool)), _1408718), hAPP(hAPP(c_COMBB(tc_fun(_1408716, tc_HOL_Obool), tc_fun(_1408716, tc_HOL_Obool), _1408714), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408716, tc_HOL_Obool)), _1408720)), _1408722)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408716, tc_HOL_Obool)), _1408720), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408714, tc_fun(_1408716, tc_HOL_Obool)), _1408718), _1408722)))], (32050 ^ _781404) ^ [_1358357, _1358359, _1358361] : [class_Orderings_Olinorder(_1358357), 32053 ^ _781404 : [(32060 ^ _781404) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358357), _1358359), _1358361) = _1358361, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358357), _1358359), _1358361)))], (32054 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358357), _1358359), _1358361)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358357), _1358359), _1358361) = _1358361)]]], (38278 ^ _781404) ^ [_1507485, _1507487, _1507489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507485, _1507485), tc_HOL_Obool)), _1507487), _1507489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1507485, tc_HOL_Obool)), c_Wellfounded_Oacc(_1507485, _1507489)), c_Wellfounded_Oacc(_1507485, _1507487))))], (52506 ^ _781404) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (46530 ^ _781404) ^ [_1716265, _1716267, _1716269, _1716271] : [-(hAPP(c_List_Ofilter(_1716265, _1716267), hAPP(c_List_Ofilter(_1716265, _1716269), _1716271)) = hAPP(c_List_Ofilter(_1716265, hAPP(hAPP(c_COMBS(_1716265, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1716265), c_fconj), _1716269)), _1716267)), _1716271))], (8776 ^ _781404) ^ [_929404, _929406] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929404, tc_HOL_Obool)), _929406), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_929404, tc_HOL_Obool)), _929406)) = c_Orderings_Obot__class_Obot(tc_fun(_929404, tc_HOL_Obool)))], (52798 ^ _781404) ^ [_1843141, _1843143] : [hBOOL(hAPP(hAPP(c_fdisj, _1843141), _1843143)), -(hBOOL(_1843141)), -(hBOOL(_1843143))], (23329 ^ _781404) ^ [_1199468, _1199470] : [-(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), _1199468)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1199470)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1199468))) = 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), _1199470)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1199468)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (26527 ^ _781404) ^ [_1254272, _1254274] : [c_Nat__Transfer_Onat__set(_1254272), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1254274), _1254272)), -(c_Nat__Transfer_Ois__nat(_1254274))], (39185 ^ _781404) ^ [_1531939, _1531941] : [class_Complete__Lattice_Ocomplete__lattice(_1531939), -(c_Complete__Lattice_OSup__class_OSup(_1531939, _1531941) = c_Complete__Lattice_OInf__class_OInf(_1531939, hAPP(c_Set_OCollect(_1531939), hAPP(hAPP(c_COMBB(tc_fun(_1531939, tc_HOL_Obool), tc_HOL_Obool, _1531939), c_HOL_OAll(_1531939)), hAPP(hAPP(c_COMBB(tc_fun(_1531939, tc_HOL_Obool), tc_fun(_1531939, tc_HOL_Obool), _1531939), hAPP(c_COMBS(_1531939, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1531939), c_fimplies), hAPP(hAPP(c_COMBC(_1531939, tc_fun(_1531939, tc_HOL_Obool), tc_HOL_Obool), c_member(_1531939)), _1531941)))), hAPP(c_COMBC(_1531939, _1531939, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1531939)))))))], (34887 ^ _781404) ^ [_1430009, _1430011, _1430013, _1430015] : [class_Groups_Oab__group__add(_1430009), 34890 ^ _781404 : [(34897 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1430011), _1430013))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1430009), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1430009, _1430009), hAPP(hAPP(c_COMBB(_1430009, tc_fun(_1430009, _1430009), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1430009)), _1430015)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1430009, tc_Nat_Onat), _1430015), 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, _1430011, _1430013)) = c_Groups_Ozero__class_Ozero(_1430009))], (34891 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1430011), _1430013)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1430009), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1430009, _1430009), hAPP(hAPP(c_COMBB(_1430009, tc_fun(_1430009, _1430009), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1430009)), _1430015)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1430009, tc_Nat_Onat), _1430015), 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, _1430011, _1430013)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1430009), hAPP(_1430015, _1430011)), hAPP(_1430015, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430013), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (12800 ^ _781404) ^ [_1003156, _1003158, _1003160, _1003162, _1003164, _1003166] : [hBOOL(hAPP(hAPP(c_member(_1003156), _1003158), _1003160)), -(hAPP(c_Set_Oimage(_1003156, _1003162, c_Fun_Ofun__upd(_1003156, _1003162, _1003164, _1003158, _1003166)), _1003160) = hAPP(hAPP(c_Set_Oinsert(_1003162), _1003166), hAPP(c_Set_Oimage(_1003156, _1003162, _1003164), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1003156, tc_HOL_Obool)), _1003160), hAPP(hAPP(c_Set_Oinsert(_1003156), _1003158), c_Orderings_Obot__class_Obot(tc_fun(_1003156, tc_HOL_Obool)))))))], (31966 ^ _781404) ^ [_1356676, _1356678, _1356680] : [class_Orderings_Olinorder(_1356676), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356676), _1356678), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356676), _1356678), _1356680)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356676), _1356678), _1356680))], (34241 ^ _781404) ^ [_1413145, _1413147, _1413149, _1413151, _1413153] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413145, tc_fun(_1413147, tc_HOL_Obool)), _1413149), hAPP(hAPP(c_COMBB(tc_fun(_1413147, tc_HOL_Obool), tc_fun(_1413147, tc_HOL_Obool), _1413145), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413147, tc_HOL_Obool)), _1413151)), _1413153)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413147, tc_HOL_Obool)), _1413151), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413145, tc_fun(_1413147, tc_HOL_Obool)), _1413149), _1413153)))], (20121 ^ _781404) ^ [_1138710, _1138712] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1138710)), c_Int_OBit0(_1138712)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1138710), _1138712)))], (44800 ^ _781404) ^ [_1677643, _1677645, _1677647] : [class_Orderings_Olinorder(_1677643), -(c_Big__Operators_Olinorder__class_OMin(_1677643, hAPP(c_List_Oset(_1677643), hAPP(hAPP(c_List_Olist_OCons(_1677643), _1677645), _1677647))) = hAPP(c_List_Ofoldl(_1677643, _1677643, c_Orderings_Oord__class_Omin(_1677643), _1677645), _1677647))], (28395 ^ _781404) ^ [_1289152, _1289154, _1289156, _1289158] : [class_Fields_Ofield(_1289152), -(_1289154 = c_Groups_Ozero__class_Ozero(_1289152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1289156), _1289158)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1289152), _1289154), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1289158), _1289156)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289152), hAPP(hAPP(c_Power_Opower__class_Opower(_1289152), _1289154), _1289158)), hAPP(hAPP(c_Power_Opower__class_Opower(_1289152), _1289154), _1289156)))], (8968 ^ _781404) ^ [_933262] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _933262)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _933262)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _933262)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (42644 ^ _781404) ^ [_1627145, _1627147, _1627149, _1627151] : [42647 ^ _781404 : [(42652 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627145, _1627145)), hAPP(hAPP(c_Product__Type_OPair(_1627145, _1627145), 42646 ^ [_1627145, _1627147, _1627149, _1627151]), 42645 ^ [_1627145, _1627147, _1627149, _1627151])), _1627147))], (42650 ^ _781404) ^ [] : [42645 ^ [_1627145, _1627147, _1627149, _1627151] = 42646 ^ [_1627145, _1627147, _1627149, _1627151]], (42648 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627145, _1627145)), hAPP(hAPP(c_Product__Type_OPair(_1627145, _1627145), 42645 ^ [_1627145, _1627147, _1627149, _1627151]), 42646 ^ [_1627145, _1627147, _1627149, _1627151])), _1627147))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627145), tc_List_Olist(_1627145))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627145), tc_List_Olist(_1627145)), _1627149), _1627151)), c_List_Olexord(_1627145, _1627147)))), -(_1627149 = _1627151), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627145), tc_List_Olist(_1627145))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627145), tc_List_Olist(_1627145)), _1627151), _1627149)), c_List_Olexord(_1627145, _1627147))))], (39514 ^ _781404) ^ [_1545928, _1545930, _1545932] : [-(hAPP(c_Fun_Ocomp(_1545928, _1545930, _1545928, _1545932), c_Fun_Oid(_1545928)) = _1545932)], (33851 ^ _781404) ^ [] : [-(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)))], (17369 ^ _781404) ^ [_1091267, _1091269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091267), _1091269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091267)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091269))))], (34491 ^ _781404) ^ [_1420754] : [class_Orderings_Olinorder(_1420754), -(c_Orderings_Oord_Omin(_1420754, hAPP(c_COMBC(_1420754, _1420754, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1420754))) = c_Orderings_Oord__class_Omax(_1420754))], (12150 ^ _781404) ^ [_990203, _990205, _990207, _990209] : [hBOOL(hAPP(hAPP(c_member(_990203), _990205), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990203, tc_HOL_Obool)), _990207), _990209))), -(hBOOL(hAPP(hAPP(c_member(_990203), _990205), _990207)))], (10085 ^ _781404) ^ [_953343, _953345, _953347] : [class_Orderings_Olinorder(_953343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953343), _953345), _953347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953343), _953347), _953345))], (23477 ^ _781404) ^ [_1202851, _1202853] : [class_Divides_Osemiring__div(_1202851), -(c_Divides_Odiv__class_Omod(_1202851, c_Groups_Ozero__class_Ozero(_1202851), _1202853) = c_Groups_Ozero__class_Ozero(_1202851))], (41600 ^ _781404) ^ [_1597468, _1597470, _1597472] : [-(hAPP(c_Relation_ORange(_1597468, _1597470), _1597472) = hAPP(c_Relation_ODomain(_1597470, _1597468), hAPP(c_Relation_Oconverse(_1597468, _1597470), _1597472)))], (42473 ^ _781404) ^ [_1622053, _1622055, _1622057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1622053, _1622053), tc_HOL_Obool)), _1622055), _1622057)), c_Relation_Orefl__on(_1622053, c_Orderings_Otop__class_Otop(tc_fun(_1622053, tc_HOL_Obool)), _1622057), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1622053), tc_List_Olist(_1622053)), tc_HOL_Obool)), c_List_Olistrel1(_1622053, _1622055)), c_List_Olistrel(_1622053, _1622057))))], (22965 ^ _781404) ^ [_1192063, _1192065] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1192063), hAPP(c_Int_Onumber__class_Onumber__of(_1192063), _1192065)), 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(_1192063), hAPP(c_Int_Onumber__class_Onumber__of(_1192063), _1192065)), hAPP(c_Int_Onumber__class_Onumber__of(_1192063), _1192065))), class_Groups_Omonoid__mult(_1192063), class_Int_Onumber(_1192063)], (46427 ^ _781404) ^ [_1713049, _1713051] : [-(hAPP(c_List_Oset(_1713049), c_List_Oconcat(_1713049, _1713051)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1713049), tc_fun(_1713049, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1713049)), _1713051)), c_List_Oset(_1713049)))], (7025 ^ _781404) ^ [_894959, _894961, _894963, _894965] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894959, tc_HOL_Obool)), _894961), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894959, tc_HOL_Obool)), _894963), _894965)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894959, tc_HOL_Obool)), _894963), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894959, tc_HOL_Obool)), _894961), _894965)))], (26577 ^ _781404) ^ [_1255033, _1255035] : [class_Rings_Olinordered__idom(_1255033), 26580 ^ _781404 : [(26587 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255033), c_Groups_Ozero__class_Ozero(_1255033)), hAPP(c_Int_Oring__1__class_Oof__int(_1255033), _1255035))))], (26581 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255033), c_Groups_Ozero__class_Ozero(_1255033)), hAPP(c_Int_Oring__1__class_Oof__int(_1255033), _1255035))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255035)))]]], (41026 ^ _781404) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (49051 ^ _781404) ^ [_1770436, _1770438, _1770440, _1770442] : [-(hAPP(hAPP(c_List_Omap(_1770436, _1770438), hAPP(c_COMBK(_1770438, _1770436), _1770440)), _1770442) = c_List_Oreplicate(_1770438, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770436)), _1770442), _1770440))], (33400 ^ _781404) ^ [_1387829, _1387831, _1387833, _1387835] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1387829, tc_fun(_1387831, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1387829, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1387831, tc_HOL_Obool), tc_fun(_1387831, tc_HOL_Obool), _1387829), hAPP(c_COMBC(_1387831, tc_fun(_1387831, tc_HOL_Obool), tc_HOL_Obool), c_member(_1387831))), _1387833)), _1387835)), -(hBOOL(hAPP(hAPP(c_member(_1387831), _1387835), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1387829, tc_fun(_1387831, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1387829, tc_HOL_Obool))), _1387833))))], (39898 ^ _781404) ^ [_1557006, _1557008, _1557010] : [c_Wellfounded_Owf(_1557006, _1557008), hBOOL(hAPP(hAPP(c_member(tc_prod(_1557006, _1557006)), hAPP(hAPP(c_Product__Type_OPair(_1557006, _1557006), _1557010), _1557010)), _1557008))], (47718 ^ _781404) ^ [_1741063, _1741065, _1741067, _1741069, _1741071] : [-(c_List_OtakeWhile(_1741063, _1741065, hAPP(hAPP(c_List_Omap(_1741067, _1741063), _1741069), _1741071)) = hAPP(hAPP(c_List_Omap(_1741067, _1741063), _1741069), c_List_OtakeWhile(_1741067, hAPP(c_Fun_Ocomp(_1741063, tc_HOL_Obool, _1741067, _1741065), _1741069), _1741071)))], (45158 ^ _781404) ^ [_1684498, _1684500] : [-(_1684498 = c_List_Olist_ONil(_1684500)), -(c_Random_Oselect__weight(_1684500, hAPP(hAPP(c_List_Omap(_1684500, tc_prod(tc_Code__Numeral_Ocode__numeral, _1684500)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1684500), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1684498)) = c_Random_Oselect(_1684500, _1684498))], (25736 ^ _781404) ^ [_1241304, _1241306] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1241304, _1241306)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1241306), _1241304)))], (37514 ^ _781404) ^ [_1488067, _1488069, _1488071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1488067, _1488067), tc_HOL_Obool)), _1488069), _1488071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488067, tc_HOL_Obool)), hAPP(c_Relation_OField(_1488067), _1488069)), hAPP(c_Relation_OField(_1488067), _1488071))))], (52326 ^ _781404) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (21083 ^ _781404) ^ [_1155726] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155726), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1156 ^ _781404) ^ [_798894, _798896] : [-(class_Lattices_Obounded__lattice(_798894)), _798896 = _798894, class_Lattices_Obounded__lattice(_798896)], (9318 ^ _781404) ^ [_940800, _940802, _940804] : [class_Orderings_Olinorder(_940800), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940800), _940802), _940804)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940800, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_940800), _940802)), c_SetInterval_Oord__class_OgreaterThanLessThan(_940800, _940802, _940804)) = hAPP(c_SetInterval_Oord__class_OlessThan(_940800), _940804))], (42161 ^ _781404) ^ [_1612042, _1612044, _1612046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1612042), c_Nitpick_Oplus__frac(_1612042, _1612044, c_Nitpick_Ouminus__frac(_1612042, _1612046)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1612042, _1612044, _1612046))], (40080 ^ _781404) ^ [_1560781, _1560783] : [c_FunDef_Oreduction__pair(_1560781, _1560783), 40083 ^ _781404 : [(40086 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1560781, _1560781), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1560781, _1560781, _1560781), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1560781, _1560781), tc_HOL_Obool), tc_fun(tc_prod(_1560781, _1560781), tc_HOL_Obool)), _1560783)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1560781, _1560781), tc_HOL_Obool), tc_fun(tc_prod(_1560781, _1560781), tc_HOL_Obool)), _1560783))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1560781, _1560781), tc_HOL_Obool), tc_fun(tc_prod(_1560781, _1560781), tc_HOL_Obool)), _1560783))))], (40084 ^ _781404) ^ [] : [-(c_Wellfounded_Owf(_1560781, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1560781, _1560781), tc_HOL_Obool), tc_fun(tc_prod(_1560781, _1560781), tc_HOL_Obool)), _1560783)))]]], (1646 ^ _781404) ^ [_805019, _805021] : [-(class_Rings_Oordered__cancel__semiring(_805019)), _805021 = _805019, class_Rings_Oordered__cancel__semiring(_805021)], (37178 ^ _781404) ^ [_1479016] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1479016)), -(_1479016 = 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))), _1479016)), c_FunDef_Omax__strict)))], (27207 ^ _781404) ^ [_1267136, _1267138] : [class_Rings_Olinordered__idom(_1267136), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267136), c_Groups_Osgn__class_Osgn(_1267136, _1267138)), hAPP(c_Groups_Oabs__class_Oabs(_1267136), _1267138)) = _1267138)], (33173 ^ _781404) ^ [_1380495, _1380497, _1380499, _1380501] : [class_Fields_Olinordered__field(_1380495), -(hAPP(c_Groups_Oabs__class_Oabs(_1380495), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380497, _1380495), _1380499), _1380501)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380497, _1380495), hAPP(hAPP(c_COMBB(_1380495, _1380495, _1380497), c_Groups_Oabs__class_Oabs(_1380495)), _1380499)), _1380501))], (30814 ^ _781404) ^ [_1335297, _1335299, _1335301, _1335303, _1335305] : [class_Orderings_Olinorder(_1335297), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335297), _1335299), _1335301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335297), _1335303), _1335305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335297), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1335297), _1335299), _1335303)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1335297), _1335301), _1335305))))], (41219 ^ _781404) ^ [_1588358, _1588360] : [-(c_Relation_Orefl__on(_1588358, c_Orderings_Otop__class_Otop(tc_fun(_1588358, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588358, _1588360)))], (46550 ^ _781404) ^ [_1716581, _1716583, _1716585] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1716581), tc_List_Olist(_1716581)), c_List_Opartition(_1716581, _1716583, _1716585)) = hAPP(c_List_Ofilter(_1716581, _1716583), _1716585))], (39576 ^ _781404) ^ [_1547070, _1547072] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1547070), _1547072)), -(_1547072 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1547070, 39580 ^ [_1547070, _1547072]), 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)), 39579 ^ [_1547070, _1547072]))))], (8471 ^ _781404) ^ [_924265] : [_924265 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _924265), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14150 ^ _781404) ^ [_1028335, _1028337, _1028339, _1028341, _1028343] : [class_Groups_Ocomm__monoid__add(_1028335), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028337), _1028339)), hBOOL(hAPP(hAPP(c_member(_1028337), _1028341), _1028339)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028337, _1028335), _1028343), _1028339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028335), hAPP(_1028343, _1028341)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028337, _1028335), _1028343), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1028337, tc_HOL_Obool)), _1028339), hAPP(hAPP(c_Set_Oinsert(_1028337), _1028341), c_Orderings_Obot__class_Obot(tc_fun(_1028337, tc_HOL_Obool)))))))], (33591 ^ _781404) ^ [_1393233, _1393235, _1393237, _1393239, _1393241] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393233, tc_fun(_1393235, tc_HOL_Obool)), _1393237), _1393239), _1393241))), 33592 ^ _781404 : [(33593 ^ _781404) ^ [_1393305] : [hBOOL(hAPP(hAPP(c_member(_1393233), _1393305), _1393237)), hBOOL(hAPP(hAPP(_1393239, _1393305), _1393241))]]], (21909 ^ _781404) ^ [_1171110, _1171112, _1171114, _1171116, _1171118, _1171120] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1171110), -(_1171112 = c_Groups_Ozero__class_Ozero(_1171110)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171110), _1171114), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171110), _1171112), _1171118)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171110), _1171116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171110), _1171112), _1171120)), _1171114 = _1171116, -(_1171118 = _1171120)], (39796 ^ _781404) ^ [_1555082, _1555084, _1555086, _1555088] : [39797 ^ _781404 : [(39798 ^ _781404) ^ [_1555136] : [hBOOL(hAPP(hAPP(_1555086, _1555136), _1555088))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1555082, _1555084, _1555086), _1555088)))], (17519 ^ _781404) ^ [_1093811] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1093811) = _1093811)], (38377 ^ _781404) ^ [_1509462, _1509464, _1509466, _1509468, _1509470, _1509472] : [c_Typedef_Otype__definition(_1509462, _1509464, _1509466, _1509468, _1509470), hBOOL(hAPP(hAPP(c_member(_1509464), _1509472), _1509470)), -(hAPP(_1509466, hAPP(_1509468, _1509472)) = _1509472)], (2100 ^ _781404) ^ [_811828, _811830, _811832, _811834] : [-(c_SMT_Oz3div(_811834, _811830) = c_SMT_Oz3div(_811832, _811828)), _811834 = _811832, _811830 = _811828], (44625 ^ _781404) ^ [_1674026, _1674028] : [hBOOL(hAPP(c_List_Odistinct(_1674026), _1674028)), -(hBOOL(hAPP(c_List_Odistinct(_1674026), hAPP(c_List_Otl(_1674026), _1674028))))], (20525 ^ _781404) ^ [_1145542] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1145542)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1145542) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4056 ^ _781404) ^ [_842710, _842712, _842714, _842716, _842718, _842720, _842722, _842724] : [-(c_New__DSequence_Oneg__bind(_842724, _842720, _842716, _842712) = c_New__DSequence_Oneg__bind(_842722, _842718, _842714, _842710)), _842724 = _842722, _842720 = _842718, _842716 = _842714, _842712 = _842710], (15669 ^ _781404) ^ [_1058555, _1058557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1058555), _1058557))), 15672 ^ _781404 : [(15675 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1058555), _1058557)))], (15673 ^ _781404) ^ [] : [_1058557 = c_Orderings_Obot__class_Obot(tc_fun(_1058555, tc_HOL_Obool))]]], (20937 ^ _781404) ^ [_1153220, _1153222, _1153224, _1153226, _1153228] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1153220), 20940 ^ _781404 : [(20941 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153220), _1153222), _1153226)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153220), _1153224), _1153228)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153220), _1153222), _1153228)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153220), _1153224), _1153226)), -(_1153222 = _1153224), -(_1153226 = _1153228)], (20951 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153220), _1153222), _1153226)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153220), _1153224), _1153228)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153220), _1153222), _1153228)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153220), _1153224), _1153226))), 20954 ^ _781404 : [(20957 ^ _781404) ^ [] : [_1153226 = _1153228], (20955 ^ _781404) ^ [] : [_1153222 = _1153224]]]]], (20373 ^ _781404) ^ [_1143016, _1143018] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1143016)), c_Int_OBit1(_1143018)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1143016), c_Int_Osucc(_1143018))))], (21803 ^ _781404) ^ [_1169135, _1169137, _1169139] : [class_Rings_Olinordered__ring__strict(_1169135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169135), _1169137), c_Groups_Ozero__class_Ozero(_1169135))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169135), _1169139), c_Groups_Ozero__class_Ozero(_1169135))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169135), c_Groups_Ozero__class_Ozero(_1169135)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169135), _1169137), _1169139))))], (40174 ^ _781404) ^ [_1563516, _1563518, _1563520, _1563522] : [40175 ^ _781404 : [(40176 ^ _781404) ^ [_1563570] : [hBOOL(hAPP(hAPP(_1563520, _1563522), _1563570))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1563516, _1563518, _1563520), _1563522)))], (12654 ^ _781404) ^ [_1000131, _1000133, _1000135, _1000137] : [c_Fun_Oinj__on(_1000131, _1000133, _1000135, c_Orderings_Otop__class_Otop(tc_fun(_1000131, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1000131, _1000133, c_Orderings_Otop__class_Otop(tc_fun(_1000131, tc_HOL_Obool)), _1000135), hAPP(_1000135, _1000137)) = _1000137)], (7383 ^ _781404) ^ [_901829, _901831] : [class_Groups_Oordered__ab__group__add(_901829), -(hAPP(c_Set_Oimage(_901829, _901829, c_Groups_Ouminus__class_Ouminus(_901829)), hAPP(c_SetInterval_Oord__class_OatMost(_901829), _901831)) = hAPP(c_SetInterval_Oord__class_OatLeast(_901829), hAPP(c_Groups_Ouminus__class_Ouminus(_901829), _901831)))], (36816 ^ _781404) ^ [_1470383, _1470385, _1470387] : [class_Orderings_Owellorder(_1470383), hBOOL(hAPP(_1470385, _1470387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1470383), c_Orderings_Oord__class_OLeast(_1470383, _1470385)), _1470387)))], (35083 ^ _781404) ^ [_1434731, _1434733, _1434735] : [-(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), _1434731)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1434733))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1434735))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1434735), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1434731), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1434731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1434735), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1434733)))))], (2 ^ _781404) ^ [_781431] : [-(_781431 = _781431)], (41093 ^ _781404) ^ [_1584412, _1584414, _1584416, _1584418, _1584420] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584412, _1584412)), hAPP(hAPP(c_Product__Type_OPair(_1584412, _1584412), _1584414), _1584416)), _1584418)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584412, _1584412)), hAPP(hAPP(c_Product__Type_OPair(_1584412, _1584412), _1584416), _1584420)), c_Transitive__Closure_Otrancl(_1584412, _1584418))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584412, _1584412)), hAPP(hAPP(c_Product__Type_OPair(_1584412, _1584412), _1584414), _1584420)), c_Transitive__Closure_Otrancl(_1584412, _1584418))))], (50717 ^ _781404) ^ [_1806729] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50713 ^ [_1806729]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (36466 ^ _781404) ^ [_1462846] : [-(hAPP(c_Int_Onat, _1462846) = 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, _1462846)), 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)))))))], (25431 ^ _781404) ^ [_1236022, _1236024, _1236026] : [-(hBOOL(hAPP(_1236022, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1236024), _1236026)))), 25434 ^ _781404 : [(25437 ^ _781404) ^ [] : [hBOOL(hAPP(_1236022, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25435 ^ _781404) ^ [] : [-(_1236026 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25438 ^ _781404 : [(25443 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25441 ^ [_1236022, _1236024, _1236026]), _1236026)))], (25445 ^ _781404) ^ [] : [-(_1236024 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1236026), 25440 ^ [_1236022, _1236024, _1236026])), 25441 ^ [_1236022, _1236024, _1236026]))], (25447 ^ _781404) ^ [] : [hBOOL(hAPP(_1236022, 25440 ^ [_1236022, _1236024, _1236026]))], (25439 ^ _781404) ^ [] : [_1236026 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (14595 ^ _781404) ^ [_1037191, _1037193, _1037195] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037191), _1037195)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1037191), hAPP(hAPP(c_Set_Oinsert(_1037191), _1037193), _1037195))))], (40456 ^ _781404) ^ [_1569632, _1569634] : [-(c_Hilbert__Choice_OEps(_1569632, hAPP(c_fequal, _1569634)) = _1569634)], (23463 ^ _781404) ^ [_1202568, _1202570, _1202572, _1202574, _1202576, _1202578] : [class_Divides_Osemiring__div(_1202568), c_Divides_Odiv__class_Omod(_1202568, _1202570, _1202572) = c_Divides_Odiv__class_Omod(_1202568, _1202574, _1202572), c_Divides_Odiv__class_Omod(_1202568, _1202576, _1202572) = c_Divides_Odiv__class_Omod(_1202568, _1202578, _1202572), -(c_Divides_Odiv__class_Omod(_1202568, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202568), _1202570), _1202576), _1202572) = c_Divides_Odiv__class_Omod(_1202568, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202568), _1202574), _1202578), _1202572))], (25037 ^ _781404) ^ [_1229684] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1229684), c_Int_OMin) = c_Int_Opred(_1229684))], (12624 ^ _781404) ^ [_999685, _999687, _999689, _999691, _999693] : [c_Fun_Oinj__on(_999685, _999687, _999689, c_Orderings_Otop__class_Otop(tc_fun(_999685, tc_HOL_Obool))), 12627 ^ _781404 : [(12634 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_999685), _999691), _999693)), -(hBOOL(hAPP(hAPP(c_member(_999687), hAPP(_999689, _999691)), hAPP(c_Set_Oimage(_999685, _999687, _999689), _999693))))], (12628 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_999687), hAPP(_999689, _999691)), hAPP(c_Set_Oimage(_999685, _999687, _999689), _999693))), -(hBOOL(hAPP(hAPP(c_member(_999685), _999691), _999693)))]]], (32826 ^ _781404) ^ [_1372829, _1372831, _1372833] : [class_Orderings_Olinorder(_1372829), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372829), _1372831)), -(hBOOL(hAPP(hAPP(c_member(_1372829), _1372833), _1372831))), -(c_Big__Operators_Olattice_OSup__fin(_1372829, c_Orderings_Oord__class_Omax(_1372829), hAPP(hAPP(c_Set_Oinsert(_1372829), _1372833), _1372831)) = hAPP(hAPP(c_Finite__Set_Ofold(_1372829, _1372829, c_Orderings_Oord__class_Omax(_1372829)), _1372833), _1372831))], (8978 ^ _781404) ^ [_933480, _933482, _933484, _933486] : [class_Orderings_Oorder(_933480), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933480, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_933480, _933482, _933484)), c_SetInterval_Oord__class_OgreaterThanLessThan(_933480, _933484, _933486)) = c_Orderings_Obot__class_Obot(tc_fun(_933480, tc_HOL_Obool)))], (49211 ^ _781404) ^ [_1773330, _1773332, _1773334, _1773336] : [-(hBOOL(hAPP(hAPP(c_member(_1773330), _1773332), hAPP(c_List_Oset(_1773330), c_List_Oreplicate(_1773330, _1773334, _1773336))))), _1773332 = _1773336, -(_1773334 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42276 ^ _781404) ^ [_1616034, _1616036, _1616038, _1616040] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1616034), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1616036), _1616038)))), -(hAPP(c_Random_Opick(_1616036, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1616036)), _1616038), _1616040)), _1616034) = hAPP(c_Random_Opick(_1616036, _1616040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1616034), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1616036), _1616038))))], (21145 ^ _781404) ^ [_1156862, _1156864, _1156866] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156862), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1156864), _1156866)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156862), _1156864)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156862), _1156866)))], (24632 ^ _781404) ^ [_1223150, _1223152] : [class_Int_Onumber__ring(_1223150), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1223150), hAPP(c_Int_Onumber__class_Onumber__of(_1223150), 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)))), _1223152))) = hAPP(c_Int_Onumber__class_Onumber__of(_1223150), c_Int_OMin))], (30380 ^ _781404) ^ [_1327188, _1327190, _1327192, _1327194] : [class_Lattices_Osemilattice__inf(_1327188), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327188), _1327190)), 30390 ^ _781404 : [(30393 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327188), _1327192), 30389 ^ [_1327188, _1327190, _1327192, _1327194]))], (30391 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327188), 30389 ^ [_1327188, _1327190, _1327192, _1327194]), _1327190)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327188), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1327188), _1327192), _1327194)), hAPP(hAPP(c_Finite__Set_Ofold(_1327188, _1327188, c_Lattices_Osemilattice__inf__class_Oinf(_1327188)), _1327194), _1327190))))], (24648 ^ _781404) ^ [_1223550, _1223552, _1223554] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1223550), _1223552)), _1223554) = 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), _1223550), _1223554)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223552), _1223554))), 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, _1223550, _1223554)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223552, _1223554))), _1223554)))], (37351 ^ _781404) ^ [_1483755, _1483757, _1483759, _1483761, _1483763] : [class_Groups_Ocomm__monoid__add(_1483755), class_Groups_Ocomm__monoid__mult(_1483755), _1483757 = _1483759, c_Nat__Transfer_Onat__set(_1483759), 37369 ^ _781404 : [(37372 ^ _781404) ^ [] : [hAPP(_1483761, 37368 ^ [_1483755, _1483757, _1483759, _1483761, _1483763]) = hAPP(_1483763, 37368 ^ [_1483755, _1483757, _1483759, _1483761, _1483763])], (37370 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37368 ^ [_1483755, _1483757, _1483759, _1483761, _1483763])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1483755), _1483761), _1483757) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1483755), _1483763), _1483759))], (19492 ^ _781404) ^ [_1128060] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1128060)), -(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)), _1128060))))], (11659 ^ _781404) ^ [_980974, _980976, _980978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_980974, tc_HOL_Obool)), _980976), _980978)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_980974, tc_HOL_Obool)), _980976), hAPP(c_Set_OPow(_980974), _980978))))], (35099 ^ _781404) ^ [_1435175, _1435177, _1435179] : [class_Int_Onumber__ring(_1435175), 35102 ^ _781404 : [(35109 ^ _781404) ^ [] : [-(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), _1435177)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435175), hAPP(c_Int_Onumber__class_Onumber__of(_1435175), _1435179)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1435177))) = c_Groups_Oone__class_Oone(_1435175))], (35103 ^ _781404) ^ [] : [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), _1435177))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435175), hAPP(c_Int_Onumber__class_Onumber__of(_1435175), _1435179)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1435177))) = hAPP(hAPP(c_HOL_OLet(_1435175, _1435175), hAPP(hAPP(c_Power_Opower__class_Opower(_1435175), hAPP(c_Int_Onumber__class_Onumber__of(_1435175), _1435179)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435177))), hAPP(hAPP(c_COMBS(_1435175, _1435175, _1435175), hAPP(hAPP(c_COMBB(_1435175, tc_fun(_1435175, _1435175), _1435175), c_Groups_Otimes__class_Otimes(_1435175)), hAPP(c_Groups_Otimes__class_Otimes(_1435175), hAPP(c_Int_Onumber__class_Onumber__of(_1435175), _1435179)))), c_COMBI(_1435175))))]]], (29245 ^ _781404) ^ [_1304774, _1304776, _1304778, _1304780, _1304782] : [class_Fields_Olinordered__field(_1304774), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304774), c_Groups_Ozero__class_Ozero(_1304774)), _1304776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304774), _1304776), _1304778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304774), c_Groups_Ozero__class_Ozero(_1304774)), _1304780)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304774), _1304780), _1304782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304774), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304774), _1304776), _1304782)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304774), _1304778), _1304780))))], (37589 ^ _781404) ^ [_1490273, _1490275, _1490277, _1490279] : [_1490273 = _1490275, hBOOL(hAPP(hAPP(c_member(_1490277), _1490273), _1490279)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1490277, _1490277)), hAPP(hAPP(c_Product__Type_OPair(_1490277, _1490277), _1490273), _1490275)), c_Relation_OId__on(_1490277, _1490279))))], (46018 ^ _781404) ^ [_1704453, _1704455, _1704457, _1704459] : [_1704459 = c_List_Olist_ONil(_1704453), -(c_List_Olist__all2(_1704453, _1704455, _1704457, _1704459, c_List_Olist_ONil(_1704455)))], (41103 ^ _781404) ^ [_1584679, _1584681, _1584683, _1584685, _1584687] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584679, _1584679)), hAPP(hAPP(c_Product__Type_OPair(_1584679, _1584679), _1584681), _1584683)), _1584685)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584679, _1584679)), hAPP(hAPP(c_Product__Type_OPair(_1584679, _1584679), _1584683), _1584687)), _1584685)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584679, _1584679)), hAPP(hAPP(c_Product__Type_OPair(_1584679, _1584679), _1584681), _1584687)), c_Transitive__Closure_Otrancl(_1584679, _1584685))))], (24979 ^ _781404) ^ [_1228869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1228869)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228869), c_Int_OMin)))], (9699 ^ _781404) ^ [_947063, _947065, _947067] : [class_Orderings_Olinorder(_947063), 9702 ^ _781404 : [(9703 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947063), _947065), _947067))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947063), _947067), _947065))), -(_947065 = _947067)], (9713 ^ _781404) ^ [] : [9714 ^ _781404 : [(9717 ^ _781404) ^ [] : [_947065 = _947067], (9715 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947063), _947067), _947065))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947063), _947065), _947067))]]], (25881 ^ _781404) ^ [_1243944, _1243946] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1243944))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1243946)) = 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)))), _1243944), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1243946)))], (14833 ^ _781404) ^ [_1041731, _1041733] : [class_Rings_Olinordered__idom(_1041731), 14836 ^ _781404 : [(14843 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041731), _1041733), c_Groups_Ozero__class_Ozero(_1041731))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041731), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041731), _1041733), _1041733)), c_Groups_Ozero__class_Ozero(_1041731))))], (14837 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041731), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041731), _1041733), _1041733)), c_Groups_Ozero__class_Ozero(_1041731))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041731), _1041733), c_Groups_Ozero__class_Ozero(_1041731))))]]], (12400 ^ _781404) ^ [_995166, _995168, _995170, _995172] : [-(hBOOL(hAPP(hAPP(c_member(_995166), hAPP(_995168, _995170)), hAPP(c_Set_Oimage(_995172, _995166, _995168), c_Orderings_Otop__class_Otop(tc_fun(_995172, tc_HOL_Obool))))))], (30363 ^ _781404) ^ [_1326783, _1326785, _1326787, _1326789, _1326791, _1326793] : [class_Groups_Oab__semigroup__mult(_1326783), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326785), _1326787)), 30373 ^ _781404 : [(30376 ^ _781404) ^ [] : [hAPP(_1326789, 30372 ^ [_1326783, _1326785, _1326787, _1326789, _1326791, _1326793]) = hAPP(_1326791, 30372 ^ [_1326783, _1326785, _1326787, _1326789, _1326791, _1326793])], (30374 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1326785), 30372 ^ [_1326783, _1326785, _1326787, _1326789, _1326791, _1326793]), _1326787)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1326783, _1326785, c_Groups_Otimes__class_Otimes(_1326783)), _1326789), _1326793), _1326787) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1326783, _1326785, c_Groups_Otimes__class_Otimes(_1326783)), _1326791), _1326793), _1326787))], (1226 ^ _781404) ^ [_799769, _799771] : [-(class_Rings_Olinordered__semiring__1(_799769)), _799771 = _799769, class_Rings_Olinordered__semiring__1(_799771)], (19637 ^ _781404) ^ [_1130422, _1130424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130422), _1130424)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1130424)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1130422)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130424), _1130422)))], (7627 ^ _781404) ^ [_906687, _906689, _906691] : [class_Complete__Lattice_Ocomplete__lattice(_906687), -(c_Complete__Lattice_OInf__class_OInf(_906687, hAPP(hAPP(c_Set_Oinsert(_906687), _906689), _906691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_906687), _906689), c_Complete__Lattice_OInf__class_OInf(_906687, _906691)))], (42822 ^ _781404) ^ [_1631696, _1631698, _1631700] : [-(c_List_Osublist(_1631696, _1631698, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1631700)) = hAPP(hAPP(c_List_Otake(_1631696), _1631700), _1631698))], (37528 ^ _781404) ^ [_1488388, _1488390] : [-(c_Relation_OId__on(_1488388, _1488390) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1488388, tc_fun(tc_prod(_1488388, _1488388), tc_HOL_Obool)), _1488390), hAPP(hAPP(c_COMBC(_1488388, tc_fun(tc_prod(_1488388, _1488388), tc_HOL_Obool), tc_fun(tc_prod(_1488388, _1488388), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1488388, _1488388), tc_fun(tc_fun(tc_prod(_1488388, _1488388), tc_HOL_Obool), tc_fun(tc_prod(_1488388, _1488388), tc_HOL_Obool)), _1488388), c_Set_Oinsert(tc_prod(_1488388, _1488388))), hAPP(hAPP(c_COMBS(_1488388, _1488388, tc_prod(_1488388, _1488388)), c_Product__Type_OPair(_1488388, _1488388)), c_COMBI(_1488388)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1488388, _1488388), tc_HOL_Obool)))))], (21983 ^ _781404) ^ [_1172740, _1172742, _1172744, _1172746] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172740), hAPP(c_Int_Onumber__class_Onumber__of(_1172740), _1172742)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172740), _1172744), _1172746)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172740), hAPP(c_Int_Onumber__class_Onumber__of(_1172740), _1172742)), _1172744)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172740), hAPP(c_Int_Onumber__class_Onumber__of(_1172740), _1172742)), _1172746))), class_Int_Onumber(_1172740), class_Rings_Osemiring(_1172740)], (6249 ^ _781404) ^ [_880824, _880826, _880828] : [class_Orderings_Olinorder(_880824), 6252 ^ _781404 : [(6259 ^ _781404) ^ [] : [_880826 = _880828, -(hAPP(c_SetInterval_Oord__class_OatLeast(_880824), _880826) = hAPP(c_SetInterval_Oord__class_OatLeast(_880824), _880828))], (6253 ^ _781404) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_880824), _880826) = hAPP(c_SetInterval_Oord__class_OatLeast(_880824), _880828), -(_880826 = _880828)]]], (46030 ^ _781404) ^ [_1704662, _1704664, _1704666, _1704668] : [_1704668 = c_List_Olist_ONil(_1704664), -(c_List_Olist__all2(_1704662, _1704664, _1704666, c_List_Olist_ONil(_1704662), _1704668))], (28531 ^ _781404) ^ [_1291800, _1291802, _1291804, _1291806] : [class_Fields_Olinordered__field__inverse__zero(_1291800), class_Int_Onumber(_1291800), 28538 ^ _781404 : [(28539 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291800), hAPP(c_Int_Onumber__class_Onumber__of(_1291800), _1291802)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291800), _1291804), _1291806))), 28542 ^ _781404 : [(28549 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291800), c_Groups_Ozero__class_Ozero(_1291800)), _1291806))), 28552 ^ _781404 : [(28559 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291800), _1291806), c_Groups_Ozero__class_Ozero(_1291800)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291800), hAPP(c_Int_Onumber__class_Onumber__of(_1291800), _1291802)), c_Groups_Ozero__class_Ozero(_1291800))))], (28553 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291800), _1291806), c_Groups_Ozero__class_Ozero(_1291800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291800), _1291804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1291800), hAPP(c_Int_Onumber__class_Onumber__of(_1291800), _1291802)), _1291806))))]]], (28543 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291800), c_Groups_Ozero__class_Ozero(_1291800)), _1291806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1291800), hAPP(c_Int_Onumber__class_Onumber__of(_1291800), _1291802)), _1291806)), _1291804)))]]], (28565 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291800), hAPP(c_Int_Onumber__class_Onumber__of(_1291800), _1291802)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291800), _1291804), _1291806)))), 28568 ^ _781404 : [(28571 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1291800), hAPP(c_Int_Onumber__class_Onumber__of(_1291800), _1291802)), _1291806)), _1291804))], (28569 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291800), c_Groups_Ozero__class_Ozero(_1291800)), _1291806)))]], 28572 ^ _781404 : [(28575 ^ _781404) ^ [] : [28576 ^ _781404 : [(28579 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291800), _1291804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1291800), hAPP(c_Int_Onumber__class_Onumber__of(_1291800), _1291802)), _1291806)))], (28577 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291800), _1291806), c_Groups_Ozero__class_Ozero(_1291800))))]], 28580 ^ _781404 : [(28583 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291800), hAPP(c_Int_Onumber__class_Onumber__of(_1291800), _1291802)), c_Groups_Ozero__class_Ozero(_1291800)))], (28581 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291800), _1291806), c_Groups_Ozero__class_Ozero(_1291800)))]]], (28573 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291800), c_Groups_Ozero__class_Ozero(_1291800)), _1291806))]]]]], (34753 ^ _781404) ^ [_1427000] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1427000) = 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), _1427000), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (44611 ^ _781404) ^ [_1673756, _1673758, _1673760] : [-(hAPP(c_List_Otl(_1673756), hAPP(hAPP(c_List_Olist_OCons(_1673756), _1673758), _1673760)) = _1673760)], (40279 ^ _781404) ^ [_1565985, _1565987] : [c_Wellfounded_OwfP(_1565985, _1565987), -(c_Wellfounded_Oacyclic(_1565985, hAPP(c_Set_OCollect(tc_prod(_1565985, _1565985)), hAPP(c_Product__Type_Oprod_Oprod__case(_1565985, _1565985, tc_HOL_Obool), _1565987))))], (35575 ^ _781404) ^ [_1445317, _1445319] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1445317))), 35578 ^ _781404 : [(35585 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1445319))), -(c_Divides_Odivmod__int(_1445317, _1445319) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445317), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445319))))], (35579 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1445319)), -(c_Divides_Odivmod__int(_1445317, _1445319) = c_Divides_OnegDivAlg(_1445317, _1445319))]]], (46660 ^ _781404) ^ [_1719231, _1719233, _1719235, _1719237] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1719231)), c_List_Otranspose__rel(_1719231)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1719231)), hAPP(hAPP(c_List_Olist_OCons(_1719231), _1719233), _1719235)), _1719237))), -(c_List_Otranspose(_1719231, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1719231)), hAPP(hAPP(c_List_Olist_OCons(_1719231), _1719233), _1719235)), _1719237)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1719231)), hAPP(hAPP(c_List_Olist_OCons(_1719231), _1719233), c_List_Oconcat(_1719231, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719231), tc_List_Olist(_1719231)), c_List_Olist_Olist__case(tc_List_Olist(_1719231), _1719231, c_List_Olist_ONil(_1719231), hAPP(hAPP(c_COMBB(tc_List_Olist(_1719231), tc_fun(tc_List_Olist(_1719231), tc_List_Olist(_1719231)), _1719231), c_COMBK(tc_List_Olist(_1719231), tc_List_Olist(_1719231))), hAPP(hAPP(c_COMBC(_1719231, tc_List_Olist(_1719231), tc_List_Olist(_1719231)), c_List_Olist_OCons(_1719231)), c_List_Olist_ONil(_1719231))))), _1719237)))), c_List_Otranspose(_1719231, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1719231)), _1719235), c_List_Oconcat(tc_List_Olist(_1719231), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719231), tc_List_Olist(tc_List_Olist(_1719231))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1719231)), _1719231, c_List_Olist_ONil(tc_List_Olist(_1719231)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1719231), tc_List_Olist(tc_List_Olist(_1719231))), _1719231), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719231), tc_List_Olist(tc_List_Olist(_1719231)), tc_List_Olist(tc_List_Olist(_1719231))), c_List_Olist_OCons(tc_List_Olist(_1719231))), c_List_Olist_ONil(tc_List_Olist(_1719231)))))), _1719237))))))], (15463 ^ _781404) ^ [_1055001, _1055003] : [15464 ^ _781404 : [(15467 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1055001), _1055003)))], (15465 ^ _781404) ^ [] : [_1055003 = c_Orderings_Obot__class_Obot(tc_fun(_1055001, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1055001), _1055003) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5426 ^ _781404) ^ [_864269, _864271, _864273, _864275, _864277, _864279, _864281, _864283] : [-(c_SetInterval_Oord_OatLeastAtMost(_864283, _864279, _864275, _864271) = c_SetInterval_Oord_OatLeastAtMost(_864281, _864277, _864273, _864269)), _864283 = _864281, _864279 = _864277, _864275 = _864273, _864271 = _864269], (23509 ^ _781404) ^ [_1203335, _1203337, _1203339] : [class_Divides_Osemiring__div(_1203335), -(c_Divides_Odiv__class_Omod(_1203335, c_Divides_Odiv__class_Omod(_1203335, _1203337, _1203339), _1203339) = c_Divides_Odiv__class_Omod(_1203335, _1203337, _1203339))], (49151 ^ _781404) ^ [_1772241, _1772243, _1772245, _1772247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1772241), _1772243)), -(hAPP(hAPP(c_List_Onth(_1772245), c_List_Oreplicate(_1772245, _1772243, _1772247)), _1772241) = _1772247)], (44104 ^ _781404) ^ [_1661382, _1661384, _1661386] : [-(c_List_Olist_ONil(_1661382) = hAPP(hAPP(c_List_Oappend(_1661382), _1661384), _1661386)), _1661384 = c_List_Olist_ONil(_1661382), _1661386 = c_List_Olist_ONil(_1661382)], (52394 ^ _781404) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (5410 ^ _781404) ^ [_864035, _864037, _864039, _864041] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_864041, _864037) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_864039, _864035)), _864041 = _864039, _864037 = _864035], (42232 ^ _781404) ^ [_1614320, _1614322, _1614324] : [hAPP(hAPP(c_List_Olist_OCons(_1614320), _1614322), _1614324) = _1614324], (24764 ^ _781404) ^ [_1225555, _1225557, _1225559] : [-(_1225555 = 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), _1225555), _1225557)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1225555), _1225559)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1225557), _1225559))], (42499 ^ _781404) ^ [_1622837, _1622839, _1622841, _1622843] : [c_List_Olistrelp(_1622837, hAPP(hAPP(c_COMBC(_1622837, tc_fun(tc_prod(_1622837, _1622837), tc_HOL_Obool), tc_fun(_1622837, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1622837, tc_fun(tc_fun(tc_prod(_1622837, _1622837), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1622837, _1622837), tc_HOL_Obool), tc_fun(_1622837, tc_HOL_Obool)), _1622837), c_COMBC(_1622837, tc_fun(tc_prod(_1622837, _1622837), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1622837, tc_prod(_1622837, _1622837)), tc_fun(_1622837, tc_fun(tc_fun(tc_prod(_1622837, _1622837), tc_HOL_Obool), tc_HOL_Obool)), _1622837), hAPP(c_COMBB(tc_prod(_1622837, _1622837), tc_fun(tc_fun(tc_prod(_1622837, _1622837), tc_HOL_Obool), tc_HOL_Obool), _1622837), c_member(tc_prod(_1622837, _1622837)))), c_Product__Type_OPair(_1622837, _1622837)))), _1622839), _1622841, _1622843), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622837), tc_List_Olist(_1622837))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622837), tc_List_Olist(_1622837)), _1622841), _1622843)), c_List_Olistrel(_1622837, _1622839))))], (32989 ^ _781404) ^ [_1376136, _1376138, _1376140, _1376142, _1376144, _1376146] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1376136, tc_fun(_1376138, tc_HOL_Obool)), _1376140), _1376142), _1376144)), hBOOL(hAPP(hAPP(c_member(_1376136), _1376146), _1376140)), -(hBOOL(hAPP(hAPP(_1376142, _1376146), _1376144)))], (25007 ^ _781404) ^ [_1229309, _1229311] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229309), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229311)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1229309, _1229311)))], (52728 ^ _781404) ^ [_1842126, _1842128, _1842130, _1842132] : [-(hAPP(hAPP(c_COMBK(_1842126, _1842128), _1842130), _1842132) = _1842130)], (5584 ^ _781404) ^ [_866784, _866786, _866788, _866790] : [-(tc_Nitpick_Opair__box(_866790, _866786) = tc_Nitpick_Opair__box(_866788, _866784)), _866790 = _866788, _866786 = _866784], (20243 ^ _781404) ^ [_1140837, _1140839] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1140837)), c_Int_OBit0(_1140839)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1140837), _1140839)))], (33299 ^ _781404) ^ [_1383871, _1383873, _1383875, _1383877, _1383879] : [-(_1383871 = c_Orderings_Obot__class_Obot(tc_fun(_1383873, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1383873, tc_fun(_1383875, tc_HOL_Obool)), _1383871), hAPP(hAPP(c_COMBC(_1383873, tc_fun(_1383875, tc_HOL_Obool), tc_fun(_1383875, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383875, tc_HOL_Obool), tc_fun(tc_fun(_1383875, tc_HOL_Obool), tc_fun(_1383875, tc_HOL_Obool)), _1383873), c_Groups_Ominus__class_Ominus(tc_fun(_1383875, tc_HOL_Obool))), _1383877)), _1383879)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1383875, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1383873, tc_fun(_1383875, tc_HOL_Obool)), _1383871), _1383877)), _1383879))], (39473 ^ _781404) ^ [_1543650, _1543652] : [c_Relation_Orefl__on(_1543650, c_Orderings_Otop__class_Otop(tc_fun(_1543650, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1543650, _1543650)), hAPP(c_Product__Type_Oprod_Oprod__case(_1543650, _1543650, tc_HOL_Obool), _1543652))), -(c_Predicate_Oreflp(_1543650, _1543652))], (42414 ^ _781404) ^ [_1620310, _1620312, _1620314, _1620316, _1620318, _1620320] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1620310), tc_List_Olist(_1620310))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1620310), tc_List_Olist(_1620310)), hAPP(hAPP(c_List_Olist_OCons(_1620310), _1620312), _1620314)), hAPP(hAPP(c_List_Olist_OCons(_1620310), _1620316), _1620318))), c_List_Olistrel1(_1620310, _1620320)))), 42415 ^ _781404 : [(42422 ^ _781404) ^ [] : [_1620312 = _1620316, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1620310), tc_List_Olist(_1620310))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1620310), tc_List_Olist(_1620310)), _1620314), _1620318)), c_List_Olistrel1(_1620310, _1620320)))], (42416 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620310, _1620310)), hAPP(hAPP(c_Product__Type_OPair(_1620310, _1620310), _1620312), _1620316)), _1620320)), _1620314 = _1620318]]], (47750 ^ _781404) ^ [_1741606, _1741608, _1741610, _1741612, _1741614] : [hBOOL(hAPP(hAPP(c_member(_1741606), _1741608), hAPP(c_List_Oset(_1741606), _1741610))), -(hBOOL(hAPP(_1741612, _1741608))), -(c_List_OtakeWhile(_1741606, _1741612, hAPP(hAPP(c_List_Oappend(_1741606), _1741610), _1741614)) = c_List_OtakeWhile(_1741606, _1741612, _1741610))], (33335 ^ _781404) ^ [_1384708, _1384710, _1384712, _1384714, _1384716, _1384718] : [-(hAPP(c_Set_Oimage(_1384708, _1384710, _1384712), hAPP(c_Set_Oimage(_1384714, _1384708, _1384716), _1384718)) = hAPP(c_Set_Oimage(_1384714, _1384710, hAPP(hAPP(c_COMBB(_1384708, _1384710, _1384714), _1384712), _1384716)), _1384718))], (13193 ^ _781404) ^ [_1010460, _1010462, _1010464, _1010466] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1010460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010460), _1010462), _1010464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010460), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010460), _1010466), _1010462)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010460), _1010466), _1010464))))], (24160 ^ _781404) ^ [_1214720, _1214722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214720)), -(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, _1214722, _1214720))))], (40714 ^ _781404) ^ [_1575147, _1575149, _1575151, _1575153] : [class_Complete__Lattice_Ocomplete__lattice(_1575147), _1575149 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1575147, _1575151), c_Orderings_Oorder__class_Omono(_1575147, _1575147, _1575151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1575147), _1575153), hAPP(_1575151, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1575147), _1575153), _1575149)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1575147), _1575153), _1575149)))], (8858 ^ _781404) ^ [_930996, _930998, _931000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930996, tc_HOL_Obool)), _930998), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_930996, tc_HOL_Obool)), _931000))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930996, tc_HOL_Obool)), _930998), _931000) = c_Orderings_Obot__class_Obot(tc_fun(_930996, tc_HOL_Obool)))], (15755 ^ _781404) ^ [_1060410, _1060412, _1060414] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1060410), _1060412)), -(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(_1060410), _1060414)), hAPP(c_Finite__Set_Ocard(_1060410), _1060412))), hAPP(c_Finite__Set_Ocard(_1060410), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1060410, tc_HOL_Obool)), _1060414), _1060412)))))], (39035 ^ _781404) ^ [_1527264, _1527266, _1527268] : [hBOOL(hAPP(hAPP(c_member(_1527264), _1527266), hAPP(c_Set_OCollect(_1527264), _1527268))), -(hBOOL(hAPP(_1527268, _1527266)))], (9188 ^ _781404) ^ [_937876, _937878, _937880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937876, tc_HOL_Obool)), _937878), _937880)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937876, tc_HOL_Obool)), _937878), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937876, tc_HOL_Obool)), _937880), _937878)) = _937880)], (31756 ^ _781404) ^ [_1352863, _1352865, _1352867] : [class_Orderings_Olinorder(_1352863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352863), _1352865)), hBOOL(hAPP(hAPP(c_member(_1352863), _1352867), _1352865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1352863), _1352867), c_Big__Operators_Olinorder__class_OMax(_1352863, _1352865))))], (47517 ^ _781404) ^ [_1736804, _1736806, _1736808] : [hAPP(c_List_Orev(_1736804), _1736806) = hAPP(c_List_Orev(_1736804), _1736808), -(_1736806 = _1736808)], (2970 ^ _781404) ^ [_825469, _825471] : [_825471 = _825469, -(c_Nitpick_Ofrac(_825471) = c_Nitpick_Ofrac(_825469))], (37296 ^ _781404) ^ [_1481863, _1481865, _1481867] : [-(c_Wellfounded_Omlex__prod(_1481863, _1481865, _1481867) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1481863), _1481863), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1481863, c_Wellfounded_Oless__than, _1481867)), hAPP(hAPP(c_COMBS(_1481863, _1481863, tc_prod(tc_Nat_Onat, _1481863)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1481863, tc_prod(tc_Nat_Onat, _1481863)), _1481863), c_Product__Type_OPair(tc_Nat_Onat, _1481863)), _1481865)), c_COMBI(_1481863))))], (4952 ^ _781404) ^ [_856854, _856856] : [_856856 = _856854, -(c_HOL_OEx(_856856) = c_HOL_OEx(_856854))], (26621 ^ _781404) ^ [] : [-(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))], (13452 ^ _781404) ^ [_1015407, _1015409] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015407), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015407), _1015409))))], (33692 ^ _781404) ^ [_1395890, _1395892, _1395894] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395890, tc_fun(_1395892, tc_HOL_Obool)), _1395894), hAPP(c_COMBK(tc_fun(_1395892, tc_HOL_Obool), _1395890), c_Orderings_Obot__class_Obot(tc_fun(_1395892, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1395892, tc_HOL_Obool)))], (46856 ^ _781404) ^ [_1723911, _1723913] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1723911, _1723913) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1723911, hAPP(c_Nat_OSuc, _1723913))))], (36683 ^ _781404) ^ [_1467420, _1467422, _1467424] : [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), _1467420), _1467422))), -(hBOOL(hAPP(hAPP(_1467424, _1467420), _1467422))), 36690 ^ _781404 : [(36693 ^ _781404) ^ [] : [-(36689 ^ [_1467420, _1467422, _1467424] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1467424, 36689 ^ [_1467420, _1467422, _1467424]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 36688 ^ [_1467420, _1467422, _1467424], 36689 ^ [_1467420, _1467422, _1467424]))))], (36699 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1467424, 36688 ^ [_1467420, _1467422, _1467424]), 36689 ^ [_1467420, _1467422, _1467424]))], (36691 ^ _781404) ^ [] : [-(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), 36688 ^ [_1467420, _1467422, _1467424]), 36689 ^ [_1467420, _1467422, _1467424]))))]]], (11441 ^ _781404) ^ [_976698, _976700, _976702, _976704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976698, tc_HOL_Obool)), _976700), hAPP(hAPP(c_Set_Oinsert(_976698), _976702), _976704))), 11444 ^ _781404 : [(11451 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_976698), _976702), _976700))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976698, tc_HOL_Obool)), _976700), _976704)))], (11445 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_976698), _976702), _976700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976698, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976698, tc_HOL_Obool)), _976700), hAPP(hAPP(c_Set_Oinsert(_976698), _976702), c_Orderings_Obot__class_Obot(tc_fun(_976698, tc_HOL_Obool))))), _976704)))]]], (7259 ^ _781404) ^ [_899495, _899497, _899499, _899501] : [class_Orderings_Olinorder(_899495), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899495), _899497), _899499)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899495), _899499), _899501)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899495, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_899495, _899497), _899499)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_899495, _899499), _899501)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_899495, _899497), _899501))], (43533 ^ _781404) ^ [_1649183, _1649185] : [-(hAPP(hAPP(c_List_Otake(_1649183), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1649185) = c_List_Olist_ONil(_1649183))], (34349 ^ _781404) ^ [_1417167, _1417169, _1417171, _1417173, _1417175] : [class_Groups_Ocomm__monoid__add(_1417167), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417169), _1417171)), 34356 ^ _781404 : [(34363 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417169), _1417173), _1417171))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417169, _1417167), hAPP(hAPP(c_COMBC(_1417169, _1417167, _1417167), hAPP(hAPP(c_COMBS(_1417169, _1417167, tc_fun(_1417167, _1417167)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417167, tc_fun(_1417167, _1417167)), _1417169), c_If(_1417167)), hAPP(c_fequal, _1417173))), _1417175)), c_Groups_Ozero__class_Ozero(_1417167))), _1417171) = c_Groups_Ozero__class_Ozero(_1417167))], (34357 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1417169), _1417173), _1417171)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417169, _1417167), hAPP(hAPP(c_COMBC(_1417169, _1417167, _1417167), hAPP(hAPP(c_COMBS(_1417169, _1417167, tc_fun(_1417167, _1417167)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417167, tc_fun(_1417167, _1417167)), _1417169), c_If(_1417167)), hAPP(c_fequal, _1417173))), _1417175)), c_Groups_Ozero__class_Ozero(_1417167))), _1417171) = hAPP(_1417175, _1417173))]]], (29773 ^ _781404) ^ [_1314758, _1314760, _1314762, _1314764] : [class_Fields_Olinordered__field(_1314758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314758), c_Groups_Ozero__class_Ozero(_1314758)), _1314760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314758), _1314762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1314758), _1314764), _1314760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314758), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314758), _1314762), _1314760)), _1314764)))], (23505 ^ _781404) ^ [_1203280] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1203280, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1203280)], (45817 ^ _781404) ^ [_1699925, _1699927, _1699929, _1699931] : [hBOOL(hAPP(c_List_Olistsp(_1699925, _1699927), _1699929)), hBOOL(hAPP(c_List_Olistsp(_1699925, _1699931), _1699929)), -(hBOOL(hAPP(c_List_Olistsp(_1699925, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1699925, tc_HOL_Obool)), _1699927), _1699931)), _1699929)))], (37543 ^ _781404) ^ [_1488956, _1488958, _1488960] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1488956, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1488956), _1488958), _1488960), -(_1488958 = c_Orderings_Obot__class_Obot(tc_fun(_1488956, tc_HOL_Obool)))], (46235 ^ _781404) ^ [_1709323, _1709325] : [-(hAPP(c_List_Oset(_1709323), c_List_Oremdups(_1709323, _1709325)) = hAPP(c_List_Oset(_1709323), _1709325))], (48052 ^ _781404) ^ [_1747980, _1747982, _1747984] : [hBOOL(hAPP(c_List_Odistinct(_1747980), _1747982)), -(hBOOL(hAPP(c_List_Odistinct(_1747980), c_List_Oinsert(_1747980, _1747984, _1747982))))], (45186 ^ _781404) ^ [_1685202, _1685204, _1685206, _1685208, _1685210, _1685212] : [-(hAPP(hAPP(c_List_Ozip(_1685202, _1685204), hAPP(hAPP(c_List_Omap(_1685206, _1685202), _1685208), _1685210)), _1685212) = hAPP(hAPP(c_List_Omap(tc_prod(_1685206, _1685204), tc_prod(_1685202, _1685204)), hAPP(c_Product__Type_Oprod_Oprod__case(_1685206, _1685204, tc_prod(_1685202, _1685204)), hAPP(hAPP(c_COMBB(_1685202, tc_fun(_1685204, tc_prod(_1685202, _1685204)), _1685206), c_Product__Type_OPair(_1685202, _1685204)), _1685208))), hAPP(hAPP(c_List_Ozip(_1685206, _1685204), _1685210), _1685212)))], (47760 ^ _781404) ^ [_1741764, _1741766, _1741768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741764)), c_List_OtakeWhile(_1741764, _1741766, _1741768))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741764)), _1741768))), hBOOL(hAPP(_1741766, hAPP(hAPP(c_List_Onth(_1741764), _1741768), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741764)), c_List_OtakeWhile(_1741764, _1741766, _1741768)))))], (12288 ^ _781404) ^ [_992787, _992789, _992791, _992793] : [hAPP(c_Set_Oimage(_992787, _992789, _992791), c_Orderings_Otop__class_Otop(tc_fun(_992787, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_992789, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_992787, _992789, _992791), hAPP(c_Set_Ovimage(_992787, _992789, _992791), _992793)) = _992793)], (33476 ^ _781404) ^ [_1390131, _1390133, _1390135, _1390137] : [_1390131 = c_Orderings_Obot__class_Obot(tc_fun(_1390133, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390133, tc_fun(_1390135, tc_HOL_Obool)), _1390131), hAPP(c_COMBK(tc_fun(_1390135, tc_HOL_Obool), _1390133), _1390137)) = c_Orderings_Otop__class_Otop(tc_fun(_1390135, tc_HOL_Obool)))], (6562 ^ _781404) ^ [_886076, _886078] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886076, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886076, tc_HOL_Obool)), _886078)) = _886078)], (36709 ^ _781404) ^ [_1468126, _1468128, _1468130, _1468132, _1468134] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1468126, _1468128, _1468130), _1468132), _1468134) = c_HOL_OThe(_1468128, c_Finite__Set_Ofold__graph(_1468126, _1468128, _1468130, _1468132, _1468134)))], (50415 ^ _781404) ^ [_1799653, _1799655, _1799657, _1799659] : [c_Equiv__Relations_Opart__equivp(_1799653, _1799655), hBOOL(hAPP(hAPP(_1799655, _1799657), _1799659)), -(hBOOL(hAPP(hAPP(_1799655, _1799659), _1799657)))], (1526 ^ _781404) ^ [_803519, _803521] : [-(class_Groups_Ouminus(_803519)), _803521 = _803519, class_Groups_Ouminus(_803521)], (25967 ^ _781404) ^ [_1245431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1245431)), -(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), _1245431), 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)))))))], (30344 ^ _781404) ^ [_1326421, _1326423, _1326425] : [30346 ^ _781404 : [(30351 ^ _781404) ^ [] : [hBOOL(hAPP(_1326423, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 30345 ^ [_1326421, _1326423, _1326425]), _1326421)))], (30349 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1326423, 30345 ^ [_1326421, _1326423, _1326425])))], (30347 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30345 ^ [_1326421, _1326423, _1326425]), _1326421)))]], hBOOL(hAPP(_1326423, _1326425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1326425), _1326421)), -(hBOOL(hAPP(_1326423, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49596 ^ _781404) ^ [_1781797, _1781799, _1781801, _1781803] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1781797), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1781799, _1781801, _1781797, _1781803) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1781799, 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(_1781799)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1781801, _1781803)), 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(_1781799)))), 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(_1781799)))), 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(_1781799)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1781799, 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(_1781799)))), 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(_1781799)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1781799, _1781801, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1781797), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1781803))), 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(_1781799)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1781799))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1781799)))), 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(_1781799)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1781799, 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(_1781799)))), 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(_1781799)))), 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(_1781799))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1781799)))), 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(_1781799)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1781799)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1781799))))), tc_prod(_1781799, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1781799)), hAPP(hAPP(c_COMBB(_1781799, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1781799)))), tc_prod(_1781799, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1781799)), c_Product__Type_Ofst(_1781799, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (18175 ^ _781404) ^ [_1105266, _1105268] : [class_Power_Opower(_1105266), class_Rings_Osemiring__0(_1105266), 18182 ^ _781404 : [(18189 ^ _781404) ^ [] : [-(_1105268 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1105266), c_Groups_Ozero__class_Ozero(_1105266)), _1105268) = c_Groups_Ozero__class_Ozero(_1105266))], (18183 ^ _781404) ^ [] : [_1105268 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1105266), c_Groups_Ozero__class_Ozero(_1105266)), _1105268) = c_Groups_Oone__class_Oone(_1105266))]]], (8712 ^ _781404) ^ [_928236, _928238, _928240] : [class_Orderings_Oorder(_928236), _928238 = _928240, -(c_SetInterval_Oord__class_OatLeastAtMost(_928236, _928238, _928240) = hAPP(hAPP(c_Set_Oinsert(_928236), _928238), c_Orderings_Obot__class_Obot(tc_fun(_928236, tc_HOL_Obool))))], (52368 ^ _781404) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (9050 ^ _781404) ^ [_934857, _934859] : [class_Groups_Ogroup__add(_934857), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_934857), _934859), c_Groups_Ozero__class_Ozero(_934857)) = _934859)], (28807 ^ _781404) ^ [_1297069, _1297071, _1297073] : [class_Fields_Ofield__inverse__zero(_1297069), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1297069), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297069), _1297071), _1297073)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297069), _1297071), hAPP(c_Groups_Ouminus__class_Ouminus(_1297069), _1297073)))], (16262 ^ _781404) ^ [_1070491, _1070493, _1070495, _1070497] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1070491, _1070495)), c_Sum__Type_OPlus(_1070491, _1070495, _1070493, _1070497)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1070491), _1070493)), hAPP(c_Finite__Set_Ocard(_1070495), _1070497))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070491), _1070493)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070495), _1070497))], (50642 ^ _781404) ^ [_1804826, _1804828, _1804830] : [hAPP(c_Set_Oimage(_1804826, _1804828, _1804830), c_Orderings_Otop__class_Otop(tc_fun(_1804826, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1804828, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1804826, _1804828, _1804828, _1804830), c_Hilbert__Choice_Oinv__into(_1804826, _1804828, c_Orderings_Otop__class_Otop(tc_fun(_1804826, tc_HOL_Obool)), _1804830)) = c_Fun_Oid(_1804828))], (20839 ^ _781404) ^ [_1151532, _1151534] : [class_Lattices_Oab__semigroup__idem__mult(_1151532), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151532), _1151534), _1151534) = _1151534)], (25955 ^ _781404) ^ [_1245243] : [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, _1245243, 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, _1245243, 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))], (3450 ^ _781404) ^ [_832921, _832923, _832925, _832927, _832929, _832931] : [-(c_Enum_On__lists(_832931, _832927, _832923) = c_Enum_On__lists(_832929, _832925, _832921)), _832931 = _832929, _832927 = _832925, _832923 = _832921], (37978 ^ _781404) ^ [_1499262, _1499264, _1499266, _1499268, _1499270, _1499272, _1499274, _1499276] : [c_Equiv__Relations_Oequiv(_1499262, _1499264, _1499266), c_Equiv__Relations_Ocongruent2(_1499262, _1499268, _1499270, _1499266, _1499272, _1499274), hBOOL(hAPP(hAPP(c_member(_1499262), _1499276), _1499264)), -(c_Equiv__Relations_Ocongruent(_1499268, _1499270, _1499272, hAPP(_1499274, _1499276)))], (11595 ^ _781404) ^ [_979795, _979797, _979799, _979801] : [hBOOL(hAPP(hAPP(c_member(_979795), _979797), _979799)), -(hBOOL(hAPP(hAPP(c_member(_979795), _979797), _979801))), -(hBOOL(hAPP(hAPP(c_member(_979795), _979797), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979795, tc_HOL_Obool)), _979799), _979801))))], (50463 ^ _781404) ^ [_1800707, _1800709, _1800711] : [hAPP(c_Fun_Ocomp(_1800709, _1800707, _1800707, c_Hilbert__Choice_Oinv__into(_1800707, _1800709, c_Orderings_Otop__class_Otop(tc_fun(_1800707, tc_HOL_Obool)), _1800711)), _1800711) = c_Fun_Oid(_1800707), -(c_Fun_Oinj__on(_1800707, _1800709, _1800711, c_Orderings_Otop__class_Otop(tc_fun(_1800707, tc_HOL_Obool))))], (8852 ^ _781404) ^ [_930853, _930855, _930857] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930853, tc_HOL_Obool)), _930855), _930857) = c_Orderings_Obot__class_Obot(tc_fun(_930853, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930853, tc_HOL_Obool)), _930855), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_930853, tc_HOL_Obool)), _930857))))], (3202 ^ _781404) ^ [_829067, _829069, _829071, _829073] : [-(c_Big__Operators_Olattice__class_OInf__fin(_829073, _829069) = c_Big__Operators_Olattice__class_OInf__fin(_829071, _829067)), _829073 = _829071, _829069 = _829067], (42282 ^ _781404) ^ [_1616122, _1616124, _1616126] : [-(c_Random_Oselect__weight(_1616122, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1616122)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1616122), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1616124)), _1616126)) = c_Random_Oselect__weight(_1616122, _1616126))], (12258 ^ _781404) ^ [_992189, _992191] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_992189, tc_HOL_Obool)), _992191), hAPP(c_Set_OPow(_992189), _992191))))], (50612 ^ _781404) ^ [_1804111, _1804113, _1804115, _1804117, _1804119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1804111, tc_HOL_Obool)), _1804113), hAPP(c_Set_Oimage(_1804115, _1804111, _1804117), _1804119))), -(c_Fun_Oinj__on(_1804111, _1804115, c_Hilbert__Choice_Oinv__into(_1804115, _1804111, _1804119, _1804117), _1804113))], (46629 ^ _781404) ^ [_1718337, _1718339, _1718341] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1718337, tc_HOL_Obool)), hAPP(c_List_Oset(_1718337), _1718339)), hAPP(hAPP(c_Set_Oinsert(_1718337), _1718341), c_Orderings_Obot__class_Obot(tc_fun(_1718337, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1718337), hAPP(c_List_Ofilter(_1718337, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1718337), c_fNot), hAPP(hAPP(c_COMBC(_1718337, _1718337, tc_HOL_Obool), c_fequal), _1718341))), _1718339)))], (39646 ^ _781404) ^ [_1549471, _1549473, _1549475, _1549477] : [hAPP(hAPP(c_Relation_Orel__comp(_1549471, _1549471, _1549471), _1549473), _1549475) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549471, _1549471), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1549471, _1549471, _1549471), _1549477), _1549475) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549471, _1549471), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1549471, _1549471, _1549471), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1549471, _1549471), tc_HOL_Obool)), _1549473), _1549477)), _1549475) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549471, _1549471), tc_HOL_Obool)))], (36235 ^ _781404) ^ [_1457760, _1457762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1457760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1457762)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1457760, _1457762) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1457760, _1457762)))], (44619 ^ _781404) ^ [_1673917, _1673919, _1673921] : [hBOOL(hAPP(c_List_Odistinct(_1673917), _1673921)), -(hBOOL(hAPP(c_List_Odistinct(_1673917), hAPP(c_List_Orotate(_1673917, _1673919), _1673921))))], (24074 ^ _781404) ^ [_1213235, _1213237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213235), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24077 ^ _781404 : [(24084 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213237), 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), _1213237), _1213235))))], (24078 ^ _781404) ^ [] : [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), _1213237), _1213235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213237), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (5746 ^ _781404) ^ [_872194, _872196, _872198] : [-(c_Hoare__Mirabelle_Ohoare__valids(_872194, _872196, _872198)), 5748 ^ _781404 : [(5749 ^ _781404) ^ [_872340] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_872194)), _872340), _872196)), -(c_Hoare__Mirabelle_Otriple__valid(_872194, 5747 ^ [_872194, _872196, _872198], _872340))], (5758 ^ _781404) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_872194, 5747 ^ [_872194, _872196, _872198], 5754 ^ [_872194, _872196, _872198])], (5756 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_872194)), 5754 ^ [_872194, _872196, _872198]), _872198)))]]], (6393 ^ _781404) ^ [_883050, _883052] : [_883050 = _883052, -(hAPP(c_Nat_OSuc, _883050) = hAPP(c_Nat_OSuc, _883052))], (52626 ^ _781404) ^ [_1841175, _1841177] : [-(class_Nat_Osize(tc_prod(_1841175, _1841177)))], (48937 ^ _781404) ^ [_1767334, _1767336, _1767338, _1767340, _1767342, _1767344, _1767346] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1767334, _1767336, _1767338, _1767340), _1767342), _1767344), _1767346) = c_New__DSequence_Opos__bind(_1767334, _1767336, hAPP(hAPP(hAPP(_1767338, _1767342), _1767344), _1767346), hAPP(hAPP(c_COMBC(_1767334, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1767336))), hAPP(hAPP(c_COMBC(_1767334, 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(_1767336)))), hAPP(hAPP(c_COMBC(_1767334, 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(_1767336))))), _1767340), _1767342)), _1767344)), _1767346)))], (6945 ^ _781404) ^ [_893177, _893179, _893181, _893183] : [6947 ^ _781404 : [(6950 ^ _781404) ^ [] : [hBOOL(hAPP(_893183, 6946 ^ [_893177, _893179, _893181, _893183]))], (6948 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893177), 6946 ^ [_893177, _893179, _893181, _893183]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_893177, tc_HOL_Obool)), _893179), _893181))))]], 6951 ^ _781404 : [(6958 ^ _781404) ^ [_893494] : [hBOOL(hAPP(hAPP(c_member(_893177), _893494), _893181)), -(hBOOL(hAPP(_893183, _893494)))], (6952 ^ _781404) ^ [_893397] : [hBOOL(hAPP(hAPP(c_member(_893177), _893397), _893179)), -(hBOOL(hAPP(_893183, _893397)))]]], (8996 ^ _781404) ^ [_933865, _933867, _933869, _933871] : [class_Orderings_Oorder(_933865), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933865, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_933865, _933867, _933869)), c_SetInterval_Oord__class_OatLeastAtMost(_933865, _933869, _933871)) = c_Orderings_Obot__class_Obot(tc_fun(_933865, tc_HOL_Obool)))], (20039 ^ _781404) ^ [_1137323, _1137325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1137323)), c_Int_OBit0(_1137325))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137323), _1137325)))], (34233 ^ _781404) ^ [_1412747, _1412749, _1412751, _1412753, _1412755] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412747, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412749, tc_fun(_1412747, tc_HOL_Obool)), _1412751), _1412753)), _1412755) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412749, tc_fun(_1412747, tc_HOL_Obool)), _1412751), hAPP(hAPP(c_COMBC(_1412749, tc_fun(_1412747, tc_HOL_Obool), tc_fun(_1412747, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412747, tc_HOL_Obool), tc_fun(tc_fun(_1412747, tc_HOL_Obool), tc_fun(_1412747, tc_HOL_Obool)), _1412749), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412747, tc_HOL_Obool))), _1412753)), _1412755)))], (52536 ^ _781404) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (47812 ^ _781404) ^ [_1742971, _1742973, _1742975] : [hBOOL(hAPP(c_List_Odistinct(_1742971), _1742973)), hBOOL(hAPP(hAPP(c_member(_1742971), _1742975), hAPP(c_List_Oset(_1742971), _1742973))), -(c_List_OdropWhile(_1742971, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1742971), c_fNot), hAPP(hAPP(c_COMBC(_1742971, _1742971, tc_HOL_Obool), c_fequal), _1742975)), hAPP(c_List_Orev(_1742971), _1742973)) = hAPP(hAPP(c_List_Olist_OCons(_1742971), _1742975), hAPP(c_List_Orev(_1742971), c_List_OtakeWhile(_1742971, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1742971), c_fNot), hAPP(hAPP(c_COMBC(_1742971, _1742971, tc_HOL_Obool), c_fequal), _1742975)), _1742973))))], (9228 ^ _781404) ^ [_938974, _938976, _938978] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938974, tc_HOL_Obool)), _938976), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938974, tc_HOL_Obool)), _938978)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938974, tc_HOL_Obool)), _938976), _938978))], (4322 ^ _781404) ^ [_846851, _846853, _846855, _846857] : [-(c_List_Omap(_846857, _846853) = c_List_Omap(_846855, _846851)), _846857 = _846855, _846853 = _846851], (24174 ^ _781404) ^ [_1214950, _1214952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214950)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214950), _1214952)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1214950, _1214952) = _1214950)], (49386 ^ _781404) ^ [_1777103, _1777105, _1777107, _1777109] : [49387 ^ _781404 : [(49390 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1777103), _1777107), _1777109))], (49388 ^ _781404) ^ [] : [_1777105 = _1777109]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1777103), hAPP(hAPP(c_List_Olist_OCons(_1777103), _1777105), _1777107)), _1777109)))], (6534 ^ _781404) ^ [_885573, _885575, _885577, _885579, _885581] : [class_Orderings_Oorder(_885573), 6537 ^ _781404 : [(6550 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885573, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_885573, _885575, _885577)), c_SetInterval_Oord__class_OatLeastAtMost(_885573, _885579, _885581)))), 6551 ^ _781404 : [(6554 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885573), _885579), _885575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885573), _885577), _885581))], (6552 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885573), _885575), _885577)))]]], (6538 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885573, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_885573, _885575, _885577)), c_SetInterval_Oord__class_OatLeastAtMost(_885573, _885579, _885581))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885573), _885575), _885577)), 6545 ^ _781404 : [(6548 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885573), _885577), _885581)))], (6546 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885573), _885579), _885575)))]]]]], (3742 ^ _781404) ^ [_837499, _837501, _837503, _837505] : [-(c_List_Oremdups(_837505, _837501) = c_List_Oremdups(_837503, _837499)), _837505 = _837503, _837501 = _837499], (49027 ^ _781404) ^ [_1769396, _1769398, _1769400, _1769402, _1769404] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1769396, _1769398, hAPP(hAPP(c_COMBC(_1769396, tc_fun(tc_prod(_1769396, _1769398), tc_HOL_Obool), tc_fun(_1769398, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769398, tc_fun(tc_fun(tc_prod(_1769396, _1769398), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1769396, _1769398), tc_HOL_Obool), tc_fun(_1769398, tc_HOL_Obool)), _1769396), c_COMBC(_1769398, tc_fun(tc_prod(_1769396, _1769398), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769398, tc_prod(_1769396, _1769398)), tc_fun(_1769398, tc_fun(tc_fun(tc_prod(_1769396, _1769398), tc_HOL_Obool), tc_HOL_Obool)), _1769396), hAPP(c_COMBB(tc_prod(_1769396, _1769398), tc_fun(tc_fun(tc_prod(_1769396, _1769398), tc_HOL_Obool), tc_HOL_Obool), _1769398), c_member(tc_prod(_1769396, _1769398)))), c_Product__Type_OPair(_1769396, _1769398)))), _1769400)), _1769402), _1769404)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769398, _1769396)), hAPP(hAPP(c_Product__Type_OPair(_1769398, _1769396), _1769402), _1769404)), hAPP(c_Relation_Oconverse(_1769396, _1769398), _1769400))))], (52354 ^ _781404) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (43499 ^ _781404) ^ [_1648647, _1648649, _1648651, _1648653] : [-(_1648647 = _1648649), -(c_List_Oremove1(_1648651, _1648647, hAPP(hAPP(c_List_Olist_OCons(_1648651), _1648649), _1648653)) = hAPP(hAPP(c_List_Olist_OCons(_1648651), _1648649), c_List_Oremove1(_1648651, _1648647, _1648653)))], (43805 ^ _781404) ^ [_1654793] : [class_Orderings_Olinorder(_1654793), -(c_List_Olinorder__class_Osorted__list__of__set(_1654793, c_Orderings_Obot__class_Obot(tc_fun(_1654793, tc_HOL_Obool))) = c_List_Olist_ONil(_1654793))], (27973 ^ _781404) ^ [_1281609, _1281611, _1281613] : [class_Fields_Ofield__inverse__zero(_1281609), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281609), c_Groups_Oone__class_Oone(_1281609)), hAPP(hAPP(c_Power_Opower__class_Opower(_1281609), _1281611), _1281613)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1281609), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281609), c_Groups_Oone__class_Oone(_1281609)), _1281611)), _1281613))], (3478 ^ _781404) ^ [_833363, _833365, _833367, _833369] : [-(c_List_OremoveAll(_833369, _833365) = c_List_OremoveAll(_833367, _833363)), _833369 = _833367, _833365 = _833363], (45247 ^ _781404) ^ [_1687026, _1687028, _1687030, _1687032] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687026)), hAPP(hAPP(c_List_Omap(_1687028, _1687026), _1687030), _1687032)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687028)), _1687032))], (34737 ^ _781404) ^ [_1426755, _1426757] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1426755))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1426757)), hAPP(c_Int_Onat, _1426755)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1426757), _1426755)), 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)))], (20241 ^ _781404) ^ [_1140804] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1140804)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1140804)))], (52300 ^ _781404) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (23381 ^ _781404) ^ [_1200691, _1200693, _1200695] : [class_Divides_Osemiring__div(_1200691), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200691), c_Divides_Odiv__class_Omod(_1200691, _1200693, _1200695)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200691), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200691), _1200693), _1200695)), _1200695)) = _1200693)], (7497 ^ _781404) ^ [_903959, _903961, _903963, _903965] : [class_Lattices_Olattice(_903959), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903959), _903961), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903959), _903963), _903965)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903959), _903963), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903959), _903961), _903965)))], (14510 ^ _781404) ^ [_1035585, _1035587, _1035589, _1035591] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1035585), hAPP(c_Set_Ovimage(_1035585, _1035587, _1035589), _1035591))), hAPP(c_Set_Oimage(_1035585, _1035587, _1035589), c_Orderings_Otop__class_Otop(tc_fun(_1035585, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1035587, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035587), _1035591)))], (15761 ^ _781404) ^ [_1060571, _1060573, _1060575] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1060571), _1060573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1060571, tc_HOL_Obool)), _1060575), _1060573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1060571), _1060575)), hAPP(c_Finite__Set_Ocard(_1060571), _1060573))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1060571, tc_HOL_Obool)), _1060575), _1060573)))], (20509 ^ _781404) ^ [_1145249] : [-(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)))), _1145249) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1145249)))], (47861 ^ _781404) ^ [_1744036, _1744038, _1744040, _1744042] : [-(hBOOL(hAPP(_1744036, _1744038))), -(c_List_OdropWhile(_1744040, _1744036, hAPP(hAPP(c_List_Olist_OCons(_1744040), _1744038), _1744042)) = hAPP(hAPP(c_List_Olist_OCons(_1744040), _1744038), _1744042))], (41881 ^ _781404) ^ [_1604339, _1604341, _1604343, _1604345] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604339, _1604339)), _1604341), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604339, _1604339), tc_HOL_Obool), _1604343), _1604345))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604339, _1604339)), _1604341), c_Transitive__Closure_Ortrancl(_1604339, _1604345))))], (11129 ^ _781404) ^ [_970351, _970353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970351), _970353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970351), hAPP(c_Nat_OSuc, _970353))))], (24242 ^ _781404) ^ [_1216012, _1216014, _1216016, _1216018] : [class_Divides_Osemiring__div(_1216012), -(_1216014 = c_Groups_Ozero__class_Ozero(_1216012)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216012), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216012), _1216016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216012), _1216014), _1216018))), _1216014) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216012), _1216018), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216012), _1216016), _1216014)))], (39417 ^ _781404) ^ [_1541066, _1541068, _1541070] : [class_Orderings_Olinorder(_1541066), hBOOL(hAPP(c_Finite__Set_Ofinite(_1541066), _1541068)), -(_1541068 = c_Orderings_Obot__class_Obot(tc_fun(_1541066, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1541066), _1541070)), -(_1541070 = c_Orderings_Obot__class_Obot(tc_fun(_1541066, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1541066), c_Big__Operators_Olattice_OSup__fin(_1541066, c_Orderings_Oord__class_Omax(_1541066), _1541068)), c_Big__Operators_Olattice_OSup__fin(_1541066, c_Orderings_Oord__class_Omax(_1541066), _1541070)) = c_Big__Operators_Olattice_OSup__fin(_1541066, c_Orderings_Oord__class_Omax(_1541066), hAPP(c_Set_OCollect(_1541066), hAPP(hAPP(c_COMBB(tc_fun(_1541066, tc_HOL_Obool), tc_HOL_Obool, _1541066), c_HOL_OEx(_1541066)), hAPP(hAPP(c_COMBB(tc_fun(_1541066, tc_fun(_1541066, tc_HOL_Obool)), tc_fun(_1541066, tc_HOL_Obool), _1541066), hAPP(c_COMBB(tc_fun(_1541066, tc_HOL_Obool), tc_HOL_Obool, _1541066), c_HOL_OEx(_1541066))), hAPP(hAPP(c_COMBC(_1541066, tc_fun(_1541066, tc_fun(_1541066, tc_HOL_Obool)), tc_fun(_1541066, tc_fun(_1541066, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1541066, tc_fun(tc_fun(_1541066, tc_HOL_Obool), tc_fun(_1541066, tc_HOL_Obool))), tc_fun(tc_fun(_1541066, tc_fun(_1541066, tc_HOL_Obool)), tc_fun(_1541066, tc_fun(_1541066, tc_HOL_Obool))), _1541066), c_COMBS(_1541066, tc_fun(_1541066, tc_HOL_Obool), tc_fun(_1541066, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1541066, tc_fun(_1541066, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1541066, tc_fun(tc_fun(_1541066, tc_HOL_Obool), tc_fun(_1541066, tc_HOL_Obool))), _1541066), hAPP(c_COMBB(tc_fun(_1541066, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1541066, tc_HOL_Obool), tc_fun(_1541066, tc_HOL_Obool)), _1541066), c_COMBS(_1541066, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1541066, tc_fun(_1541066, tc_HOL_Obool)), tc_fun(_1541066, tc_fun(_1541066, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1541066), hAPP(c_COMBB(tc_fun(_1541066, tc_HOL_Obool), tc_fun(_1541066, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1541066), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541066), c_fconj))), hAPP(hAPP(c_COMBC(_1541066, tc_fun(_1541066, tc_fun(_1541066, _1541066)), tc_fun(_1541066, tc_fun(_1541066, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1541066, _1541066), tc_fun(_1541066, tc_HOL_Obool)), tc_fun(tc_fun(_1541066, tc_fun(_1541066, _1541066)), tc_fun(_1541066, tc_fun(_1541066, tc_HOL_Obool))), _1541066), c_COMBB(tc_fun(_1541066, _1541066), tc_fun(_1541066, tc_HOL_Obool), _1541066)), hAPP(hAPP(c_COMBB(tc_fun(_1541066, tc_HOL_Obool), tc_fun(tc_fun(_1541066, _1541066), tc_fun(_1541066, tc_HOL_Obool)), _1541066), c_COMBB(_1541066, tc_HOL_Obool, _1541066)), c_fequal))), c_Orderings_Oord__class_Omin(_1541066)))))), hAPP(hAPP(c_COMBC(_1541066, tc_fun(_1541066, tc_HOL_Obool), tc_fun(_1541066, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1541066, tc_HOL_Obool), tc_fun(_1541066, tc_HOL_Obool)), _1541066), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1541066)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541066), c_fconj), hAPP(hAPP(c_COMBC(_1541066, tc_fun(_1541066, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541066)), _1541068)))), hAPP(hAPP(c_COMBC(_1541066, tc_fun(_1541066, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541066)), _1541070))))))))], (52684 ^ _781404) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (5506 ^ _781404) ^ [_865649, _865651] : [_865651 = _865649, -(c_Orderings_Obot__class_Obot(_865651) = c_Orderings_Obot__class_Obot(_865649))], (47535 ^ _781404) ^ [_1737113, _1737115, _1737117] : [_1737115 = hAPP(c_List_Orev(_1737113), _1737117), -(hAPP(c_List_Orev(_1737113), _1737115) = _1737117)], (24682 ^ _781404) ^ [] : [c_Int_OPls = c_Int_OMin], (21047 ^ _781404) ^ [_1155229, _1155231, _1155233] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155229), _1155231) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155229), _1155233), -(_1155231 = _1155233), -(_1155229 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14192 ^ _781404) ^ [_1029240, _1029242, _1029244] : [class_Groups_Oordered__comm__monoid__add(_1029240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029240), _1029242), c_Groups_Ozero__class_Ozero(_1029240))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029240), _1029244), c_Groups_Ozero__class_Ozero(_1029240))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029240), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029240), _1029242), _1029244)), c_Groups_Ozero__class_Ozero(_1029240))))], (34109 ^ _781404) ^ [_1407739, _1407741, _1407743, _1407745, _1407747, _1407749] : [-(c_Nitpick_Opair__box_OPairBox(_1407739, _1407741, _1407743, _1407745) = c_Nitpick_Opair__box_OPairBox(_1407739, _1407741, _1407747, _1407749)), _1407743 = _1407747, _1407745 = _1407749], (38994 ^ _781404) ^ [_1526358, _1526360] : [-(hBOOL(hAPP(_1526360, 38995 ^ [_1526358, _1526360]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1526358, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1526358), _1526360))], (7731 ^ _781404) ^ [_908581, _908583, _908585] : [class_Lattices_Osemilattice__inf(_908581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908581), _908583), _908585)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_908581), _908585), _908583) = _908583)], (36949 ^ _781404) ^ [_1473823, _1473825, _1473827, _1473829, _1473831, _1473833, _1473835] : [hBOOL(hAPP(_1473823, _1473825)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1473827, _1473827)), hAPP(hAPP(c_Product__Type_OPair(_1473827, _1473827), _1473829), _1473831)), hAPP(_1473833, _1473825))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1473835, _1473827), tc_prod(_1473835, _1473827))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1473835, _1473827), tc_prod(_1473835, _1473827)), hAPP(hAPP(c_Product__Type_OPair(_1473835, _1473827), _1473825), _1473829)), hAPP(hAPP(c_Product__Type_OPair(_1473835, _1473827), _1473825), _1473831))), c_Recdef_Osame__fst(_1473835, _1473827, _1473823, _1473833))))], (38209 ^ _781404) ^ [_1505717, _1505719, _1505721, _1505723] : [c_Relation_Orefl__on(_1505717, _1505719, _1505721), hBOOL(hAPP(hAPP(c_member(_1505717), _1505723), _1505719)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1505717, _1505717)), hAPP(hAPP(c_Product__Type_OPair(_1505717, _1505717), _1505723), _1505723)), _1505721)))], (10283 ^ _781404) ^ [_956264, _956266, _956268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956264), _956266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956264), _956268)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956266), _956268))))], (39735 ^ _781404) ^ [_1552735, _1552737, _1552739, _1552741] : [hBOOL(hAPP(hAPP(c_member(_1552735), _1552737), hAPP(c_Relation_ORange(_1552739, _1552735), _1552741))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1552739, _1552735)), hAPP(hAPP(c_Product__Type_OPair(_1552739, _1552735), 39738 ^ [_1552735, _1552737, _1552739, _1552741]), _1552737)), _1552741)))], (13393 ^ _781404) ^ [_1014262, _1014264, _1014266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014262), _1014264)), _1014266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014264), _1014266)))], (46259 ^ _781404) ^ [_1709774, _1709776] : [_1709776 = c_List_Olist_ONil(_1709774), -(c_List_Olist_ONil(_1709774) = c_List_Oremdups(_1709774, _1709776))], (12903 ^ _781404) ^ [_1005363] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1005363))))], (25690 ^ _781404) ^ [_1240481, _1240483] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1240481) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1240483)), _1240481 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1240483)), 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), _1240483)))], (10945 ^ _781404) ^ [_967271, _967273] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967271), _967273) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967271), _967273)))], (39614 ^ _781404) ^ [_1548530, _1548532] : [-(hAPP(c_Relation_ORange(_1548530, _1548530), c_Relation_OId__on(_1548530, _1548532)) = _1548532)], (516 ^ _781404) ^ [_789154, _789156, _789158, _789160, _789162, _789164] : [-(c_Nitpick_Oless__frac(_789162, _789158, _789154)), c_Nitpick_Oless__frac(_789164, _789160, _789156), _789164 = _789162, _789160 = _789158, _789156 = _789154], (52386 ^ _781404) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (15923 ^ _781404) ^ [_1063494, _1063496, _1063498, _1063500] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1063494), _1063496)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063498), _1063500)), 15930 ^ _781404 : [(15931 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1063494), _1063496)), hAPP(c_Finite__Set_Ocard(_1063498), _1063500)))), 15932 ^ _781404 : [(15933 ^ _781404) ^ [_1063705] : [c_Fun_Oinj__on(_1063494, _1063498, _1063705, _1063496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1063498, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1063494, _1063498, _1063705), _1063496)), _1063500))]]], (15941 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1063494), _1063496)), hAPP(c_Finite__Set_Ocard(_1063498), _1063500))), 15945 ^ _781404 : [(15948 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1063498, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1063494, _1063498, 15944 ^ [_1063494, _1063496, _1063498, _1063500]), _1063496)), _1063500)))], (15946 ^ _781404) ^ [] : [-(c_Fun_Oinj__on(_1063494, _1063498, 15944 ^ [_1063494, _1063496, _1063498, _1063500], _1063496))]]]]], (5626 ^ _781404) ^ [_867401, _867403, _867405, _867407, _867409, _867411] : [-(c_COMBB(_867411, _867407, _867403) = c_COMBB(_867409, _867405, _867401)), _867411 = _867409, _867407 = _867405, _867403 = _867401], (21149 ^ _781404) ^ [_1156976, _1156978, _1156980, _1156982] : [class_Groups_Ocomm__monoid__mult(_1156976), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1156976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156976), _1156978), _1156980)), _1156982) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156976), hAPP(hAPP(c_Power_Opower__class_Opower(_1156976), _1156978), _1156982)), hAPP(hAPP(c_Power_Opower__class_Opower(_1156976), _1156980), _1156982)))], (21999 ^ _781404) ^ [_1173128, _1173130, _1173132] : [class_Rings_Ocomm__semiring__1(_1173128), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173128), _1173130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173128), _1173132), _1173130)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173128), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173128), _1173132), c_Groups_Oone__class_Oone(_1173128))), _1173130))], (48931 ^ _781404) ^ [_1767160, _1767162, _1767164, _1767166, _1767168] : [-(hAPP(c_New__DSequence_Opos__bind(_1767160, _1767162, _1767164, _1767166), _1767168) = hAPP(c_Lazy__Sequence_Obind(_1767160, _1767162, hAPP(_1767164, _1767168)), hAPP(hAPP(c_COMBC(_1767160, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1767162)), _1767166), _1767168)))], (5182 ^ _781404) ^ [_860455, _860457, _860459, _860461, _860463, _860465] : [-(c_Product__Type_Oprod_Oprod__case(_860465, _860461, _860457) = c_Product__Type_Oprod_Oprod__case(_860463, _860459, _860455)), _860465 = _860463, _860461 = _860459, _860457 = _860455], (14621 ^ _781404) ^ [_1037642, _1037644] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037642), c_Orderings_Otop__class_Otop(tc_fun(_1037642, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1037644), c_Orderings_Otop__class_Otop(tc_fun(_1037644, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1037642, _1037644)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1037642, _1037644), tc_HOL_Obool)))))], (48745 ^ _781404) ^ [_1763331, _1763333, _1763335] : [c_List_Olist__all(_1763331, _1763333, _1763335), -(c_List_Olist__all(_1763331, _1763333, hAPP(c_List_Orev(_1763331), _1763335)))], (3330 ^ _781404) ^ [_831101, _831103, _831105, _831107] : [-(c_Code__Numeral_Onat__of__aux(_831107, _831103) = c_Code__Numeral_Onat__of__aux(_831105, _831101)), _831107 = _831105, _831103 = _831101], (52454 ^ _781404) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (9180 ^ _781404) ^ [_937659, _937661, _937663] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937659, tc_HOL_Obool)), _937661), _937663) = c_Orderings_Obot__class_Obot(tc_fun(_937659, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937659, tc_HOL_Obool)), _937661), _937663) = _937661)], (12909 ^ _781404) ^ [_1005450, _1005452] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1005450, _1005452))))], (35261 ^ _781404) ^ [_1438132, _1438134, _1438136, _1438138, _1438140] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1438132, tc_fun(_1438134, tc_HOL_Obool)), _1438136), _1438138), _1438140)), 35264 ^ _781404 : [(35265 ^ _781404) ^ [_1438241] : [hBOOL(hAPP(hAPP(c_member(_1438132), _1438241), _1438136)), -(hBOOL(hAPP(hAPP(_1438138, _1438241), _1438140)))]]], (1966 ^ _781404) ^ [_809019, _809021] : [-(class_Rings_Odvd(_809019)), _809021 = _809019, class_Rings_Odvd(_809021)], (12726 ^ _781404) ^ [_1001622, _1001624, _1001626, _1001628, _1001630] : [hBOOL(hAPP(hAPP(c_member(_1001622), _1001624), c_SetInterval_Oord_OgreaterThanLessThan(_1001622, _1001626, _1001628, _1001630))), 12729 ^ _781404 : [(12732 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1001626, _1001624), _1001630)))], (12730 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1001626, _1001628), _1001624)))]]], (34187 ^ _781404) ^ [_1411160, _1411162, _1411164, _1411166] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411160, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1411160, tc_fun(_1411160, tc_HOL_Obool), tc_HOL_Obool), c_member(_1411160)), _1411162)), hAPP(hAPP(c_COMBC(_1411160, tc_fun(_1411160, tc_HOL_Obool), tc_HOL_Obool), c_member(_1411160)), _1411164)), _1411166)), -(hBOOL(hAPP(hAPP(c_member(_1411160), _1411166), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411160, tc_HOL_Obool)), _1411162), _1411164))))], (10 ^ _781404) ^ [_781527, _781529, _781531] : [-(_781531 = _781527), _781531 = _781529, _781529 = _781527], (47911 ^ _781404) ^ [_1744999, _1745001, _1745003] : [-(c_List_OdropWhile(_1744999, _1745001, _1745003) = hAPP(hAPP(c_List_Odrop(_1744999), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744999)), c_List_OtakeWhile(_1744999, _1745001, _1745003))), _1745003))], (30306 ^ _781404) ^ [_1325660, _1325662, _1325664, _1325666, _1325668, _1325670] : [c_Finite__Set_Ofun__left__comm__idem(_1325660, _1325662, _1325664), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325660), _1325666)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1325660, _1325662, _1325664), _1325668), hAPP(hAPP(c_Set_Oinsert(_1325660), _1325670), _1325666)) = hAPP(hAPP(_1325664, _1325670), hAPP(hAPP(c_Finite__Set_Ofold(_1325660, _1325662, _1325664), _1325668), _1325666)))], (9999 ^ _781404) ^ [_952175, _952177, _952179, _952181] : [class_Orderings_Opreorder(_952175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952175), _952177), _952179)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952175), _952179), _952181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952175), _952177), _952181)))], (41604 ^ _781404) ^ [_1597558, _1597560, _1597562] : [-(hAPP(c_Relation_ORange(_1597558, _1597560), hAPP(c_Relation_Oconverse(_1597560, _1597558), _1597562)) = hAPP(c_Relation_ODomain(_1597560, _1597558), _1597562))], (38878 ^ _781404) ^ [_1523176, _1523178, _1523180, _1523182, _1523184, _1523186, _1523188, _1523190] : [-(hAPP(c_Product__Type_Omap__pair(_1523176, _1523178, _1523180, _1523182, _1523184, _1523186), hAPP(hAPP(c_Product__Type_OPair(_1523176, _1523180), _1523188), _1523190)) = hAPP(hAPP(c_Product__Type_OPair(_1523178, _1523182), hAPP(_1523184, _1523188)), hAPP(_1523186, _1523190)))], (33418 ^ _781404) ^ [_1388474, _1388476, _1388478, _1388480, _1388482] : [class_Groups_Ominus(_1388474), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388476, _1388474)), _1388478), _1388480), _1388482) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388474), hAPP(_1388478, _1388482)), hAPP(_1388480, _1388482)))], (27195 ^ _781404) ^ [_1266928, _1266930] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1266928), _1266930)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1266928) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (11117 ^ _781404) ^ [_970132, _970134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970132), _970134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _970132)), _970134)))], (16346 ^ _781404) ^ [_1071765] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1071765)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1071765)], (35622 ^ _781404) ^ [_1446188, _1446190] : [-(_1446188 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35625 ^ _781404 : [(35632 ^ _781404) ^ [] : [-(_1446190 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1446188, _1446190) = 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, _1446190))), 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)), _1446190)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1446188))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446190), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446188), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1446188, _1446190)), 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), _1446190))))), c_Divides_Opdivmod(_1446188, _1446190)))))], (35626 ^ _781404) ^ [] : [_1446190 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1446188, _1446190) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1446188))]]], (37429 ^ _781404) ^ [_1485760, _1485762, _1485764, _1485766, _1485768] : [hBOOL(hAPP(hAPP(c_member(_1485760), _1485762), hAPP(c_Relation_OImage(_1485764, _1485760, _1485766), hAPP(hAPP(c_Set_Oinsert(_1485764), _1485768), c_Orderings_Obot__class_Obot(tc_fun(_1485764, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1485764, _1485760)), hAPP(hAPP(c_Product__Type_OPair(_1485764, _1485760), _1485768), _1485762)), _1485766)))], (18685 ^ _781404) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14783 ^ _781404) ^ [_1040796, _1040798, _1040800] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040796), _1040798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1040796, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1040796, _1040796, _1040800), _1040798)), _1040798)), c_Fun_Oinj__on(_1040796, _1040796, _1040800, _1040798), -(hAPP(c_Set_Oimage(_1040796, _1040796, _1040800), _1040798) = _1040798)], (23503 ^ _781404) ^ [_1203254] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203254), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8309 ^ _781404) ^ [_921505, _921507, _921509] : [-(hAPP(c_Set_Oimage(_921505, _921507, _921509), c_Orderings_Obot__class_Obot(tc_fun(_921505, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_921507, tc_HOL_Obool)))], (27691 ^ _781404) ^ [_1276161, _1276163, _1276165, _1276167] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1276161, _1276163, hAPP(hAPP(c_Set_Oinsert(_1276161), _1276165), c_Orderings_Obot__class_Obot(tc_fun(_1276161, tc_HOL_Obool)))), _1276167)), -(_1276165 = _1276167)], (4306 ^ _781404) ^ [_846617, _846619, _846621, _846623] : [-(c_List_Oconcat(_846623, _846619) = c_List_Oconcat(_846621, _846617)), _846623 = _846621, _846619 = _846617], (30472 ^ _781404) ^ [_1328947, _1328949] : [_1328947 = _1328949, -(c_Random_Oinc__shift(_1328947, _1328949) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (49880 ^ _781404) ^ [_1789955, _1789957, _1789959, _1789961] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1789955), _1789957)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1789955), _1789959)), -(_1789959 = c_Orderings_Obot__class_Obot(tc_fun(_1789955, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1789955, _1789961, _1789957, _1789959)), 49894 ^ _781404 : [(49897 ^ _781404) ^ [_1790300] : [hBOOL(hAPP(hAPP(c_member(_1789955), _1790300), _1789959)), hBOOL(hAPP(hAPP(_1789961, 49893 ^ [_1789955, _1789957, _1789959, _1789961]), _1790300))], (49895 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1789955), 49893 ^ [_1789955, _1789957, _1789959, _1789961]), _1789957)))]]], (3212 ^ _781404) ^ [_829216, _829218, _829220, _829222] : [-(c_Big__Operators_Olinorder__class_OMin(_829222, _829218) = c_Big__Operators_Olinorder__class_OMin(_829220, _829216)), _829222 = _829220, _829218 = _829216], (24282 ^ _781404) ^ [_1216711, _1216713, _1216715] : [hBOOL(hAPP(_1216711, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1216713), _1216715))), 24285 ^ _781404 : [(24310 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216715), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24313 ^ _781404 : [(24314 ^ _781404) ^ [_1217375] : [-(hBOOL(hAPP(_1216711, _1217375))), 24315 ^ _781404 : [(24316 ^ _781404) ^ [_1217449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216715), _1217449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1217449), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1216713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1216715), _1217375)), _1217449)]]]]], (24292 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216715)), 24295 ^ _781404 : [(24296 ^ _781404) ^ [_1217045] : [-(hBOOL(hAPP(_1216711, _1217045))), 24297 ^ _781404 : [(24298 ^ _781404) ^ [_1217116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217116), _1216715)), _1216713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1216715), _1217045)), _1217116)]]]]], (24286 ^ _781404) ^ [] : [_1216715 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1216711, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (38741 ^ _781404) ^ [_1518963, _1518965, _1518967, _1518969, _1518971, _1518973, _1518975, _1518977] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1518963, _1518965), tc_fun(tc_prod(_1518967, _1518969), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518963, _1518965), _1518971), hAPP(c_COMBK(tc_fun(_1518965, tc_HOL_Obool), _1518963), _1518973))), hAPP(c_Product__Type_Oprod_Oprod__case(_1518963, _1518965, tc_fun(tc_prod(_1518967, _1518969), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1518963, tc_fun(_1518965, tc_fun(_1518967, tc_fun(_1518969, tc_HOL_Obool))), tc_fun(_1518965, tc_fun(tc_prod(_1518967, _1518969), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1518967, tc_fun(_1518969, tc_HOL_Obool)), tc_fun(tc_prod(_1518967, _1518969), tc_HOL_Obool)), tc_fun(tc_fun(_1518965, tc_fun(_1518967, tc_fun(_1518969, tc_HOL_Obool))), tc_fun(_1518965, tc_fun(tc_prod(_1518967, _1518969), tc_HOL_Obool))), _1518963), c_COMBB(tc_fun(_1518967, tc_fun(_1518969, tc_HOL_Obool)), tc_fun(tc_prod(_1518967, _1518969), tc_HOL_Obool), _1518965)), hAPP(hAPP(c_COMBB(tc_fun(_1518967, tc_HOL_Obool), tc_fun(tc_fun(_1518967, tc_fun(_1518969, tc_HOL_Obool)), tc_fun(tc_prod(_1518967, _1518969), tc_HOL_Obool)), _1518963), c_Product__Type_OSigma(_1518967, _1518969)), _1518975))), hAPP(hAPP(c_COMBB(tc_fun(_1518969, tc_HOL_Obool), tc_fun(_1518967, tc_fun(_1518969, tc_HOL_Obool)), _1518965), c_COMBK(tc_fun(_1518969, tc_HOL_Obool), _1518967)), _1518977)))) = hAPP(hAPP(c_Product__Type_OSigma(_1518967, _1518969), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1518963, tc_fun(_1518967, tc_HOL_Obool)), _1518971), _1518975)), hAPP(c_COMBK(tc_fun(_1518969, tc_HOL_Obool), _1518967), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1518965, tc_fun(_1518969, tc_HOL_Obool)), _1518973), _1518977))))], (33875 ^ _781404) ^ [_1401428, _1401430, _1401432, _1401434, _1401436] : [class_Complete__Lattice_Ocomplete__lattice(_1401428), 33878 ^ _781404 : [(33879 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401428), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401430, _1401428), _1401432), _1401434)), _1401436)), 33882 ^ _781404 : [(33883 ^ _781404) ^ [_1401609] : [hBOOL(hAPP(hAPP(c_member(_1401430), _1401609), _1401432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401428), hAPP(_1401434, _1401609)), _1401436)))]]], (33889 ^ _781404) ^ [] : [33891 ^ _781404 : [(33894 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401428), hAPP(_1401434, 33890 ^ [_1401428, _1401430, _1401432, _1401434, _1401436])), _1401436))], (33892 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401430), 33890 ^ [_1401428, _1401430, _1401432, _1401434, _1401436]), _1401432)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401428), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401430, _1401428), _1401432), _1401434)), _1401436)))]]], (27897 ^ _781404) ^ [_1280497, _1280499] : [class_Rings_Odivision__ring__inverse__zero(_1280497), 27900 ^ _781404 : [(27907 ^ _781404) ^ [] : [-(_1280499 = c_Groups_Ozero__class_Ozero(_1280497)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280497), _1280499), _1280499) = c_Groups_Oone__class_Oone(_1280497))], (27901 ^ _781404) ^ [] : [_1280499 = c_Groups_Ozero__class_Ozero(_1280497), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280497), _1280499), _1280499) = c_Groups_Ozero__class_Ozero(_1280497))]]], (52520 ^ _781404) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (52374 ^ _781404) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (25483 ^ _781404) ^ [_1236947, _1236949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236947)), 25486 ^ _781404 : [(25493 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236947), _1236949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1236947)), hAPP(c_Int_Onat, _1236949))))], (25487 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1236947)), hAPP(c_Int_Onat, _1236949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236947), _1236949)))]]], (27857 ^ _781404) ^ [_1279841, _1279843, _1279845, _1279847] : [class_Rings_Odivision__ring(_1279841), -(_1279843 = c_Groups_Ozero__class_Ozero(_1279841)), 27864 ^ _781404 : [(27871 ^ _781404) ^ [] : [_1279845 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279841), _1279847), _1279843), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279841), _1279845), _1279843) = _1279847)], (27865 ^ _781404) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279841), _1279845), _1279843) = _1279847, -(_1279845 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279841), _1279847), _1279843))]]], (46006 ^ _781404) ^ [_1704224, _1704226, _1704228, _1704230, _1704232] : [c_List_Olist__all2(_1704224, _1704226, _1704228, _1704230, _1704232), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704224)), _1704230) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704226)), _1704232))], (22241 ^ _781404) ^ [_1177899, _1177901] : [_1177899 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177899), _1177901), -(_1177901 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1177899 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52378 ^ _781404) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (39729 ^ _781404) ^ [_1552378, _1552380, _1552382, _1552384] : [hBOOL(hAPP(hAPP(c_member(_1552380), _1552384), hAPP(c_Relation_ORange(_1552378, _1552380), _1552382))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1552378, _1552380, hAPP(hAPP(c_COMBC(_1552378, tc_fun(tc_prod(_1552378, _1552380), tc_HOL_Obool), tc_fun(_1552380, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552380, tc_fun(tc_fun(tc_prod(_1552378, _1552380), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1552378, _1552380), tc_HOL_Obool), tc_fun(_1552380, tc_HOL_Obool)), _1552378), c_COMBC(_1552380, tc_fun(tc_prod(_1552378, _1552380), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552380, tc_prod(_1552378, _1552380)), tc_fun(_1552380, tc_fun(tc_fun(tc_prod(_1552378, _1552380), tc_HOL_Obool), tc_HOL_Obool)), _1552378), hAPP(c_COMBB(tc_prod(_1552378, _1552380), tc_fun(tc_fun(tc_prod(_1552378, _1552380), tc_HOL_Obool), tc_HOL_Obool), _1552380), c_member(tc_prod(_1552378, _1552380)))), c_Product__Type_OPair(_1552378, _1552380)))), _1552382)), _1552384)))], (15166 ^ _781404) ^ [_1048844, _1048846, _1048848, _1048850, _1048852, _1048854, _1048856, _1048858] : [c_Finite__Set_Ofolding__image__simple(_1048844, _1048846, _1048848, _1048850, _1048852, _1048854), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048846), _1048856)), -(hAPP(_1048854, hAPP(hAPP(c_Set_Oinsert(_1048846), _1048858), _1048856)) = hAPP(hAPP(_1048848, hAPP(_1048852, _1048858)), hAPP(_1048854, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048846, tc_HOL_Obool)), _1048856), hAPP(hAPP(c_Set_Oinsert(_1048846), _1048858), c_Orderings_Obot__class_Obot(tc_fun(_1048846, tc_HOL_Obool)))))))], (41827 ^ _781404) ^ [_1603034, _1603036, _1603038, _1603040, _1603042] : [c_Relation_Osingle__valued(_1603034, _1603036, hAPP(c_Relation_Oconverse(_1603036, _1603034), _1603038)), -(hAPP(c_Relation_OImage(_1603036, _1603034, _1603038), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1603036, tc_HOL_Obool)), _1603040), _1603042)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1603034, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1603036, _1603034, _1603038), _1603040)), hAPP(c_Relation_OImage(_1603036, _1603034, _1603038), _1603042)))], (39836 ^ _781404) ^ [_1555828, _1555830] : [-(c_Wellfounded_Owf(_1555828, hAPP(c_Wellfounded_Omeasure(_1555828), _1555830)))], (39530 ^ _781404) ^ [_1546195, _1546197] : [-(hAPP(c_Fun_Oid(_1546195), _1546197) = _1546197)], (29223 ^ _781404) ^ [_1304351, _1304353, _1304355, _1304357, _1304359] : [class_Fields_Olinordered__field(_1304351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304351), c_Groups_Ozero__class_Ozero(_1304351)), _1304353)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304351), _1304353), _1304355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304351), c_Groups_Ozero__class_Ozero(_1304351)), _1304357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304351), _1304357), _1304359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304351), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304351), _1304353), _1304359)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304351), _1304355), _1304357))))], (41461 ^ _781404) ^ [_1594039] : [-(c_Relation_OId(_1594039) = hAPP(c_Set_OCollect(tc_prod(_1594039, _1594039)), hAPP(hAPP(c_COMBB(tc_fun(_1594039, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1594039, _1594039)), c_HOL_OEx(_1594039)), hAPP(hAPP(c_COMBC(tc_prod(_1594039, _1594039), tc_fun(_1594039, tc_prod(_1594039, _1594039)), tc_fun(_1594039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1594039, _1594039), tc_HOL_Obool), tc_fun(tc_fun(_1594039, tc_prod(_1594039, _1594039)), tc_fun(_1594039, tc_HOL_Obool)), tc_prod(_1594039, _1594039)), c_COMBB(tc_prod(_1594039, _1594039), tc_HOL_Obool, _1594039)), c_fequal)), hAPP(hAPP(c_COMBS(_1594039, _1594039, tc_prod(_1594039, _1594039)), c_Product__Type_OPair(_1594039, _1594039)), c_COMBI(_1594039))))))], (52736 ^ _781404) ^ [_1842323, _1842325] : [hBOOL(hAPP(hAPP(c_fequal, _1842323), _1842325)), -(_1842323 = _1842325)], (27793 ^ _781404) ^ [_1278563, _1278565, _1278567, _1278569] : [class_Rings_Odivision__ring(_1278563), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278563), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1278563), _1278565), _1278567)), _1278569) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1278563), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278563), _1278565), _1278569)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278563), _1278567), _1278569)))], (49563 ^ _781404) ^ [_1781181, _1781183, _1781185] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1781181), _1781183, _1781185)), -(c_List_Olist__ex(tc_Int_Oint, _1781181, c_List_Oupto(_1781183, _1781185)))], (43643 ^ _781404) ^ [_1651122, _1651124] : [-(c_List_Osublist(_1651122, _1651124, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1651122))], (15251 ^ _781404) ^ [_1050612, _1050614, _1050616] : [class_Lattices_Olattice(_1050612), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050612), _1050614)), hBOOL(hAPP(hAPP(c_member(_1050612), _1050616), _1050614)), 15262 ^ _781404 : [(15269 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050612, tc_HOL_Obool)), _1050614), hAPP(hAPP(c_Set_Oinsert(_1050612), _1050616), c_Orderings_Obot__class_Obot(tc_fun(_1050612, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1050612, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1050612, _1050614) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1050612), _1050616), c_Big__Operators_Olattice__class_OInf__fin(_1050612, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050612, tc_HOL_Obool)), _1050614), hAPP(hAPP(c_Set_Oinsert(_1050612), _1050616), c_Orderings_Obot__class_Obot(tc_fun(_1050612, tc_HOL_Obool)))))))], (15263 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050612, tc_HOL_Obool)), _1050614), hAPP(hAPP(c_Set_Oinsert(_1050612), _1050616), c_Orderings_Obot__class_Obot(tc_fun(_1050612, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1050612, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1050612, _1050614) = _1050616)]]], (8566 ^ _781404) ^ [_925857, _925859] : [class_Lattices_Obounded__lattice__bot(_925857), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925857), _925859), c_Orderings_Obot__class_Obot(_925857)) = c_Orderings_Obot__class_Obot(_925857))], (52774 ^ _781404) ^ [_1842793, _1842795] : [hBOOL(hAPP(hAPP(c_fconj, _1842793), _1842795)), -(hBOOL(_1842793))], (42173 ^ _781404) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26931 ^ _781404) ^ [_1262112, _1262114, _1262116] : [class_Rings_Olinordered__idom(_1262112), -(hAPP(c_Groups_Oabs__class_Oabs(_1262112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262112), _1262114), _1262116)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262112), hAPP(c_Groups_Oabs__class_Oabs(_1262112), _1262114)), hAPP(c_Groups_Oabs__class_Oabs(_1262112), _1262116)))], (15984 ^ _781404) ^ [_1064838, _1064840, _1064842] : [class_Lattices_Olattice(_1064838), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064838), _1064840)), -(hBOOL(hAPP(hAPP(c_member(_1064838), _1064842), _1064840))), -(_1064840 = c_Orderings_Obot__class_Obot(tc_fun(_1064838, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1064838, hAPP(hAPP(c_Set_Oinsert(_1064838), _1064842), _1064840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064838), _1064842), c_Big__Operators_Olattice__class_OSup__fin(_1064838, _1064840)))], (27391 ^ _781404) ^ [_1270552, _1270554] : [class_Lattices_Olattice(_1270552), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270552), _1270554)), -(c_Big__Operators_Olattice__class_OSup__fin(_1270552, _1270554) = hAPP(c_Finite__Set_Ofold1(_1270552, c_Lattices_Osemilattice__sup__class_Osup(_1270552)), _1270554))], (41237 ^ _781404) ^ [_1588810, _1588812, _1588814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588810, _1588810), tc_HOL_Obool)), _1588812), _1588814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588810, _1588810), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588810, _1588812)), c_Transitive__Closure_Ortrancl(_1588810, _1588814))))], (122 ^ _781404) ^ [_783285, _783287, _783289, _783291] : [-(c_Int_Oiszero(_783289, _783285)), c_Int_Oiszero(_783291, _783287), _783291 = _783289, _783287 = _783285], (50197 ^ _781404) ^ [_1796021, _1796023] : [c_Relation_Osym(_1796021, _1796023), -(c_Relation_Osym(tc_List_Olist(_1796021), c_List_Olistrel(_1796021, _1796023)))], (42764 ^ _781404) ^ [_1630375, _1630377, _1630379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630375)), _1630377)), _1630379)), -(hAPP(hAPP(c_List_Otake(_1630375), _1630379), _1630377) = _1630377)], (14585 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (7389 ^ _781404) ^ [_901952, _901954] : [class_Groups_Oordered__ab__group__add(_901952), -(hAPP(c_Set_Oimage(_901952, _901952, c_Groups_Ouminus__class_Ouminus(_901952)), hAPP(c_SetInterval_Oord__class_OatLeast(_901952), _901954)) = hAPP(c_SetInterval_Oord__class_OatMost(_901952), hAPP(c_Groups_Ouminus__class_Ouminus(_901952), _901954)))], (2850 ^ _781404) ^ [_823641, _823643, _823645, _823647] : [-(c_Inductive_Ocomplete__lattice__class_Olfp(_823647, _823643) = c_Inductive_Ocomplete__lattice__class_Olfp(_823645, _823641)), _823647 = _823645, _823643 = _823641], (19907 ^ _781404) ^ [_1135000, _1135002, _1135004] : [class_Rings_Olinordered__idom(_1135000), 19910 ^ _781404 : [(19911 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135000), c_Groups_Ozero__class_Ozero(_1135000)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135000), hAPP(hAPP(c_Power_Opower__class_Opower(_1135000), _1135002), 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(_1135000), _1135004), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1135002 = c_Groups_Ozero__class_Ozero(_1135000), _1135004 = c_Groups_Ozero__class_Ozero(_1135000)], (19921 ^ _781404) ^ [] : [19922 ^ _781404 : [(19925 ^ _781404) ^ [] : [-(_1135004 = c_Groups_Ozero__class_Ozero(_1135000))], (19923 ^ _781404) ^ [] : [-(_1135002 = c_Groups_Ozero__class_Ozero(_1135000))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135000), c_Groups_Ozero__class_Ozero(_1135000)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135000), hAPP(hAPP(c_Power_Opower__class_Opower(_1135000), _1135002), 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(_1135000), _1135004), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (19216 ^ _781404) ^ [_1123147] : [hBOOL(hAPP(_1123147, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 19217 ^ [_1123147]))), 19220 ^ _781404 : [(19221 ^ _781404) ^ [_1123247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1123247)), -(hBOOL(hAPP(_1123147, _1123247)))]]], (45088 ^ _781404) ^ [_1683138, _1683140, _1683142] : [-(c_List_Olast(_1683138, hAPP(hAPP(c_List_Oappend(_1683138), _1683140), hAPP(hAPP(c_List_Olist_OCons(_1683138), _1683142), c_List_Olist_ONil(_1683138)))) = _1683142)], (7503 ^ _781404) ^ [_904102, _904104, _904106, _904108] : [class_Lattices_Osemilattice__inf(_904102), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904102), _904104), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904102), _904106), _904108)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904102), _904106), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904102), _904104), _904108)))], (4846 ^ _781404) ^ [_855169, _855171, _855173, _855175] : [-(c_Complete__Lattice_OSup__class_OSup(_855175, _855171) = c_Complete__Lattice_OSup__class_OSup(_855173, _855169)), _855175 = _855173, _855171 = _855169], (30085 ^ _781404) ^ [_1320960, _1320962, _1320964, _1320966, _1320968] : [class_Groups_Ocomm__monoid__mult(_1320960), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320962), _1320964)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320962), _1320966)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320962, tc_HOL_Obool)), _1320964), _1320966) = c_Orderings_Obot__class_Obot(tc_fun(_1320962, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1320962, _1320960), _1320968), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320962, tc_HOL_Obool)), _1320964), _1320966)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1320960), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1320962, _1320960), _1320968), _1320964)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1320962, _1320960), _1320968), _1320966)))], (52428 ^ _781404) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (39707 ^ _781404) ^ [_1551100, _1551102, _1551104, _1551106] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1551100, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1551102, _1551100), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1551102, _1551100), tc_HOL_Obool)), _1551104), _1551106))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1551100, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1551102, _1551100), _1551104)), hAPP(c_Relation_ORange(_1551102, _1551100), _1551106)))))], (7205 ^ _781404) ^ [_898337, _898339, _898341, _898343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898337, tc_HOL_Obool)), _898339), _898341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898337, tc_HOL_Obool)), _898343), _898341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898337, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898337, tc_HOL_Obool)), _898339), _898343)), _898341)))], (40224 ^ _781404) ^ [_1564641, _1564643] : [c_Wellfounded_Owf(_1564641, hAPP(c_Set_OCollect(tc_prod(_1564641, _1564641)), hAPP(c_Product__Type_Oprod_Oprod__case(_1564641, _1564641, tc_HOL_Obool), _1564643))), -(c_Wellfounded_OwfP(_1564641, _1564643))], (7934 ^ _781404) ^ [_913174, _913176, _913178, _913180] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913174, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913174, tc_HOL_Obool)), _913176), _913178)), _913180) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913174, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913174, tc_HOL_Obool)), _913176), _913180)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913174, tc_HOL_Obool)), _913178), _913180)))], (38528 ^ _781404) ^ [_1513173, _1513175, _1513177] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1513173, _1513175), _1513177), hAPP(c_COMBK(tc_fun(_1513175, tc_HOL_Obool), _1513173), c_Orderings_Obot__class_Obot(tc_fun(_1513175, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513173, _1513175), tc_HOL_Obool)))], (32366 ^ _781404) ^ [_1364482, _1364484, _1364486, _1364488] : [class_Orderings_Olinorder(_1364482), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364482, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1364482), _1364484)), c_SetInterval_Oord__class_OatLeastAtMost(_1364482, _1364486, _1364488)) = c_SetInterval_Oord__class_OatLeastAtMost(_1364482, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364482), _1364484), _1364486), _1364488))], (41303 ^ _781404) ^ [_1590363, _1590365, _1590367, _1590369, _1590371] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590363, _1590363)), hAPP(hAPP(c_Product__Type_OPair(_1590363, _1590363), _1590365), _1590367)), c_Transitive__Closure_Ortrancl(_1590363, _1590369))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590363, _1590363)), hAPP(hAPP(c_Product__Type_OPair(_1590363, _1590363), _1590367), _1590371)), c_Transitive__Closure_Otrancl(_1590363, _1590369))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590363, _1590363)), hAPP(hAPP(c_Product__Type_OPair(_1590363, _1590363), _1590365), _1590371)), c_Transitive__Closure_Otrancl(_1590363, _1590369))))], (41229 ^ _781404) ^ [_1588572, _1588574] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588572, _1588572), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588572, _1588574)), c_Relation_OId(_1588572)) = c_Transitive__Closure_Ortrancl(_1588572, _1588574))], (43653 ^ _781404) ^ [_1651313, _1651315] : [-(_1651315 = c_List_Olist_ONil(_1651313)), -(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(_1651313)), _1651315))))], (44373 ^ _781404) ^ [_1668404, _1668406] : [-(hAPP(c_List_Oset(_1668404), hAPP(c_List_Orotate1(_1668404), _1668406)) = hAPP(c_List_Oset(_1668404), _1668406))], (45176 ^ _781404) ^ [_1684747, _1684749, _1684751, _1684753, _1684755, _1684757, _1684759] : [-(hAPP(c_List_Ofoldl(_1684747, _1684749, _1684751, _1684753), hAPP(hAPP(c_List_Omap(_1684755, _1684749), _1684757), _1684759)) = hAPP(c_List_Ofoldl(_1684747, _1684755, hAPP(hAPP(c_COMBC(_1684747, tc_fun(_1684755, _1684749), tc_fun(_1684755, _1684747)), hAPP(hAPP(c_COMBB(tc_fun(_1684749, _1684747), tc_fun(tc_fun(_1684755, _1684749), tc_fun(_1684755, _1684747)), _1684747), c_COMBB(_1684749, _1684747, _1684755)), _1684751)), _1684757), _1684753), _1684759))], (41854 ^ _781404) ^ [_1603666, _1603668, _1603670, _1603672] : [-(hAPP(_1603666, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1603668, _1603668), _1603670), _1603666), _1603672)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1603668, _1603668), _1603670), _1603666), hAPP(_1603666, _1603672)))], (18711 ^ _781404) ^ [_1115070, _1115072] : [class_Int_Onumber__ring(_1115070), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115070), _1115072), hAPP(c_Int_Onumber__class_Onumber__of(_1115070), c_Int_OPls)) = _1115072)], (20769 ^ _781404) ^ [_1149873, _1149875, _1149877, _1149879, _1149881] : [class_Rings_Ocomm__semiring__1(_1149873), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149873), _1149875), _1149877)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149873), _1149879), _1149881)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149873), _1149875), _1149879)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149873), _1149877), _1149881)))], (30708 ^ _781404) ^ [_1333483, _1333485, _1333487] : [class_Orderings_Olinorder(_1333483), 30711 ^ _781404 : [(30718 ^ _781404) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333483), _1333485), _1333487) = _1333485, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333483), _1333485), _1333487)))], (30712 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333483), _1333485), _1333487)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333483), _1333485), _1333487) = _1333485)]]], (33982 ^ _781404) ^ [_1404962, _1404964, _1404966, _1404968, _1404970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404962, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404964, tc_fun(_1404962, tc_HOL_Obool)), _1404966), _1404968)), _1404970)), 33985 ^ _781404 : [(33986 ^ _781404) ^ [_1405095] : [hBOOL(hAPP(hAPP(c_member(_1404964), _1405095), _1404966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404962, tc_HOL_Obool)), hAPP(_1404968, _1405095)), _1404970)))]]], (43118 ^ _781404) ^ [_1640225, _1640227, _1640229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1640225), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640227)), _1640229))), -(c_List_Obutlast(_1640227, hAPP(hAPP(c_List_Otake(_1640227), _1640225), _1640229)) = hAPP(hAPP(c_List_Otake(_1640227), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1640225), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1640229))], (40021 ^ _781404) ^ [_1559508, _1559510] : [c_Wellfounded_Owf(_1559508, _1559510), 40025 ^ _781404 : [(40026 ^ _781404) ^ [_1559644] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559508, _1559508)), hAPP(hAPP(c_Product__Type_OPair(_1559508, _1559508), hAPP(_1559644, hAPP(c_Nat_OSuc, 40024 ^ [_1559508, _1559510, _1559644]))), hAPP(_1559644, 40024 ^ [_1559508, _1559510, _1559644]))), _1559510))]]], (38504 ^ _781404) ^ [_1512504, _1512506, _1512508, _1512510, _1512512, _1512514] : [hBOOL(hAPP(hAPP(c_member(_1512504), _1512506), _1512508)), 38507 ^ _781404 : [(38514 ^ _781404) ^ [] : [_1512512 = _1512514, -(hAPP(hAPP(c_Product__Type_OSigma(_1512510, _1512504), _1512512), hAPP(c_COMBK(tc_fun(_1512504, tc_HOL_Obool), _1512510), _1512508)) = hAPP(hAPP(c_Product__Type_OSigma(_1512510, _1512504), _1512514), hAPP(c_COMBK(tc_fun(_1512504, tc_HOL_Obool), _1512510), _1512508)))], (38508 ^ _781404) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1512510, _1512504), _1512512), hAPP(c_COMBK(tc_fun(_1512504, tc_HOL_Obool), _1512510), _1512508)) = hAPP(hAPP(c_Product__Type_OSigma(_1512510, _1512504), _1512514), hAPP(c_COMBK(tc_fun(_1512504, tc_HOL_Obool), _1512510), _1512508)), -(_1512512 = _1512514)]]], (7045 ^ _781404) ^ [_895400, _895402, _895404, _895406, _895408] : [class_Lattices_Osemilattice__sup(_895400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895400), _895402), _895404)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895400), _895406), _895408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895400), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895400), _895402), _895406)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895400), _895404), _895408))))], (33293 ^ _781404) ^ [_1383664, _1383666, _1383668, _1383670, _1383672] : [_1383664 = c_Orderings_Obot__class_Obot(tc_fun(_1383666, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1383666, tc_fun(_1383668, tc_HOL_Obool)), _1383664), hAPP(hAPP(c_COMBC(_1383666, tc_fun(_1383668, tc_HOL_Obool), tc_fun(_1383668, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383668, tc_HOL_Obool), tc_fun(tc_fun(_1383668, tc_HOL_Obool), tc_fun(_1383668, tc_HOL_Obool)), _1383666), c_Groups_Ominus__class_Ominus(tc_fun(_1383668, tc_HOL_Obool))), _1383670)), _1383672)) = c_Orderings_Otop__class_Otop(tc_fun(_1383668, tc_HOL_Obool)))], (48957 ^ _781404) ^ [_1767891, _1767893] : [c_Wellfounded_Oacyclic(_1767891, hAPP(c_Set_OCollect(tc_prod(_1767891, _1767891)), hAPP(c_Product__Type_Oprod_Oprod__case(_1767891, _1767891, tc_HOL_Obool), c_Predicate_Oconversep(_1767891, _1767891, _1767893)))), -(c_Wellfounded_Oacyclic(_1767891, hAPP(c_Set_OCollect(tc_prod(_1767891, _1767891)), hAPP(c_Product__Type_Oprod_Oprod__case(_1767891, _1767891, tc_HOL_Obool), _1767893))))], (13243 ^ _781404) ^ [_1011425, _1011427, _1011429] : [class_Groups_Ogroup__add(_1011425), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011425), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011425), _1011427), _1011429)), _1011429) = _1011427)], (41927 ^ _781404) ^ [_1605681, _1605683, _1605685] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605681, _1605681)), _1605683), c_Transitive__Closure_Otrancl(_1605681, _1605685))), 41931 ^ _781404 : [(41934 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605681, _1605681)), _1605683), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605681, _1605681), tc_HOL_Obool), 41930 ^ [_1605681, _1605683, _1605685]), _1605685))))], (41932 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41930 ^ [_1605681, _1605683, _1605685])))]]], (6059 ^ _781404) ^ [_877469, _877471, _877473] : [6061 ^ _781404 : [(6064 ^ _781404) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_877469, hAPP(c_Nat_OSuc, _877473), 6060 ^ [_877469, _877471, _877473])], (6062 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_877469)), 6060 ^ [_877469, _877471, _877473]), _877471)))]], 6065 ^ _781404 : [(6066 ^ _781404) ^ [_877642] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_877469)), _877642), _877471)), -(c_Hoare__Mirabelle_Otriple__valid(_877469, _877473, _877642))]]], (48969 ^ _781404) ^ [_1768179, _1768181, _1768183, _1768185] : [-(c_Predicate_Oconversep(_1768179, _1768181, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1768179, tc_fun(_1768181, tc_HOL_Obool))), _1768183), _1768185)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1768181, tc_fun(_1768179, tc_HOL_Obool))), c_Predicate_Oconversep(_1768179, _1768181, _1768183)), c_Predicate_Oconversep(_1768179, _1768181, _1768185)))], (13339 ^ _781404) ^ [_1013198, _1013200, _1013202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013198), _1013200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013198), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013202), _1013200))))], (39928 ^ _781404) ^ [_1557505, _1557507] : [c_Wellfounded_Owf(_1557505, _1557507), -(c_Wellfounded_Owf(tc_fun(_1557505, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1557505, _1557507)))], (22031 ^ _781404) ^ [_1173890, _1173892] : [class_Rings_Ocomm__ring__1(_1173890), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1173890), _1173892) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173890), hAPP(c_Groups_Ouminus__class_Ouminus(_1173890), c_Groups_Oone__class_Oone(_1173890))), _1173892))], (35828 ^ _781404) ^ [_1450333, _1450335, _1450337, _1450339, _1450341] : [class_Orderings_Oorder(_1450333), c_Orderings_Oorder__class_Omono(_1450333, tc_fun(_1450335, tc_HOL_Obool), _1450337), -(c_Orderings_Oorder__class_Omono(_1450333, tc_fun(_1450335, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1450333, tc_fun(_1450335, tc_HOL_Obool), tc_fun(_1450335, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450335, tc_HOL_Obool), tc_fun(tc_fun(_1450335, tc_HOL_Obool), tc_fun(_1450335, tc_HOL_Obool)), _1450333), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450335, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1450333, tc_fun(_1450335, tc_HOL_Obool), tc_fun(_1450335, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450335, tc_HOL_Obool), tc_fun(tc_fun(_1450335, tc_HOL_Obool), tc_fun(_1450335, tc_HOL_Obool)), _1450333), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450335, tc_HOL_Obool))), _1450337)), _1450339))), _1450341)))], (45096 ^ _781404) ^ [_1683338, _1683340, _1683342, _1683344] : [hAPP(hAPP(c_List_Oappend(_1683338), _1683340), hAPP(hAPP(c_List_Olist_OCons(_1683338), _1683342), c_List_Olist_ONil(_1683338))) = _1683344, 45099 ^ _781404 : [(45104 ^ _781404) ^ [] : [-(c_List_Olast(_1683338, _1683344) = _1683342)], (45102 ^ _781404) ^ [] : [-(c_List_Obutlast(_1683338, _1683344) = _1683340)], (45100 ^ _781404) ^ [] : [_1683344 = c_List_Olist_ONil(_1683338)]]], (27913 ^ _781404) ^ [_1280719, _1280721] : [class_Rings_Odivision__ring(_1280719), -(_1280721 = c_Groups_Ozero__class_Ozero(_1280719)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280719), _1280721), _1280721) = c_Groups_Oone__class_Oone(_1280719))], (5296 ^ _781404) ^ [_862244, _862246, _862248, _862250, _862252, _862254] : [-(c_Lazy__Sequence_Obind(_862254, _862250, _862246) = c_Lazy__Sequence_Obind(_862252, _862248, _862244)), _862254 = _862252, _862250 = _862248, _862246 = _862244], (21887 ^ _781404) ^ [_1170735, _1170737, _1170739] : [class_Rings_Olinordered__ring__strict(_1170735), 21890 ^ _781404 : [(21899 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170735), _1170737), _1170737)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170735), _1170739), _1170739)) = c_Groups_Ozero__class_Ozero(_1170735)), _1170737 = c_Groups_Ozero__class_Ozero(_1170735), _1170739 = c_Groups_Ozero__class_Ozero(_1170735)], (21891 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170735), _1170737), _1170737)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170735), _1170739), _1170739)) = c_Groups_Ozero__class_Ozero(_1170735), 21894 ^ _781404 : [(21897 ^ _781404) ^ [] : [-(_1170739 = c_Groups_Ozero__class_Ozero(_1170735))], (21895 ^ _781404) ^ [] : [-(_1170737 = c_Groups_Ozero__class_Ozero(_1170735))]]]]], (51094 ^ _781404) ^ [_1814088, _1814090, _1814092, _1814094, _1814096, _1814098] : [c_Fun_Obij__betw(_1814088, _1814090, _1814092, c_Orderings_Otop__class_Otop(tc_fun(_1814088, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1814090, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1814088, _1814090, _1814092), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1814094, tc_fun(_1814088, tc_HOL_Obool)), _1814096), _1814098)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1814094, tc_fun(_1814090, tc_HOL_Obool)), _1814096), hAPP(hAPP(c_COMBB(tc_fun(_1814088, tc_HOL_Obool), tc_fun(_1814090, tc_HOL_Obool), _1814094), c_Set_Oimage(_1814088, _1814090, _1814092)), _1814098)))], (47453 ^ _781404) ^ [_1735309, _1735311, _1735313] : [hAPP(c_List_Orev(_1735309), _1735311) = hAPP(hAPP(c_List_Olist_OCons(_1735309), _1735313), c_List_Olist_ONil(_1735309)), -(_1735311 = hAPP(hAPP(c_List_Olist_OCons(_1735309), _1735313), c_List_Olist_ONil(_1735309)))], (9274 ^ _781404) ^ [_939914, _939916, _939918] : [class_Orderings_Olinorder(_939914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939914), _939916), _939918)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_939914, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_939914, _939916, _939918)), hAPP(hAPP(c_Set_Oinsert(_939914), _939918), c_Orderings_Obot__class_Obot(tc_fun(_939914, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_939914, _939916, _939918))], (14745 ^ _781404) ^ [_1040063, _1040065, _1040067, _1040069] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040063), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1040063, tc_HOL_Obool)), _1040065), _1040069))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040063), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1040063, tc_HOL_Obool)), _1040065), hAPP(hAPP(c_Set_Oinsert(_1040063), _1040067), _1040069)))))], (37333 ^ _781404) ^ [_1483279, _1483281, _1483283, _1483285, _1483287, _1483289] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1483285, _1483285)), hAPP(hAPP(c_Product__Type_OPair(_1483285, _1483285), hAPP(_1483289, _1483281)), hAPP(_1483289, _1483283))), _1483287)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1483279, _1483279)), hAPP(hAPP(c_Product__Type_OPair(_1483279, _1483279), _1483281), _1483283)), hAPP(hAPP(c_Relation_Oinv__image(_1483285, _1483279), _1483287), _1483289))))], (4448 ^ _781404) ^ [_848936, _848938] : [_848938 = _848936, -(c_Lazy__Sequence_Osingle(_848938) = c_Lazy__Sequence_Osingle(_848936))], (3104 ^ _781404) ^ [_827566, _827568, _827570, _827572] : [-(c_Nitpick_Ocard_H(_827572, _827568) = c_Nitpick_Ocard_H(_827570, _827566)), _827572 = _827570, _827568 = _827566], (41003 ^ _781404) ^ [_1582364, _1582366] : [-(c_Wellfounded_Owf(_1582364, _1582366)), 41006 ^ _781404 : [(41009 ^ _781404) ^ [_1582584] : [hBOOL(hAPP(hAPP(c_member(_1582364), _1582584), 41004 ^ [_1582364, _1582366])), 41013 ^ _781404 : [(41016 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1582364), 41012 ^ [_1582364, _1582366, _1582584]), 41004 ^ [_1582364, _1582366])))], (41014 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582364, _1582364)), hAPP(hAPP(c_Product__Type_OPair(_1582364, _1582364), 41012 ^ [_1582364, _1582366, _1582584]), _1582584)), _1582366)))]]], (41007 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1582364), 41005 ^ [_1582364, _1582366]), 41004 ^ [_1582364, _1582366])))]]], (33512 ^ _781404) ^ [_1391091, _1391093, _1391095, _1391097] : [-(hAPP(c_Set_OPow(_1391091), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391093, tc_fun(_1391091, tc_HOL_Obool)), _1391095), _1391097)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391093, tc_fun(tc_fun(_1391091, tc_HOL_Obool), tc_HOL_Obool)), _1391095), hAPP(hAPP(c_COMBB(tc_fun(_1391091, tc_HOL_Obool), tc_fun(tc_fun(_1391091, tc_HOL_Obool), tc_HOL_Obool), _1391093), c_Set_OPow(_1391091)), _1391097)))], (37532 ^ _781404) ^ [_1488668, _1488670, _1488672, _1488674, _1488676] : [hBOOL(hAPP(hAPP(c_member(_1488668), _1488670), hAPP(c_Relation_OImage(_1488672, _1488668, _1488674), _1488676))), 37536 ^ _781404 : [(37539 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488672), 37535 ^ [_1488668, _1488670, _1488672, _1488674, _1488676]), _1488676)))], (37537 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1488672, _1488668)), hAPP(hAPP(c_Product__Type_OPair(_1488672, _1488668), 37535 ^ [_1488668, _1488670, _1488672, _1488674, _1488676]), _1488670)), _1488674)))]]], (49251 ^ _781404) ^ [_1774258, _1774260] : [-(c_Predicate_Opred__comp(_1774258, _1774258, _1774258, c_fequal, c_Predicate_Opred__comp(_1774258, _1774258, _1774258, _1774260, c_fequal)) = _1774260)], (17274 ^ _781404) ^ [_1089463, _1089465, _1089467, _1089469, _1089471, _1089473, _1089475, _1089477] : [c_Finite__Set_Ofolding__image__simple__idem(_1089463, _1089465, _1089467, _1089469, _1089471, _1089473), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089465), _1089475)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089465), _1089477)), -(hAPP(_1089473, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1089465, tc_HOL_Obool)), _1089475), _1089477)) = hAPP(hAPP(_1089467, hAPP(_1089473, _1089475)), hAPP(_1089473, _1089477)))], (38760 ^ _781404) ^ [_1519888, _1519890, _1519892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519888, _1519888), tc_HOL_Obool)), _1519890), hAPP(hAPP(c_Product__Type_OSigma(_1519888, _1519888), _1519892), hAPP(c_COMBK(tc_fun(_1519888, tc_HOL_Obool), _1519888), _1519892)))), 38766 ^ _781404 : [(38769 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1519888, _1519888)), hAPP(hAPP(c_Product__Type_OPair(_1519888, _1519888), 38765 ^ [_1519888, _1519890, _1519892]), 38765 ^ [_1519888, _1519890, _1519892])), _1519890))], (38767 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519888), 38765 ^ [_1519888, _1519890, _1519892]), _1519892)))]], -(c_Relation_Orefl__on(_1519888, _1519892, _1519890))], (25005 ^ _781404) ^ [_1229267, _1229269] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1229267, _1229269)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229267), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229269)))], (17659 ^ _781404) ^ [_1096116, _1096118, _1096120, _1096122] : [class_Lattices_Osemilattice__sup(_1096116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096116), _1096118)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1096116, _1096116, c_Lattices_Osemilattice__sup__class_Osup(_1096116)), _1096120), hAPP(hAPP(c_Set_Oinsert(_1096116), _1096122), _1096118)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1096116), _1096122), hAPP(hAPP(c_Finite__Set_Ofold(_1096116, _1096116, c_Lattices_Osemilattice__sup__class_Osup(_1096116)), _1096120), _1096118)))], (8142 ^ _781404) ^ [_918044, _918046] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_918044, tc_HOL_Obool)), _918046)))], (13985 ^ _781404) ^ [_1025240, _1025242] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025240), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025242), _1025240)))))], (24640 ^ _781404) ^ [_1223346, _1223348, _1223350] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223346, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223348), _1223350)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223348), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223346), _1223348), _1223350))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223346, _1223348)))], (12846 ^ _781404) ^ [_1004220, _1004222, _1004224, _1004226] : [-(_1004220 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1004222, tc_HOL_Obool), tc_HOL_Obool))), 12852 ^ _781404 : [(12855 ^ _781404) ^ [] : [c_Fun_Oinj__on(_1004222, _1004224, _1004226, 12851 ^ [_1004220, _1004222, _1004224, _1004226])], (12853 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1004222, tc_HOL_Obool)), 12851 ^ [_1004220, _1004222, _1004224, _1004226]), _1004220)))]], -(c_Fun_Oinj__on(_1004222, _1004224, _1004226, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1004222, tc_HOL_Obool), _1004220)))], (42511 ^ _781404) ^ [_1623597, _1623599, _1623601, _1623603, _1623605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623597), tc_List_Olist(_1623597))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623597), tc_List_Olist(_1623597)), _1623599), hAPP(hAPP(c_List_Olist_OCons(_1623597), _1623601), _1623603))), c_List_Olistrel(_1623597, _1623605))), 42516 ^ _781404 : [(42521 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623597), tc_List_Olist(_1623597))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623597), tc_List_Olist(_1623597)), 42515 ^ [_1623597, _1623599, _1623601, _1623603, _1623605]), _1623603)), c_List_Olistrel(_1623597, _1623605))))], (42519 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623597, _1623597)), hAPP(hAPP(c_Product__Type_OPair(_1623597, _1623597), 42514 ^ [_1623597, _1623599, _1623601, _1623603, _1623605]), _1623601)), _1623605)))], (42517 ^ _781404) ^ [] : [-(_1623599 = hAPP(hAPP(c_List_Olist_OCons(_1623597), 42514 ^ [_1623597, _1623599, _1623601, _1623603, _1623605]), 42515 ^ [_1623597, _1623599, _1623601, _1623603, _1623605]))]]], (39536 ^ _781404) ^ [_1546300, _1546302] : [-(c_Product__Type_Omap__pair(_1546300, _1546300, _1546302, _1546302, c_COMBI(_1546300), c_COMBI(_1546302)) = c_Fun_Oid(tc_prod(_1546300, _1546302)))], (2986 ^ _781404) ^ [_825703, _825705, _825707, _825709, _825711, _825713] : [-(c_Nitpick_Oplus__frac(_825713, _825709, _825705) = c_Nitpick_Oplus__frac(_825711, _825707, _825703)), _825713 = _825711, _825709 = _825707, _825705 = _825703], (10613 ^ _781404) ^ [_961865, _961867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961865), _961867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961865), hAPP(c_Nat_OSuc, _961867))))], (35950 ^ _781404) ^ [_1452113, _1452115, _1452117, _1452119, _1452121, _1452123, _1452125] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1452113, _1452115), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1452117), _1452119))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1452121, _1452115), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1452123), _1452125))), -(_1452115 = 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), _1452113), _1452121), _1452115), 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), _1452117), _1452123)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1452119), _1452125)), _1452115))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1452119), _1452125), _1452115)))))], (39967 ^ _781404) ^ [_1558183, _1558185, _1558187] : [c_Wellfounded_Owf(_1558183, _1558185), -(hBOOL(hAPP(hAPP(c_member(_1558183), _1558187), c_Wellfounded_Oacc(_1558183, _1558185))))], (46810 ^ _781404) ^ [_1723068, _1723070] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1723068, _1723070)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1723070), _1723068))], (47919 ^ _781404) ^ [_1745236, _1745238, _1745240, _1745242, _1745244] : [class_Groups_Omonoid__add(_1745236), 47925 ^ _781404 : [(47930 ^ _781404) ^ [] : [hAPP(_1745244, 47924 ^ [_1745236, _1745238, _1745240, _1745242, _1745244]) = c_Groups_Ozero__class_Ozero(_1745236)], (47928 ^ _781404) ^ [] : [hBOOL(hAPP(_1745242, 47924 ^ [_1745236, _1745238, _1745240, _1745242, _1745244]))], (47926 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745238), 47924 ^ [_1745236, _1745238, _1745240, _1745242, _1745244]), hAPP(c_List_Oset(_1745238), _1745240))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1745236), hAPP(hAPP(c_List_Omap(_1745238, _1745236), _1745244), hAPP(c_List_Ofilter(_1745238, _1745242), _1745240))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1745236), hAPP(hAPP(c_List_Omap(_1745238, _1745236), _1745244), _1745240)))], (22819 ^ _781404) ^ [_1189313, _1189315, _1189317, _1189319, _1189321, _1189323] : [class_Rings_Olinordered__semiring__1(_1189313), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189313), _1189315), _1189317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189313), _1189319), _1189317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189313), c_Groups_Ozero__class_Ozero(_1189313)), _1189321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189313), c_Groups_Ozero__class_Ozero(_1189313)), _1189323)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1189313), _1189321), _1189323) = c_Groups_Oone__class_Oone(_1189313), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189313), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1189313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189313), _1189321), _1189315)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189313), _1189323), _1189319))), _1189317)))], (52704 ^ _781404) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (45273 ^ _781404) ^ [_1687926, _1687928, _1687930] : [class_Groups_Omonoid__add(_1687926), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687926), hAPP(hAPP(c_List_Omap(_1687928, _1687926), hAPP(c_COMBK(_1687926, _1687928), c_Groups_Ozero__class_Ozero(_1687926))), _1687930)) = c_Groups_Ozero__class_Ozero(_1687926))], (52250 ^ _781404) ^ [_1837414, _1837416] : [class_Groups_Ouminus(_1837414), -(class_Groups_Ouminus(tc_fun(_1837416, _1837414)))], (49779 ^ _781404) ^ [_1786371, _1786373] : [49780 ^ _781404 : [(49781 ^ _781404) ^ [_1786437] : [hBOOL(hAPP(_1786373, _1786437))]], 49783 ^ _781404 : [(49786 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1786373, 49782 ^ [_1786371, _1786373])))], (49784 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786371), 49782 ^ [_1786371, _1786373]), c_Orderings_Otop__class_Otop(tc_fun(_1786371, tc_HOL_Obool)))))]]], (19121 ^ _781404) ^ [_1121703] : [c_Int_OBit1(_1121703) = c_Int_OPls], (25734 ^ _781404) ^ [] : [-(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)))))], (2598 ^ _781404) ^ [_819675, _819677, _819679, _819681, _819683, _819685, _819687, _819689, _819691, _819693] : [-(c_Product__Type_Oprod_Oprod__rec(_819693, _819689, _819685, _819681, _819677) = c_Product__Type_Oprod_Oprod__rec(_819691, _819687, _819683, _819679, _819675)), _819693 = _819691, _819689 = _819687, _819685 = _819683, _819681 = _819679, _819677 = _819675], (43087 ^ _781404) ^ [_1639566, _1639568] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1639566), _1639568) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1639566, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1639568), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (33534 ^ _781404) ^ [_1391692, _1391694, _1391696, _1391698, _1391700, _1391702] : [class_Complete__Lattice_Ocomplete__lattice(_1391692), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391694, tc_fun(_1391696, _1391692)), _1391698), _1391700), _1391702) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391694, _1391692), _1391698), hAPP(hAPP(c_COMBC(_1391694, _1391696, _1391692), _1391700), _1391702)))], (33267 ^ _781404) ^ [_1383048, _1383050, _1383052, _1383054, _1383056] : [_1383048 = c_Orderings_Obot__class_Obot(tc_fun(_1383050, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383050, tc_fun(_1383052, tc_HOL_Obool)), _1383048), hAPP(hAPP(c_COMBB(tc_fun(_1383052, tc_HOL_Obool), tc_fun(_1383052, tc_HOL_Obool), _1383050), hAPP(c_Set_Oinsert(_1383052), _1383054)), _1383056)) = c_Orderings_Obot__class_Obot(tc_fun(_1383052, tc_HOL_Obool)))], (49745 ^ _781404) ^ [_1785452, _1785454, _1785456, _1785458] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785452), _1785454)), 49748 ^ _781404 : [(49749 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785456), hAPP(c_Set_OCollect(_1785456), hAPP(hAPP(c_COMBB(tc_fun(_1785452, tc_HOL_Obool), tc_HOL_Obool, _1785456), c_HOL_OEx(_1785452)), hAPP(hAPP(c_COMBB(tc_fun(_1785452, tc_HOL_Obool), tc_fun(_1785452, tc_HOL_Obool), _1785456), hAPP(c_COMBS(_1785452, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1785452), c_fconj), hAPP(hAPP(c_COMBC(_1785452, tc_fun(_1785452, tc_HOL_Obool), tc_HOL_Obool), c_member(_1785452)), _1785454)))), _1785458))))), 49752 ^ _781404 : [(49753 ^ _781404) ^ [_1785760] : [hBOOL(hAPP(hAPP(c_member(_1785452), _1785760), _1785454)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1785456), hAPP(c_Set_OCollect(_1785456), hAPP(hAPP(c_COMBC(_1785456, _1785452, tc_HOL_Obool), _1785458), _1785760)))))]]], (49759 ^ _781404) ^ [] : [49761 ^ _781404 : [(49764 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785456), hAPP(c_Set_OCollect(_1785456), hAPP(hAPP(c_COMBC(_1785456, _1785452, tc_HOL_Obool), _1785458), 49760 ^ [_1785452, _1785454, _1785456, _1785458]))))], (49762 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785452), 49760 ^ [_1785452, _1785454, _1785456, _1785458]), _1785454)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1785456), hAPP(c_Set_OCollect(_1785456), hAPP(hAPP(c_COMBB(tc_fun(_1785452, tc_HOL_Obool), tc_HOL_Obool, _1785456), c_HOL_OEx(_1785452)), hAPP(hAPP(c_COMBB(tc_fun(_1785452, tc_HOL_Obool), tc_fun(_1785452, tc_HOL_Obool), _1785456), hAPP(c_COMBS(_1785452, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1785452), c_fconj), hAPP(hAPP(c_COMBC(_1785452, tc_fun(_1785452, tc_HOL_Obool), tc_HOL_Obool), c_member(_1785452)), _1785454)))), _1785458))))))]]], (1376 ^ _781404) ^ [_801644, _801646] : [-(class_Rings_Oring__1(_801644)), _801646 = _801644, class_Rings_Oring__1(_801646)], (23063 ^ _781404) ^ [_1194227, _1194229, _1194231, _1194233, _1194235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1194227), _1194229)), -(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), _1194229), _1194231)), _1194233)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194227), _1194231)), _1194235)) = 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), _1194229), _1194227)), _1194231)), _1194233)), _1194235))], (17437 ^ _781404) ^ [_1092413, _1092415] : [17438 ^ _781404 : [(17441 ^ _781404) ^ [] : [_1092413 = _1092415], (17439 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092413), _1092415))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092413), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1092415), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (34135 ^ _781404) ^ [_1408333, _1408335, _1408337, _1408339, _1408341] : [_1408333 = c_Orderings_Obot__class_Obot(tc_fun(_1408335, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408337, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408335, tc_fun(_1408337, tc_HOL_Obool)), _1408333), _1408339)), _1408341) = _1408341)], (13997 ^ _781404) ^ [_1025492, _1025494, _1025496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025492), _1025496)), _1025494)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025492), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025494), _1025496))))], (42820 ^ _781404) ^ [_1631643, _1631645, _1631647] : [-(hAPP(c_List_Oset(_1631643), hAPP(hAPP(c_List_Olist_OCons(_1631643), _1631645), _1631647)) = hAPP(hAPP(c_Set_Oinsert(_1631643), _1631645), hAPP(c_List_Oset(_1631643), _1631647)))], (4 ^ _781404) ^ [_781454, _781456] : [_781456 = _781454, -(_781454 = _781456)], (10347 ^ _781404) ^ [_957427, _957429, _957431, _957433, _957435] : [class_Groups_Oordered__ab__group__add(_957427), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_957427), _957429), _957431) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_957427), _957433), _957435), 10354 ^ _781404 : [(10361 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957427), _957433), _957435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957427), _957429), _957431)))], (10355 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957427), _957429), _957431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957427), _957433), _957435)))]]], (43435 ^ _781404) ^ [_1647497, _1647499, _1647501, _1647503] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647497) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1647499), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647497)), hAPP(hAPP(c_List_Olist_OCons(_1647499), _1647501), _1647503)) = c_List_Olist_ONil(_1647499))], (47657 ^ _781404) ^ [_1739637, _1739639, _1739641] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1739637), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1739637))), _1739639))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1739641), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1739637))), _1739639))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1739637))), hAPP(c_List_Ofilter(tc_List_Olist(_1739637), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1739637)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1739641)), c_Nat_Osize__class_Osize(tc_List_Olist(_1739637)))), c_List_Otranspose(_1739637, _1739639))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739637)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1739637)), _1739639), _1739641)))], (36715 ^ _781404) ^ [_1468250, _1468252, _1468254] : [-(c_HOL_OThe(tc_prod(_1468250, _1468252), hAPP(c_Product__Type_Oprod_Oprod__case(_1468250, _1468252, tc_HOL_Obool), _1468254)) = c_HOL_OThe(tc_prod(_1468250, _1468252), hAPP(hAPP(c_COMBS(tc_prod(_1468250, _1468252), _1468252, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1468250, tc_fun(_1468252, tc_HOL_Obool), tc_prod(_1468250, _1468252)), _1468254), c_Product__Type_Ofst(_1468250, _1468252))), c_Product__Type_Osnd(_1468250, _1468252))))], (41686 ^ _781404) ^ [_1599767, _1599769, _1599771] : [c_Relation_Ototal__on(_1599767, _1599769, _1599771), -(c_Relation_Ototal__on(_1599767, _1599769, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1599767, _1599767), tc_HOL_Obool)), _1599771), c_Relation_OId(_1599767))))], (50257 ^ _781404) ^ [_1796977, _1796979, _1796981] : [c_Relation_Orefl__on(_1796977, _1796979, _1796981), c_Relation_Osym(_1796977, _1796981), c_Relation_Otrans(_1796977, _1796981), -(c_Equiv__Relations_Oequiv(_1796977, _1796979, _1796981))], (33430 ^ _781404) ^ [_1388758, _1388760, _1388762, _1388764, _1388766] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388758, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388760, tc_fun(_1388758, tc_HOL_Obool)), _1388762), _1388764)), _1388766) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388760, tc_fun(_1388758, tc_HOL_Obool)), _1388762), hAPP(hAPP(c_COMBC(_1388760, tc_fun(_1388758, tc_HOL_Obool), tc_fun(_1388758, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1388758, tc_HOL_Obool), tc_fun(tc_fun(_1388758, tc_HOL_Obool), tc_fun(_1388758, tc_HOL_Obool)), _1388760), c_Groups_Ominus__class_Ominus(tc_fun(_1388758, tc_HOL_Obool))), _1388764)), _1388766)))], (38588 ^ _781404) ^ [_1515099, _1515101] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1515099, _1515099), tc_HOL_Obool)), c_Relation_OId__on(_1515099, _1515101)), hAPP(hAPP(c_Product__Type_OSigma(_1515099, _1515099), _1515101), hAPP(c_COMBK(tc_fun(_1515099, tc_HOL_Obool), _1515099), _1515101)))))], (17421 ^ _781404) ^ [_1092191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1092191)), -(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)), _1092191))))], (8219 ^ _781404) ^ [_919630, _919632, _919634, _919636] : [c_Hoare__Mirabelle_Ohoare__derivs(_919630, _919632, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_919630)), _919634), _919636)), 8222 ^ _781404 : [(8225 ^ _781404) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_919630, _919632, _919636))], (8223 ^ _781404) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_919630, _919632, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_919630)), _919634), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_919630), tc_HOL_Obool)))))]]], (33680 ^ _781404) ^ [_1395685, _1395687, _1395689, _1395691] : [_1395685 = c_Orderings_Obot__class_Obot(tc_fun(_1395687, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395687, tc_fun(_1395689, tc_HOL_Obool)), _1395685), hAPP(c_COMBK(tc_fun(_1395689, tc_HOL_Obool), _1395687), _1395691)) = c_Orderings_Obot__class_Obot(tc_fun(_1395689, tc_HOL_Obool)))], (45333 ^ _781404) ^ [_1689217, _1689219, _1689221, _1689223, _1689225] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1689217), tc_List_Olist(_1689219), tc_List_Olist(_1689221), hAPP(c_List_Omap(_1689217, _1689219), _1689223)), hAPP(c_List_Omap(_1689221, _1689217), _1689225)) = hAPP(c_List_Omap(_1689221, _1689219), hAPP(c_Fun_Ocomp(_1689217, _1689219, _1689221, _1689223), _1689225)))], (44717 ^ _781404) ^ [_1675932, _1675934, _1675936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1675932), _1675934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1675932), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1675934), _1675936))))], (40956 ^ _781404) ^ [_1581098, _1581100, _1581102, _1581104, _1581106] : [-(_1581098 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1581100, _1581102, _1581098, _1581104), _1581106) = hAPP(hAPP(c_Product__Type_Oscomp(_1581102, _1581100, _1581102, tc_prod(_1581100, _1581102)), hAPP(_1581104, _1581106)), c_Random_Oiterate(_1581100, _1581102, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1581098), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1581104)))], (49666 ^ _781404) ^ [_1783790, _1783792] : [c_Relation_Otrans(_1783790, _1783792), 49669 ^ _781404 : [(49670 ^ _781404) ^ [_1783926, _1783928] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1783790, _1783790)), hAPP(hAPP(c_Product__Type_OPair(_1783790, _1783790), _1783928), _1783926)), _1783792)), 49673 ^ _781404 : [(49674 ^ _781404) ^ [_1784069] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1783790, _1783790)), hAPP(hAPP(c_Product__Type_OPair(_1783790, _1783790), _1783926), _1784069)), _1783792)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783790, _1783790)), hAPP(hAPP(c_Product__Type_OPair(_1783790, _1783790), _1783928), _1784069)), _1783792)))]]]]], (4210 ^ _781404) ^ [_845205, _845207, _845209, _845211] : [-(c_New__DSequence_Opos__single(_845211, _845207) = c_New__DSequence_Opos__single(_845209, _845205)), _845211 = _845209, _845207 = _845205], (8096 ^ _781404) ^ [_917042, _917044, _917046] : [class_Orderings_Olinorder(_917042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917042), _917044), _917046)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917042, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_917042, _917044), _917046)), hAPP(hAPP(c_Set_Oinsert(_917042), _917046), c_Orderings_Obot__class_Obot(tc_fun(_917042, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_917042, _917044, _917046))], (25041 ^ _781404) ^ [_1229733] : [class_Int_Onumber__ring(_1229733), c_Int_Oiszero(_1229733, hAPP(c_Int_Onumber__class_Onumber__of(_1229733), c_Int_OMin))], (25463 ^ _781404) ^ [_1236632, _1236634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236632)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236634)), 25470 ^ _781404 : [(25477 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236632), _1236634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1236632)), hAPP(c_Int_Onat, _1236634))))], (25471 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1236632)), hAPP(c_Int_Onat, _1236634))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236632), _1236634)))]]], (21447 ^ _781404) ^ [_1162688, _1162690, _1162692, _1162694] : [class_Rings_Oordered__semiring(_1162688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162688), _1162690), _1162692)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162688), c_Groups_Ozero__class_Ozero(_1162688)), _1162694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162688), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162688), _1162690), _1162694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162688), _1162692), _1162694))))], (26005 ^ _781404) ^ [_1246046, _1246048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246046)), 26014 ^ _781404 : [(26017 ^ _781404) ^ [] : [hBOOL(hAPP(_1246048, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26010 ^ [_1246046, _1246048]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 26011 ^ [_1246046, _1246048]), _1246046))))], (26015 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1246048, 26010 ^ [_1246046, _1246048])))]], 26018 ^ _781404 : [(26021 ^ _781404) ^ [] : [hBOOL(hAPP(_1246048, 26010 ^ [_1246046, _1246048]))], (26019 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1246048, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26010 ^ [_1246046, _1246048]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 26011 ^ [_1246046, _1246048]), _1246046)))))]], 26022 ^ _781404 : [(26032 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1246048, 26039 ^ [_1246046, _1246048]))), 26033 ^ _781404 : [(26034 ^ _781404) ^ [_1246593] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1246593), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1246046))), hBOOL(hAPP(_1246048, _1246593))]]], (26023 ^ _781404) ^ [] : [26024 ^ _781404 : [(26025 ^ _781404) ^ [_1246478] : [hBOOL(hAPP(_1246048, _1246478))]], 26027 ^ _781404 : [(26030 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1246048, 26026 ^ [_1246046, _1246048])))], (26028 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26026 ^ [_1246046, _1246048]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1246046))))]]]]], (3084 ^ _781404) ^ [_827268, _827270, _827272, _827274] : [-(c_List_Olexn(_827274, _827270) = c_List_Olexn(_827272, _827268)), _827274 = _827272, _827270 = _827268], (31884 ^ _781404) ^ [_1355110, _1355112, _1355114] : [class_Orderings_Olinorder(_1355110), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355110), _1355112), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355110), _1355112), _1355114)) = _1355112)], (36846 ^ _781404) ^ [] : [-(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))], (7900 ^ _781404) ^ [_912229, _912231, _912233, _912235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912229, tc_HOL_Obool)), _912231), _912233)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912229, tc_HOL_Obool)), _912231), _912235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912229, tc_HOL_Obool)), _912231), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912229, tc_HOL_Obool)), _912233), _912235))))], (3766 ^ _781404) ^ [_837869, _837871, _837873, _837875, _837877, _837879, _837881, _837883] : [-(c_List_Omaps(_837883, _837879, _837875, _837871) = c_List_Omaps(_837881, _837877, _837873, _837869)), _837883 = _837881, _837879 = _837877, _837875 = _837873, _837871 = _837869], (39812 ^ _781404) ^ [_1555421, _1555423, _1555425] : [-(hAPP(c_Relation_ODomain(_1555421, _1555423), hAPP(c_Set_OCollect(tc_prod(_1555421, _1555423)), hAPP(c_Product__Type_Oprod_Oprod__case(_1555421, _1555423, tc_HOL_Obool), _1555425))) = hAPP(c_Set_OCollect(_1555421), hAPP(hAPP(c_COMBB(tc_fun(_1555423, tc_HOL_Obool), tc_HOL_Obool, _1555421), c_HOL_OEx(_1555423)), _1555425)))], (35115 ^ _781404) ^ [_1435573, _1435575] : [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), _1435573))), 35118 ^ _781404 : [(35125 ^ _781404) ^ [] : [-(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), _1435575)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435573))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435575), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435573)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435573)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435575), 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), _1435573)))))], (35119 ^ _781404) ^ [] : [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), _1435575)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435573)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435575), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435573)) = 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), _1435575)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435573))))]]], (25353 ^ _781404) ^ [_1234694] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1234694)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1234694)))], (20301 ^ _781404) ^ [_1141686] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1141686)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141686))))], (44154 ^ _781404) ^ [_1662463, _1662465, _1662467, _1662469] : [44155 ^ _781404 : [(44158 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1662463), _1662465), hAPP(c_List_Oset(_1662463), c_List_Obutlast(_1662463, _1662469))))], (44156 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1662463), _1662465), hAPP(c_List_Oset(_1662463), c_List_Obutlast(_1662463, _1662467))))]], -(hBOOL(hAPP(hAPP(c_member(_1662463), _1662465), hAPP(c_List_Oset(_1662463), c_List_Obutlast(_1662463, hAPP(hAPP(c_List_Oappend(_1662463), _1662467), _1662469))))))], (2830 ^ _781404) ^ [_823343, _823345, _823347, _823349] : [-(c_Wellfounded_Omax__ext(_823349, _823345) = c_Wellfounded_Omax__ext(_823347, _823343)), _823349 = _823347, _823345 = _823343], (30503 ^ _781404) ^ [_1329500, _1329502, _1329504, _1329506] : [class_Rings_Olinordered__semidom(_1329500), 30509 ^ _781404 : [(30512 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329500), c_Groups_Ozero__class_Ozero(_1329500)), hAPP(_1329506, 30508 ^ [_1329500, _1329502, _1329504, _1329506])))], (30510 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329502), 30508 ^ [_1329500, _1329502, _1329504, _1329506]), _1329504)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329500), c_Groups_Ozero__class_Ozero(_1329500)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329502, _1329500), _1329506), _1329504))))], (24919 ^ _781404) ^ [_1227939] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1227939) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1227939)))], (30598 ^ _781404) ^ [_1331334] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1331334) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30135 ^ _781404) ^ [_1322075, _1322077, _1322079, _1322081, _1322083] : [class_Fields_Ofield(_1322075), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322077), _1322079)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322077), _1322081)), 30149 ^ _781404 : [(30152 ^ _781404) ^ [] : [-(hAPP(_1322083, 30148 ^ [_1322075, _1322077, _1322079, _1322081, _1322083]) = c_Groups_Ozero__class_Ozero(_1322075))], (30150 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322077), 30148 ^ [_1322075, _1322077, _1322079, _1322081, _1322083]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322077, tc_HOL_Obool)), _1322079), _1322081))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1322077, _1322075), _1322083), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322077, tc_HOL_Obool)), _1322079), _1322081)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322075), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322075), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1322077, _1322075), _1322083), _1322079)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1322077, _1322075), _1322083), _1322081))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1322077, _1322075), _1322083), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322077, tc_HOL_Obool)), _1322079), _1322081))))], (44788 ^ _781404) ^ [_1677385, _1677387, _1677389] : [class_Lattices_Olattice(_1677385), -(c_Big__Operators_Olattice__class_OSup__fin(_1677385, hAPP(c_List_Oset(_1677385), hAPP(hAPP(c_List_Olist_OCons(_1677385), _1677387), _1677389))) = hAPP(c_List_Ofoldl(_1677385, _1677385, c_Lattices_Osemilattice__sup__class_Osup(_1677385), _1677387), _1677389))], (12923 ^ _781404) ^ [_1005705, _1005707, _1005709, _1005711, _1005713, _1005715] : [-(c_Fun_Ofun__upd(_1005705, _1005707, c_Fun_Ofun__upd(_1005705, _1005707, _1005709, _1005711, _1005713), _1005711, _1005715) = c_Fun_Ofun__upd(_1005705, _1005707, _1005709, _1005711, _1005715))], (34549 ^ _781404) ^ [_1422145, _1422147, _1422149, _1422151, _1422153] : [c_Fun_Oinj__on(_1422145, _1422147, _1422149, c_Orderings_Otop__class_Otop(tc_fun(_1422145, tc_HOL_Obool))), c_Fun_Oinj__on(_1422151, _1422145, _1422153, c_Orderings_Otop__class_Otop(tc_fun(_1422151, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1422151, _1422147, hAPP(c_Fun_Ocomp(_1422145, _1422147, _1422151, _1422149), _1422153), c_Orderings_Otop__class_Otop(tc_fun(_1422151, tc_HOL_Obool))))], (11831 ^ _781404) ^ [_983888, _983890, _983892, _983894] : [_983888 = _983890, 11834 ^ _781404 : [(11841 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_983892), _983890), _983894)), -(hBOOL(hAPP(hAPP(c_member(_983892), _983888), _983894)))], (11835 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_983892), _983888), _983894)), -(hBOOL(hAPP(hAPP(c_member(_983892), _983890), _983894)))]]], (23649 ^ _781404) ^ [_1206191, _1206193, _1206195, _1206197] : [class_Divides_Osemiring__div(_1206191), -(c_Divides_Odiv__class_Omod(_1206191, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206191), _1206193), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206191), _1206195), _1206197)), _1206197) = c_Divides_Odiv__class_Omod(_1206191, _1206193, _1206197))], (45457 ^ _781404) ^ [_1692032, _1692034, _1692036, _1692038] : [class_Groups_Ocomm__monoid__add(_1692032), 45460 ^ _781404 : [(45467 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1692034), _1692036))), -(c_Nitpick_Osetsum_H(_1692034, _1692032, _1692038, _1692036) = c_Groups_Ozero__class_Ozero(_1692032))], (45461 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1692034), _1692036)), -(c_Nitpick_Osetsum_H(_1692034, _1692032, _1692038, _1692036) = hAPP(c_List_Omonoid__add__class_Olistsum(_1692032), hAPP(hAPP(c_List_Omap(_1692034, _1692032), _1692038), c_Hilbert__Choice_OEps(tc_List_Olist(_1692034), hAPP(hAPP(c_COMBS(tc_List_Olist(_1692034), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1692034)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1692034), tc_fun(_1692034, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1692034, tc_HOL_Obool), tc_fun(tc_fun(_1692034, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1692034)), c_fequal), c_List_Oset(_1692034))), _1692036))), c_List_Odistinct(_1692034))))))]]], (27103 ^ _781404) ^ [_1265182, _1265184, _1265186] : [class_Groups_Oordered__ab__group__add__abs(_1265182), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265182), hAPP(c_Groups_Oabs__class_Oabs(_1265182), _1265184)), hAPP(c_Groups_Oabs__class_Oabs(_1265182), _1265186))), hAPP(c_Groups_Oabs__class_Oabs(_1265182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265182), _1265184), _1265186)))))], (19703 ^ _781404) ^ [_1131563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1131563)), -(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), _1131563))))], (6855 ^ _781404) ^ [_891237, _891239, _891241] : [class_Lattices_Osemilattice__sup(_891237), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891237), _891239), _891241) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891237), _891241), _891239))], (48943 ^ _781404) ^ [_1767550, _1767552, _1767554, _1767556, _1767558] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1767550), _1767552), _1767554), _1767556), _1767558) = c_New__DSequence_Opos__single(_1767550, _1767552))], (4014 ^ _781404) ^ [_842023, _842025, _842027, _842029, _842031, _842033, _842035, _842037] : [-(c_Lazy__Sequence_Ohb__bind(_842037, _842033, _842029, _842025) = c_Lazy__Sequence_Ohb__bind(_842035, _842031, _842027, _842023)), _842037 = _842035, _842033 = _842031, _842029 = _842027, _842025 = _842023], (36500 ^ _781404) ^ [_1463540, _1463542] : [hAPP(c_Int_ORep__Integ, _1463540) = hAPP(c_Int_ORep__Integ, _1463542), -(_1463540 = _1463542)], (48560 ^ _781404) ^ [_1759785, _1759787, _1759789] : [c_List_Olist__ex(_1759785, _1759787, _1759789), 48564 ^ _781404 : [(48567 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1759787, 48563 ^ [_1759785, _1759787, _1759789])))], (48565 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759785), 48563 ^ [_1759785, _1759787, _1759789]), hAPP(c_List_Oset(_1759785), _1759789))))]]], (24670 ^ _781404) ^ [_1224015, _1224017, _1224019] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1224015), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1224017, _1224019)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1224015), _1224017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1224015), _1224019)))], (52332 ^ _781404) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (26889 ^ _781404) ^ [_1261321, _1261323] : [class_Groups_Oordered__ab__group__add__abs(_1261321), -(hAPP(c_Groups_Oabs__class_Oabs(_1261321), hAPP(c_Groups_Oabs__class_Oabs(_1261321), _1261323)) = hAPP(c_Groups_Oabs__class_Oabs(_1261321), _1261323))], (52168 ^ _781404) ^ [_1836337, _1836339] : [class_Lattices_Obounded__lattice(_1836337), -(class_Lattices_Obounded__lattice__top(tc_fun(_1836339, _1836337)))], (52034 ^ _781404) ^ [_1834105, _1834107, _1834109] : [class_Rings_Olinordered__idom(_1834105), 52037 ^ _781404 : [(52044 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834105), _1834107), _1834109)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834105), hAPP(c_Groups_Oabs__class_Oabs(_1834105), _1834107)), _1834109)))], (52038 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834105), hAPP(c_Groups_Oabs__class_Oabs(_1834105), _1834107)), _1834109)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834105), _1834107), _1834109)))]]], (10581 ^ _781404) ^ [_961374, _961376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961374), _961376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961374)), hAPP(c_Nat_OSuc, _961376))))], (25979 ^ _781404) ^ [_1245655] : [_1245655 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1245655) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25205 ^ _781404) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48451 ^ _781404) ^ [_1757446, _1757448, _1757450] : [class_Enum_Oenum(_1757446), class_Enum_Oenum(_1757448), 48458 ^ _781404 : [(48465 ^ _781404) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1757448), hAPP(hAPP(c_COMBB(tc_fun(_1757446, tc_HOL_Obool), tc_HOL_Obool, _1757448), c_Enum_Oenum__class_Oenum__all(_1757446)), hAPP(hAPP(c_COMBB(tc_fun(_1757446, tc_prod(_1757448, _1757446)), tc_fun(_1757446, tc_HOL_Obool), _1757448), hAPP(c_COMBB(tc_prod(_1757448, _1757446), tc_HOL_Obool, _1757446), _1757450)), c_Product__Type_OPair(_1757448, _1757446))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1757448, _1757446)), _1757450)))], (48459 ^ _781404) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1757448, _1757446)), _1757450)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1757448), hAPP(hAPP(c_COMBB(tc_fun(_1757446, tc_HOL_Obool), tc_HOL_Obool, _1757448), c_Enum_Oenum__class_Oenum__all(_1757446)), hAPP(hAPP(c_COMBB(tc_fun(_1757446, tc_prod(_1757448, _1757446)), tc_fun(_1757446, tc_HOL_Obool), _1757448), hAPP(c_COMBB(tc_prod(_1757448, _1757446), tc_HOL_Obool, _1757446), _1757450)), c_Product__Type_OPair(_1757448, _1757446))))))]]], (51934 ^ _781404) ^ [_1832364, _1832366] : [51935 ^ _781404 : [(51938 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832366), _1832364))], (51936 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832364), _1832366)))]], -(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)))), _1832364, _1832366) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (33089 ^ _781404) ^ [_1378287, _1378289, _1378291, _1378293] : [class_Groups_Oordered__ab__group__add__abs(_1378287), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378287), hAPP(c_Groups_Oabs__class_Oabs(_1378287), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1378289, _1378287), _1378291), _1378293))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1378289, _1378287), hAPP(hAPP(c_COMBB(_1378287, _1378287, _1378289), c_Groups_Oabs__class_Oabs(_1378287)), _1378291)), _1378293))))], (25009 ^ _781404) ^ [] : [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)], (14908 ^ _781404) ^ [_1043347, _1043349, _1043351, _1043353, _1043355] : [class_Groups_Ocomm__monoid__add(_1043347), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043349), _1043351)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043349), _1043353)), 14922 ^ _781404 : [(14925 ^ _781404) ^ [] : [hAPP(_1043355, 14921 ^ [_1043347, _1043349, _1043351, _1043353, _1043355]) = c_Groups_Ozero__class_Ozero(_1043347)], (14923 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1043349), 14921 ^ [_1043347, _1043349, _1043351, _1043353, _1043355]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1043349, tc_HOL_Obool)), _1043351), _1043353))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043349, _1043347), _1043355), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1043349, tc_HOL_Obool)), _1043351), _1043353)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043347), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043349, _1043347), _1043355), _1043351)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043349, _1043347), _1043355), _1043353)))], (12402 ^ _781404) ^ [_995217, _995219, _995221, _995223, _995225] : [_995217 = hAPP(_995219, _995221), -(hBOOL(hAPP(hAPP(c_member(_995223), _995217), hAPP(c_Set_Oimage(_995225, _995223, _995219), c_Orderings_Otop__class_Otop(tc_fun(_995225, tc_HOL_Obool))))))], (49800 ^ _781404) ^ [_1786729, _1786731] : [c_Relation_Otrans(_1786729, _1786731), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1786729, _1786729), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1786729, _1786729, _1786729), _1786731), _1786731)), _1786731)))], (18679 ^ _781404) ^ [_1114679] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114679), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114679)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1114679)))], (46560 ^ _781404) ^ [_1716850, _1716852] : [-(hAPP(c_List_Ofilter(_1716850, _1716852), c_List_Olist_ONil(_1716850)) = c_List_Olist_ONil(_1716850))], (1506 ^ _781404) ^ [_803269, _803271] : [-(class_Orderings_Otop(_803269)), _803271 = _803269, class_Orderings_Otop(_803271)], (48123 ^ _781404) ^ [_1749855, _1749857, _1749859, _1749861, _1749863] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1749855, _1749855)), hAPP(hAPP(c_Product__Type_OPair(_1749855, _1749855), _1749857), _1749859)), c_List_Omeasures(_1749855, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1749855, tc_Nat_Onat)), _1749861), _1749863)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1749861, _1749857)), hAPP(_1749861, _1749859)))), 48130 ^ _781404 : [(48133 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1749855, _1749855)), hAPP(hAPP(c_Product__Type_OPair(_1749855, _1749855), _1749857), _1749859)), c_List_Omeasures(_1749855, _1749863))))], (48131 ^ _781404) ^ [] : [-(hAPP(_1749861, _1749857) = hAPP(_1749861, _1749859))]]], (13446 ^ _781404) ^ [_1015293, _1015295] : [13447 ^ _781404 : [(13448 ^ _781404) ^ [_1015343] : [_1015295 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015293), _1015343)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015293), _1015295)))], (41459 ^ _781404) ^ [_1593992, _1593994] : [-(c_Relation_Orefl__on(_1593992, c_Orderings_Otop__class_Otop(tc_fun(_1593992, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593992, _1593992), tc_HOL_Obool)), _1593994), c_Relation_OId(_1593992))))], (43210 ^ _781404) ^ [_1642288, _1642290, _1642292, _1642294, _1642296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642288), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642290)), _1642292))), 43213 ^ _781404 : [(43220 ^ _781404) ^ [] : [-(_1642288 = _1642294), -(hAPP(hAPP(c_List_Onth(_1642290), hAPP(hAPP(c_List_Olist__update(_1642290, _1642292), _1642288), _1642296)), _1642294) = hAPP(hAPP(c_List_Onth(_1642290), _1642292), _1642294))], (43214 ^ _781404) ^ [] : [_1642288 = _1642294, -(hAPP(hAPP(c_List_Onth(_1642290), hAPP(hAPP(c_List_Olist__update(_1642290, _1642292), _1642288), _1642296)), _1642294) = _1642296)]]], (52660 ^ _781404) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (39047 ^ _781404) ^ [_1527492, _1527494, _1527496] : [hBOOL(hAPP(_1527496, _1527494)), -(hBOOL(hAPP(hAPP(c_member(_1527492), _1527494), hAPP(c_Set_OCollect(_1527492), _1527496))))], (37832 ^ _781404) ^ [_1495740, _1495742, _1495744, _1495746, _1495748] : [c_Equiv__Relations_Oequiv(_1495740, _1495742, _1495744), hBOOL(hAPP(hAPP(c_member(tc_prod(_1495740, _1495740)), hAPP(hAPP(c_Product__Type_OPair(_1495740, _1495740), _1495746), _1495748)), _1495744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495740, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1495740, _1495740, _1495744), hAPP(hAPP(c_Set_Oinsert(_1495740), _1495746), c_Orderings_Obot__class_Obot(tc_fun(_1495740, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1495740, _1495740, _1495744), hAPP(hAPP(c_Set_Oinsert(_1495740), _1495748), c_Orderings_Obot__class_Obot(tc_fun(_1495740, tc_HOL_Obool)))))))], (47311 ^ _781404) ^ [_1732217, _1732219, _1732221, _1732223] : [class_Orderings_Olinorder(_1732217), c_List_Olinorder__class_Osorted(_1732217, _1732219), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1732221), _1732223)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732223), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732217)), _1732219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732217), hAPP(hAPP(c_List_Onth(_1732217), _1732219), _1732221)), hAPP(hAPP(c_List_Onth(_1732217), _1732219), _1732223))))], (20171 ^ _781404) ^ [_1139550, _1139552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1139550), _1139552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1139550)), c_Int_OBit1(_1139552))))], (10897 ^ _781404) ^ [_966399, _966401, _966403, _966405, _966407] : [c_Fun_Oinj__on(_966399, _966401, _966403, c_Orderings_Otop__class_Otop(tc_fun(_966399, tc_HOL_Obool))), 10900 ^ _781404 : [(10907 ^ _781404) ^ [] : [_966405 = _966407, -(hAPP(c_Set_Oimage(_966399, _966401, _966403), _966405) = hAPP(c_Set_Oimage(_966399, _966401, _966403), _966407))], (10901 ^ _781404) ^ [] : [hAPP(c_Set_Oimage(_966399, _966401, _966403), _966405) = hAPP(c_Set_Oimage(_966399, _966401, _966403), _966407), -(_966405 = _966407)]]], (11195 ^ _781404) ^ [_971344, _971346, _971348] : [class_Orderings_Oorder(_971344), 11198 ^ _781404 : [(11205 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971344), _971346), _971348))), -(c_Orderings_Obot__class_Obot(tc_fun(_971344, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_971344, _971346, _971348))], (11199 ^ _781404) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_971344, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_971344, _971346, _971348), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971344), _971346), _971348))]]], (27566 ^ _781404) ^ [_1273646, _1273648] : [class_Rings_Olinordered__idom(_1273646), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1273646), hAPP(c_Groups_Oabs__class_Oabs(_1273646), _1273648)), 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(_1273646), _1273648), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19504 ^ _781404) ^ [_1128236] : [class_Nat_Osemiring__char__0(_1128236), -(c_Fun_Oinj__on(tc_Nat_Onat, _1128236, c_Nat_Osemiring__1__class_Oof__nat(_1128236), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (18445 ^ _781404) ^ [_1110268, _1110270, _1110272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110268)), 18448 ^ _781404 : [(18449 ^ _781404) ^ [_1110402] : [18451 ^ _781404 : [(18457 ^ _781404) ^ [] : [-(_1110402 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 18453 ^ [_1110268, _1110270, _1110272, _1110402]), 18450 ^ [_1110268, _1110270, _1110272, _1110402]))], (18455 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18453 ^ [_1110268, _1110270, _1110272, _1110402]), _1110270)))], (18452 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18450 ^ [_1110268, _1110270, _1110272, _1110402]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1110268))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110272), _1110402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110272), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1110402), _1110268))))]]], (49444 ^ _781404) ^ [_1778398, _1778400, _1778402, _1778404] : [class_Groups_Ocomm__monoid__add(_1778398), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1778400, tc_HOL_Obool)), _1778402)), 49454 ^ _781404 : [(49457 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1778400), 49453 ^ [_1778398, _1778400, _1778402, _1778404]))], (49455 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1778400, tc_HOL_Obool)), 49453 ^ [_1778398, _1778400, _1778402, _1778404]), _1778402)))]], 49461 ^ _781404 : [(49465 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1778400, tc_HOL_Obool)), 49463 ^ [_1778398, _1778400, _1778402, _1778404]), _1778402)))], (49462 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1778400, tc_HOL_Obool)), 49460 ^ [_1778398, _1778400, _1778402, _1778404]), _1778402)))], (49474 ^ _781404) ^ [] : [hAPP(_1778404, 49468 ^ [_1778398, _1778400, _1778402, _1778404]) = c_Groups_Ozero__class_Ozero(_1778398)], (49470 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1778400), 49468 ^ [_1778398, _1778400, _1778402, _1778404]), 49460 ^ [_1778398, _1778400, _1778402, _1778404])))], (49472 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1778400), 49468 ^ [_1778398, _1778400, _1778402, _1778404]), 49463 ^ [_1778398, _1778400, _1778402, _1778404])))], (49467 ^ _781404) ^ [] : [49460 ^ [_1778398, _1778400, _1778402, _1778404] = 49463 ^ [_1778398, _1778400, _1778402, _1778404]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1778400, _1778398), _1778404), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1778400, tc_HOL_Obool), _1778402)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1778400, tc_HOL_Obool), _1778398), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1778400, _1778398), _1778404)), _1778402))], (9172 ^ _781404) ^ [_937409, _937411, _937413, _937415] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937409, tc_HOL_Obool)), _937411), hAPP(hAPP(c_Set_Oinsert(_937409), _937413), _937415)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937409, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937409, tc_HOL_Obool)), _937411), hAPP(hAPP(c_Set_Oinsert(_937409), _937413), c_Orderings_Obot__class_Obot(tc_fun(_937409, tc_HOL_Obool))))), _937415))], (6570 ^ _781404) ^ [_886242, _886244, _886246] : [_886244 = _886246, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886242, tc_HOL_Obool)), _886244) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886242, tc_HOL_Obool)), _886246))], (1586 ^ _781404) ^ [_804269, _804271] : [-(class_Rings_Olinordered__comm__semiring__strict(_804269)), _804271 = _804269, class_Rings_Olinordered__comm__semiring__strict(_804271)], (24740 ^ _781404) ^ [_1225135, _1225137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225137)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1225135), hAPP(c_Int_Onat, _1225137)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1225135, _1225137)))], (13387 ^ _781404) ^ [_1014151, _1014153, _1014155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014151), _1014153)), _1014155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014151), _1014155)))], (20757 ^ _781404) ^ [_1149603, _1149605, _1149607] : [class_Int_Onumber__ring(_1149603), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149603), hAPP(c_Int_Onumber__class_Onumber__of(_1149603), _1149605)), hAPP(c_Int_Onumber__class_Onumber__of(_1149603), _1149607)) = hAPP(c_Int_Onumber__class_Onumber__of(_1149603), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1149605), _1149607)))], (43034 ^ _781404) ^ [_1638451, _1638453, _1638455, _1638457, _1638459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1638451), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638453)), _1638455))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1638451), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638457)), _1638459))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1638453, _1638457)), hAPP(hAPP(c_List_Ozip(_1638453, _1638457), _1638455), _1638459)), _1638451) = hAPP(hAPP(c_Product__Type_OPair(_1638453, _1638457), hAPP(hAPP(c_List_Onth(_1638453), _1638455), _1638451)), hAPP(hAPP(c_List_Onth(_1638457), _1638459), _1638451)))], (46195 ^ _781404) ^ [_1708521, _1708523, _1708525, _1708527, _1708529] : [c_Finite__Set_Ofun__left__comm(_1708521, _1708523, _1708525), -(hAPP(hAPP(c_Finite__Set_Ofold(_1708521, _1708523, _1708525), _1708527), hAPP(c_List_Oset(_1708521), _1708529)) = hAPP(c_List_Ofoldl(_1708523, _1708521, hAPP(c_COMBC(_1708521, _1708523, _1708523), _1708525), _1708527), c_List_Oremdups(_1708521, _1708529)))], (42971 ^ _781404) ^ [_1636774, _1636776, _1636778] : [_1636774 = _1636776, 42974 ^ _781404 : [(42977 ^ _781404) ^ [_1636930] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636778, _1636778)), _1636930), hAPP(c_List_Oset(tc_prod(_1636778, _1636778)), hAPP(hAPP(c_List_Ozip(_1636778, _1636778), _1636774), _1636776)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1636778, _1636778, tc_HOL_Obool), c_fequal), _1636930)))], (42975 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636778)), _1636774) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636778)), _1636776))]]], (13305 ^ _781404) ^ [_1012549, _1012551] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012549), hAPP(c_Nat_OSuc, _1012551)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012549), _1012551)))], (32880 ^ _781404) ^ [_1373914, _1373916, _1373918] : [class_Orderings_Olinorder(_1373914), hAPP(_1373916, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373914), 32885 ^ [_1373914, _1373916, _1373918]), 32886 ^ [_1373914, _1373916, _1373918])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373914), hAPP(_1373916, 32885 ^ [_1373914, _1373916, _1373918])), hAPP(_1373916, 32886 ^ [_1373914, _1373916, _1373918])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373914), _1373918)), -(_1373918 = c_Orderings_Obot__class_Obot(tc_fun(_1373914, tc_HOL_Obool))), -(hAPP(_1373916, c_Big__Operators_Olinorder__class_OMax(_1373914, _1373918)) = c_Big__Operators_Olinorder__class_OMax(_1373914, hAPP(c_Set_Oimage(_1373914, _1373914, _1373916), _1373918)))], (24881 ^ _781404) ^ [_1227335, _1227337] : [24882 ^ _781404 : [(24883 ^ _781404) ^ [_1227384] : [_1227335 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227337), _1227384)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1227335, _1227337) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44481 ^ _781404) ^ [_1670929, _1670931, _1670933, _1670935, _1670937] : [-(hAPP(hAPP(c_List_Oappend(_1670929), _1670931), _1670933) = hAPP(hAPP(c_List_Oappend(_1670929), _1670935), _1670937)), 44484 ^ _781404 : [(44487 ^ _781404) ^ [] : [_1670931 = hAPP(hAPP(c_List_Otake(_1670929), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670929)), _1670931)), _1670935), _1670933 = hAPP(hAPP(c_List_Oappend(_1670929), hAPP(hAPP(c_List_Odrop(_1670929), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670929)), _1670931)), _1670935)), _1670937)], (44485 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670929)), _1670931)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670929)), _1670935))))]], 44492 ^ _781404 : [(44495 ^ _781404) ^ [] : [hAPP(hAPP(c_List_Otake(_1670929), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670929)), _1670935)), _1670931) = _1670935, hAPP(hAPP(c_List_Oappend(_1670929), hAPP(hAPP(c_List_Odrop(_1670929), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670929)), _1670935)), _1670931)), _1670933) = _1670937], (44493 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670929)), _1670931)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670929)), _1670935)))]]], (18421 ^ _781404) ^ [_1109784, _1109786, _1109788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109784)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1109786), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1109788)), 18428 ^ _781404 : [(18429 ^ _781404) ^ [_1109992] : [18431 ^ _781404 : [(18437 ^ _781404) ^ [] : [-(_1109992 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 18433 ^ [_1109784, _1109786, _1109788, _1109992]), 18430 ^ [_1109784, _1109786, _1109788, _1109992]))], (18435 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18433 ^ [_1109784, _1109786, _1109788, _1109992]), _1109788)))], (18432 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18430 ^ [_1109784, _1109786, _1109788, _1109992]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1109784))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109786), _1109992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109786), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1109992), _1109784))))]]], (27313 ^ _781404) ^ [_1269274, _1269276, _1269278] : [class_Rings_Olinordered__idom(_1269274), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269274), c_Groups_Ozero__class_Ozero(_1269274)), hAPP(hAPP(c_Power_Opower__class_Opower(_1269274), hAPP(c_Groups_Oabs__class_Oabs(_1269274), _1269276)), _1269278))))], (40188 ^ _781404) ^ [_1563739, _1563741, _1563743] : [c_Wellfounded_Owf(_1563739, _1563741), -(c_Wellfounded_Owf(tc_List_Olist(_1563739), hAPP(c_List_Olexn(_1563739, _1563741), _1563743)))], (9298 ^ _781404) ^ [_940392, _940394, _940396] : [class_Orderings_Olinorder(_940392), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940392), _940394), _940396)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940392, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_940392), _940394), c_Orderings_Obot__class_Obot(tc_fun(_940392, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_940392, _940394, _940396)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_940392, _940394), _940396))], (50209 ^ _781404) ^ [_1796208, _1796210] : [c_Relation_Osym(_1796208, _1796210), -(c_Relation_Osym(_1796208, hAPP(c_Relation_Oconverse(_1796208, _1796208), _1796210)))], (40636 ^ _781404) ^ [_1573604, _1573606, _1573608, _1573610] : [hBOOL(hAPP(hAPP(c_member(_1573604), _1573606), _1573608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1573604, tc_HOL_Obool)), _1573608), hAPP(_1573610, _1573608))), -(hBOOL(hAPP(hAPP(c_member(_1573604), _1573606), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1573604, tc_HOL_Obool), _1573610))))], (26545 ^ _781404) ^ [_1254518, _1254520] : [class_Rings_Olinordered__idom(_1254518), 26548 ^ _781404 : [(26555 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254520), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254518), hAPP(c_Int_Oring__1__class_Oof__int(_1254518), _1254520)), c_Groups_Ozero__class_Ozero(_1254518))))], (26549 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254518), hAPP(c_Int_Oring__1__class_Oof__int(_1254518), _1254520)), c_Groups_Ozero__class_Ozero(_1254518))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254520), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (11779 ^ _781404) ^ [_982903, _982905, _982907] : [hBOOL(hAPP(hAPP(c_member(_982903), _982905), hAPP(c_fequal, _982907))), -(_982905 = _982907)], (21927 ^ _781404) ^ [_1171448, _1171450, _1171452] : [class_Rings_Olinordered__semidom(_1171448), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171448), c_Groups_Oone__class_Oone(_1171448)), _1171450)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171448), c_Groups_Oone__class_Oone(_1171448)), _1171452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171448), c_Groups_Oone__class_Oone(_1171448)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171448), _1171450), _1171452))))], (29289 ^ _781404) ^ [_1305620, _1305622, _1305624] : [class_Fields_Olinordered__field(_1305620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305620), c_Groups_Ozero__class_Ozero(_1305620)), _1305622)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305620), _1305624), c_Groups_Ozero__class_Ozero(_1305620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305620), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305620), _1305622), _1305624)), c_Groups_Ozero__class_Ozero(_1305620))))], (7555 ^ _781404) ^ [_905138, _905140, _905142] : [class_Orderings_Otop(_905138), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_905140, _905138)), _905142) = c_Orderings_Otop__class_Otop(_905138))], (11030 ^ _781404) ^ [_968700, _968702] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968700), hAPP(c_Nat_OSuc, _968702)))), 11031 ^ _781404 : [(11034 ^ _781404) ^ [_968788] : [_968700 = hAPP(c_Nat_OSuc, _968788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968788), _968702))], (11032 ^ _781404) ^ [] : [_968700 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (19189 ^ _781404) ^ [] : [-(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))], (37467 ^ _781404) ^ [_1486808, _1486810, _1486812, _1486814] : [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), _1486808), _1486810)), 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), _1486812), _1486814)), 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), _1486808), _1486814)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1486812), _1486810))))], (30642 ^ _781404) ^ [_1332205, _1332207, _1332209, _1332211] : [class_Orderings_Olinorder(_1332205), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332205), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332205), _1332207), _1332209)), _1332211) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332205), _1332207), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332205), _1332209), _1332211)))], (15861 ^ _781404) ^ [_1062229, _1062231, _1062233] : [class_Lattices_Olattice(_1062229), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062229), _1062231)), -(_1062231 = c_Orderings_Obot__class_Obot(tc_fun(_1062229, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062229), _1062233)), -(_1062233 = c_Orderings_Obot__class_Obot(tc_fun(_1062229, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1062229, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062229, tc_HOL_Obool)), _1062231), _1062233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062229), c_Big__Operators_Olattice__class_OInf__fin(_1062229, _1062231)), c_Big__Operators_Olattice__class_OInf__fin(_1062229, _1062233)))], (51942 ^ _781404) ^ [_1832527, _1832529] : [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)))), _1832527, _1832529) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832527), _1832529)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832529), _1832527)))], (16662 ^ _781404) ^ [_1077930] : [class_Rings_Oring__1(_1077930), -(hBOOL(hAPP(hAPP(c_member(_1077930), c_Groups_Oone__class_Oone(_1077930)), c_Int_Oring__1__class_OInts(_1077930))))], (10531 ^ _781404) ^ [_960673] : [-(_960673 = 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)), _960673)))], (45313 ^ _781404) ^ [_1688744, _1688746, _1688748, _1688750, _1688752] : [-(hAPP(hAPP(c_List_Omap(_1688744, _1688746), _1688748), hAPP(hAPP(c_List_Olist_OCons(_1688744), _1688750), _1688752)) = hAPP(hAPP(c_List_Olist_OCons(_1688746), hAPP(_1688748, _1688750)), hAPP(hAPP(c_List_Omap(_1688744, _1688746), _1688748), _1688752)))], (22603 ^ _781404) ^ [_1184809, _1184811, _1184813, _1184815, _1184817, _1184819] : [class_Rings_Oordered__ring(_1184809), 22606 ^ _781404 : [(22613 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184809), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1184809), _1184811), _1184817)), _1184813)), _1184815)), _1184819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184809), _1184811), _1184813)), _1184815)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184809), _1184817), _1184813)), _1184819))))], (22607 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184809), _1184811), _1184813)), _1184815)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184809), _1184817), _1184813)), _1184819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184809), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1184809), _1184811), _1184817)), _1184813)), _1184815)), _1184819)))]]], (47706 ^ _781404) ^ [_1740748, _1740750, _1740752, _1740754] : [hBOOL(hAPP(hAPP(c_member(_1740748), _1740750), hAPP(c_List_Oset(_1740748), c_List_OtakeWhile(_1740748, _1740752, _1740754)))), 47709 ^ _781404 : [(47712 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1740752, _1740750)))], (47710 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740748), _1740750), hAPP(c_List_Oset(_1740748), _1740754))))]]], (11491 ^ _781404) ^ [_977806, _977808, _977810, _977812] : [c_Fun_Oinj__on(_977806, _977808, _977810, _977812), -(hAPP(c_Set_Oimage(_977808, _977806, c_Fun_Othe__inv__into(_977806, _977808, _977812, _977810)), hAPP(c_Set_Oimage(_977806, _977808, _977810), _977812)) = _977812)], (10289 ^ _781404) ^ [_956387, _956389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956387), _956389)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956389), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956389), _956387)) = _956387)], (22707 ^ _781404) ^ [_1187293, _1187295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1187293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1187295)), -(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), _1187295), _1187293))))], (51844 ^ _781404) ^ [_1830911, _1830913, _1830915] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830911, _1830913) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1830915), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1830911 = _1830913, _1830913 = _1830915], (17589 ^ _781404) ^ [_1095009, _1095011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095009), _1095011)), 17592 ^ _781404 : [(17595 ^ _781404) ^ [] : [_1095009 = _1095011], (17593 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095009), _1095011)))]]], (2094 ^ _781404) ^ [_811743, _811745] : [_811745 = _811743, -(c_Nat_Osemiring__1__class_ONats(_811745) = c_Nat_Osemiring__1__class_ONats(_811743))], (6747 ^ _781404) ^ [_889478, _889480, _889482] : [class_Lattices_Oboolean__algebra(_889478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889478), _889480), _889482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889478), hAPP(c_Groups_Ouminus__class_Ouminus(_889478), _889482)), hAPP(c_Groups_Ouminus__class_Ouminus(_889478), _889480))))], (36636 ^ _781404) ^ [_1466248, _1466250, _1466252] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1466248, _1466250), _1466252))), _1466248 = 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), _1466252)), _1466250)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1466252)), 36643 ^ _781404 : [(36646 ^ _781404) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1466252) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36644 ^ _781404) ^ [] : [-(_1466250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 36647 ^ _781404 : [(36650 ^ _781404) ^ [] : [36651 ^ _781404 : [(36654 ^ _781404) ^ [] : [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), _1466252))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1466252)), _1466250))], (36652 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1466250)))]], 36659 ^ _781404 : [(36662 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1466250), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1466252))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1466252)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (36660 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1466250))]]], (36648 ^ _781404) ^ [] : [_1466250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (26731 ^ _781404) ^ [_1258149, _1258151, _1258153, _1258155, _1258157, _1258159] : [class_Groups_Oab__semigroup__mult(_1258149), hBOOL(hAPP(c_Finite__Set_Ofinite(_1258151), _1258153)), -(hBOOL(hAPP(hAPP(c_member(_1258151), _1258155), _1258153))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1258149, _1258151, c_Groups_Otimes__class_Otimes(_1258149)), _1258157), _1258159), hAPP(hAPP(c_Set_Oinsert(_1258151), _1258155), _1258153)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1258149), hAPP(_1258157, _1258155)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1258149, _1258151, c_Groups_Otimes__class_Otimes(_1258149)), _1258157), _1258159), _1258153)))], (51748 ^ _781404) ^ [_1829175, _1829177, _1829179, _1829181] : [class_Divides_Osemiring__div(_1829175), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829175), _1829177), _1829179)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829175), _1829181), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1829175), _1829179), _1829177)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1829175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829175), _1829181), _1829179)), _1829177))], (44349 ^ _781404) ^ [_1667794, _1667796, _1667798] : [hBOOL(hAPP(c_List_Odistinct(_1667794), _1667796)), -(hBOOL(hAPP(c_List_Odistinct(_1667794), hAPP(hAPP(c_List_Odrop(_1667794), _1667798), _1667796))))], (35748 ^ _781404) ^ [_1448646, _1448648, _1448650] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1448646, _1448648), _1448650)), -(c_Divides_Odivmod__nat(_1448646, _1448648) = _1448650)], (20247 ^ _781404) ^ [_1140923] : [-(c_Int_Opred(c_Int_OBit0(_1140923)) = c_Int_OBit1(c_Int_Opred(_1140923)))], (23093 ^ _781404) ^ [_1194860, _1194862, _1194864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1194860)), 23096 ^ _781404 : [(23103 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1194862), _1194864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194860), _1194862)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194860), _1194864))))], (23097 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194860), _1194862)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194860), _1194864))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1194862), _1194864)))]]], (42613 ^ _781404) ^ [_1626129, _1626131, _1626133] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1626129)), _1626131), c_List_Olists(_1626129, c_Wellfounded_Oacc(_1626129, _1626133)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1626129)), _1626131), c_Wellfounded_Oacc(tc_List_Olist(_1626129), c_List_Olistrel1(_1626129, _1626133)))))], (23347 ^ _781404) ^ [_1199828, _1199830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1199828), 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)))), _1199830))), 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)))), _1199828)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199830), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1199828))], (22175 ^ _781404) ^ [_1176484, _1176486, _1176488] : [class_Rings_Ocomm__semiring__1(_1176484), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1176484), _1176486), hAPP(c_Nat_OSuc, _1176488)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176484), _1176486), hAPP(hAPP(c_Power_Opower__class_Opower(_1176484), _1176486), _1176488)))], (36223 ^ _781404) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12306 ^ _781404) ^ [_993184, _993186, _993188] : [hBOOL(hAPP(hAPP(c_member(_993184), _993186), hAPP(hAPP(c_Set_Oinsert(_993184), _993188), c_Orderings_Obot__class_Obot(tc_fun(_993184, tc_HOL_Obool))))), -(_993186 = _993188)], (46874 ^ _781404) ^ [_1724275, _1724277, _1724279, _1724281] : [class_Groups_Ocomm__monoid__add(_1724275), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1724275), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1724275), _1724277), c_List_Oupt(_1724279, _1724281))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1724275), _1724277), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1724279, _1724281))))], (1206 ^ _781404) ^ [_799519, _799521] : [-(class_Rings_Olinordered__ring__strict(_799519)), _799521 = _799519, class_Rings_Olinordered__ring__strict(_799521)], (34653 ^ _781404) ^ [_1424594, _1424596, _1424598] : [class_Int_Onumber__ring(_1424594), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424594), hAPP(c_Int_Onumber__class_Onumber__of(_1424594), _1424596)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1424598))) = hAPP(hAPP(c_HOL_OLet(_1424594, _1424594), hAPP(hAPP(c_Power_Opower__class_Opower(_1424594), hAPP(c_Int_Onumber__class_Onumber__of(_1424594), _1424596)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424598))), hAPP(hAPP(c_COMBS(_1424594, _1424594, _1424594), c_Groups_Otimes__class_Otimes(_1424594)), c_COMBI(_1424594))))], (43298 ^ _781404) ^ [_1644354, _1644356, _1644358, _1644360] : [hBOOL(hAPP(c_List_Odistinct(_1644354), _1644356)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1644354, _1644358)), hAPP(hAPP(c_List_Ozip(_1644354, _1644358), _1644356), _1644360))))], (21205 ^ _781404) ^ [_1158225, _1158227, _1158229, _1158231] : [class_Rings_Ocomm__semiring__1(_1158225), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1158225), hAPP(hAPP(c_Power_Opower__class_Opower(_1158225), _1158227), _1158229)), _1158231) = hAPP(hAPP(c_Power_Opower__class_Opower(_1158225), _1158227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158229), _1158231)))], (49715 ^ _781404) ^ [_1784981, _1784983] : [c_Relation_Otrans(_1784981, _1784983), -(c_Relation_Otrans(tc_List_Olist(_1784981), c_List_Olexord(_1784981, _1784983)))], (33237 ^ _781404) ^ [_1382120, _1382122, _1382124, _1382126] : [-(_1382120 = c_Orderings_Obot__class_Obot(tc_fun(_1382122, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1382122, _1382124, hAPP(c_COMBK(_1382124, _1382122), _1382126)), _1382120) = hAPP(hAPP(c_Set_Oinsert(_1382124), _1382126), c_Orderings_Obot__class_Obot(tc_fun(_1382124, tc_HOL_Obool))))], (9100 ^ _781404) ^ [_935648, _935650] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935648, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_935648, tc_HOL_Obool))), _935650) = c_Orderings_Obot__class_Obot(tc_fun(_935648, tc_HOL_Obool)))], (50618 ^ _781404) ^ [_1804242, _1804244, _1804246, _1804248, _1804250] : [c_Fun_Oinj__on(_1804242, _1804244, _1804246, _1804248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1804242, tc_HOL_Obool)), _1804250), _1804248)), -(hAPP(c_Set_Oimage(_1804244, _1804242, c_Hilbert__Choice_Oinv__into(_1804242, _1804244, _1804248, _1804246)), hAPP(c_Set_Oimage(_1804242, _1804244, _1804246), _1804250)) = _1804250)], (37282 ^ _781404) ^ [_1481545, _1481547, _1481549, _1481551] : [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), _1481545), _1481547)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1481549), _1481551))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1481545), _1481551) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1481549), _1481547))], (13367 ^ _781404) ^ [_1013778, _1013780, _1013782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013778), _1013780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013778), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013780), _1013782))))], (15445 ^ _781404) ^ [_1054686, _1054688] : [class_Lattices_Olattice(_1054686), -(c_Big__Operators_Olattice__class_OSup__fin(_1054686, hAPP(hAPP(c_Set_Oinsert(_1054686), _1054688), c_Orderings_Obot__class_Obot(tc_fun(_1054686, tc_HOL_Obool)))) = _1054688)], (4332 ^ _781404) ^ [_847000, _847002, _847004, _847006] : [-(c_List_Oupt(_847006, _847002) = c_List_Oupt(_847004, _847000)), _847006 = _847004, _847002 = _847000], (33436 ^ _781404) ^ [_1389066, _1389068, _1389070, _1389072, _1389074] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389066, tc_fun(_1389068, tc_HOL_Obool)), _1389070), hAPP(hAPP(c_COMBB(tc_fun(_1389068, tc_HOL_Obool), tc_fun(_1389068, tc_HOL_Obool), _1389066), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1389068, tc_HOL_Obool)), _1389072)), _1389074)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1389068, tc_HOL_Obool)), _1389072), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389066, tc_fun(_1389068, tc_HOL_Obool)), _1389070), _1389074)))], (52232 ^ _781404) ^ [_1837177, _1837179] : [class_Orderings_Otop(_1837177), -(class_Orderings_Otop(tc_fun(_1837179, _1837177)))], (41073 ^ _781404) ^ [_1583872, _1583874, _1583876, _1583878, _1583880] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583872, _1583872)), hAPP(hAPP(c_Product__Type_OPair(_1583872, _1583872), _1583874), _1583876)), c_Transitive__Closure_Otrancl(_1583872, _1583878))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583872, _1583872)), hAPP(hAPP(c_Product__Type_OPair(_1583872, _1583872), _1583876), _1583880)), c_Transitive__Closure_Otrancl(_1583872, _1583878))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583872, _1583872)), hAPP(hAPP(c_Product__Type_OPair(_1583872, _1583872), _1583874), _1583880)), c_Transitive__Closure_Otrancl(_1583872, _1583878))))], (45479 ^ _781404) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50568 ^ _781404) ^ [_1802997, _1802999, _1803001, _1803003, _1803005, _1803007] : [hAPP(c_Set_Oimage(_1802997, _1802999, _1803001), _1803003) = _1803005, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802999, tc_HOL_Obool)), _1803007), _1803005)), -(hAPP(c_Set_Oimage(_1802997, _1802999, _1803001), hAPP(c_Set_Oimage(_1802999, _1802997, c_Hilbert__Choice_Oinv__into(_1802997, _1802999, _1803003, _1803001)), _1803007)) = _1803007)], (35519 ^ _781404) ^ [_1444181, _1444183, _1444185] : [hBOOL(hAPP(_1444181, hAPP(hAPP(c_Product__Type_OPair(_1444183, _1444185), 35520 ^ [_1444181, _1444183, _1444185]), 35521 ^ [_1444181, _1444183, _1444185]))), 35524 ^ _781404 : [(35525 ^ _781404) ^ [_1444328] : [-(hBOOL(hAPP(_1444181, _1444328)))]]], (24100 ^ _781404) ^ [_1213656, _1213658, _1213660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213656), 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)), _1213658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213658), _1213660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213656), _1213658)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213656), _1213660))))], (37304 ^ _781404) ^ [_1482044, _1482046, _1482048, _1482050, _1482052, _1482054, _1482056, _1482058] : [class_Groups_Ocomm__monoid__mult(_1482044), c_Fun_Oinj__on(_1482046, _1482048, _1482050, _1482052), _1482054 = hAPP(c_Set_Oimage(_1482046, _1482048, _1482050), _1482052), 37318 ^ _781404 : [(37321 ^ _781404) ^ [] : [hAPP(_1482056, 37317 ^ [_1482044, _1482046, _1482048, _1482050, _1482052, _1482054, _1482056, _1482058]) = hAPP(hAPP(c_Fun_Ocomp(_1482048, _1482044, _1482046, _1482058), _1482050), 37317 ^ [_1482044, _1482046, _1482048, _1482050, _1482052, _1482054, _1482056, _1482058])], (37319 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482046), 37317 ^ [_1482044, _1482046, _1482048, _1482050, _1482052, _1482054, _1482056, _1482058]), _1482052)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1482048, _1482044), _1482058), _1482054) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1482046, _1482044), _1482056), _1482052))], (5931 ^ _781404) ^ [_875439, _875441, _875443, _875445] : [class_Orderings_Oord(_875439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875439), _875441), _875443)), _875443 = _875445, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875439), _875441), _875445)))], (29335 ^ _781404) ^ [_1306489, _1306491, _1306493, _1306495] : [class_Fields_Olinordered__field(_1306489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306489), _1306491), _1306493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306489), c_Groups_Ozero__class_Ozero(_1306489)), _1306495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306489), c_Groups_Ozero__class_Ozero(_1306489)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306489), _1306493), _1306491))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306489), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306489), _1306495), _1306493)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306489), _1306495), _1306491))))], (36261 ^ _781404) ^ [_1458215, _1458217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1458215), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1458217), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1458215, _1458217) = 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), _1458215), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1458217)))))], (12110 ^ _781404) ^ [_989336, _989338, _989340, _989342] : [-(hBOOL(hAPP(hAPP(c_member(_989336), _989338), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989336, tc_HOL_Obool)), _989340), _989342)))), hBOOL(hAPP(hAPP(c_member(_989336), _989338), _989340)), hBOOL(hAPP(hAPP(c_member(_989336), _989338), _989342))], (7023 ^ _781404) ^ [_894886, _894888, _894890, _894892] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894886, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894886, tc_HOL_Obool)), _894888), _894890)), _894892) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894886, tc_HOL_Obool)), _894888), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894886, tc_HOL_Obool)), _894890), _894892)))], (13620 ^ _781404) ^ [_1018775, _1018777, _1018779] : [class_Groups_Oordered__comm__monoid__add(_1018775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018775), c_Groups_Ozero__class_Ozero(_1018775)), _1018777)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018775), c_Groups_Ozero__class_Ozero(_1018775)), _1018779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018775), c_Groups_Ozero__class_Ozero(_1018775)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018775), _1018777), _1018779))))], (50556 ^ _781404) ^ [_1802687, _1802689, _1802691, _1802693] : [hAPP(c_Set_Oimage(_1802687, _1802689, _1802691), c_Orderings_Otop__class_Otop(tc_fun(_1802687, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1802689, tc_HOL_Obool)), -(hAPP(_1802691, hAPP(c_Hilbert__Choice_Oinv__into(_1802687, _1802689, c_Orderings_Otop__class_Otop(tc_fun(_1802687, tc_HOL_Obool)), _1802691), _1802693)) = _1802693)], (19647 ^ _781404) ^ [_1130587, _1130589] : [class_Rings_Osemiring__1(_1130587), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130587), hAPP(c_Nat_OSuc, _1130589)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130587), c_Groups_Oone__class_Oone(_1130587)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130587), _1130589)))], (21271 ^ _781404) ^ [_1159421, _1159423, _1159425] : [class_Rings_Olinordered__idom(_1159421), -(c_Groups_Osgn__class_Osgn(_1159421, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159421), _1159423), _1159425)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159421), c_Groups_Osgn__class_Osgn(_1159421, _1159423)), c_Groups_Osgn__class_Osgn(_1159421, _1159425)))], (52284 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (47549 ^ _781404) ^ [_1737354, _1737356] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737354)), hAPP(c_List_Orev(_1737354), _1737356)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737354)), _1737356))], (31658 ^ _781404) ^ [_1351005, _1351007] : [class_Orderings_Olinorder(_1351005), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351005), _1351007)), -(_1351007 = c_Orderings_Obot__class_Obot(tc_fun(_1351005, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1351005), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1351005), 31671 ^ [_1351005, _1351007]), 31672 ^ [_1351005, _1351007])), hAPP(hAPP(c_Set_Oinsert(_1351005), 31671 ^ [_1351005, _1351007]), hAPP(hAPP(c_Set_Oinsert(_1351005), 31672 ^ [_1351005, _1351007]), c_Orderings_Obot__class_Obot(tc_fun(_1351005, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1351005), c_Big__Operators_Olinorder__class_OMin(_1351005, _1351007)), _1351007)))], (40415 ^ _781404) ^ [_1568600, _1568602, _1568604, _1568606, _1568608, _1568610] : [hBOOL(hAPP(hAPP(c_member(_1568600), _1568602), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1568604, _1568606, tc_fun(_1568600, tc_HOL_Obool)), _1568608), _1568610))), 40420 ^ _781404 : [(40423 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568600), _1568602), hAPP(hAPP(_1568608, 40418 ^ [_1568600, _1568602, _1568604, _1568606, _1568608, _1568610]), 40419 ^ [_1568600, _1568602, _1568604, _1568606, _1568608, _1568610]))))], (40421 ^ _781404) ^ [] : [-(_1568610 = hAPP(hAPP(c_Product__Type_OPair(_1568604, _1568606), 40418 ^ [_1568600, _1568602, _1568604, _1568606, _1568608, _1568610]), 40419 ^ [_1568600, _1568602, _1568604, _1568606, _1568608, _1568610]))]]], (20333 ^ _781404) ^ [_1142299, _1142301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1142299)), c_Int_OBit1(_1142301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1142299), _1142301)))], (31700 ^ _781404) ^ [_1351910, _1351912] : [-(c_Nitpick_Onat__lcm(_1351910, _1351912) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1351910), _1351912)), c_Nitpick_Onat__gcd(_1351910, _1351912)))], (29161 ^ _781404) ^ [_1303234, _1303236, _1303238, _1303240, _1303242] : [class_Fields_Ofield(_1303234), -(_1303236 = c_Groups_Ozero__class_Ozero(_1303234)), -(_1303238 = c_Groups_Ozero__class_Ozero(_1303234)), 29172 ^ _781404 : [(29179 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303234), _1303240), _1303238) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303234), _1303242), _1303236), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303234), _1303240), _1303236) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303234), _1303242), _1303238))], (29173 ^ _781404) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303234), _1303240), _1303236) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303234), _1303242), _1303238), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303234), _1303240), _1303238) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303234), _1303242), _1303236))]]], (50715 ^ _781404) ^ [_1806701] : [-(_1806701 = hAPP(c_Code__Numeral_Oof__nat, 50713 ^ [_1806701]))], (15749 ^ _781404) ^ [_1060215, _1060217, _1060219] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1060215), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1060215, tc_HOL_Obool)), _1060217), _1060219))), -(hAPP(c_Finite__Set_Ocard(_1060215), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1060215, tc_HOL_Obool)), _1060217), _1060219)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1060215), _1060217)), hAPP(c_Finite__Set_Ocard(_1060215), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1060215, tc_HOL_Obool)), _1060217), _1060219))))], (21301 ^ _781404) ^ [_1159936, _1159938, _1159940] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159936), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159936)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159938)), _1159940)) = 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), _1159936), _1159938))), _1159940))], (43286 ^ _781404) ^ [_1644130, _1644132, _1644134] : [hBOOL(hAPP(c_List_Odistinct(_1644130), _1644132)), -(hBOOL(hAPP(c_List_Odistinct(_1644130), c_List_Osublist(_1644130, _1644132, _1644134))))], (12933 ^ _781404) ^ [_1005914, _1005916, _1005918, _1005920, _1005922, _1005924] : [-(_1005914 = _1005916), -(hAPP(c_Fun_Ofun__upd(_1005918, _1005920, _1005922, _1005916, _1005924), _1005914) = hAPP(_1005922, _1005914))], (42296 ^ _781404) ^ [_1616529, _1616531, _1616533, _1616535, _1616537, _1616539] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616529), tc_List_Olist(_1616529))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616529), tc_List_Olist(_1616529)), hAPP(hAPP(c_List_Olist_OCons(_1616529), _1616531), _1616533)), hAPP(hAPP(c_List_Olist_OCons(_1616529), _1616535), _1616537))), c_List_Olexord(_1616529, _1616539)))), 42297 ^ _781404 : [(42300 ^ _781404) ^ [] : [_1616531 = _1616535, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616529), tc_List_Olist(_1616529))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616529), tc_List_Olist(_1616529)), _1616533), _1616537)), c_List_Olexord(_1616529, _1616539)))], (42298 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616529, _1616529)), hAPP(hAPP(c_Product__Type_OPair(_1616529, _1616529), _1616531), _1616535)), _1616539))]]], (44216 ^ _781404) ^ [_1664097, _1664099, _1664101, _1664103] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1664097), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664099)), _1664101)))), -(hAPP(hAPP(c_List_Onth(_1664099), hAPP(hAPP(c_List_Oappend(_1664099), _1664101), _1664103)), _1664097) = hAPP(hAPP(c_List_Onth(_1664099), _1664103), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1664097), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664099)), _1664101))))], (38484 ^ _781404) ^ [_1511822, _1511824, _1511826, _1511828, _1511830, _1511832] : [hBOOL(hAPP(hAPP(c_member(_1511822), _1511824), _1511826)), hBOOL(hAPP(hAPP(c_member(_1511828), _1511830), hAPP(_1511832, _1511824))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1511822, _1511828)), hAPP(hAPP(c_Product__Type_OPair(_1511822, _1511828), _1511824), _1511830)), hAPP(hAPP(c_Product__Type_OSigma(_1511822, _1511828), _1511826), _1511832))))], (46987 ^ _781404) ^ [_1726510, _1726512] : [class_Orderings_Olinorder(_1726510), c_List_Olinorder__class_Osorted(_1726510, _1726512), -(c_List_Olinorder__class_Osorted(_1726510, hAPP(c_List_Otl(_1726510), _1726512)))], (46313 ^ _781404) ^ [_1710702, _1710704, _1710706] : [hBOOL(hAPP(hAPP(c_member(_1710702), _1710704), hAPP(c_List_Oset(_1710702), _1710706))), -(c_List_Oremdups(_1710702, hAPP(hAPP(c_List_Olist_OCons(_1710702), _1710704), _1710706)) = c_List_Oremdups(_1710702, _1710706))], (52074 ^ _781404) ^ [_1834779, _1834781, _1834783, _1834785] : [class_Divides_Osemiring__div(_1834779), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834779), _1834781), _1834783)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834779), _1834781), _1834785)), 52085 ^ _781404 : [(52092 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834779), _1834783), _1834785)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834779), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834779), _1834783), _1834781)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834779), _1834785), _1834781))))], (52086 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834779), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834779), _1834783), _1834781)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834779), _1834785), _1834781))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834779), _1834783), _1834785)))]]], (43549 ^ _781404) ^ [_1649459, _1649461, _1649463] : [-(hAPP(hAPP(c_List_Ozip(_1649459, _1649461), _1649463), c_List_Olist_ONil(_1649461)) = c_List_Olist_ONil(tc_prod(_1649459, _1649461)))], (24712 ^ _781404) ^ [_1224637] : [c_Int_OBit0(_1224637) = c_Int_OMin], (23317 ^ _781404) ^ [_1199259, _1199261] : [-(_1199259 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1199259, _1199261) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1199259), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1199261)))], (52786 ^ _781404) ^ [_1842967, _1842969] : [hBOOL(_1842967), -(hBOOL(hAPP(hAPP(c_fdisj, _1842967), _1842969)))], (44164 ^ _781404) ^ [_1662736, _1662738, _1662740, _1662742, _1662744, _1662746] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662736), tc_List_Olist(_1662736))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662736), tc_List_Olist(_1662736)), hAPP(hAPP(c_List_Oappend(_1662736), _1662738), _1662744)), hAPP(hAPP(c_List_Oappend(_1662736), _1662740), _1662746))), c_List_Olistrel1(_1662736, _1662742)))), 44165 ^ _781404 : [(44172 ^ _781404) ^ [] : [_1662738 = _1662740, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662736), tc_List_Olist(_1662736))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662736), tc_List_Olist(_1662736)), _1662744), _1662746)), c_List_Olistrel1(_1662736, _1662742)))], (44166 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662736), tc_List_Olist(_1662736))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662736), tc_List_Olist(_1662736)), _1662738), _1662740)), c_List_Olistrel1(_1662736, _1662742))), _1662744 = _1662746]]], (7858 ^ _781404) ^ [_911286, _911288, _911290] : [class_Groups_Oordered__ab__group__add(_911286), -(hAPP(c_Set_Oimage(_911286, _911286, c_Groups_Ouminus__class_Ouminus(_911286)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_911286, _911288), _911290)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_911286, hAPP(c_Groups_Ouminus__class_Ouminus(_911286), _911290), hAPP(c_Groups_Ouminus__class_Ouminus(_911286), _911288)))], (36901 ^ _781404) ^ [_1472375, _1472377, _1472379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472375, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472375, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36902 ^ [_1472375, _1472377, _1472379])), _1472377)), _1472379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472375, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472375, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1472377)), _1472379)))], (35380 ^ _781404) ^ [_1440847, _1440849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1440847)), 35383 ^ _781404 : [(35390 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440849), _1440847))), -(c_Divides_OposDivAlg(_1440849, _1440847) = hAPP(c_Divides_Oadjust(_1440847), c_Divides_OposDivAlg(_1440849, 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)))), _1440847))))], (35384 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440849), _1440847)), -(c_Divides_OposDivAlg(_1440849, _1440847) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1440849))]]], (35710 ^ _781404) ^ [_1447827, _1447829, _1447831, _1447833, _1447835] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1447827, _1447829), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1447831), _1447833))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1447829)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1447835), _1447827), _1447829), 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), _1447835), _1447831)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1447835), _1447833)), _1447829))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1447835), _1447833), _1447829)))))], (47589 ^ _781404) ^ [_1738227, _1738229, _1738231] : [-(hAPP(c_List_Orotate(_1738227, _1738229), hAPP(c_List_Orev(_1738227), _1738231)) = hAPP(c_List_Orev(_1738227), hAPP(c_List_Orotate(_1738227, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738227)), _1738231)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1738229, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738227)), _1738231)))), _1738231)))], (52648 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (3632 ^ _781404) ^ [_835804, _835806, _835808, _835810] : [-(c_List_Olinorder__class_Osorted__list__of__set(_835810, _835806) = c_List_Olinorder__class_Osorted__list__of__set(_835808, _835804)), _835810 = _835808, _835806 = _835804], (30606 ^ _781404) ^ [_1331451, _1331453, _1331455] : [class_Orderings_Olinorder(_1331451), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331451), _1331453), _1331455) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331451), _1331455), _1331453))], (39345 ^ _781404) ^ [_1537896, _1537898, _1537900] : [class_Lattices_Odistrib__lattice(_1537896), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537896), _1537898)), -(_1537898 = c_Orderings_Obot__class_Obot(tc_fun(_1537896, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537896), _1537900)), -(_1537900 = c_Orderings_Obot__class_Obot(tc_fun(_1537896, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1537896), c_Big__Operators_Olattice__class_OInf__fin(_1537896, _1537898)), c_Big__Operators_Olattice__class_OInf__fin(_1537896, _1537900)) = c_Big__Operators_Olattice__class_OInf__fin(_1537896, hAPP(c_Set_OCollect(_1537896), hAPP(hAPP(c_COMBB(tc_fun(_1537896, tc_HOL_Obool), tc_HOL_Obool, _1537896), c_HOL_OEx(_1537896)), hAPP(hAPP(c_COMBB(tc_fun(_1537896, tc_fun(_1537896, tc_HOL_Obool)), tc_fun(_1537896, tc_HOL_Obool), _1537896), hAPP(c_COMBB(tc_fun(_1537896, tc_HOL_Obool), tc_HOL_Obool, _1537896), c_HOL_OEx(_1537896))), hAPP(hAPP(c_COMBC(_1537896, tc_fun(_1537896, tc_fun(_1537896, tc_HOL_Obool)), tc_fun(_1537896, tc_fun(_1537896, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1537896, tc_fun(tc_fun(_1537896, tc_HOL_Obool), tc_fun(_1537896, tc_HOL_Obool))), tc_fun(tc_fun(_1537896, tc_fun(_1537896, tc_HOL_Obool)), tc_fun(_1537896, tc_fun(_1537896, tc_HOL_Obool))), _1537896), c_COMBS(_1537896, tc_fun(_1537896, tc_HOL_Obool), tc_fun(_1537896, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1537896, tc_fun(_1537896, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1537896, tc_fun(tc_fun(_1537896, tc_HOL_Obool), tc_fun(_1537896, tc_HOL_Obool))), _1537896), hAPP(c_COMBB(tc_fun(_1537896, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1537896, tc_HOL_Obool), tc_fun(_1537896, tc_HOL_Obool)), _1537896), c_COMBS(_1537896, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1537896, tc_fun(_1537896, tc_HOL_Obool)), tc_fun(_1537896, tc_fun(_1537896, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1537896), hAPP(c_COMBB(tc_fun(_1537896, tc_HOL_Obool), tc_fun(_1537896, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1537896), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1537896), c_fconj))), hAPP(hAPP(c_COMBC(_1537896, tc_fun(_1537896, tc_fun(_1537896, _1537896)), tc_fun(_1537896, tc_fun(_1537896, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1537896, _1537896), tc_fun(_1537896, tc_HOL_Obool)), tc_fun(tc_fun(_1537896, tc_fun(_1537896, _1537896)), tc_fun(_1537896, tc_fun(_1537896, tc_HOL_Obool))), _1537896), c_COMBB(tc_fun(_1537896, _1537896), tc_fun(_1537896, tc_HOL_Obool), _1537896)), hAPP(hAPP(c_COMBB(tc_fun(_1537896, tc_HOL_Obool), tc_fun(tc_fun(_1537896, _1537896), tc_fun(_1537896, tc_HOL_Obool)), _1537896), c_COMBB(_1537896, tc_HOL_Obool, _1537896)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1537896)))))), hAPP(hAPP(c_COMBC(_1537896, tc_fun(_1537896, tc_HOL_Obool), tc_fun(_1537896, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1537896, tc_HOL_Obool), tc_fun(_1537896, tc_HOL_Obool)), _1537896), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1537896)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1537896), c_fconj), hAPP(hAPP(c_COMBC(_1537896, tc_fun(_1537896, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537896)), _1537898)))), hAPP(hAPP(c_COMBC(_1537896, tc_fun(_1537896, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537896)), _1537900))))))))], (47415 ^ _781404) ^ [_1734649, _1734651] : [hBOOL(hAPP(c_List_Odistinct(_1734649), hAPP(c_List_Orev(_1734649), _1734651))), -(hBOOL(hAPP(c_List_Odistinct(_1734649), _1734651)))], (47875 ^ _781404) ^ [_1744235, _1744237, _1744239] : [-(c_List_OdropWhile(_1744235, _1744237, _1744239) = c_List_Olist_ONil(_1744235)), hBOOL(hAPP(_1744237, hAPP(c_List_Ohd(_1744235), c_List_OdropWhile(_1744235, _1744237, _1744239))))], (47505 ^ _781404) ^ [_1736558, _1736560, _1736562, _1736564, _1736566] : [c_List_Olist__all2(_1736558, _1736560, _1736562, hAPP(c_List_Orev(_1736558), _1736564), hAPP(c_List_Orev(_1736560), _1736566)), -(c_List_Olist__all2(_1736558, _1736560, _1736562, _1736564, _1736566))], (52444 ^ _781404) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (24710 ^ _781404) ^ [_1224603] : [c_Int_OMin = c_Int_OBit0(_1224603)], (34625 ^ _781404) ^ [_1423738, _1423740, _1423742] : [hBOOL(hAPP(c_Predicate_OPowp(_1423738, hAPP(hAPP(c_COMBC(_1423738, tc_fun(_1423738, tc_HOL_Obool), tc_HOL_Obool), c_member(_1423738)), _1423740)), _1423742)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1423738, tc_HOL_Obool)), _1423742), hAPP(c_Set_OPow(_1423738), _1423740))))], (8086 ^ _781404) ^ [_916833, _916835, _916837] : [class_Orderings_Olinorder(_916833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916833), _916835), _916837)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916833, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_916833), _916835), c_Orderings_Obot__class_Obot(tc_fun(_916833, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_916833, _916835, _916837)) = c_SetInterval_Oord__class_OatLeastAtMost(_916833, _916835, _916837))], (2920 ^ _781404) ^ [_824708, _824710, _824712, _824714, _824716, _824718] : [-(c_Nitpick_Otimes__frac(_824718, _824714, _824710) = c_Nitpick_Otimes__frac(_824716, _824712, _824708)), _824718 = _824716, _824714 = _824712, _824710 = _824708], (21405 ^ _781404) ^ [_1161881, _1161883, _1161885, _1161887] : [class_Rings_Oordered__ring(_1161881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), _1161883), _1161885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), _1161887), c_Groups_Ozero__class_Ozero(_1161881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161881), _1161885), _1161887)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161881), _1161883), _1161887))))], (23609 ^ _781404) ^ [_1205440, _1205442] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1205440, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205442)) = 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), _1205440), _1205442)))], (3260 ^ _781404) ^ [_829956, _829958, _829960, _829962, _829964, _829966, _829968, _829970, _829972, _829974] : [-(c_Fun_Ofun__upd(_829974, _829970, _829966, _829962, _829958) = c_Fun_Ofun__upd(_829972, _829968, _829964, _829960, _829956)), _829974 = _829972, _829970 = _829968, _829966 = _829964, _829962 = _829960, _829958 = _829956], (38894 ^ _781404) ^ [_1523758, _1523760, _1523762, _1523764, _1523766, _1523768] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1523758, _1523760), _1523758, tc_prod(_1523762, _1523764), c_Product__Type_Ofst(_1523758, _1523760)), c_Product__Type_Omap__pair(_1523762, _1523758, _1523764, _1523760, _1523766, _1523768)) = hAPP(c_Fun_Ocomp(_1523762, _1523758, tc_prod(_1523762, _1523764), _1523766), c_Product__Type_Ofst(_1523762, _1523764)))], (29970 ^ _781404) ^ [_1318566, _1318568, _1318570] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318566), _1318568)), 29973 ^ _781404 : [(29974 ^ _781404) ^ [] : [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(_1318566, tc_Nat_Onat), _1318570), _1318568))), 29977 ^ _781404 : [(29978 ^ _781404) ^ [_1318734] : [hBOOL(hAPP(hAPP(c_member(_1318566), _1318734), _1318568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1318570, _1318734))))]]], (29984 ^ _781404) ^ [] : [29986 ^ _781404 : [(29989 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1318570, 29985 ^ [_1318566, _1318568, _1318570])))], (29987 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318566), 29985 ^ [_1318566, _1318568, _1318570]), _1318568)))]], -(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(_1318566, tc_Nat_Onat), _1318570), _1318568))))]]], (49608 ^ _781404) ^ [_1782318, _1782320, _1782322, _1782324] : [-(c_Random__Sequence_Omap(_1782318, _1782320, _1782322, _1782324) = c_Random__Sequence_Obind(_1782318, _1782320, _1782324, hAPP(c_Fun_Ocomp(_1782320, 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(_1782320)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1782318, c_Random__Sequence_Osingle(_1782320)), _1782322)))], (13972 ^ _781404) ^ [_1025007, _1025009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025007), _1025009)), -(_1025009 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025007), 13975 ^ [_1025007, _1025009])))], (1306 ^ _781404) ^ [_800769, _800771] : [-(class_Groups_Ogroup__add(_800769)), _800771 = _800769, class_Groups_Ogroup__add(_800771)], (52324 ^ _781404) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (1826 ^ _781404) ^ [_807269, _807271] : [-(class_Orderings_Olinorder(_807269)), _807271 = _807269, class_Orderings_Olinorder(_807271)], (8806 ^ _781404) ^ [_929985, _929987] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_929985, tc_HOL_Obool), tc_HOL_Obool)), _929987), hAPP(c_Set_OPow(_929985), c_Complete__Lattice_OSup__class_OSup(tc_fun(_929985, tc_HOL_Obool), _929987)))))], (38969 ^ _781404) ^ [_1525907, _1525909, _1525911, _1525913] : [-(hAPP(c_Set_Ovimage(_1525907, _1525909, _1525911), hAPP(c_Set_OCollect(_1525909), _1525913)) = hAPP(c_Set_OCollect(_1525907), hAPP(hAPP(c_COMBB(_1525909, tc_HOL_Obool, _1525907), _1525913), _1525911)))], (13427 ^ _781404) ^ [_1014927, _1014929, _1014931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014927), _1014929)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014927), _1014931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014929), _1014931)))], (13025 ^ _781404) ^ [_1007365, _1007367, _1007369, _1007371] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1007365), 13028 ^ _781404 : [(13035 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007365), _1007367), _1007371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007365), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007365), _1007367), _1007369)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007365), _1007371), _1007369))))], (13029 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007365), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007365), _1007367), _1007369)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007365), _1007371), _1007369))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007365), _1007367), _1007371)))]]], (19269 ^ _781404) ^ [_1124088, _1124090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124088), _1124090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124088)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124090))))], (41856 ^ _781404) ^ [_1603725, _1603727, _1603729, _1603731] : [-(hAPP(hAPP(c_Nat_Ocompow(_1603725, _1603725), _1603727), hAPP(hAPP(c_Nat_Ocompow(_1603725, _1603725), _1603729), _1603731)) = hAPP(hAPP(c_Nat_Ocompow(_1603725, _1603725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1603729), _1603727)), _1603731))], (44134 ^ _781404) ^ [_1661969, _1661971, _1661973, _1661975, _1661977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661969), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661971)), _1661973))), -(hAPP(hAPP(c_List_Olist__update(_1661971, hAPP(hAPP(c_List_Oappend(_1661971), _1661973), _1661975)), _1661969), _1661977) = hAPP(hAPP(c_List_Oappend(_1661971), hAPP(hAPP(c_List_Olist__update(_1661971, _1661973), _1661969), _1661977)), _1661975))], (33019 ^ _781404) ^ [_1376757, _1376759, _1376761, _1376763, _1376765, _1376767, _1376769, _1376771] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1376757, tc_fun(_1376759, tc_fun(_1376761, tc_HOL_Obool))), _1376763), _1376765), _1376767), _1376769)), -(hBOOL(hAPP(hAPP(hAPP(_1376765, _1376771), _1376767), _1376769))), hBOOL(hAPP(hAPP(c_member(_1376757), _1376771), _1376763))], (20237 ^ _781404) ^ [_1140718, _1140720] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1140718)), c_Int_OBit0(_1140720)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140718), _1140720)))], (33556 ^ _781404) ^ [_1392400, _1392402, _1392404, _1392406, _1392408, _1392410, _1392412] : [hAPP(c_Fun_Ocomp(_1392400, _1392402, _1392404, _1392406), _1392408) = _1392410, -(hAPP(_1392406, hAPP(_1392408, _1392412)) = hAPP(_1392410, _1392412))], (47435 ^ _781404) ^ [_1734991, _1734993] : [_1734993 = c_List_Olist_ONil(_1734991), -(c_List_Olist_ONil(_1734991) = hAPP(c_List_Orev(_1734991), _1734993))], (45188 ^ _781404) ^ [_1685306, _1685308, _1685310, _1685312, _1685314, _1685316, _1685318, _1685320] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1685306, _1685308), _1685310), _1685312), hAPP(hAPP(c_List_Ozip(_1685306, _1685308), hAPP(hAPP(c_List_Omap(_1685314, _1685306), _1685316), _1685318)), _1685320)) = hAPP(hAPP(c_List_Omap(tc_prod(_1685314, _1685308), _1685310), hAPP(c_Product__Type_Oprod_Oprod__case(_1685314, _1685308, _1685310), hAPP(hAPP(c_COMBB(tc_fun(_1685308, tc_prod(_1685306, _1685308)), tc_fun(_1685308, _1685310), _1685314), hAPP(c_COMBB(tc_prod(_1685306, _1685308), _1685310, _1685308), _1685312)), hAPP(hAPP(c_COMBB(_1685306, tc_fun(_1685308, tc_prod(_1685306, _1685308)), _1685314), c_Product__Type_OPair(_1685306, _1685308)), _1685316)))), hAPP(hAPP(c_List_Ozip(_1685314, _1685308), _1685318), _1685320)))], (26999 ^ _781404) ^ [_1263335, _1263337, _1263339, _1263341, _1263343, _1263345, _1263347] : [c_Finite__Set_Ofun__left__comm(_1263335, _1263337, _1263339), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1263335, _1263337, _1263339, _1263341, _1263343), _1263345)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1263335, _1263337, _1263339, _1263341, _1263343), _1263347)), -(_1263347 = _1263345)], (20827 ^ _781404) ^ [_1151316, _1151318, _1151320] : [class_Lattices_Oab__semigroup__idem__mult(_1151316), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151316), _1151318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151316), _1151318), _1151320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151316), _1151318), _1151320))], (19123 ^ _781404) ^ [_1121737] : [c_Int_OPls = c_Int_OBit1(_1121737)], (46540 ^ _781404) ^ [_1716435, _1716437, _1716439, _1716441, _1716443, _1716445] : [class_Orderings_Olinorder(_1716435), -(hBOOL(hAPP(_1716437, _1716439))), -(hAPP(c_List_Ofilter(_1716441, _1716437), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1716441, _1716435, _1716443), _1716439), _1716445)) = hAPP(c_List_Ofilter(_1716441, _1716437), _1716445))], (12001 ^ _781404) ^ [_987112, _987114, _987116] : [hBOOL(hAPP(hAPP(c_member(_987112), _987114), _987116)), -(hAPP(hAPP(c_Set_Oinsert(_987112), _987114), _987116) = _987116)], (50245 ^ _781404) ^ [_1796795, _1796797] : [-(c_Relation_Osym(_1796795, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1796795, _1796795), tc_HOL_Obool)), _1796797), hAPP(c_Relation_Oconverse(_1796795, _1796795), _1796797))))], (44130 ^ _781404) ^ [_1661821, _1661823, _1661825, _1661827] : [-(hAPP(hAPP(c_List_Onth(_1661821), hAPP(hAPP(c_List_Oappend(_1661821), _1661823), _1661825)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661821)), _1661823)), _1661827)) = hAPP(hAPP(c_List_Onth(_1661821), _1661825), _1661827))], (26135 ^ _781404) ^ [_1248137, _1248139] : [c_Nat__Transfer_Onat__set(_1248137), c_Nat__Transfer_Onat__set(_1248139), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1248137), _1248139)))], (11613 ^ _781404) ^ [_980130, _980132, _980134] : [-(hBOOL(hAPP(hAPP(c_member(_980130), _980132), _980134))), -(hBOOL(hAPP(hAPP(c_member(_980130), _980132), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_980130, tc_HOL_Obool)), _980134))))], (6689 ^ _781404) ^ [_888450, _888452, _888454] : [class_Groups_Oordered__ab__group__add(_888450), 6692 ^ _781404 : [(6699 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888450), hAPP(c_Groups_Ouminus__class_Ouminus(_888450), _888454)), _888452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888450), hAPP(c_Groups_Ouminus__class_Ouminus(_888450), _888452)), _888454)))], (6693 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888450), hAPP(c_Groups_Ouminus__class_Ouminus(_888450), _888452)), _888454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888450), hAPP(c_Groups_Ouminus__class_Ouminus(_888450), _888454)), _888452)))]]], (23735 ^ _781404) ^ [_1207656, _1207658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1207656)), 23738 ^ _781404 : [(23745 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1207658), 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), _1207658), _1207656)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23739 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1207658), _1207656)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1207658), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (42489 ^ _781404) ^ [_1622481, _1622483, _1622485, _1622487, _1622489, _1622491] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622481, _1622481)), hAPP(hAPP(c_Product__Type_OPair(_1622481, _1622481), _1622483), _1622485)), _1622487)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622481), tc_List_Olist(_1622481))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622481), tc_List_Olist(_1622481)), _1622489), _1622491)), c_List_Olistrel(_1622481, _1622487))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622481), tc_List_Olist(_1622481))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622481), tc_List_Olist(_1622481)), hAPP(hAPP(c_List_Olist_OCons(_1622481), _1622483), _1622489)), hAPP(hAPP(c_List_Olist_OCons(_1622481), _1622485), _1622491))), c_List_Olistrel(_1622481, _1622487))))], (12684 ^ _781404) ^ [_1000769, _1000771, _1000773, _1000775] : [hBOOL(hAPP(hAPP(c_member(_1000769), _1000771), c_SetInterval_Oord_OlessThan(_1000769, _1000773, _1000775))), -(hBOOL(hAPP(hAPP(_1000773, _1000771), _1000775)))], (37339 ^ _781404) ^ [_1483487, _1483489] : [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)), _1483487), 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)), _1483489), 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)), _1483487), _1483489)), c_Int_Ointrel)))], (35318 ^ _781404) ^ [_1439611, _1439613, _1439615, _1439617, _1439619, _1439621] : [hBOOL(hAPP(hAPP(_1439611, _1439613), _1439615)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439617, tc_fun(_1439619, tc_HOL_Obool))), _1439611), _1439621), _1439613), _1439615)))], (27067 ^ _781404) ^ [_1264410, _1264412] : [class_Groups_Oordered__ab__group__add__abs(_1264410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264410), c_Groups_Ozero__class_Ozero(_1264410)), _1264412)), -(hAPP(c_Groups_Oabs__class_Oabs(_1264410), _1264412) = _1264412)], (8251 ^ _781404) ^ [_920321, _920323, _920325, _920327, _920329] : [hAPP(hAPP(c_Set_Oinsert(_920321), _920323), hAPP(hAPP(c_Set_Oinsert(_920321), _920325), c_Orderings_Obot__class_Obot(tc_fun(_920321, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_920321), _920327), hAPP(hAPP(c_Set_Oinsert(_920321), _920329), c_Orderings_Obot__class_Obot(tc_fun(_920321, tc_HOL_Obool)))), 8256 ^ _781404 : [(8259 ^ _781404) ^ [] : [-(_920325 = _920329)], (8257 ^ _781404) ^ [] : [-(_920323 = _920327)]], 8260 ^ _781404 : [(8263 ^ _781404) ^ [] : [-(_920325 = _920327)], (8261 ^ _781404) ^ [] : [-(_920323 = _920329)]]], (46666 ^ _781404) ^ [_1719764, _1719766] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1719764)), c_List_Otranspose__rel(_1719764)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1719764)), c_List_Olist_ONil(_1719764)), _1719766))), -(c_List_Otranspose(_1719764, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1719764)), c_List_Olist_ONil(_1719764)), _1719766)) = c_List_Otranspose(_1719764, _1719766))], (46229 ^ _781404) ^ [_1709232, _1709234] : [hBOOL(hAPP(c_List_Odistinct(_1709232), _1709234)), -(c_List_Oremdups(_1709232, _1709234) = _1709234)], (42171 ^ _781404) ^ [_1612229, _1612231, _1612233] : [-(c_Product__Type_Ointernal__split(_1612229, _1612231, _1612233) = c_Product__Type_Oprod_Oprod__case(_1612229, _1612231, _1612233))], (10475 ^ _781404) ^ [_959741, _959743, _959745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_959741, tc_HOL_Obool)), _959743), _959745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959741, tc_HOL_Obool)), _959743), _959745)))], (47901 ^ _781404) ^ [_1744785, _1744787, _1744789, _1744791, _1744793] : [-(c_List_OdropWhile(_1744785, _1744787, _1744789) = hAPP(hAPP(c_List_Olist_OCons(_1744785), _1744791), _1744793)), _1744789 = hAPP(hAPP(c_List_Oappend(_1744785), c_List_OtakeWhile(_1744785, _1744787, _1744789)), hAPP(hAPP(c_List_Olist_OCons(_1744785), _1744791), _1744793)), -(hBOOL(hAPP(_1744787, _1744791)))], (33725 ^ _781404) ^ [_1396591, _1396593, _1396595, _1396597, _1396599, _1396601] : [hBOOL(hAPP(hAPP(c_member(_1396591), _1396593), _1396595)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396591, tc_fun(_1396597, tc_HOL_Obool)), _1396595), hAPP(hAPP(c_COMBB(tc_fun(_1396597, tc_HOL_Obool), tc_fun(_1396597, tc_HOL_Obool), _1396591), hAPP(c_Set_Oinsert(_1396597), _1396599)), _1396601)) = hAPP(hAPP(c_Set_Oinsert(_1396597), _1396599), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396591, tc_fun(_1396597, tc_HOL_Obool)), _1396595), _1396601)))], (51472 ^ _781404) ^ [_1823832, _1823834, _1823836, _1823838, _1823840] : [class_Groups_Ocomm__monoid__mult(_1823832), class_Rings_Odvd(_1823832), hBOOL(hAPP(c_Finite__Set_Ofinite(_1823834), _1823836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1823834, tc_HOL_Obool)), _1823838), _1823836)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823832), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1823834, _1823832), _1823840), _1823838)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1823834, _1823832), _1823840), _1823836))))], (34779 ^ _781404) ^ [_1427559, _1427561, _1427563, _1427565] : [class_Groups_Ocomm__monoid__add(_1427559), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1427561), _1427563)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1427559), _1427565), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1427561, _1427563)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427559), hAPP(_1427565, _1427561)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1427559), _1427565), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1427561, _1427563))))], (11747 ^ _781404) ^ [_982451, _982453] : [-(_982451 = _982453), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982451), _982453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982453), _982451)))], (26981 ^ _781404) ^ [_1263001] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1263001)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1263001))], (7878 ^ _781404) ^ [_911738, _911740, _911742, _911744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911738, tc_HOL_Obool)), _911740), _911742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911738, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_911738), _911744), _911740)), hAPP(hAPP(c_Set_Oinsert(_911738), _911744), _911742))))], (38896 ^ _781404) ^ [_1523829, _1523831, _1523833, _1523835, _1523837, _1523839] : [-(c_Product__Type_Omap__pair(_1523829, _1523831, _1523833, _1523835, _1523837, _1523839) = hAPP(c_Product__Type_Oprod_Oprod__case(_1523829, _1523833, tc_prod(_1523831, _1523835)), hAPP(hAPP(c_COMBC(_1523829, tc_fun(_1523833, _1523835), tc_fun(_1523833, tc_prod(_1523831, _1523835))), hAPP(hAPP(c_COMBB(tc_fun(_1523835, tc_prod(_1523831, _1523835)), tc_fun(tc_fun(_1523833, _1523835), tc_fun(_1523833, tc_prod(_1523831, _1523835))), _1523829), c_COMBB(_1523835, tc_prod(_1523831, _1523835), _1523833)), hAPP(hAPP(c_COMBB(_1523831, tc_fun(_1523835, tc_prod(_1523831, _1523835)), _1523829), c_Product__Type_OPair(_1523831, _1523835)), _1523837))), _1523839)))], (4724 ^ _781404) ^ [_853258, _853260, _853262, _853264, _853266, _853268, _853270, _853272] : [-(c_Random__Sequence_Omap(_853272, _853268, _853264, _853260) = c_Random__Sequence_Omap(_853270, _853266, _853262, _853258)), _853272 = _853270, _853268 = _853266, _853264 = _853262, _853260 = _853258], (6879 ^ _781404) ^ [_891689, _891691, _891693] : [class_Lattices_Olattice(_891689), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891689), _891691), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891689), _891691), _891693)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891689), _891691), _891693))], (42018 ^ _781404) ^ [_1608230, _1608232, _1608234, _1608236, _1608238] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608230, _1608230)), hAPP(hAPP(c_Product__Type_OPair(_1608230, _1608230), _1608232), _1608234)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608230, _1608230), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1608236)), _1608238))), 42022 ^ _781404 : [(42025 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608230, _1608230)), hAPP(hAPP(c_Product__Type_OPair(_1608230, _1608230), 42021 ^ [_1608230, _1608232, _1608234, _1608236, _1608238]), _1608234)), _1608238)))], (42023 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608230, _1608230)), hAPP(hAPP(c_Product__Type_OPair(_1608230, _1608230), _1608232), 42021 ^ [_1608230, _1608232, _1608234, _1608236, _1608238])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608230, _1608230), tc_HOL_Obool), _1608236), _1608238))))]]], (2262 ^ _781404) ^ [_814343, _814345] : [_814345 = _814343, -(c_SetInterval_Oord__class_OgreaterThan(_814345) = c_SetInterval_Oord__class_OgreaterThan(_814343))], (40950 ^ _781404) ^ [_1580993, _1580995, _1580997, _1580999, _1581001] : [_1580993 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1580995, _1580997, _1580993, _1580999), _1581001) = hAPP(c_Product__Type_OPair(_1580995, _1580997), _1581001))], (38674 ^ _781404) ^ [_1517220, _1517222, _1517224, _1517226] : [_1517220 = c_Orderings_Obot__class_Obot(tc_fun(_1517222, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1517224, _1517222), _1517224, c_Product__Type_Ofst(_1517224, _1517222)), hAPP(hAPP(c_Product__Type_OSigma(_1517224, _1517222), _1517226), hAPP(c_COMBK(tc_fun(_1517222, tc_HOL_Obool), _1517224), _1517220))) = c_Orderings_Obot__class_Obot(tc_fun(_1517224, tc_HOL_Obool)))], (6825 ^ _781404) ^ [_890770, _890772, _890774, _890776] : [6826 ^ _781404 : [(6829 ^ _781404) ^ [] : [hBOOL(hAPP(_890774, _890772))], (6827 ^ _781404) ^ [] : [hBOOL(hAPP(_890770, _890772))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890776, tc_HOL_Obool)), _890774), _890770), _890772)))], (238 ^ _781404) ^ [_785131, _785133] : [-(class_Rings_Odivision__ring(_785131)), _785133 = _785131, class_Rings_Odivision__ring(_785133)], (44675 ^ _781404) ^ [_1675048, _1675050, _1675052] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1675048, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675050)), _1675052)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1675050, _1675048), _1675052) = _1675052)], (27600 ^ _781404) ^ [_1274317, _1274319, _1274321] : [class_Groups_Oab__semigroup__mult(_1274317), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274317), _1274319)), -(_1274319 = c_Orderings_Obot__class_Obot(tc_fun(_1274317, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274317), _1274321)), -(_1274321 = c_Orderings_Obot__class_Obot(tc_fun(_1274317, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1274317, tc_HOL_Obool)), _1274319), _1274321) = c_Orderings_Obot__class_Obot(tc_fun(_1274317, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1274317, c_Groups_Otimes__class_Otimes(_1274317)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274317, tc_HOL_Obool)), _1274319), _1274321)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274317), hAPP(c_Finite__Set_Ofold1(_1274317, c_Groups_Otimes__class_Otimes(_1274317)), _1274319)), hAPP(c_Finite__Set_Ofold1(_1274317, c_Groups_Otimes__class_Otimes(_1274317)), _1274321)))], (18725 ^ _781404) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48935 ^ _781404) ^ [_1767286, _1767288, _1767290, _1767292, _1767294] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1767286), _1767288), _1767290), _1767292), _1767294) = c_New__DSequence_Oneg__single(_1767286, _1767288))], (10153 ^ _781404) ^ [_954358, _954360, _954362] : [class_Orderings_Olinorder(_954358), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954358), _954360), _954362))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954358), _954362), _954360)))], (4464 ^ _781404) ^ [_849170, _849172, _849174, _849176] : [-(c_Lazy__Sequence_Osmall__lazy_H(_849176, _849172) = c_Lazy__Sequence_Osmall__lazy_H(_849174, _849170)), _849176 = _849174, _849172 = _849170], (49711 ^ _781404) ^ [_1784925, _1784927] : [-(c_Relation_Otrans(_1784925, c_Relation_OId__on(_1784925, _1784927)))], (25889 ^ _781404) ^ [] : [-(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)))))], (47427 ^ _781404) ^ [_1734853] : [-(hAPP(c_List_Orev(_1734853), c_List_Olist_ONil(_1734853)) = c_List_Olist_ONil(_1734853))], (5334 ^ _781404) ^ [_862835, _862837] : [_862837 = _862835, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_862837) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_862835))], (11547 ^ _781404) ^ [_978844, _978846] : [-(hBOOL(hAPP(hAPP(c_member(_978844), _978846), c_Orderings_Otop__class_Otop(tc_fun(_978844, tc_HOL_Obool)))))], (52484 ^ _781404) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (12252 ^ _781404) ^ [_992065, _992067, _992069] : [hBOOL(hAPP(hAPP(c_member(_992065), _992067), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_992065, tc_HOL_Obool)), _992069))), hBOOL(hAPP(hAPP(c_member(_992065), _992067), _992069))], (47959 ^ _781404) ^ [_1746119, _1746121, _1746123, _1746125] : [47961 ^ _781404 : [(47966 ^ _781404) ^ [] : [hBOOL(hAPP(_1746125, hAPP(hAPP(c_List_Onth(_1746121), _1746123), 47960 ^ [_1746119, _1746121, _1746123, _1746125])))], (47964 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47960 ^ [_1746119, _1746121, _1746123, _1746125]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746121)), _1746123))))], (47962 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47960 ^ [_1746119, _1746121, _1746123, _1746125]), _1746119)))]], 47969 ^ _781404 : [(47972 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1746125, hAPP(hAPP(c_List_Onth(_1746121), _1746123), _1746119))))], (47970 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746119), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746121)), _1746123))))]], -(c_List_OtakeWhile(_1746121, _1746125, _1746123) = hAPP(hAPP(c_List_Otake(_1746121), _1746119), _1746123))], (29915 ^ _781404) ^ [_1317680, _1317682, _1317684] : [class_Groups_Ocomm__monoid__mult(_1317680), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317682, _1317680), _1317684), c_Orderings_Obot__class_Obot(tc_fun(_1317682, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1317680))], (50759 ^ _781404) ^ [_1807530, _1807532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1807530), _1807532)), -(c_Quickcheck_Obeyond(_1807530, _1807532) = _1807532)], (40116 ^ _781404) ^ [_1561792, _1561794, _1561796, _1561798] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1561792, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1561792, _1561794), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1561792, _1561794), tc_HOL_Obool)), _1561796), _1561798))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1561792, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1561792, _1561794), _1561796)), hAPP(c_Relation_ODomain(_1561792, _1561794), _1561798)))))], (38303 ^ _781404) ^ [_1508133, _1508135, _1508137, _1508139] : [hBOOL(hAPP(hAPP(c_member(_1508133), _1508135), c_Wellfounded_Oacc(_1508133, _1508137))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508133, _1508133)), hAPP(hAPP(c_Product__Type_OPair(_1508133, _1508133), _1508139), _1508135)), _1508137)), -(hBOOL(hAPP(hAPP(c_member(_1508133), _1508139), c_Wellfounded_Oacc(_1508133, _1508137))))], (9539 ^ _781404) ^ [_944803, _944805, _944807, _944809] : [class_Orderings_Oord(_944803), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944803), _944805), _944807)), _944807 = _944809, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944803), _944805), _944809)))], (4942 ^ _781404) ^ [_856705, _856707, _856709, _856711] : [-(c_Relation_Oconverse(_856711, _856707) = c_Relation_Oconverse(_856709, _856705)), _856711 = _856709, _856707 = _856705], (14067 ^ _781404) ^ [_1026836, _1026838, _1026840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026836), _1026838)), 14070 ^ _781404 : [(14077 ^ _781404) ^ [] : [_1026838 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026840), _1026836), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026838), _1026836) = _1026840)], (14071 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026838), _1026836) = _1026840, -(_1026838 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026840), _1026836))]]], (9767 ^ _781404) ^ [_948067, _948069, _948071, _948073] : [9769 ^ _781404 : [(9773 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_948067), 9771 ^ [_948067, _948069, _948071, _948073]), _948073)))], (9775 ^ _781404) ^ [] : [-(hAPP(_948071, 9768 ^ [_948067, _948069, _948071, _948073]) = hAPP(_948071, 9771 ^ [_948067, _948069, _948071, _948073]))], (9777 ^ _781404) ^ [] : [9768 ^ [_948067, _948069, _948071, _948073] = 9771 ^ [_948067, _948069, _948071, _948073]], (9770 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_948067), 9768 ^ [_948067, _948069, _948071, _948073]), _948073)))]], -(c_Fun_Oinj__on(_948067, _948069, _948071, _948073))], (51195 ^ _781404) ^ [_1816316, _1816318, _1816320, _1816322, _1816324, _1816326] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1816316, _1816318, _1816320, _1816322), _1816324), _1816326) = hAPP(_1816322, hAPP(hAPP(c_Product__Type_OPair(_1816316, _1816318), _1816324), _1816326)))], (21249 ^ _781404) ^ [_1159090, _1159092] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159090), _1159092), 21252 ^ _781404 : [(21255 ^ _781404) ^ [] : [-(_1159092 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (21253 ^ _781404) ^ [] : [-(_1159090 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (39816 ^ _781404) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (52306 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (50189 ^ _781404) ^ [_1795910, _1795912] : [c_Relation_Osym(_1795910, _1795912), -(c_Relation_Osym(_1795910, c_Transitive__Closure_Otrancl(_1795910, _1795912)))], (584 ^ _781404) ^ [_790170, _790172] : [-(class_Lattices_Oab__semigroup__idem__mult(_790170)), _790172 = _790170, class_Lattices_Oab__semigroup__idem__mult(_790172)], (8188 ^ _781404) ^ [_918823, _918825, _918827] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_918823, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_918823, tc_HOL_Obool)), _918825), _918827)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_918823, tc_HOL_Obool)), _918825), c_Complete__Lattice_OSup__class_OSup(tc_fun(_918823, tc_HOL_Obool), _918827)))], (51239 ^ _781404) ^ [_1817208, _1817210, _1817212] : [hBOOL(hAPP(hAPP(_1817210, _1817212), _1817212)), -(hBOOL(hAPP(c_Quotient_ORespects(_1817208, _1817210), _1817212)))], (35547 ^ _781404) ^ [_1444894, _1444896] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1444894, _1444896) = 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), _1444894), _1444896)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1444894, _1444896)))], (8483 ^ _781404) ^ [_924470, _924472] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_924470, _924472, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_924470), tc_HOL_Obool))))], (45385 ^ _781404) ^ [_1690374, _1690376, _1690378, _1690380] : [-(hBOOL(hAPP(c_List_Odistinct(_1690374), hAPP(hAPP(c_List_Omap(_1690376, _1690374), _1690378), _1690380)))), hBOOL(hAPP(c_List_Odistinct(_1690376), _1690380)), c_Fun_Oinj__on(_1690376, _1690374, _1690378, hAPP(c_List_Oset(_1690376), _1690380))], (42449 ^ _781404) ^ [_1621299, _1621301, _1621303, _1621305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621299), tc_List_Olist(_1621299))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621299), tc_List_Olist(_1621299)), _1621301), _1621303)), c_List_Olistrel(_1621299, _1621305))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621299)), _1621301) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621299)), _1621303))], (11105 ^ _781404) ^ [_969915, _969917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969915), _969917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969915), hAPP(c_Nat_OSuc, _969917))))], (22881 ^ _781404) ^ [_1190589, _1190591] : [_1190589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1190589), _1190591) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40251 ^ _781404) ^ [_1565102, _1565104, _1565106] : [c_Wellfounded_OwfP(_1565102, _1565104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1565102, tc_fun(_1565102, tc_HOL_Obool))), _1565106), _1565104)), -(c_Wellfounded_OwfP(_1565102, _1565106))], (12120 ^ _781404) ^ [_989539, _989541, _989543, _989545] : [hBOOL(hAPP(hAPP(c_member(_989539), _989541), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989539, tc_HOL_Obool)), _989543), _989545))), -(hBOOL(hAPP(hAPP(c_member(_989539), _989541), _989543)))], (43573 ^ _781404) ^ [_1649886, _1649888] : [hAPP(c_List_Oset(_1649886), _1649888) = c_Orderings_Obot__class_Obot(tc_fun(_1649886, tc_HOL_Obool)), -(_1649888 = c_List_Olist_ONil(_1649886))], (666 ^ _781404) ^ [_791403, _791405, _791407, _791409, _791411, _791413, _791415, _791417, _791419, _791421] : [-(c_List_Olist__all2(_791419, _791415, _791411, _791407, _791403)), c_List_Olist__all2(_791421, _791417, _791413, _791409, _791405), _791421 = _791419, _791417 = _791415, _791413 = _791411, _791409 = _791407, _791405 = _791403], (12072 ^ _781404) ^ [_988547, _988549, _988551, _988553] : [hBOOL(hAPP(hAPP(c_member(_988547), _988549), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_988547, tc_HOL_Obool)), _988551), _988553))), -(hBOOL(hAPP(hAPP(c_member(_988547), _988549), _988551))), -(hBOOL(hAPP(hAPP(c_member(_988547), _988549), _988553)))], (9104 ^ _781404) ^ [_935735, _935737] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935735, tc_HOL_Obool)), _935737), _935737) = c_Orderings_Obot__class_Obot(tc_fun(_935735, tc_HOL_Obool)))], (43132 ^ _781404) ^ [_1640541, _1640543, _1640545, _1640547, _1640549] : [-(_1640541 = _1640543), -(hAPP(hAPP(c_List_Onth(_1640545), hAPP(hAPP(c_List_Olist__update(_1640545, _1640547), _1640541), _1640549)), _1640543) = hAPP(hAPP(c_List_Onth(_1640545), _1640547), _1640543))], (20993 ^ _781404) ^ [_1154368, _1154370] : [class_Rings_Ocomm__semiring__1(_1154368), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154368), _1154370), c_Groups_Oone__class_Oone(_1154368)) = _1154370)], (8417 ^ _781404) ^ [_923270, _923272] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923270, tc_HOL_Obool)), _923272), c_Orderings_Obot__class_Obot(tc_fun(_923270, tc_HOL_Obool))) = _923272)], (40357 ^ _781404) ^ [_1567352, _1567354] : [-(c_Nitpick_Owf_H(_1567352, _1567354)), c_Wellfounded_Oacyclic(_1567352, _1567354), 40362 ^ _781404 : [(40365 ^ _781404) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (40363 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1567352, _1567352)), _1567354))]]], (11803 ^ _781404) ^ [_983407, _983409, _983411, _983413, _983415] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_983407, _983409, _983411), _983413), _983415)), -(hBOOL(hAPP(_983413, hAPP(_983411, _983415))))], (32118 ^ _781404) ^ [_1359512, _1359514, _1359516] : [class_Orderings_Olinorder(_1359512), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359512), _1359514), _1359516)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359512), _1359516), _1359514) = _1359516)], (45419 ^ _781404) ^ [_1691165, _1691167, _1691169] : [c_Fun_Oinj__on(tc_List_Olist(_1691165), tc_List_Olist(_1691167), hAPP(c_List_Omap(_1691165, _1691167), _1691169), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1691165), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1691165, _1691167, _1691169, c_Orderings_Otop__class_Otop(tc_fun(_1691165, tc_HOL_Obool))))], (9409 ^ _781404) ^ [_942721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _942721))))], (45323 ^ _781404) ^ [_1688946, _1688948, _1688950, _1688952, _1688954] : [-(hAPP(hAPP(c_List_Odrop(_1688946), _1688948), hAPP(hAPP(c_List_Omap(_1688950, _1688946), _1688952), _1688954)) = hAPP(hAPP(c_List_Omap(_1688950, _1688946), _1688952), hAPP(hAPP(c_List_Odrop(_1688950), _1688948), _1688954)))], (34333 ^ _781404) ^ [_1416788, _1416790, _1416792, _1416794] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1416788), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1416790, tc_Nat_Onat), _1416792), _1416794)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1416790, _1416788), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1416788, _1416790), c_Nat_Osemiring__1__class_Oof__nat(_1416788)), _1416792)), _1416794)), class_Groups_Ocomm__monoid__mult(_1416788), class_Rings_Osemiring__1(_1416788)], (3730 ^ _781404) ^ [_837329, _837331] : [_837331 = _837329, -(c_List_Oembed__list(_837331) = c_List_Oembed__list(_837329))], (52558 ^ _781404) ^ [_1840302, _1840304] : [-(class_Finite__Set_Ofinite(tc_sum(_1840302, _1840304))), class_Finite__Set_Ofinite(_1840302), class_Finite__Set_Ofinite(_1840304)], (38745 ^ _781404) ^ [_1519517, _1519519, _1519521] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1519517), _1519519)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519517, _1519517), tc_HOL_Obool)), _1519521), hAPP(hAPP(c_Product__Type_OSigma(_1519517, _1519517), _1519519), hAPP(c_COMBK(tc_fun(_1519517, tc_HOL_Obool), _1519517), _1519519)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1519517, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1519517), _1519519), _1519521))))], (45692 ^ _781404) ^ [_1696822] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1696822)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1696822))], (37027 ^ _781404) ^ [_1475601, _1475603, _1475605, _1475607, _1475609, _1475611] : [c_Finite__Set_Ofolding__idem(_1475601, _1475603, _1475605, _1475607), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475601), _1475609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475601, tc_HOL_Obool)), _1475611), _1475609)), -(hAPP(c_Fun_Ocomp(_1475603, _1475603, _1475603, hAPP(_1475607, _1475609)), hAPP(_1475607, _1475611)) = hAPP(_1475607, _1475609))], (49175 ^ _781404) ^ [_1772688, _1772690] : [-(c_List_Oreplicate(_1772688, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1772690) = c_List_Olist_ONil(_1772688))], (46690 ^ _781404) ^ [_1720622, _1720624, _1720626, _1720628, _1720630, _1720632] : [-(c_List_Ofoldr(_1720622, _1720624, _1720626, hAPP(hAPP(c_List_Olist_OCons(_1720622), _1720628), _1720630), _1720632) = hAPP(hAPP(_1720626, _1720628), c_List_Ofoldr(_1720622, _1720624, _1720626, _1720630, _1720632)))], (11757 ^ _781404) ^ [_982500, _982502] : [11758 ^ _781404 : [(11761 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982502), _982500))], (11759 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982500), _982502))]], _982500 = _982502], (41887 ^ _781404) ^ [_1604490, _1604492, _1604494] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604490, _1604490), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1604492)), _1604494) = hAPP(hAPP(c_Relation_Orel__comp(_1604490, _1604490, _1604490), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604490, _1604490), tc_HOL_Obool), _1604492), _1604494)), _1604494))], (14817 ^ _781404) ^ [_1041417, _1041419] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041417), c_Orderings_Otop__class_Otop(tc_fun(_1041417, tc_HOL_Obool)))), c_Fun_Oinj__on(_1041417, _1041417, _1041419, c_Orderings_Otop__class_Otop(tc_fun(_1041417, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1041417, _1041417, _1041419), c_Orderings_Otop__class_Otop(tc_fun(_1041417, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041417, tc_HOL_Obool)))], (19057 ^ _781404) ^ [_1120559, _1120561] : [c_Int_Oiszero(_1120559, hAPP(c_Int_Onumber__class_Onumber__of(_1120559), c_Int_OBit1(_1120561))), class_Int_Onumber__ring(_1120559), class_Int_Oring__char__0(_1120559)], (51048 ^ _781404) ^ [_1813170, _1813172, _1813174] : [c_Fun_Obij__betw(_1813170, _1813170, c_Fun_Oid(_1813170), _1813172, _1813174), -(_1813172 = _1813174)], (23785 ^ _781404) ^ [_1208403, _1208405] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1208403))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1208405))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1208403)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1208405)))], (21219 ^ _781404) ^ [_1158565] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158565), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1158565)], (27979 ^ _781404) ^ [_1281758, _1281760, _1281762, _1281764] : [class_Fields_Ofield__inverse__zero(_1281758), class_Int_Onumber(_1281758), 27986 ^ _781404 : [(27987 ^ _781404) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281758), _1281760), hAPP(c_Int_Onumber__class_Onumber__of(_1281758), _1281762)) = _1281764, 27990 ^ _781404 : [(27997 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1281758), _1281762) = c_Groups_Ozero__class_Ozero(_1281758), -(_1281764 = c_Groups_Ozero__class_Ozero(_1281758))], (27991 ^ _781404) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1281758), _1281762) = c_Groups_Ozero__class_Ozero(_1281758)), -(_1281760 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281758), _1281764), hAPP(c_Int_Onumber__class_Onumber__of(_1281758), _1281762)))]]], (28003 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281758), _1281760), hAPP(c_Int_Onumber__class_Onumber__of(_1281758), _1281762)) = _1281764), 28006 ^ _781404 : [(28009 ^ _781404) ^ [] : [_1281760 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281758), _1281764), hAPP(c_Int_Onumber__class_Onumber__of(_1281758), _1281762))], (28007 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1281758), _1281762) = c_Groups_Ozero__class_Ozero(_1281758)]], 28010 ^ _781404 : [(28013 ^ _781404) ^ [] : [_1281764 = c_Groups_Ozero__class_Ozero(_1281758)], (28011 ^ _781404) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1281758), _1281762) = c_Groups_Ozero__class_Ozero(_1281758))]]]]], (49604 ^ _781404) ^ [_1782208, _1782210, _1782212] : [-(c_Random__Sequence_Oempty(_1782208, _1782210, _1782212) = 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(_1782208)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1782208)))], (46597 ^ _781404) ^ [_1717572, _1717574, _1717576, _1717578] : [-(hBOOL(hAPP(_1717572, _1717574))), -(hAPP(c_List_OremoveAll(_1717576, _1717574), hAPP(c_List_Ofilter(_1717576, _1717572), _1717578)) = hAPP(c_List_Ofilter(_1717576, _1717572), _1717578))], (30466 ^ _781404) ^ [_1328883, _1328885, _1328887] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1328883), _1328885))), -(c_Random_Ominus__shift(_1328887, _1328883, _1328885) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1328883), _1328885))], (11529 ^ _781404) ^ [_978494, _978496, _978498, _978500] : [11530 ^ _781404 : [(11533 ^ _781404) ^ [] : [_978496 = _978500], (11531 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_978494), _978496), _978498))]], -(hBOOL(hAPP(hAPP(c_member(_978494), _978496), hAPP(hAPP(c_Set_Oinsert(_978494), _978500), _978498))))], (46435 ^ _781404) ^ [_1713242, _1713244, _1713246] : [-(c_List_Oconcat(_1713242, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1713242)), _1713244), _1713246)) = hAPP(hAPP(c_List_Oappend(_1713242), c_List_Oconcat(_1713242, _1713244)), c_List_Oconcat(_1713242, _1713246)))], (35342 ^ _781404) ^ [_1440143, _1440145, _1440147] : [_1440143 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1440145, _1440145), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1440145, _1440145), tc_HOL_Obool)), _1440143), _1440147)))], (7651 ^ _781404) ^ [_907212, _907214, _907216] : [class_Lattices_Olattice(_907212), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907212), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_907212), _907214), _907216)), _907216)))], (23125 ^ _781404) ^ [_1195396, _1195398, _1195400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1195396)), 23128 ^ _781404 : [(23135 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1195398), _1195400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195396), _1195398)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195396), _1195400))))], (23129 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195396), _1195398)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195396), _1195400))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1195398), _1195400)))]]], (47465 ^ _781404) ^ [_1735583, _1735585, _1735587] : [hAPP(hAPP(c_List_Olist_OCons(_1735583), _1735585), c_List_Olist_ONil(_1735583)) = hAPP(c_List_Orev(_1735583), _1735587), -(_1735587 = hAPP(hAPP(c_List_Olist_OCons(_1735583), _1735585), c_List_Olist_ONil(_1735583)))], (20153 ^ _781404) ^ [_1139262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1139262))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1139262)))], (46631 ^ _781404) ^ [_1718424, _1718426, _1718428] : [hBOOL(hAPP(c_List_Odistinct(_1718424), _1718426)), -(hAPP(c_List_Ofilter(_1718424, hAPP(hAPP(c_COMBC(_1718424, tc_fun(_1718424, tc_HOL_Obool), tc_HOL_Obool), c_member(_1718424)), hAPP(c_List_Oset(_1718424), c_List_Osublist(_1718424, _1718426, _1718428)))), _1718426) = c_List_Osublist(_1718424, _1718426, _1718428))], (6891 ^ _781404) ^ [_891939, _891941, _891943, _891945] : [class_Lattices_Osemilattice__sup(_891939), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891939), _891941), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891939), _891943), _891945)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891939), _891943), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891939), _891941), _891945)))], (41793 ^ _781404) ^ [_1602062, _1602064, _1602066] : [41795 ^ _781404 : [(41796 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602062), 41794 ^ [_1602062, _1602064, _1602066]), _1602064)))], (41801 ^ _781404) ^ [] : [41794 ^ [_1602062, _1602064, _1602066] = 41797 ^ [_1602062, _1602064, _1602066]], (41805 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602062, _1602062)), hAPP(hAPP(c_Product__Type_OPair(_1602062, _1602062), 41797 ^ [_1602062, _1602064, _1602066]), 41794 ^ [_1602062, _1602064, _1602066])), _1602066))], (41803 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602062, _1602062)), hAPP(hAPP(c_Product__Type_OPair(_1602062, _1602062), 41794 ^ [_1602062, _1602064, _1602066]), 41797 ^ [_1602062, _1602064, _1602066])), _1602066))], (41799 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602062), 41797 ^ [_1602062, _1602064, _1602066]), _1602064)))]], -(c_Relation_Ototal__on(_1602062, _1602064, _1602066))], (33704 ^ _781404) ^ [_1396198, _1396200, _1396202, _1396204] : [33706 ^ _781404 : [(33709 ^ _781404) ^ [] : [hAPP(_1396204, 33705 ^ [_1396198, _1396200, _1396202, _1396204]) = c_Orderings_Obot__class_Obot(tc_fun(_1396198, tc_HOL_Obool))], (33707 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1396200), 33705 ^ [_1396198, _1396200, _1396202, _1396204]), _1396202)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1396198, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396200, tc_fun(_1396198, tc_HOL_Obool)), _1396202), _1396204))], (39540 ^ _781404) ^ [_1546359, _1546361] : [-(hAPP(c_Set_Oimage(_1546359, _1546359, c_Fun_Oid(_1546359)), _1546361) = _1546361)], (9487 ^ _781404) ^ [_943958, _943960, _943962] : [class_Orderings_Opreorder(_943958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943958), _943960), _943962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943958), _943962), _943960))], (4698 ^ _781404) ^ [_852867, _852869, _852871, _852873, _852875, _852877] : [-(c_Random__Sequence_Oempty(_852877, _852873, _852869) = c_Random__Sequence_Oempty(_852875, _852871, _852867)), _852877 = _852875, _852873 = _852871, _852869 = _852867], (24899 ^ _781404) ^ [_1227596, _1227598] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227596), _1227598))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1227596, _1227598) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1227596), _1227598), _1227598))], (42541 ^ _781404) ^ [_1624367, _1624369, _1624371, _1624373, _1624375, _1624377] : [hBOOL(hAPP(hAPP(_1624367, _1624369), _1624371)), c_List_Olistrelp(_1624373, _1624367, _1624375, _1624377), -(c_List_Olistrelp(_1624373, _1624367, hAPP(hAPP(c_List_Olist_OCons(_1624373), _1624369), _1624375), hAPP(hAPP(c_List_Olist_OCons(_1624373), _1624371), _1624377)))], (43471 ^ _781404) ^ [_1648192] : [-(hBOOL(hAPP(c_List_Odistinct(_1648192), c_List_Olist_ONil(_1648192))))], (23569 ^ _781404) ^ [_1204593, _1204595, _1204597, _1204599] : [class_Divides_Osemiring__div(_1204593), -(c_Divides_Odiv__class_Omod(_1204593, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204593), c_Divides_Odiv__class_Omod(_1204593, _1204595, _1204597)), _1204599), _1204597) = c_Divides_Odiv__class_Omod(_1204593, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204593), _1204595), _1204599), _1204597))], (49263 ^ _781404) ^ [_1774458, _1774460, _1774462, _1774464] : [-(hAPP(c_New__DSequence_Opos__union(_1774458, _1774460, _1774462), _1774464) = c_Lazy__Sequence_Oappend(_1774458, hAPP(_1774460, _1774464), hAPP(_1774462, _1774464)))], (44697 ^ _781404) ^ [_1675458, _1675460, _1675462] : [-(hAPP(c_List_Orotate(_1675458, _1675460), _1675462) = hAPP(hAPP(c_List_Oappend(_1675458), hAPP(hAPP(c_List_Odrop(_1675458), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1675460, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675458)), _1675462))), _1675462)), hAPP(hAPP(c_List_Otake(_1675458), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1675460, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675458)), _1675462))), _1675462)))], (9380 ^ _781404) ^ [_942177, _942179, _942181] : [c_List_Oall__interval__nat(_942177, _942179, _942181), 9383 ^ _781404 : [(9384 ^ _781404) ^ [_942257] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _942257), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _942179), _942181))), -(hBOOL(hAPP(_942177, _942257)))]]], (52670 ^ _781404) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (25035 ^ _781404) ^ [_1229656] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1229656) = c_Int_Opred(_1229656))], (45267 ^ _781404) ^ [_1687743, _1687745, _1687747, _1687749, _1687751] : [class_Rings_Osemiring__0(_1687743), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687743), hAPP(hAPP(c_List_Omap(_1687745, _1687743), hAPP(hAPP(c_COMBB(_1687743, _1687743, _1687745), hAPP(c_Groups_Otimes__class_Otimes(_1687743), _1687747)), _1687749)), _1687751)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1687743), _1687747), hAPP(c_List_Omonoid__add__class_Olistsum(_1687743), hAPP(hAPP(c_List_Omap(_1687745, _1687743), _1687749), _1687751))))], (23033 ^ _781404) ^ [_1193607, _1193609, _1193611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193607)), _1193607 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193609), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193607), _1193611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193611), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (45327 ^ _781404) ^ [_1689046] : [-(hAPP(c_List_Omap(_1689046, _1689046), c_Fun_Oid(_1689046)) = c_Fun_Oid(tc_List_Olist(_1689046)))], (15821 ^ _781404) ^ [_1061566, _1061568, _1061570] : [class_Lattices_Olattice(_1061566), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061566), _1061568)), -(_1061570 = c_Orderings_Obot__class_Obot(tc_fun(_1061566, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1061566, tc_HOL_Obool)), _1061570), _1061568)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1061566), c_Big__Operators_Olattice__class_OInf__fin(_1061566, _1061570)), c_Big__Operators_Olattice__class_OInf__fin(_1061566, _1061568)) = c_Big__Operators_Olattice__class_OInf__fin(_1061566, _1061568))], (25919 ^ _781404) ^ [_1244668, _1244670] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244668))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244668)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244670)) = 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), _1244670)))], (22415 ^ _781404) ^ [_1181175, _1181177, _1181179, _1181181, _1181183] : [class_Rings_Olinordered__semiring__strict(_1181175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181175), _1181177), _1181179)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181175), _1181181), _1181183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181175), c_Groups_Ozero__class_Ozero(_1181175)), _1181177)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181175), c_Groups_Ozero__class_Ozero(_1181175)), _1181181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181175), _1181177), _1181181)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181175), _1181179), _1181183))))], (41449 ^ _781404) ^ [_1593766, _1593768, _1593770, _1593772] : [-(c_Wellfounded_Oacyclic(_1593766, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593766, _1593766)), hAPP(hAPP(c_Product__Type_OPair(_1593766, _1593766), _1593768), _1593770)), _1593772))), c_Wellfounded_Oacyclic(_1593766, _1593772), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593766, _1593766)), hAPP(hAPP(c_Product__Type_OPair(_1593766, _1593766), _1593770), _1593768)), c_Transitive__Closure_Ortrancl(_1593766, _1593772))))], (37790 ^ _781404) ^ [_1494807, _1494809, _1494811, _1494813, _1494815] : [hAPP(c_Relation_OImage(_1494807, _1494807, _1494809), hAPP(hAPP(c_Set_Oinsert(_1494807), _1494811), c_Orderings_Obot__class_Obot(tc_fun(_1494807, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1494807, _1494807, _1494809), hAPP(hAPP(c_Set_Oinsert(_1494807), _1494813), c_Orderings_Obot__class_Obot(tc_fun(_1494807, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1494807, _1494815, _1494809), hBOOL(hAPP(hAPP(c_member(_1494807), _1494813), _1494815)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494807, _1494807)), hAPP(hAPP(c_Product__Type_OPair(_1494807, _1494807), _1494811), _1494813)), _1494809)))], (36154 ^ _781404) ^ [_1456206, _1456208, _1456210] : [36156 ^ _781404 : [(36159 ^ _781404) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1456206, _1456208), 36155 ^ [_1456206, _1456208, _1456210]))], (36157 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1456208, 36155 ^ [_1456206, _1456208, _1456210]), _1456210)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1456206, _1456208), _1456210)))], (2200 ^ _781404) ^ [_813350, _813352, _813354, _813356, _813358, _813360] : [-(c_Random_Ominus__shift(_813360, _813356, _813352) = c_Random_Ominus__shift(_813358, _813354, _813350)), _813360 = _813358, _813356 = _813354, _813352 = _813350], (19035 ^ _781404) ^ [_1120231, _1120233] : [_1120231 = _1120233, -(c_Int_OBit1(_1120231) = c_Int_OBit1(_1120233))], (27259 ^ _781404) ^ [_1268217, _1268219, _1268221, _1268223, _1268225] : [class_Groups_Oordered__ab__group__add__abs(_1268217), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268217), hAPP(c_Groups_Oabs__class_Oabs(_1268217), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1268217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1268217), _1268219), _1268221)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1268217), _1268223), _1268225)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1268217), hAPP(c_Groups_Oabs__class_Oabs(_1268217), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1268217), _1268219), _1268223))), hAPP(c_Groups_Oabs__class_Oabs(_1268217), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1268217), _1268221), _1268225))))))], (3736 ^ _781404) ^ [_837414, _837416] : [_837416 = _837414, -(c_List_Omonoid__add__class_Olistsum(_837416) = c_List_Omonoid__add__class_Olistsum(_837414))], (39197 ^ _781404) ^ [_1532407, _1532409, _1532411, _1532413] : [-(hAPP(c_Relation_OImage(_1532407, _1532409, _1532411), hAPP(hAPP(c_Set_Oinsert(_1532407), _1532413), c_Orderings_Obot__class_Obot(tc_fun(_1532407, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1532409), hAPP(hAPP(c_COMBC(_1532409, tc_fun(tc_prod(_1532407, _1532409), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1532407, _1532409), tc_fun(tc_fun(tc_prod(_1532407, _1532409), tc_HOL_Obool), tc_HOL_Obool), _1532409), c_member(tc_prod(_1532407, _1532409))), hAPP(c_Product__Type_OPair(_1532407, _1532409), _1532413))), _1532411)))], (40267 ^ _781404) ^ [_1565361, _1565363] : [c_Wellfounded_OwfP(_1565361, hAPP(hAPP(c_COMBC(_1565361, tc_fun(tc_prod(_1565361, _1565361), tc_HOL_Obool), tc_fun(_1565361, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565361, tc_fun(tc_fun(tc_prod(_1565361, _1565361), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1565361, _1565361), tc_HOL_Obool), tc_fun(_1565361, tc_HOL_Obool)), _1565361), c_COMBC(_1565361, tc_fun(tc_prod(_1565361, _1565361), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565361, tc_prod(_1565361, _1565361)), tc_fun(_1565361, tc_fun(tc_fun(tc_prod(_1565361, _1565361), tc_HOL_Obool), tc_HOL_Obool)), _1565361), hAPP(c_COMBB(tc_prod(_1565361, _1565361), tc_fun(tc_fun(tc_prod(_1565361, _1565361), tc_HOL_Obool), tc_HOL_Obool), _1565361), c_member(tc_prod(_1565361, _1565361)))), c_Product__Type_OPair(_1565361, _1565361)))), _1565363)), -(c_Wellfounded_Owf(_1565361, _1565363))], (6458 ^ _781404) ^ [_884109, _884111, _884113, _884115, _884117] : [class_Complete__Lattice_Ocomplete__lattice(_884109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884111, tc_HOL_Obool)), _884113), _884115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884109), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_884111, _884109), _884115), _884117)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_884111, _884109), _884113), _884117))))], (24684 ^ _781404) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (44900 ^ _781404) ^ [_1680017, _1680019, _1680021, _1680023, _1680025, _1680027] : [class_Orderings_Olinorder(_1680017), -(hAPP(_1680019, _1680021) = hAPP(_1680019, _1680023)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680025, _1680017, _1680019), _1680023), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680025, _1680017, _1680019), _1680021), _1680027)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680025, _1680017, _1680019), _1680021), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680025, _1680017, _1680019), _1680023), _1680027)))], (34157 ^ _781404) ^ [_1409093, _1409095, _1409097, _1409099, _1409101] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409093, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409095, tc_fun(_1409093, tc_HOL_Obool)), _1409097), _1409099)), _1409101) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409095, tc_fun(_1409093, tc_HOL_Obool)), _1409097), hAPP(hAPP(c_COMBC(_1409095, tc_fun(_1409093, tc_HOL_Obool), tc_fun(_1409093, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409093, tc_HOL_Obool), tc_fun(tc_fun(_1409093, tc_HOL_Obool), tc_fun(_1409093, tc_HOL_Obool)), _1409095), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409093, tc_HOL_Obool))), _1409099)), _1409101)))], (3572 ^ _781404) ^ [_834808, _834810, _834812, _834814, _834816, _834818] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_834818, _834814, _834810) = c_SetInterval_Oord__class_OgreaterThanLessThan(_834816, _834812, _834808)), _834818 = _834816, _834814 = _834812, _834810 = _834808], (45547 ^ _781404) ^ [_1693810, _1693812] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1693810)), hAPP(c_Code__Numeral_Oof__nat, _1693812)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1693810), _1693812)))], (34529 ^ _781404) ^ [_1421607, _1421609] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1421607), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1421609))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1421607), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421609))), 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))))], (27943 ^ _781404) ^ [_1281135, _1281137, _1281139] : [class_Rings_Odivision__ring(_1281135), -(_1281137 = c_Groups_Ozero__class_Ozero(_1281135)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281135), hAPP(c_Groups_Ouminus__class_Ouminus(_1281135), _1281139)), hAPP(c_Groups_Ouminus__class_Ouminus(_1281135), _1281137)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281135), _1281139), _1281137))], (318 ^ _781404) ^ [_786301, _786303, _786305, _786307] : [-(c_Nitpick_Orefl_H(_786305, _786301)), c_Nitpick_Orefl_H(_786307, _786303), _786307 = _786305, _786303 = _786301], (22103 ^ _781404) ^ [_1175041, _1175043, _1175045] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175041), _1175043)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175041), _1175045)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1175043), _1175045))], (48983 ^ _781404) ^ [_1768476] : [-(c_Predicate_Oconversep(_1768476, _1768476, c_fequal) = c_fequal)], (11703 ^ _781404) ^ [_981834, _981836, _981838] : [11704 ^ _781404 : [(11707 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_981838, _981836), _981834))], (11705 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981834), _981836)))]], 11710 ^ _781404 : [(11713 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_981838, _981836), _981834))], (11711 ^ _781404) ^ [] : [-(_981834 = _981836)]], 11716 ^ _781404 : [(11719 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_981838, _981836), _981834))], (11717 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981836), _981834)))]], -(hBOOL(hAPP(hAPP(_981838, _981836), _981834)))], (51289 ^ _781404) ^ [_1818131, _1818133, _1818135, _1818137, _1818139, _1818141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1818131, tc_HOL_Obool)), _1818133), _1818135)), 51295 ^ _781404 : [(51298 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1818137, tc_HOL_Obool)), hAPP(_1818139, 51294 ^ [_1818131, _1818133, _1818135, _1818137, _1818139, _1818141])), hAPP(_1818141, 51294 ^ [_1818131, _1818133, _1818135, _1818137, _1818139, _1818141])))], (51296 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1818131), 51294 ^ [_1818131, _1818133, _1818135, _1818137, _1818139, _1818141]), _1818135)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1818137, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1818131, tc_fun(_1818137, tc_HOL_Obool)), _1818135), _1818139)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1818131, tc_fun(_1818137, tc_HOL_Obool)), _1818135), _1818141))))], (25756 ^ _781404) ^ [_1241664] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1241664) = 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), _1241664))))], (12336 ^ _781404) ^ [_993804, _993806, _993808, _993810] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993804, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_993804), _993806), _993808)), _993810))), hBOOL(hAPP(hAPP(c_member(_993804), _993806), _993810)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993804, tc_HOL_Obool)), _993808), _993810))], (1286 ^ _781404) ^ [_800519, _800521] : [-(class_Rings_Oordered__ring(_800519)), _800521 = _800519, class_Rings_Oordered__ring(_800521)], (12582 ^ _781404) ^ [_998824, _998826, _998828] : [hBOOL(hAPP(hAPP(c_member(_998824), _998826), _998828)), -(hAPP(hAPP(c_Set_Oinsert(_998824), _998826), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998824, tc_HOL_Obool)), _998828), hAPP(hAPP(c_Set_Oinsert(_998824), _998826), c_Orderings_Obot__class_Obot(tc_fun(_998824, tc_HOL_Obool))))) = _998828)], (43505 ^ _781404) ^ [_1648728, _1648730, _1648732] : [hAPP(hAPP(c_List_Olist_OCons(_1648728), _1648730), _1648732) = c_List_Olist_ONil(_1648728)], (22817 ^ _781404) ^ [_1189266, _1189268] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1189266)), _1189268) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1189266), _1189268))), _1189268))], (20403 ^ _781404) ^ [] : [-(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)))))], (39467 ^ _781404) ^ [_1543535, _1543537] : [c_Predicate_Oreflp(_1543535, _1543537), -(c_Relation_Orefl__on(_1543535, c_Orderings_Otop__class_Otop(tc_fun(_1543535, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1543535, _1543535)), hAPP(c_Product__Type_Oprod_Oprod__case(_1543535, _1543535, tc_HOL_Obool), _1543537))))], (5993 ^ _781404) ^ [_876396, _876398, _876400] : [class_Orderings_Opreorder(_876396), _876398 = _876400, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876396), _876398), _876400)))], (26401 ^ _781404) ^ [_1252127, _1252129] : [class_Int_Oring__char__0(_1252127), 26404 ^ _781404 : [(26411 ^ _781404) ^ [] : [_1252129 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1252127) = hAPP(c_Int_Oring__1__class_Oof__int(_1252127), _1252129))], (26405 ^ _781404) ^ [] : [c_Groups_Ozero__class_Ozero(_1252127) = hAPP(c_Int_Oring__1__class_Oof__int(_1252127), _1252129), -(_1252129 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (32556 ^ _781404) ^ [_1367872, _1367874, _1367876] : [class_Orderings_Olinorder(_1367872), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367872), _1367874)), -(hBOOL(hAPP(hAPP(c_member(_1367872), _1367876), _1367874))), -(c_Big__Operators_Olinorder__class_OMax(_1367872, hAPP(hAPP(c_Set_Oinsert(_1367872), _1367876), _1367874)) = hAPP(hAPP(c_Finite__Set_Ofold(_1367872, _1367872, c_Orderings_Oord__class_Omax(_1367872)), _1367876), _1367874))], (35924 ^ _781404) ^ [_1451748, _1451750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451748), 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)), _1451750)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451748, _1451750), c_Divides_OnegDivAlg(_1451748, _1451750))))], (14164 ^ _781404) ^ [_1028660, _1028662, _1028664, _1028666, _1028668] : [class_Groups_Ocomm__monoid__add(_1028660), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028662), _1028664)), hBOOL(hAPP(hAPP(c_member(_1028662), _1028666), _1028664)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028662, _1028660), _1028668), _1028664) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028660), hAPP(_1028668, _1028666)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028662, _1028660), _1028668), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1028662, tc_HOL_Obool)), _1028664), hAPP(hAPP(c_Set_Oinsert(_1028662), _1028666), c_Orderings_Obot__class_Obot(tc_fun(_1028662, tc_HOL_Obool)))))))], (50997 ^ _781404) ^ [_1812303] : [-(c_Quickcheck_Obeyond(_1812303, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (14486 ^ _781404) ^ [_1035150, _1035152, _1035154, _1035156] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1035150), _1035152)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035154), hAPP(c_Set_Oimage(_1035150, _1035154, _1035156), _1035152))))], (42196 ^ _781404) ^ [_1612828, _1612830, _1612832] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612828)), _1612830) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612828)), _1612832)), _1612830 = _1612832], (4050 ^ _781404) ^ [_842625, _842627] : [_842627 = _842625, -(c_New__DSequence_Opos__empty(_842627) = c_New__DSequence_Opos__empty(_842625))], (38548 ^ _781404) ^ [_1513607, _1513609, _1513611] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1513607, _1513609), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1513607, _1513609), _1513611), hAPP(c_COMBK(tc_fun(_1513609, tc_HOL_Obool), _1513607), c_Orderings_Otop__class_Otop(tc_fun(_1513609, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1513607, _1513609), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1513607, tc_HOL_Obool)), _1513611)), hAPP(c_COMBK(tc_fun(_1513609, tc_HOL_Obool), _1513607), c_Orderings_Otop__class_Otop(tc_fun(_1513609, tc_HOL_Obool)))))], (40972 ^ _781404) ^ [_1581537, _1581539, _1581541, _1581543, _1581545, _1581547, _1581549] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1581537, _1581539, _1581541, _1581543), _1581545), _1581547), _1581549) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1581539, _1581541, _1581543), _1581547), hAPP(_1581545, _1581549)))], (40508 ^ _781404) ^ [_1570796, _1570798, _1570800] : [-(hBOOL(hAPP(hAPP(c_member(_1570796), _1570798), c_Wellfounded_Oacc(_1570796, _1570800)))), 40512 ^ _781404 : [(40515 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1570796), 40511 ^ [_1570796, _1570798, _1570800]), c_Wellfounded_Oacc(_1570796, _1570800)))], (40513 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570796, _1570796)), hAPP(hAPP(c_Product__Type_OPair(_1570796, _1570796), 40511 ^ [_1570796, _1570798, _1570800]), _1570798)), _1570800)))]]], (25841 ^ _781404) ^ [_1243266, _1243268] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1243266), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1243268)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1243266), 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)))), _1243268)))], (33109 ^ _781404) ^ [_1378799, _1378801, _1378803, _1378805, _1378807] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1378799, tc_fun(_1378801, tc_HOL_Obool)), _1378803), hAPP(hAPP(c_COMBS(_1378799, tc_fun(_1378801, tc_HOL_Obool), tc_fun(_1378801, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1378801, tc_HOL_Obool), tc_fun(tc_fun(_1378801, tc_HOL_Obool), tc_fun(_1378801, tc_HOL_Obool)), _1378799), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1378801, tc_HOL_Obool))), _1378805)), _1378807)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1378801, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1378801, tc_HOL_Obool), hAPP(c_Set_Oimage(_1378799, tc_fun(_1378801, tc_HOL_Obool), _1378805), _1378803))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1378801, tc_HOL_Obool), hAPP(c_Set_Oimage(_1378799, tc_fun(_1378801, tc_HOL_Obool), _1378807), _1378803))))], (4290 ^ _781404) ^ [_846383, _846385] : [_846385 = _846383, -(c_List_Onth(_846385) = c_List_Onth(_846383))], (20115 ^ _781404) ^ [_1138607, _1138609] : [c_Int_OBit1(_1138607) = c_Int_OBit0(_1138609)], (19462 ^ _781404) ^ [_1127499] : [-(c_Int_Osucc(c_Int_Opred(_1127499)) = _1127499)], (44375 ^ _781404) ^ [_1668444, _1668446, _1668448, _1668450] : [hBOOL(hAPP(hAPP(c_member(_1668444), _1668446), hAPP(c_List_Oset(_1668444), hAPP(hAPP(c_List_Odrop(_1668444), _1668448), _1668450)))), -(hBOOL(hAPP(hAPP(c_member(_1668444), _1668446), hAPP(c_List_Oset(_1668444), _1668450))))], (6616 ^ _781404) ^ [_887177, _887179, _887181] : [class_Complete__Lattice_Ocomplete__lattice(_887177), 6619 ^ _781404 : [(6620 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887177), _887179), c_Complete__Lattice_OInf__class_OInf(_887177, _887181))), 6623 ^ _781404 : [(6624 ^ _781404) ^ [_887335] : [hBOOL(hAPP(hAPP(c_member(_887177), _887335), _887181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887177), _887179), _887335)))]]], (6630 ^ _781404) ^ [] : [6632 ^ _781404 : [(6635 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887177), _887179), 6631 ^ [_887177, _887179, _887181]))], (6633 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887177), 6631 ^ [_887177, _887179, _887181]), _887181)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887177), _887179), c_Complete__Lattice_OInf__class_OInf(_887177, _887181))))]]], (48147 ^ _781404) ^ [_1750457, _1750459, _1750461, _1750463, _1750465, _1750467, _1750469, _1750471] : [48149 ^ _781404 : [(48152 ^ _781404) ^ [] : [hAPP(c_Fun_Ocomp(_1750461, _1750461, _1750463, hAPP(_1750465, 48148 ^ [_1750457, _1750459, _1750461, _1750463, _1750465, _1750467, _1750469, _1750471])), _1750467) = hAPP(c_Fun_Ocomp(_1750463, _1750461, _1750463, _1750467), hAPP(_1750469, 48148 ^ [_1750457, _1750459, _1750461, _1750463, _1750465, _1750467, _1750469, _1750471]))], (48150 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750457), 48148 ^ [_1750457, _1750459, _1750461, _1750463, _1750465, _1750467, _1750469, _1750471]), hAPP(c_List_Oset(_1750457), _1750459))))]], -(hAPP(c_List_Ofoldl(_1750461, _1750457, hAPP(c_COMBC(_1750457, _1750461, _1750461), _1750465), hAPP(_1750467, _1750471)), _1750459) = hAPP(_1750467, hAPP(c_List_Ofoldl(_1750463, _1750457, hAPP(c_COMBC(_1750457, _1750463, _1750463), _1750469), _1750471), _1750459)))], (2948 ^ _781404) ^ [_825150, _825152] : [_825152 = _825150, -(c_Rings_Oinverse__class_Odivide(_825152) = c_Rings_Oinverse__class_Odivide(_825150))], (8297 ^ _781404) ^ [_921277, _921279, _921281, _921283] : [hAPP(c_Set_Oimage(_921277, _921279, _921281), _921283) = c_Orderings_Obot__class_Obot(tc_fun(_921279, tc_HOL_Obool)), -(_921283 = c_Orderings_Obot__class_Obot(tc_fun(_921277, tc_HOL_Obool)))], (20273 ^ _781404) ^ [_1141305] : [-(c_Int_Osucc(c_Int_OBit1(_1141305)) = c_Int_OBit0(c_Int_Osucc(_1141305)))], (17383 ^ _781404) ^ [_1091529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1091529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1091529)))], (40400 ^ _781404) ^ [_1568160, _1568162, _1568164] : [c_Wellfounded_OwfP(_1568160, hAPP(_1568162, 40401 ^ [_1568160, _1568162, _1568164])), 40408 ^ _781404 : [(40411 ^ _781404) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568160, tc_HOL_Obool)), c_Predicate_ODomainP(_1568160, _1568160, hAPP(_1568162, 40406 ^ [_1568160, _1568162, _1568164]))), c_Predicate_ORangeP(_1568160, _1568160, hAPP(_1568162, 40407 ^ [_1568160, _1568162, _1568164]))) = c_Orderings_Obot__class_Obot(tc_fun(_1568160, tc_HOL_Obool))], (40409 ^ _781404) ^ [] : [hAPP(_1568162, 40406 ^ [_1568160, _1568162, _1568164]) = hAPP(_1568162, 40407 ^ [_1568160, _1568162, _1568164])]], -(c_Wellfounded_OwfP(_1568160, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1568164, tc_fun(_1568160, tc_fun(_1568160, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1568164, tc_HOL_Obool))), _1568162)))], (35061 ^ _781404) ^ [_1434380, _1434382] : [35062 ^ _781404 : [(35065 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434382), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35063 ^ _781404) ^ [] : [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), _1434380), _1434382)))]], -(c_Divides_OnegDivAlg(_1434380, _1434382) = 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), _1434380), _1434382)))], (52792 ^ _781404) ^ [_1843054, _1843056] : [hBOOL(_1843054), -(hBOOL(hAPP(hAPP(c_fdisj, _1843056), _1843054)))], (20019 ^ _781404) ^ [_1137006] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137006))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1137006)))))], (8828 ^ _781404) ^ [_930407, _930409] : [class_Lattices_Oboolean__algebra(_930407), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930407), _930409), hAPP(c_Groups_Ouminus__class_Ouminus(_930407), _930409)) = c_Orderings_Obot__class_Obot(_930407))], (52638 ^ _781404) ^ [_1841292] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1841292)))], (37270 ^ _781404) ^ [_1481308, _1481310] : [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), _1481308), _1481310)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1481308), _1481310)))], (38620 ^ _781404) ^ [_1515964, _1515966, _1515968, _1515970, _1515972, _1515974] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515964, _1515966)), hAPP(hAPP(c_Product__Type_OPair(_1515964, _1515966), _1515968), _1515970)), hAPP(hAPP(c_Product__Type_OSigma(_1515964, _1515966), _1515972), _1515974)))), hBOOL(hAPP(hAPP(c_member(_1515964), _1515968), _1515972)), hBOOL(hAPP(hAPP(c_member(_1515966), _1515970), hAPP(_1515974, _1515968)))], (3724 ^ _781404) ^ [_837244, _837246] : [_837246 = _837244, -(c_List_Oreturn__list(_837246) = c_List_Oreturn__list(_837244))], (49366 ^ _781404) ^ [_1776756, _1776758, _1776760] : [hBOOL(hAPP(hAPP(c_member(_1776756), _1776760), hAPP(c_List_Oset(_1776756), _1776758))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1776756), _1776758), _1776760)))], (8894 ^ _781404) ^ [_931792, _931794, _931796] : [class_Orderings_Oorder(_931792), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931792, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_931792, _931794, _931796)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_931792), _931796)) = c_Orderings_Obot__class_Obot(tc_fun(_931792, tc_HOL_Obool)))], (51189 ^ _781404) ^ [_1816191, _1816193, _1816195, _1816197, _1816199] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1816191, _1816193, tc_HOL_Obool, _1816195), _1816197), _1816199)), -(hBOOL(hAPP(_1816195, hAPP(hAPP(c_Product__Type_OPair(_1816191, _1816193), _1816197), _1816199))))], (19313 ^ _781404) ^ [_1124915, _1124917, _1124919] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124915)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124917)), _1124919)) = 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), _1124915), _1124917))), _1124919))], (42780 ^ _781404) ^ [_1630763, _1630765, _1630767, _1630769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630763), _1630765)), -(hAPP(hAPP(c_List_Onth(_1630767), hAPP(hAPP(c_List_Otake(_1630767), _1630765), _1630769)), _1630763) = hAPP(hAPP(c_List_Onth(_1630767), _1630769), _1630763))], (44357 ^ _781404) ^ [_1667954, _1667956, _1667958] : [-(c_List_Obutlast(_1667954, hAPP(hAPP(c_List_Odrop(_1667954), _1667956), _1667958)) = hAPP(hAPP(c_List_Odrop(_1667954), _1667956), c_List_Obutlast(_1667954, _1667958)))], (2710 ^ _781404) ^ [_821453, _821455, _821457, _821459, _821461, _821463, _821465, _821467] : [-(c_Product__Type_Oapsnd(_821467, _821463, _821459, _821455) = c_Product__Type_Oapsnd(_821465, _821461, _821457, _821453)), _821467 = _821465, _821463 = _821461, _821459 = _821457, _821455 = _821453], (24825 ^ _781404) ^ [_1226479] : [24827 ^ _781404 : [(24830 ^ _781404) ^ [] : [hBOOL(hAPP(_1226479, hAPP(c_Int_Onat, 24826 ^ [_1226479])))], (24828 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24826 ^ [_1226479])))]], 24831 ^ _781404 : [(24832 ^ _781404) ^ [_1226612] : [-(hBOOL(hAPP(_1226479, _1226612)))]]], (41235 ^ _781404) ^ [_1588733, _1588735, _1588737] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588733, _1588733), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588733, _1588733), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588733, _1588735)), c_Transitive__Closure_Ortrancl(_1588733, _1588737))), c_Transitive__Closure_Ortrancl(_1588733, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588733, _1588733), tc_HOL_Obool)), _1588735), _1588737)))))], (42983 ^ _781404) ^ [_1637085, _1637087, _1637089] : [-(_1637085 = _1637087), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637089)), _1637085) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637089)), _1637087), 42989 ^ _781404 : [(42992 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1637089, _1637089, tc_HOL_Obool), c_fequal), 42988 ^ [_1637085, _1637087, _1637089]))], (42990 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637089, _1637089)), 42988 ^ [_1637085, _1637087, _1637089]), hAPP(c_List_Oset(tc_prod(_1637089, _1637089)), hAPP(hAPP(c_List_Ozip(_1637089, _1637089), _1637085), _1637087)))))]]], (14573 ^ _781404) ^ [_1036844, _1036846] : [class_Finite__Set_Ofinite(_1036844), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1036844), _1036846)))], (41968 ^ _781404) ^ [_1606670, _1606672, _1606674, _1606676, _1606678] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606670, _1606670)), hAPP(hAPP(c_Product__Type_OPair(_1606670, _1606670), _1606672), _1606674)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1606670, _1606670), tc_HOL_Obool), _1606676), _1606678))), 41973 ^ _781404 : [(41976 ^ _781404) ^ [] : [-(_1606672 = _1606674)], (41974 ^ _781404) ^ [] : [-(_1606676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41979 ^ _781404 : [(41984 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606670, _1606670)), hAPP(hAPP(c_Product__Type_OPair(_1606670, _1606670), 41977 ^ [_1606670, _1606672, _1606674, _1606676, _1606678]), _1606674)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1606670, _1606670), tc_HOL_Obool), 41978 ^ [_1606670, _1606672, _1606674, _1606676, _1606678]), _1606678))))], (41982 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606670, _1606670)), hAPP(hAPP(c_Product__Type_OPair(_1606670, _1606670), _1606672), 41977 ^ [_1606670, _1606672, _1606674, _1606676, _1606678])), _1606678)))], (41980 ^ _781404) ^ [] : [-(_1606676 = hAPP(c_Nat_OSuc, 41978 ^ [_1606670, _1606672, _1606674, _1606676, _1606678]))]]], (42483 ^ _781404) ^ [_1622270, _1622272, _1622274, _1622276] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622270), tc_List_Olist(_1622270))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622270), tc_List_Olist(_1622270)), _1622272), _1622274)), c_List_Olistrel(_1622270, _1622276))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622270), tc_List_Olist(_1622270))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622270), tc_List_Olist(_1622270)), _1622272), _1622274)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1622270), c_List_Olistrel1(_1622270, _1622276)))))], (33568 ^ _781404) ^ [_1392639, _1392641, _1392643, _1392645, _1392647, _1392649] : [-(_1392639 = _1392641), -(hAPP(c_Fun_Ofun__upd(_1392643, _1392645, _1392647, _1392641, _1392649), _1392639) = hAPP(_1392647, _1392639))], (44681 ^ _781404) ^ [_1675161, _1675163, _1675165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675161)), _1675163)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1675161, _1675165), _1675163) = _1675163)], (8124 ^ _781404) ^ [_917582, _917584] : [class_Orderings_Oorder(_917582), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_917582, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_917582), _917584)), hAPP(c_SetInterval_Oord__class_OatLeast(_917582), _917584)) = hAPP(hAPP(c_Set_Oinsert(_917582), _917584), c_Orderings_Obot__class_Obot(tc_fun(_917582, tc_HOL_Obool))))], (46285 ^ _781404) ^ [_1710227, _1710229, _1710231, _1710233] : [-(_1710227 = _1710229), -(hAPP(c_List_OremoveAll(_1710231, _1710227), hAPP(hAPP(c_List_Olist_OCons(_1710231), _1710229), _1710233)) = hAPP(hAPP(c_List_Olist_OCons(_1710231), _1710229), hAPP(c_List_OremoveAll(_1710231, _1710227), _1710233)))], (43493 ^ _781404) ^ [_1648548, _1648550, _1648552, _1648554] : [_1648548 = _1648550, -(c_List_Oremove1(_1648552, _1648548, hAPP(hAPP(c_List_Olist_OCons(_1648552), _1648550), _1648554)) = _1648554)], (43166 ^ _781404) ^ [_1641301, _1641303, _1641305, _1641307] : [-(hAPP(hAPP(c_List_Olist__update(_1641301, hAPP(hAPP(c_List_Olist_OCons(_1641301), _1641303), _1641305)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1641307) = hAPP(hAPP(c_List_Olist_OCons(_1641301), _1641307), _1641305))], (49406 ^ _781404) ^ [_1777536, _1777538, _1777540] : [c_List_Olist__ex1(_1777536, _1777538, _1777540), 49410 ^ _781404 : [(49415 ^ _781404) ^ [_1777782] : [-(_1777782 = 49409 ^ [_1777536, _1777538, _1777540]), hBOOL(hAPP(hAPP(c_member(_1777536), _1777782), hAPP(c_List_Oset(_1777536), _1777540))), hBOOL(hAPP(_1777538, _1777782))], (49413 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1777538, 49409 ^ [_1777536, _1777538, _1777540])))], (49411 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777536), 49409 ^ [_1777536, _1777538, _1777540]), hAPP(c_List_Oset(_1777536), _1777540))))]]], (33829 ^ _781404) ^ [_1400041, _1400043, _1400045, _1400047, _1400049, _1400051, _1400053] : [class_Rings_Osemiring__0(_1400041), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400041), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400043, _1400041), _1400045), _1400047)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400049, _1400041), _1400051), _1400053)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400043, _1400041), hAPP(hAPP(c_COMBC(_1400043, tc_fun(_1400049, tc_HOL_Obool), _1400041), hAPP(hAPP(c_COMBB(tc_fun(_1400049, _1400041), tc_fun(tc_fun(_1400049, tc_HOL_Obool), _1400041), _1400043), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400049, _1400041)), hAPP(hAPP(c_COMBC(_1400043, tc_fun(_1400049, _1400041), tc_fun(_1400049, _1400041)), hAPP(hAPP(c_COMBB(tc_fun(_1400041, _1400041), tc_fun(tc_fun(_1400049, _1400041), tc_fun(_1400049, _1400041)), _1400043), c_COMBB(_1400041, _1400041, _1400049)), hAPP(hAPP(c_COMBB(_1400041, tc_fun(_1400041, _1400041), _1400043), c_Groups_Otimes__class_Otimes(_1400041)), _1400045))), _1400051))), _1400053)), _1400047))], (45563 ^ _781404) ^ [_1694133, _1694135, _1694137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1694133), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1694135), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1694135)), _1694137)))), -(hBOOL(hAPP(hAPP(c_member(_1694135), hAPP(c_Random_Opick(_1694135, _1694137), _1694133)), hAPP(c_List_Oset(_1694135), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1694135), _1694135), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1694135)), _1694137)))))], (20497 ^ _781404) ^ [_1145098] : [class_Rings_Osemiring__1(_1145098), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1145098), c_Groups_Ozero__class_Ozero(_1145098)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1145098))], (5729 ^ _781404) ^ [_871804, _871806, _871808] : [c_Hoare__Mirabelle_Ohoare__valids(_871804, _871806, _871808), 5732 ^ _781404 : [(5733 ^ _781404) ^ [_871913] : [5735 ^ _781404 : [(5738 ^ _781404) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_871804, _871913, 5734 ^ [_871804, _871806, _871808, _871913])], (5736 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_871804)), 5734 ^ [_871804, _871806, _871808, _871913]), _871806)))]], 5739 ^ _781404 : [(5740 ^ _781404) ^ [_872085] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_871804)), _872085), _871808)), -(c_Hoare__Mirabelle_Otriple__valid(_871804, _871913, _872085))]]]]], (48895 ^ _781404) ^ [_1766308, _1766310, _1766312, _1766314, _1766316] : [_1766308 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1766310, _1766312, _1766314, _1766316), _1766308) = c_Lazy__Sequence_Ohit__bound(_1766312))], (52358 ^ _781404) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (23507 ^ _781404) ^ [_1203309] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203309) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (46517 ^ _781404) ^ [_1715945, _1715947, _1715949] : [46519 ^ _781404 : [(46522 ^ _781404) ^ [] : [hBOOL(hAPP(_1715947, 46518 ^ [_1715945, _1715947, _1715949]))], (46520 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715945), 46518 ^ [_1715945, _1715947, _1715949]), hAPP(c_List_Oset(_1715945), _1715949))))]], -(hAPP(c_List_Ofilter(_1715945, _1715947), _1715949) = _1715949)], (43322 ^ _781404) ^ [_1644854, _1644856] : [hAPP(c_Finite__Set_Ocard(_1644854), hAPP(c_List_Oset(_1644854), _1644856)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644854)), _1644856), -(hBOOL(hAPP(c_List_Odistinct(_1644854), _1644856)))], (39556 ^ _781404) ^ [_1546669, _1546671, _1546673, _1546675] : [class_Groups_Ocomm__monoid__add(_1546669), c_Fun_Oinj__on(_1546671, _1546669, _1546673, _1546675), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1546671, _1546669), _1546673), _1546675) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1546669, _1546669), c_Fun_Oid(_1546669)), hAPP(c_Set_Oimage(_1546671, _1546669, _1546673), _1546675)))], (47033 ^ _781404) ^ [_1727163, _1727165, _1727167, _1727169] : [class_Orderings_Olinorder(_1727163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727163), _1727165), _1727167)), c_List_Olinorder__class_Osorted(_1727163, hAPP(hAPP(c_List_Olist_OCons(_1727163), _1727167), _1727169)), -(c_List_Olinorder__class_Osorted(_1727163, hAPP(hAPP(c_List_Olist_OCons(_1727163), _1727165), hAPP(hAPP(c_List_Olist_OCons(_1727163), _1727167), _1727169))))], (39630 ^ _781404) ^ [_1548997, _1548999, _1549001, _1549003, _1549005, _1549007] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1548997, _1548999, _1549001), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1548997, _1548999), tc_HOL_Obool)), _1549003), _1549005)), _1549007) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1548997, _1549001), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1548997, _1548999, _1549001), _1549003), _1549007)), hAPP(hAPP(c_Relation_Orel__comp(_1548997, _1548999, _1549001), _1549005), _1549007)))], (3352 ^ _781404) ^ [_831420, _831422, _831424, _831426] : [-(c_List_Olistsp(_831426, _831422) = c_List_Olistsp(_831424, _831420)), _831426 = _831424, _831422 = _831420], (4786 ^ _781404) ^ [_854243, _854245, _854247, _854249, _854251, _854253] : [-(c_Relation_OImage(_854253, _854249, _854245) = c_Relation_OImage(_854251, _854247, _854243)), _854253 = _854251, _854249 = _854247, _854245 = _854243], (11559 ^ _781404) ^ [_979074, _979076, _979078, _979080] : [hBOOL(hAPP(hAPP(c_member(_979074), _979076), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979074, tc_HOL_Obool)), _979078), _979080))), -(hBOOL(hAPP(hAPP(c_member(_979074), _979076), _979078))), -(hBOOL(hAPP(hAPP(c_member(_979074), _979076), _979080)))], (17679 ^ _781404) ^ [_1096562, _1096564, _1096566] : [class_Complete__Lattice_Ocomplete__lattice(_1096562), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096562), _1096564)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1096562), _1096566), c_Complete__Lattice_OSup__class_OSup(_1096562, _1096564)) = hAPP(hAPP(c_Finite__Set_Ofold(_1096562, _1096562, c_Lattices_Osemilattice__sup__class_Osup(_1096562)), _1096566), _1096564))], (15146 ^ _781404) ^ [_1048362, _1048364, _1048366, _1048368, _1048370] : [c_Finite__Set_Ofolding__one(_1048362, _1048364, _1048366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048362), _1048368)), 15153 ^ _781404 : [(15160 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048362, tc_HOL_Obool)), _1048368), hAPP(hAPP(c_Set_Oinsert(_1048362), _1048370), c_Orderings_Obot__class_Obot(tc_fun(_1048362, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1048362, tc_HOL_Obool))), -(hAPP(_1048366, hAPP(hAPP(c_Set_Oinsert(_1048362), _1048370), _1048368)) = hAPP(hAPP(_1048364, _1048370), hAPP(_1048366, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048362, tc_HOL_Obool)), _1048368), hAPP(hAPP(c_Set_Oinsert(_1048362), _1048370), c_Orderings_Obot__class_Obot(tc_fun(_1048362, tc_HOL_Obool)))))))], (15154 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048362, tc_HOL_Obool)), _1048368), hAPP(hAPP(c_Set_Oinsert(_1048362), _1048370), c_Orderings_Obot__class_Obot(tc_fun(_1048362, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1048362, tc_HOL_Obool)), -(hAPP(_1048366, hAPP(hAPP(c_Set_Oinsert(_1048362), _1048370), _1048368)) = _1048370)]]], (27923 ^ _781404) ^ [_1280833, _1280835, _1280837] : [class_Rings_Odivision__ring(_1280833), -(_1280835 = c_Groups_Ozero__class_Ozero(_1280833)), 27930 ^ _781404 : [(27937 ^ _781404) ^ [] : [_1280837 = _1280835, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280833), _1280837), _1280835) = c_Groups_Oone__class_Oone(_1280833))], (27931 ^ _781404) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280833), _1280837), _1280835) = c_Groups_Oone__class_Oone(_1280833), -(_1280837 = _1280835)]]], (27373 ^ _781404) ^ [_1270221, _1270223] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1270221), _1270223))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1270221))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1270223))))], (45497 ^ _781404) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13532 ^ _781404) ^ [_1016934, _1016936, _1016938, _1016940, _1016942] : [class_Groups_Ocomm__monoid__add(_1016934), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016936), _1016938)), -(hBOOL(hAPP(hAPP(c_member(_1016936), _1016940), _1016938))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1016936, _1016934), _1016942), hAPP(hAPP(c_Set_Oinsert(_1016936), _1016940), _1016938)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016934), hAPP(_1016942, _1016940)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1016936, _1016934), _1016942), _1016938)))], (35762 ^ _781404) ^ [_1448885, _1448887, _1448889, _1448891] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1448885, _1448887), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1448889), _1448891))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1448885), _1448887) = _1448889)], (2860 ^ _781404) ^ [_823790, _823792, _823794, _823796, _823798, _823800, _823802, _823804] : [-(c_Random_Oiterate(_823804, _823800, _823796, _823792) = c_Random_Oiterate(_823802, _823798, _823794, _823790)), _823804 = _823802, _823800 = _823798, _823796 = _823794, _823792 = _823790], (26907 ^ _781404) ^ [_1261660, _1261662] : [class_Groups_Oordered__ab__group__add__abs(_1261660), -(hAPP(c_Groups_Oabs__class_Oabs(_1261660), hAPP(c_Groups_Ouminus__class_Ouminus(_1261660), _1261662)) = hAPP(c_Groups_Oabs__class_Oabs(_1261660), _1261662))], (3048 ^ _781404) ^ [_826634, _826636, _826638, _826640] : [-(c_List_Olenlex(_826640, _826636) = c_List_Olenlex(_826638, _826634)), _826640 = _826638, _826636 = _826634], (13399 ^ _781404) ^ [_1014373, _1014375, _1014377, _1014379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014373), _1014375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014377), _1014379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014373), _1014377)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014375), _1014379))))], (5084 ^ _781404) ^ [_858938, _858940] : [_858940 = _858938, -(c_Lattices_Osemilattice__sup__class_Osup(_858940) = c_Lattices_Osemilattice__sup__class_Osup(_858938))], (32246 ^ _781404) ^ [_1361752, _1361754, _1361756, _1361758] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1361752), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361752), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361752), _1361754), _1361756)), _1361758) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361752), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361752), _1361754), _1361758)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361752), _1361756), _1361758)))], (50179 ^ _781404) ^ [_1795749, _1795751, _1795753] : [c_Relation_Osym(_1795749, _1795751), c_Relation_Osym(_1795749, _1795753), -(c_Relation_Osym(_1795749, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1795749, _1795749), tc_HOL_Obool)), _1795751), _1795753)))], (32860 ^ _781404) ^ [_1373499, _1373501, _1373503] : [class_Orderings_Olinorder(_1373499), hAPP(_1373501, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373499), 32865 ^ [_1373499, _1373501, _1373503]), 32866 ^ [_1373499, _1373501, _1373503])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373499), hAPP(_1373501, 32865 ^ [_1373499, _1373501, _1373503])), hAPP(_1373501, 32866 ^ [_1373499, _1373501, _1373503])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373499), _1373503)), -(_1373503 = c_Orderings_Obot__class_Obot(tc_fun(_1373499, tc_HOL_Obool))), -(hAPP(_1373501, c_Big__Operators_Olattice_OSup__fin(_1373499, c_Orderings_Oord__class_Omax(_1373499), _1373503)) = c_Big__Operators_Olattice_OSup__fin(_1373499, c_Orderings_Oord__class_Omax(_1373499), hAPP(c_Set_Oimage(_1373499, _1373499, _1373501), _1373503)))], (21817 ^ _781404) ^ [_1169390, _1169392, _1169394, _1169396] : [class_Rings_Olinordered__semiring__strict(_1169390), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169390), _1169392), _1169394)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169390), c_Groups_Ozero__class_Ozero(_1169390)), _1169396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169390), _1169392), _1169396)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169390), _1169394), _1169396))))], (45377 ^ _781404) ^ [_1690223, _1690225, _1690227, _1690229] : [hBOOL(hAPP(c_List_Odistinct(_1690223), hAPP(hAPP(c_List_Omap(_1690225, _1690223), _1690227), _1690229))), 45380 ^ _781404 : [(45383 ^ _781404) ^ [] : [-(c_Fun_Oinj__on(_1690225, _1690223, _1690227, hAPP(c_List_Oset(_1690225), _1690229)))], (45381 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1690225), _1690229)))]]], (11293 ^ _781404) ^ [_973239, _973241, _973243, _973245, _973247] : [c_Fun_Oinj__on(_973239, _973241, _973243, c_Orderings_Otop__class_Otop(tc_fun(_973239, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_973239, _973241, _973243), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_973239, tc_HOL_Obool)), _973245), _973247)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_973241, tc_HOL_Obool)), hAPP(c_Set_Oimage(_973239, _973241, _973243), _973245)), hAPP(c_Set_Oimage(_973239, _973241, _973243), _973247)))], (39985 ^ _781404) ^ [_1558612, _1558614, _1558616] : [c_Wellfounded_Owf(_1558612, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1558612, _1558612), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1558612, _1558612), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1558612, _1558612, _1558612), _1558614), _1558614)), hAPP(hAPP(c_Relation_Orel__comp(_1558612, _1558612, _1558612), _1558616), _1558614))), _1558616)), -(c_Wellfounded_Owf(_1558612, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1558612, _1558612), tc_HOL_Obool)), _1558614), _1558616)))], (5282 ^ _781404) ^ [_862023, _862025, _862027, _862029, _862031, _862033] : [-(c_Lazy__Sequence_Oappend(_862033, _862029, _862025) = c_Lazy__Sequence_Oappend(_862031, _862027, _862023)), _862033 = _862031, _862029 = _862027, _862025 = _862023], (11061 ^ _781404) ^ [_969205] : [11062 ^ _781404 : [(11063 ^ _781404) ^ [_969247] : [_969205 = hAPP(c_Nat_OSuc, _969247)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _969205)))], (18667 ^ _781404) ^ [_1114530, _1114532] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114530), _1114532))), -(c_Nat__Transfer_Otsub(_1114532, _1114530) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5380 ^ _781404) ^ [_863610, _863612] : [_863612 = _863610, -(c_Power_Opower__class_Opower(_863612) = c_Power_Opower__class_Opower(_863610))], (7073 ^ _781404) ^ [_895920, _895922, _895924, _895926] : [class_Lattices_Osemilattice__sup(_895920), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895920), _895922), _895924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895920), _895926), _895924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895920), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895920), _895922), _895926)), _895924)))], (26375 ^ _781404) ^ [_1251772, _1251774] : [c_Nat__Transfer_Ois__nat(_1251772), c_Nat__Transfer_Ois__nat(_1251774), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1251772, _1251774)))], (47989 ^ _781404) ^ [_1746831, _1746833] : [class_Orderings_Olinorder(_1746831), 47992 ^ _781404 : [(48013 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1746831, _1746833)), 48014 ^ _781404 : [(48017 ^ _781404) ^ [_1747391, _1747393] : [_1746833 = hAPP(hAPP(c_List_Olist_OCons(_1746831), _1747391), _1747393), 48023 ^ _781404 : [(48026 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746831), _1747391), 48022 ^ [_1746831, _1746833, _1747391, _1747393]))], (48024 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1746831), 48022 ^ [_1746831, _1746833, _1747391, _1747393]), hAPP(c_List_Oset(_1746831), _1747393))))]], c_List_Olinorder__class_Osorted(_1746831, _1747393)], (48015 ^ _781404) ^ [] : [_1746833 = c_List_Olist_ONil(_1746831)]]], (47993 ^ _781404) ^ [] : [c_List_Olinorder__class_Osorted(_1746831, _1746833), -(_1746833 = c_List_Olist_ONil(_1746831)), 48002 ^ _781404 : [(48005 ^ _781404) ^ [_1747165] : [hBOOL(hAPP(hAPP(c_member(_1746831), _1747165), hAPP(c_List_Oset(_1746831), 48000 ^ [_1746831, _1746833]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746831), 48001 ^ [_1746831, _1746833]), _1747165)))], (48011 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1746831, 48000 ^ [_1746831, _1746833]))], (48003 ^ _781404) ^ [] : [-(_1746833 = hAPP(hAPP(c_List_Olist_OCons(_1746831), 48001 ^ [_1746831, _1746833]), 48000 ^ [_1746831, _1746833]))]]]]], (32202 ^ _781404) ^ [_1361023, _1361025, _1361027, _1361029] : [class_Orderings_Olinorder(_1361023), 32205 ^ _781404 : [(32206 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361023), _1361025), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361023), _1361027), _1361029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361023), _1361025), _1361027))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361023), _1361025), _1361029)))], (32216 ^ _781404) ^ [] : [32217 ^ _781404 : [(32220 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361023), _1361025), _1361029))], (32218 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361023), _1361025), _1361027))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361023), _1361025), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361023), _1361027), _1361029))))]]], (43681 ^ _781404) ^ [_1652059, _1652061] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1652059), _1652061))), -(c_List_Oupto(_1652059, _1652061) = c_List_Olist_ONil(tc_Int_Oint))], (46798 ^ _781404) ^ [_1722857, _1722859] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1722857), _1722859)) = c_List_Oupt(_1722857, _1722859))], (5713 ^ _781404) ^ [_871524, _871526, _871528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871524, tc_HOL_Obool)), _871526), _871528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871524, tc_HOL_Obool)), _871528), _871526)), -(_871526 = _871528)], (26281 ^ _781404) ^ [_1250431, _1250433] : [class_Rings_Oring__1(_1250431), 26284 ^ _781404 : [(26291 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250433), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1250431), _1250433) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1250431), hAPP(c_Int_Onat, _1250433)))], (26285 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250433), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1250431), _1250433) = hAPP(c_Groups_Ouminus__class_Ouminus(_1250431), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1250431), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1250433)))))]]], (29947 ^ _781404) ^ [_1318146, _1318148, _1318150] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318146), _1318148)), 29950 ^ _781404 : [(29951 ^ _781404) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318146, tc_Nat_Onat), _1318150), _1318148) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 29954 ^ _781404 : [(29955 ^ _781404) ^ [_1318308] : [hBOOL(hAPP(hAPP(c_member(_1318146), _1318308), _1318148)), -(hAPP(_1318150, _1318308) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (29961 ^ _781404) ^ [] : [29963 ^ _781404 : [(29966 ^ _781404) ^ [] : [hAPP(_1318150, 29962 ^ [_1318146, _1318148, _1318150]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (29964 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318146), 29962 ^ [_1318146, _1318148, _1318150]), _1318148)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318146, tc_Nat_Onat), _1318150), _1318148) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (38743 ^ _781404) ^ [_1519237, _1519239, _1519241, _1519243] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519237, _1519239), _1519241), _1519243) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519237, tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool)), _1519241), hAPP(hAPP(c_COMBS(_1519237, tc_fun(_1519239, tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool)), tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519239, tc_HOL_Obool), tc_fun(tc_fun(_1519239, tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool)), tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool)), _1519237), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519239, tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool))), _1519243)), hAPP(hAPP(c_COMBC(_1519237, tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool), tc_fun(_1519239, tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1519239, tc_fun(tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool), tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool), tc_fun(_1519239, tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool))), _1519237), c_COMBC(_1519239, tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool), tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1519239, tc_prod(_1519237, _1519239)), tc_fun(_1519239, tc_fun(tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool), tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool))), _1519237), hAPP(c_COMBB(tc_prod(_1519237, _1519239), tc_fun(tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool), tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool)), _1519239), c_Set_Oinsert(tc_prod(_1519237, _1519239)))), c_Product__Type_OPair(_1519237, _1519239)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519237, _1519239), tc_HOL_Obool))))))], (44022 ^ _781404) ^ [_1659935, _1659937, _1659939] : [_1659935 = _1659937, -(_1659935 = hAPP(hAPP(c_List_Oappend(_1659939), c_List_Olist_ONil(_1659939)), _1659937))], (43775 ^ _781404) ^ [_1654095, _1654097, _1654099] : [class_Orderings_Olinorder(_1654095), hBOOL(hAPP(c_Finite__Set_Ofinite(_1654095), _1654097)), -(c_List_Olinorder__class_Osorted__list__of__set(_1654095, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1654095, tc_HOL_Obool)), _1654097), hAPP(hAPP(c_Set_Oinsert(_1654095), _1654099), c_Orderings_Obot__class_Obot(tc_fun(_1654095, tc_HOL_Obool))))) = c_List_Oremove1(_1654095, _1654099, c_List_Olinorder__class_Osorted__list__of__set(_1654095, _1654097)))], (28991 ^ _781404) ^ [_1300487, _1300489, _1300491] : [class_Fields_Olinordered__field(_1300487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300487), c_Groups_Ozero__class_Ozero(_1300487)), _1300489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300487), c_Groups_Ozero__class_Ozero(_1300487)), _1300491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300487), c_Groups_Ozero__class_Ozero(_1300487)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1300487), _1300489), _1300491))))], (31944 ^ _781404) ^ [_1356312] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1356312), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1356312)], (8209 ^ _781404) ^ [_919433, _919435, _919437, _919439] : [c_Hoare__Mirabelle_Ohoare__derivs(_919433, _919435, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_919433)), _919437), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_919433), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_919433, _919435, _919439), -(c_Hoare__Mirabelle_Ohoare__derivs(_919433, _919435, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_919433)), _919437), _919439)))], (20733 ^ _781404) ^ [_1149044, _1149046, _1149048] : [class_Rings_Olinordered__idom(_1149044), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149044), c_Groups_Ozero__class_Ozero(_1149044)), hAPP(hAPP(c_Power_Opower__class_Opower(_1149044), _1149046), 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)))), _1149048)))))], (36125 ^ _781404) ^ [_1455630, _1455632, _1455634] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1455630, _1455632), _1455634)), 36128 ^ _781404 : [(36129 ^ _781404) ^ [_1455715] : [hBOOL(hAPP(hAPP(_1455632, _1455715), _1455634)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1455630, _1455632), _1455715)))]]], (33671 ^ _781404) ^ [_1395440, _1395442, _1395444, _1395446] : [33673 ^ _781404 : [(33676 ^ _781404) ^ [] : [hAPP(_1395446, 33672 ^ [_1395440, _1395442, _1395444, _1395446]) = c_Orderings_Obot__class_Obot(tc_fun(_1395442, tc_HOL_Obool))], (33674 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1395440), 33672 ^ [_1395440, _1395442, _1395444, _1395446]), _1395444)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395440, tc_fun(_1395442, tc_HOL_Obool)), _1395444), _1395446) = c_Orderings_Obot__class_Obot(tc_fun(_1395442, tc_HOL_Obool)))], (42786 ^ _781404) ^ [_1630902, _1630904, _1630906, _1630908] : [-(hAPP(hAPP(c_List_Otake(_1630902), hAPP(c_Nat_OSuc, _1630904)), hAPP(hAPP(c_List_Olist_OCons(_1630902), _1630906), _1630908)) = hAPP(hAPP(c_List_Olist_OCons(_1630902), _1630906), hAPP(hAPP(c_List_Otake(_1630902), _1630904), _1630908)))], (29619 ^ _781404) ^ [_1311775, _1311777, _1311779, _1311781] : [class_Fields_Ofield(_1311775), -(_1311777 = c_Groups_Ozero__class_Ozero(_1311775)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1311775), _1311779), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311775), _1311781), _1311777)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311775), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1311775), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311775), _1311777), _1311779)), _1311781)), _1311777))], (11639 ^ _781404) ^ [_980580, _980582, _980584, _980586] : [hBOOL(hAPP(hAPP(c_member(_980580), _980582), c_Complete__Lattice_OInf__class_OInf(tc_fun(_980580, tc_HOL_Obool), _980584))), hBOOL(hAPP(hAPP(c_member(tc_fun(_980580, tc_HOL_Obool)), _980586), _980584)), -(hBOOL(hAPP(hAPP(c_member(_980580), _980582), _980586)))], (10185 ^ _781404) ^ [_954776, _954778, _954780] : [class_Orderings_Opreorder(_954776), 10188 ^ _781404 : [(10197 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954776), _954778), _954780))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954776), _954778), _954780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954776), _954780), _954778)))], (10189 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954776), _954778), _954780)), 10192 ^ _781404 : [(10195 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954776), _954780), _954778))], (10193 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954776), _954778), _954780)))]]]]], (9240 ^ _781404) ^ [_939194, _939196] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _939194)), _939196) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _939194, _939196))], (32680 ^ _781404) ^ [_1370100, _1370102, _1370104] : [class_Orderings_Olinorder(_1370100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370100), _1370102)), -(_1370104 = c_Orderings_Obot__class_Obot(tc_fun(_1370100, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1370100, tc_HOL_Obool)), _1370104), _1370102)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1370100), c_Big__Operators_Olattice_OSup__fin(_1370100, c_Orderings_Oord__class_Omax(_1370100), _1370104)), c_Big__Operators_Olattice_OSup__fin(_1370100, c_Orderings_Oord__class_Omax(_1370100), _1370102)) = c_Big__Operators_Olattice_OSup__fin(_1370100, c_Orderings_Oord__class_Omax(_1370100), _1370102))], (17415 ^ _781404) ^ [_1092076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092076), 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)), _1092076)), _1092076)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (5959 ^ _781404) ^ [_875877, _875879, _875881, _875883] : [class_Orderings_Oord(_875877), _875879 = _875881, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875877), _875881), _875883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875877), _875879), _875883)))], (41584 ^ _781404) ^ [_1597113, _1597115, _1597117, _1597119, _1597121] : [-(hAPP(c_Relation_Oconverse(_1597113, _1597115), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1597117, tc_fun(tc_prod(_1597113, _1597115), tc_HOL_Obool)), _1597119), _1597121)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1597117, tc_fun(tc_prod(_1597115, _1597113), tc_HOL_Obool)), _1597119), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1597113, _1597115), tc_HOL_Obool), tc_fun(tc_prod(_1597115, _1597113), tc_HOL_Obool), _1597117), c_Relation_Oconverse(_1597113, _1597115)), _1597121)))], (27823 ^ _781404) ^ [_1279222, _1279224, _1279226, _1279228] : [class_Fields_Ofield__inverse__zero(_1279222), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1279222), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279222), _1279224), _1279226)), _1279228) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279222), hAPP(hAPP(c_Power_Opower__class_Opower(_1279222), _1279224), _1279228)), hAPP(hAPP(c_Power_Opower__class_Opower(_1279222), _1279226), _1279228)))], (17132 ^ _781404) ^ [_1086720, _1086722, _1086724] : [class_Int_Onumber(_1086720), 17135 ^ _781404 : [(17142 ^ _781404) ^ [] : [_1086724 = hAPP(c_Int_Onumber__class_Onumber__of(_1086720), _1086722), -(hAPP(c_Int_Onumber__class_Onumber__of(_1086720), _1086722) = _1086724)], (17136 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1086720), _1086722) = _1086724, -(_1086724 = hAPP(c_Int_Onumber__class_Onumber__of(_1086720), _1086722))]]], (42139 ^ _781404) ^ [_1611571, _1611573] : [-(c_Nitpick_Oinverse__frac(_1611571, _1611573) = hAPP(hAPP(c_Nitpick_Ofrac(_1611571), hAPP(c_Nitpick_Odenom(_1611571), _1611573)), hAPP(c_Nitpick_Onum(_1611571), _1611573)))], (52316 ^ _781404) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (48070 ^ _781404) ^ [_1748332, _1748334, _1748336, _1748338] : [-(c_List_Omaps(_1748332, _1748334, _1748336, _1748338) = c_List_Oconcat(_1748334, hAPP(hAPP(c_List_Omap(_1748332, tc_List_Olist(_1748334)), _1748336), _1748338)))], (41554 ^ _781404) ^ [_1596171, _1596173, _1596175, _1596177, _1596179] : [-(hAPP(c_Relation_Oconverse(_1596171, _1596173), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596175, tc_fun(tc_prod(_1596171, _1596173), tc_HOL_Obool)), _1596177), _1596179)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596175, tc_fun(tc_prod(_1596173, _1596171), tc_HOL_Obool)), _1596177), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1596171, _1596173), tc_HOL_Obool), tc_fun(tc_prod(_1596173, _1596171), tc_HOL_Obool), _1596175), c_Relation_Oconverse(_1596171, _1596173)), _1596179)))], (22267 ^ _781404) ^ [_1178313, _1178315, _1178317] : [class_Rings_Osemiring__1(_1178313), hBOOL(hAPP(hAPP(c_member(_1178313), _1178315), c_Nat_Osemiring__1__class_ONats(_1178313))), hBOOL(hAPP(hAPP(c_member(_1178313), _1178317), c_Nat_Osemiring__1__class_ONats(_1178313))), -(hBOOL(hAPP(hAPP(c_member(_1178313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178313), _1178315), _1178317)), c_Nat_Osemiring__1__class_ONats(_1178313))))], (46383 ^ _781404) ^ [_1712058, _1712060, _1712062] : [-(c_List_Oconcat(_1712058, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1712058)), _1712060), _1712062)) = hAPP(hAPP(c_List_Oappend(_1712058), _1712060), c_List_Oconcat(_1712058, _1712062)))], (44186 ^ _781404) ^ [_1663437, _1663439, _1663441] : [hBOOL(hAPP(c_List_Odistinct(_1663437), hAPP(hAPP(c_List_Oappend(_1663437), _1663439), _1663441))), 44189 ^ _781404 : [(44194 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1663437, tc_HOL_Obool)), hAPP(c_List_Oset(_1663437), _1663439)), hAPP(c_List_Oset(_1663437), _1663441)) = c_Orderings_Obot__class_Obot(tc_fun(_1663437, tc_HOL_Obool)))], (44192 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1663437), _1663441)))], (44190 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1663437), _1663439)))]]], (6285 ^ _781404) ^ [_881370, _881372, _881374, _881376, _881378] : [class_Orderings_Oorder(_881370), class_Orderings_Olinorder(_881372), c_Orderings_Oorder__class_Ostrict__mono(_881372, _881370, _881374), 6296 ^ _781404 : [(6303 ^ _781404) ^ [] : [_881376 = _881378, -(hAPP(_881374, _881376) = hAPP(_881374, _881378))], (6297 ^ _781404) ^ [] : [hAPP(_881374, _881376) = hAPP(_881374, _881378), -(_881376 = _881378)]]], (46423 ^ _781404) ^ [_1712933, _1712935, _1712937, _1712939] : [-(hAPP(hAPP(c_List_Omap(_1712933, _1712935), _1712937), c_List_Oconcat(_1712933, _1712939)) = c_List_Oconcat(_1712935, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1712933), tc_List_Olist(_1712935)), hAPP(c_List_Omap(_1712933, _1712935), _1712937)), _1712939)))], (46251 ^ _781404) ^ [_1709642] : [-(c_List_Oremdups(_1709642, c_List_Olist_ONil(_1709642)) = c_List_Olist_ONil(_1709642))], (25379 ^ _781404) ^ [_1235122, _1235124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235122)), 25382 ^ _781404 : [(25389 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235124), _1235122))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235124), _1235122) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1235124), _1235122)), _1235122)))], (25383 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235124), _1235122)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235124), _1235122) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11517 ^ _781404) ^ [_978317, _978319] : [hBOOL(hAPP(hAPP(c_member(_978317), _978319), c_Orderings_Obot__class_Obot(tc_fun(_978317, tc_HOL_Obool))))], (13365 ^ _781404) ^ [_1013742, _1013744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013742), _1013744)), _1013742))], (17567 ^ _781404) ^ [_1094630, _1094632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094630), _1094632)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094632), _1094630)), -(_1094630 = _1094632)], (52628 ^ _781404) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (13991 ^ _781404) ^ [_1025373, _1025375, _1025377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025373), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025375), _1025377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025373), _1025377)), _1025375)))], (22235 ^ _781404) ^ [_1177762, _1177764, _1177766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1177764), _1177766)), -(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, _1177762)), _1177764)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1177762)), _1177766))))], (7579 ^ _781404) ^ [_905711, _905713, _905715, _905717] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905711, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905711, tc_HOL_Obool)), _905713), _905715)), _905717) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905711, tc_HOL_Obool)), _905713), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905711, tc_HOL_Obool)), _905715), _905717)))], (39924 ^ _781404) ^ [_1557459] : [-(c_Wellfounded_Owf(tc_fun(_1557459, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1557459)))], (11957 ^ _781404) ^ [_986344, _986346, _986348, _986350] : [hBOOL(hAPP(hAPP(c_member(_986344), _986346), hAPP(hAPP(c_Set_Oinsert(_986344), _986348), _986350))), -(_986346 = _986348), -(hBOOL(hAPP(hAPP(c_member(_986344), _986346), _986350)))], (36506 ^ _781404) ^ [_1463625, _1463627] : [_1463625 = _1463627, -(hAPP(c_Int_ORep__Integ, _1463625) = hAPP(c_Int_ORep__Integ, _1463627))], (34647 ^ _781404) ^ [_1424355, _1424357, _1424359, _1424361] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1424355), _1424357)), -(hAPP(c_Set_Oimage(_1424355, _1424359, _1424361), _1424357) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1424359, tc_HOL_Obool), _1424355, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424359, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1424355, tc_fun(_1424359, tc_HOL_Obool), tc_fun(_1424359, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1424359, tc_fun(tc_fun(_1424359, tc_HOL_Obool), tc_fun(_1424359, tc_HOL_Obool)), _1424355), c_Set_Oinsert(_1424359)), _1424361)), c_Orderings_Obot__class_Obot(tc_fun(_1424359, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1424359, tc_HOL_Obool))), _1424357))], (6233 ^ _781404) ^ [_880583, _880585, _880587] : [class_Orderings_Olinorder(_880583), 6236 ^ _781404 : [(6243 ^ _781404) ^ [] : [_880585 = _880587, -(hAPP(c_SetInterval_Oord__class_OlessThan(_880583), _880585) = hAPP(c_SetInterval_Oord__class_OlessThan(_880583), _880587))], (6237 ^ _781404) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_880583), _880585) = hAPP(c_SetInterval_Oord__class_OlessThan(_880583), _880587), -(_880585 = _880587)]]], (11665 ^ _781404) ^ [_981103, _981105, _981107] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981103), _981105)), _981107) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981103), _981107)), _981105))], (45724 ^ _781404) ^ [_1697392, _1697394] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1697392), _1697394) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1697392)), hAPP(c_Code__Numeral_Onat__of, _1697394))))], (38888 ^ _781404) ^ [_1523503, _1523505, _1523507, _1523509, _1523511, _1523513, _1523515, _1523517, _1523519, _1523521] : [-(c_Product__Type_Omap__pair(_1523503, _1523505, _1523507, _1523509, hAPP(c_Fun_Ocomp(_1523511, _1523505, _1523503, _1523513), _1523515), hAPP(c_Fun_Ocomp(_1523517, _1523509, _1523507, _1523519), _1523521)) = hAPP(c_Fun_Ocomp(tc_prod(_1523511, _1523517), tc_prod(_1523505, _1523509), tc_prod(_1523503, _1523507), c_Product__Type_Omap__pair(_1523511, _1523505, _1523517, _1523509, _1523513, _1523519)), c_Product__Type_Omap__pair(_1523503, _1523511, _1523507, _1523517, _1523515, _1523521)))], (26901 ^ _781404) ^ [_1261531, _1261533, _1261535] : [class_Rings_Olinordered__idom(_1261531), -(hAPP(c_Groups_Oabs__class_Oabs(_1261531), hAPP(hAPP(c_Power_Opower__class_Opower(_1261531), _1261533), _1261535)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1261531), hAPP(c_Groups_Oabs__class_Oabs(_1261531), _1261533)), _1261535))], (11649 ^ _781404) ^ [_980777, _980779, _980781, _980783] : [hBOOL(hAPP(hAPP(c_member(_980777), _980779), c_Complete__Lattice_OInf__class_OInf(tc_fun(_980777, tc_HOL_Obool), _980781))), hBOOL(hAPP(hAPP(c_member(tc_fun(_980777, tc_HOL_Obool)), _980783), _980781)), -(hBOOL(hAPP(hAPP(c_member(_980777), _980779), _980783)))], (22011 ^ _781404) ^ [_1173404, _1173406, _1173408, _1173410] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173404), hAPP(c_Int_Onumber__class_Onumber__of(_1173404), _1173406)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1173404), _1173408), _1173410)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1173404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173404), hAPP(c_Int_Onumber__class_Onumber__of(_1173404), _1173406)), _1173408)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173404), hAPP(c_Int_Onumber__class_Onumber__of(_1173404), _1173406)), _1173410))), class_Int_Onumber(_1173404), class_Rings_Oring(_1173404)], (30478 ^ _781404) ^ [_1329024, _1329026] : [-(_1329024 = _1329026), -(c_Random_Oinc__shift(_1329024, _1329026) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1329026), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (23525 ^ _781404) ^ [_1203623, _1203625, _1203627] : [class_Divides_Oring__div(_1203623), -(c_Divides_Odiv__class_Omod(_1203623, hAPP(c_Groups_Ouminus__class_Ouminus(_1203623), _1203625), _1203627) = c_Divides_Odiv__class_Omod(_1203623, hAPP(c_Groups_Ouminus__class_Ouminus(_1203623), c_Divides_Odiv__class_Omod(_1203623, _1203625, _1203627)), _1203627))], (8407 ^ _781404) ^ [_923083, _923085, _923087] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923083, tc_HOL_Obool)), _923085), _923087) = c_Orderings_Obot__class_Obot(tc_fun(_923083, tc_HOL_Obool))), _923085 = c_Orderings_Obot__class_Obot(tc_fun(_923083, tc_HOL_Obool)), _923087 = c_Orderings_Obot__class_Obot(tc_fun(_923083, tc_HOL_Obool))], (25263 ^ _781404) ^ [_1233360, _1233362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233360)), _1233362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1233360), hAPP(c_Int_Onat, _1233362))))], (45948 ^ _781404) ^ [_1703089, _1703091, _1703093, _1703095, _1703097, _1703099, _1703101] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703089)), _1703091) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703093)), _1703095), 45951 ^ _781404 : [(45960 ^ _781404) ^ [] : [-(c_List_Olist__all2(_1703089, _1703093, _1703097, hAPP(hAPP(c_List_Oappend(_1703089), _1703091), _1703099), hAPP(hAPP(c_List_Oappend(_1703093), _1703095), _1703101))), c_List_Olist__all2(_1703089, _1703093, _1703097, _1703091, _1703095), c_List_Olist__all2(_1703089, _1703093, _1703097, _1703099, _1703101)], (45952 ^ _781404) ^ [] : [c_List_Olist__all2(_1703089, _1703093, _1703097, hAPP(hAPP(c_List_Oappend(_1703089), _1703091), _1703099), hAPP(hAPP(c_List_Oappend(_1703093), _1703095), _1703101)), 45955 ^ _781404 : [(45958 ^ _781404) ^ [] : [-(c_List_Olist__all2(_1703089, _1703093, _1703097, _1703099, _1703101))], (45956 ^ _781404) ^ [] : [-(c_List_Olist__all2(_1703089, _1703093, _1703097, _1703091, _1703095))]]]]], (20127 ^ _781404) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (1626 ^ _781404) ^ [_804769, _804771] : [-(class_Groups_Oordered__comm__monoid__add(_804769)), _804771 = _804769, class_Groups_Oordered__comm__monoid__add(_804771)], (27297 ^ _781404) ^ [_1269034, _1269036] : [class_Groups_Oabs__if(_1269034), 27300 ^ _781404 : [(27307 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269034), _1269036), c_Groups_Ozero__class_Ozero(_1269034)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1269034), _1269036) = _1269036)], (27301 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269034), _1269036), c_Groups_Ozero__class_Ozero(_1269034))), -(hAPP(c_Groups_Oabs__class_Oabs(_1269034), _1269036) = hAPP(c_Groups_Ouminus__class_Ouminus(_1269034), _1269036))]]], (16304 ^ _781404) ^ [_1071113] : [class_Rings_Ozero__neq__one(_1071113), c_Groups_Oone__class_Oone(_1071113) = c_Groups_Ozero__class_Ozero(_1071113)], (45064 ^ _781404) ^ [_1682862, _1682864, _1682866] : [-(_1682862 = c_List_Olist_ONil(_1682864)), -(c_List_Olast(_1682864, hAPP(hAPP(c_List_Oappend(_1682864), _1682866), _1682862)) = c_List_Olast(_1682864, _1682862))], (28977 ^ _781404) ^ [_1300232, _1300234, _1300236] : [class_Fields_Olinordered__field(_1300232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300232), c_Groups_Ozero__class_Ozero(_1300232)), _1300234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300232), _1300236), c_Groups_Ozero__class_Ozero(_1300232))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300232), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1300232), _1300234), _1300236)), c_Groups_Ozero__class_Ozero(_1300232))))], (34153 ^ _781404) ^ [_1408913, _1408915, _1408917, _1408919, _1408921] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408913, tc_HOL_Obool)), _1408915), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408917, tc_fun(_1408913, tc_HOL_Obool)), _1408919), _1408921)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408917, tc_fun(_1408913, tc_HOL_Obool)), _1408919), hAPP(hAPP(c_COMBB(tc_fun(_1408913, tc_HOL_Obool), tc_fun(_1408913, tc_HOL_Obool), _1408917), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408913, tc_HOL_Obool)), _1408915)), _1408921)))], (24674 ^ _781404) ^ [_1224121] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224121)) = _1224121)], (45627 ^ _781404) ^ [_1695603, _1695605, _1695607, _1695609, _1695611] : [class_Groups_Omonoid__add(_1695603), class_Groups_Oordered__ab__semigroup__add(_1695603), 45637 ^ _781404 : [(45640 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695603), hAPP(_1695609, 45636 ^ [_1695603, _1695605, _1695607, _1695609, _1695611])), hAPP(_1695611, 45636 ^ [_1695603, _1695605, _1695607, _1695609, _1695611])))], (45638 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1695605), 45636 ^ [_1695603, _1695605, _1695607, _1695609, _1695611]), hAPP(c_List_Oset(_1695605), _1695607))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695603), hAPP(c_List_Omonoid__add__class_Olistsum(_1695603), hAPP(hAPP(c_List_Omap(_1695605, _1695603), _1695609), _1695607))), hAPP(c_List_Omonoid__add__class_Olistsum(_1695603), hAPP(hAPP(c_List_Omap(_1695605, _1695603), _1695611), _1695607)))))], (52452 ^ _781404) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (50239 ^ _781404) ^ [_1796696, _1796698, _1796700, _1796702] : [c_Relation_Osym(_1796696, _1796698), -(c_Relation_Osym(_1796700, hAPP(hAPP(c_Relation_Oinv__image(_1796696, _1796700), _1796698), _1796702)))], (2674 ^ _781404) ^ [_820851, _820853, _820855, _820857, _820859, _820861, _820863, _820865] : [-(c_Nitpick_Oprod(_820865, _820861, _820857, _820853) = c_Nitpick_Oprod(_820863, _820859, _820855, _820851)), _820865 = _820863, _820861 = _820859, _820857 = _820855, _820853 = _820851], (24923 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (8457 ^ _781404) ^ [_924051] : [hAPP(c_Nat_OSuc, _924051) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7577 ^ _781404) ^ [_905647, _905649, _905651, _905653, _905655] : [-(hAPP(c_Set_Oimage(_905647, _905649, _905651), hAPP(hAPP(c_Set_Oinsert(_905647), _905653), _905655)) = hAPP(hAPP(c_Set_Oinsert(_905649), hAPP(_905651, _905653)), hAPP(c_Set_Oimage(_905647, _905649, _905651), _905655)))], (45869 ^ _781404) ^ [_1700965, _1700967, _1700969] : [hBOOL(hAPP(c_List_Olistsp(_1700965, hAPP(hAPP(c_COMBC(_1700965, tc_fun(_1700965, tc_HOL_Obool), tc_HOL_Obool), c_member(_1700965)), _1700967)), _1700969)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1700965)), _1700969), c_List_Olists(_1700965, _1700967))))], (14975 ^ _781404) ^ [_1044905, _1044907, _1044909, _1044911, _1044913] : [14977 ^ _781404 : [(14980 ^ _781404) ^ [] : [hBOOL(hAPP(_1044913, 14976 ^ [_1044905, _1044907, _1044909, _1044911, _1044913]))], (14978 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1044905), 14976 ^ [_1044905, _1044907, _1044909, _1044911, _1044913]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044907, tc_fun(_1044905, tc_HOL_Obool)), _1044909), _1044911))))]], 14981 ^ _781404 : [(14982 ^ _781404) ^ [_1045127] : [hBOOL(hAPP(hAPP(c_member(_1044907), _1045127), _1044909)), 14985 ^ _781404 : [(14986 ^ _781404) ^ [_1045224] : [hBOOL(hAPP(hAPP(c_member(_1044905), _1045224), hAPP(_1044911, _1045127))), -(hBOOL(hAPP(_1044913, _1045224)))]]]]], (8036 ^ _781404) ^ [_915820, _915822] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915820, tc_HOL_Obool)), _915822), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_915820, tc_HOL_Obool)), _915822)) = c_Orderings_Otop__class_Otop(tc_fun(_915820, tc_HOL_Obool)))], (32999 ^ _781404) ^ [_1376333, _1376335, _1376337, _1376339, _1376341, _1376343] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1376333, tc_fun(_1376335, tc_HOL_Obool)), _1376337), _1376339), _1376341)), -(hBOOL(hAPP(hAPP(_1376339, _1376343), _1376341))), hBOOL(hAPP(hAPP(c_member(_1376333), _1376343), _1376337))], (50594 ^ _781404) ^ [_1803678, _1803680, _1803682, _1803684] : [c_Fun_Oinj__on(_1803678, _1803680, _1803682, c_Orderings_Otop__class_Otop(tc_fun(_1803678, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1803680, _1803678, c_Hilbert__Choice_Oinv__into(_1803678, _1803680, c_Orderings_Otop__class_Otop(tc_fun(_1803678, tc_HOL_Obool)), _1803682)), hAPP(c_Set_Oimage(_1803678, _1803680, _1803682), _1803684)) = _1803684)], (3232 ^ _781404) ^ [_829514, _829516, _829518, _829520, _829522, _829524] : [-(c_Big__Operators_Olattice_OInf__fin(_829524, _829520, _829516) = c_Big__Operators_Olattice_OInf__fin(_829522, _829518, _829514)), _829524 = _829522, _829520 = _829518, _829516 = _829514], (45670 ^ _781404) ^ [_1696451, _1696453] : [_1696451 = _1696453, -(hAPP(c_Code__Numeral_Onat__of, _1696451) = hAPP(c_Code__Numeral_Onat__of, _1696453))], (36476 ^ _781404) ^ [_1463056, _1463058, _1463060, _1463062] : [-(_1463056 = _1463058), hAPP(c_Product__Type_Ofst(_1463060, _1463062), _1463056) = hAPP(c_Product__Type_Ofst(_1463060, _1463062), _1463058), hAPP(c_Product__Type_Osnd(_1463060, _1463062), _1463056) = hAPP(c_Product__Type_Osnd(_1463060, _1463062), _1463058)], (34927 ^ _781404) ^ [_1431048, _1431050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1431048)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431050))), -(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(_1431050))), 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), _1431048)), c_Int_Onat))))))], (8640 ^ _781404) ^ [_927063, _927065] : [class_Groups_Oordered__ab__group__add(_927063), 8643 ^ _781404 : [(8650 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927063), _927065), c_Groups_Ozero__class_Ozero(_927063))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927063), c_Groups_Ozero__class_Ozero(_927063)), hAPP(c_Groups_Ouminus__class_Ouminus(_927063), _927065))))], (8644 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927063), c_Groups_Ozero__class_Ozero(_927063)), hAPP(c_Groups_Ouminus__class_Ouminus(_927063), _927065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927063), _927065), c_Groups_Ozero__class_Ozero(_927063))))]]], (43026 ^ _781404) ^ [_1638216, _1638218, _1638220, _1638222, _1638224, _1638226] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1638216, _1638218)), hAPP(hAPP(c_Product__Type_OPair(_1638216, _1638218), _1638220), _1638222)), hAPP(c_List_Oset(tc_prod(_1638216, _1638218)), hAPP(hAPP(c_List_Ozip(_1638216, _1638218), _1638224), _1638226)))), 43029 ^ _781404 : [(43032 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1638218), _1638222), hAPP(c_List_Oset(_1638218), _1638226))))], (43030 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1638216), _1638220), hAPP(c_List_Oset(_1638216), _1638224))))]]], (50837 ^ _781404) ^ [_1809179, _1809181, _1809183, _1809185, _1809187, _1809189, _1809191, _1809193] : [c_Fun_Obij__betw(_1809179, _1809181, _1809183, _1809185, _1809187), 50840 ^ _781404 : [(50847 ^ _781404) ^ [] : [c_Fun_Obij__betw(_1809179, _1809189, hAPP(c_Fun_Ocomp(_1809181, _1809189, _1809179, _1809191), _1809183), _1809185, _1809193), -(c_Fun_Obij__betw(_1809181, _1809189, _1809191, _1809187, _1809193))], (50841 ^ _781404) ^ [] : [c_Fun_Obij__betw(_1809181, _1809189, _1809191, _1809187, _1809193), -(c_Fun_Obij__betw(_1809179, _1809189, hAPP(c_Fun_Ocomp(_1809181, _1809189, _1809179, _1809191), _1809183), _1809185, _1809193))]]], (15070 ^ _781404) ^ [_1047112, _1047114, _1047116, _1047118, _1047120, _1047122, _1047124, _1047126] : [c_Finite__Set_Ofolding__image__simple(_1047112, _1047114, _1047116, _1047118, _1047120, _1047122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047114), _1047124)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047114), _1047126)), -(hAPP(hAPP(_1047116, hAPP(_1047122, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1047114, tc_HOL_Obool)), _1047124), _1047126))), hAPP(_1047122, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1047114, tc_HOL_Obool)), _1047124), _1047126))) = hAPP(hAPP(_1047116, hAPP(_1047122, _1047124)), hAPP(_1047122, _1047126)))], (9174 ^ _781404) ^ [_937492, _937494, _937496] : [-(hAPP(hAPP(c_Set_Oinsert(_937492), _937494), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937492, tc_HOL_Obool)), _937496), hAPP(hAPP(c_Set_Oinsert(_937492), _937494), c_Orderings_Obot__class_Obot(tc_fun(_937492, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_937492), _937494), _937496))], (43146 ^ _781404) ^ [_1640806, _1640808, _1640810, _1640812] : [-(_1640806 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640808)), _1640810)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1640808, hAPP(hAPP(c_List_Olist__update(_1640808, _1640810), _1640806), _1640812)) = hAPP(hAPP(c_List_Olist__update(_1640808, c_List_Obutlast(_1640808, _1640810)), _1640806), _1640812))], (44655 ^ _781404) ^ [_1674604, _1674606, _1674608] : [-(hAPP(c_List_Orotate1(_1674604), hAPP(c_List_Orotate(_1674604, _1674606), _1674608)) = hAPP(c_List_Orotate(_1674604, _1674606), hAPP(c_List_Orotate1(_1674604), _1674608)))], (42678 ^ _781404) ^ [_1628042, _1628044, _1628046] : [-(_1628042 = _1628044), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628046)), _1628042) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628046)), _1628044), 42684 ^ _781404 : [(42687 ^ _781404) ^ [] : [hAPP(hAPP(c_List_Onth(_1628046), _1628042), 42683 ^ [_1628042, _1628044, _1628046]) = hAPP(hAPP(c_List_Onth(_1628046), _1628044), 42683 ^ [_1628042, _1628044, _1628046])], (42685 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42683 ^ [_1628042, _1628044, _1628046]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628046)), _1628042))))]]], (2298 ^ _781404) ^ [_814875, _814877, _814879, _814881, _814883, _814885, _814887, _814889] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_814889, _814885, _814881, _814877) = c_Nat_Osemiring__1__class_Oof__nat__aux(_814887, _814883, _814879, _814875)), _814889 = _814887, _814885 = _814883, _814881 = _814879, _814877 = _814875], (47147 ^ _781404) ^ [_1729102, _1729104, _1729106, _1729108, _1729110] : [class_Orderings_Olinorder(_1729102), c_List_Olinorder__class_Osorted(_1729102, hAPP(hAPP(c_List_Omap(_1729104, _1729102), _1729106), _1729108)), -(c_List_Olinorder__class_Osorted(_1729102, hAPP(hAPP(c_List_Omap(_1729104, _1729102), _1729106), hAPP(c_List_Ofilter(_1729104, _1729110), _1729108))))], (6043 ^ _781404) ^ [_877135, _877137, _877139, _877141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877135, tc_HOL_Obool)), _877137), _877139)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877135, tc_HOL_Obool)), _877139), _877141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877135, tc_HOL_Obool)), _877137), _877141)))], (6181 ^ _781404) ^ [_879698, _879700, _879702] : [class_Orderings_Oorder(_879698), 6184 ^ _781404 : [(6191 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879698), _879700), _879702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879698, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_879698), _879700)), hAPP(c_SetInterval_Oord__class_OatMost(_879698), _879702))))], (6185 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879698, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_879698), _879700)), hAPP(c_SetInterval_Oord__class_OatMost(_879698), _879702))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879698), _879700), _879702)))]]], (17475 ^ _781404) ^ [_1093142] : [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)), _1093142)), _1093142) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (17967 ^ _781404) ^ [_1101783, _1101785, _1101787, _1101789] : [class_Rings_Olinordered__semidom(_1101783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101783), _1101785), _1101787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101783), c_Groups_Ozero__class_Ozero(_1101783)), _1101785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101783), hAPP(hAPP(c_Power_Opower__class_Opower(_1101783), _1101785), _1101789)), hAPP(hAPP(c_Power_Opower__class_Opower(_1101783), _1101787), _1101789))))], (48319 ^ _781404) ^ [_1754438, _1754440, _1754442, _1754444, _1754446] : [hAPP(c_List_Ofilter(_1754438, _1754440), _1754442) = hAPP(hAPP(c_List_Olist_OCons(_1754438), _1754444), _1754446), 48324 ^ _781404 : [(48333 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1754440, _1754444)))], (48335 ^ _781404) ^ [] : [-(_1754446 = hAPP(c_List_Ofilter(_1754438, _1754440), 48323 ^ [_1754438, _1754440, _1754442, _1754444, _1754446]))], (48327 ^ _781404) ^ [_1754752] : [hBOOL(hAPP(hAPP(c_member(_1754438), _1754752), hAPP(c_List_Oset(_1754438), 48322 ^ [_1754438, _1754440, _1754442, _1754444, _1754446]))), hBOOL(hAPP(_1754440, _1754752))], (48325 ^ _781404) ^ [] : [-(_1754442 = hAPP(hAPP(c_List_Oappend(_1754438), 48322 ^ [_1754438, _1754440, _1754442, _1754444, _1754446]), hAPP(hAPP(c_List_Olist_OCons(_1754438), _1754444), 48323 ^ [_1754438, _1754440, _1754442, _1754444, _1754446])))]]], (14761 ^ _781404) ^ [_1040393, _1040395] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040393), _1040395)), 14764 ^ _781404 : [(14771 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040393), c_Orderings_Otop__class_Otop(tc_fun(_1040393, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040393), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1040393, tc_HOL_Obool)), _1040395))))], (14765 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040393), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1040393, tc_HOL_Obool)), _1040395))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040393), c_Orderings_Otop__class_Otop(tc_fun(_1040393, tc_HOL_Obool)))))]]], (1616 ^ _781404) ^ [_804644, _804646] : [-(class_Groups_Oordered__ab__semigroup__add(_804644)), _804646 = _804644, class_Groups_Oordered__ab__semigroup__add(_804646)], (14412 ^ _781404) ^ [_1033537, _1033539, _1033541, _1033543] : [class_Groups_Ocomm__monoid__add(_1033537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1033539), _1033541)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1033537), _1033543), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1033539, _1033541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033537), hAPP(_1033543, _1033539)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1033537), _1033543), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1033539), _1033541))))], (31890 ^ _781404) ^ [_1355219, _1355221, _1355223, _1355225] : [class_Orderings_Olinorder(_1355219), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355219), _1355221), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355219), _1355223), _1355225)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355219), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355219), _1355221), _1355223)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355219), _1355221), _1355225)))], (35041 ^ _781404) ^ [_1433773, _1433775, _1433777, _1433779, _1433781] : [class_Groups_Ocomm__monoid__mult(_1433773), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433775), _1433777)), c_Fun_Oinj__on(_1433775, _1433775, _1433779, _1433777), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1433775, _1433773), _1433781), hAPP(c_Set_Oimage(_1433775, _1433775, _1433779), _1433777)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1433775, _1433773), hAPP(c_Fun_Ocomp(_1433775, _1433773, _1433775, _1433781), _1433779)), _1433777))], (52522 ^ _781404) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (47742 ^ _781404) ^ [_1741475, _1741477, _1741479] : [hBOOL(hAPP(c_List_Odistinct(_1741475), _1741477)), -(hBOOL(hAPP(c_List_Odistinct(_1741475), c_List_OtakeWhile(_1741475, _1741479, _1741477))))], (1696 ^ _781404) ^ [_805644, _805646] : [-(class_Groups_Oab__semigroup__mult(_805644)), _805646 = _805644, class_Groups_Oab__semigroup__mult(_805646)], (27249 ^ _781404) ^ [_1268016, _1268018, _1268020] : [class_Rings_Olinordered__idom(_1268016), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268016), c_Groups_Ozero__class_Ozero(_1268016)), _1268018)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1268016), hAPP(c_Groups_Oabs__class_Oabs(_1268016), _1268020)), _1268018) = hAPP(c_Groups_Oabs__class_Oabs(_1268016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1268016), _1268020), _1268018)))], (39069 ^ _781404) ^ [_1528097, _1528099, _1528101, _1528103] : [-(hBOOL(hAPP(hAPP(c_member(_1528097), _1528099), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1528097, tc_HOL_Obool)), _1528101), hAPP(c_Set_OCollect(_1528097), _1528103))))), hBOOL(hAPP(hAPP(c_member(_1528097), _1528099), _1528101)), hBOOL(hAPP(_1528103, _1528099))], (21269 ^ _781404) ^ [_1159370, _1159372, _1159374] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1159370), _1159372)), _1159374) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1159370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159372), _1159374)))], (38890 ^ _781404) ^ [_1523598, _1523600, _1523602, _1523604, _1523606, _1523608, _1523610, _1523612, _1523614, _1523616, _1523618] : [-(hAPP(c_Product__Type_Omap__pair(_1523598, _1523600, _1523602, _1523604, _1523606, _1523608), hAPP(c_Product__Type_Omap__pair(_1523610, _1523598, _1523612, _1523602, _1523614, _1523616), _1523618)) = hAPP(c_Product__Type_Omap__pair(_1523610, _1523600, _1523612, _1523604, hAPP(c_Fun_Ocomp(_1523598, _1523600, _1523610, _1523606), _1523614), hAPP(c_Fun_Ocomp(_1523602, _1523604, _1523612, _1523608), _1523616)), _1523618))], (52494 ^ _781404) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (27963 ^ _781404) ^ [_1281431, _1281433, _1281435, _1281437] : [class_Fields_Ofield(_1281431), -(_1281433 = c_Groups_Ozero__class_Ozero(_1281431)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1281431), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281431), _1281435), _1281433)), _1281437) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281431), hAPP(hAPP(c_Power_Opower__class_Opower(_1281431), _1281435), _1281437)), hAPP(hAPP(c_Power_Opower__class_Opower(_1281431), _1281433), _1281437)))], (47934 ^ _781404) ^ [_1745627, _1745629] : [class_Orderings_Olinorder(_1745627), 47941 ^ _781404 : [(47946 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1745627), hAPP(hAPP(c_List_Onth(_1745627), _1745629), 47939 ^ [_1745627, _1745629])), hAPP(hAPP(c_List_Onth(_1745627), _1745629), 47940 ^ [_1745627, _1745629])))], (47944 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47940 ^ [_1745627, _1745629]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745627)), _1745629))))], (47942 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47939 ^ [_1745627, _1745629]), 47940 ^ [_1745627, _1745629])))]], -(c_List_Olinorder__class_Osorted(_1745627, _1745629))], (52468 ^ _781404) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (38498 ^ _781404) ^ [_1512196, _1512198, _1512200, _1512202, _1512204] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1512196, _1512198), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1512196, tc_HOL_Obool)), _1512200), _1512202)), _1512204) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1512196, _1512198), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1512196, _1512198), _1512200), _1512204)), hAPP(hAPP(c_Product__Type_OSigma(_1512196, _1512198), _1512202), _1512204)))], (33580 ^ _781404) ^ [_1392970, _1392972] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1392970, tc_HOL_Obool), _1392972) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1392970, tc_HOL_Obool), tc_fun(_1392970, tc_HOL_Obool)), _1392972), c_COMBI(tc_fun(_1392970, tc_HOL_Obool))))], (9749 ^ _781404) ^ [_947682, _947684, _947686, _947688] : [c_Fun_Oinj__on(_947682, _947684, _947686, _947688), 9752 ^ _781404 : [(9753 ^ _781404) ^ [_947790] : [hBOOL(hAPP(hAPP(c_member(_947682), _947790), _947688)), 9756 ^ _781404 : [(9757 ^ _781404) ^ [_947892] : [hBOOL(hAPP(hAPP(c_member(_947682), _947892), _947688)), hAPP(_947686, _947790) = hAPP(_947686, _947892), -(_947790 = _947892)]]]]], (33339 ^ _781404) ^ [_1384849, _1384851, _1384853, _1384855, _1384857, _1384859] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384849, tc_fun(_1384851, tc_HOL_Obool)), _1384853), hAPP(hAPP(c_COMBB(_1384855, tc_fun(_1384851, tc_HOL_Obool), _1384849), _1384857), _1384859)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384855, tc_fun(_1384851, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1384849, _1384855, _1384859), _1384853)), _1384857))], (24610 ^ _781404) ^ [_1222806, _1222808] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222806))), -(c_SMT_Oz3mod(_1222808, _1222806) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1222808, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1222806)))], (23555 ^ _781404) ^ [_1204232, _1204234, _1204236, _1204238] : [class_Divides_Osemiring__div(_1204232), -(c_Divides_Odiv__class_Omod(_1204232, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204232), _1204234), _1204236), _1204238) = c_Divides_Odiv__class_Omod(_1204232, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204232), c_Divides_Odiv__class_Omod(_1204232, _1204234, _1204238)), c_Divides_Odiv__class_Omod(_1204232, _1204236, _1204238)), _1204238))], (21769 ^ _781404) ^ [_1168499, _1168501, _1168503, _1168505] : [class_Rings_Olinordered__ring__strict(_1168499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168499), _1168501), c_Groups_Ozero__class_Ozero(_1168499))), 21776 ^ _781404 : [(21783 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168499), _1168505), _1168503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168499), _1168501), _1168503)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168499), _1168501), _1168505))))], (21777 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168499), _1168501), _1168503)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168499), _1168501), _1168505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168499), _1168505), _1168503)))]]], (30516 ^ _781404) ^ [_1329796, _1329798, _1329800] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1329796), _1329798)), hBOOL(hAPP(_1329800, c_Orderings_Obot__class_Obot(tc_fun(_1329796, tc_HOL_Obool)))), 30527 ^ _781404 : [(30530 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1329796), 30525 ^ [_1329796, _1329798, _1329800]), 30526 ^ [_1329796, _1329798, _1329800]))], (30532 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1329800, 30526 ^ [_1329796, _1329798, _1329800])))], (30534 ^ _781404) ^ [] : [hBOOL(hAPP(_1329800, hAPP(hAPP(c_Set_Oinsert(_1329796), 30525 ^ [_1329796, _1329798, _1329800]), 30526 ^ [_1329796, _1329798, _1329800])))], (30528 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1329796), 30526 ^ [_1329796, _1329798, _1329800])))]], -(hBOOL(hAPP(_1329800, _1329798)))], (3000 ^ _781404) ^ [_825924, _825926, _825928, _825930] : [-(c_Nitpick_Ouminus__frac(_825930, _825926) = c_Nitpick_Ouminus__frac(_825928, _825924)), _825930 = _825928, _825926 = _825924], (1736 ^ _781404) ^ [_806144, _806146] : [-(class_Rings_Ono__zero__divisors(_806144)), _806146 = _806144, class_Rings_Ono__zero__divisors(_806146)], (27157 ^ _781404) ^ [_1266232, _1266234, _1266236] : [class_Groups_Oordered__ab__group__add__abs(_1266232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266232), hAPP(c_Groups_Oabs__class_Oabs(_1266232), _1266234)), _1266236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266232), hAPP(c_Groups_Ouminus__class_Ouminus(_1266232), _1266234)), _1266236)))], (35788 ^ _781404) ^ [_1449580, _1449582, _1449584, _1449586, _1449588, _1449590] : [-(c_Nitpick_Opair__box_Opair__box__case(_1449580, _1449582, _1449584, _1449586, c_Nitpick_Opair__box_OPairBox(_1449580, _1449582, _1449588, _1449590)) = hAPP(hAPP(_1449586, _1449588), _1449590))], (50117 ^ _781404) ^ [_1794291, _1794293] : [c_Relation_Oantisym(_1794291, _1794293), -(c_Relation_Oantisym(_1794291, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1794291, _1794291), tc_HOL_Obool)), _1794293), c_Relation_OId(_1794291))))], (44671 ^ _781404) ^ [_1674915, _1674917, _1674919] : [-(hAPP(c_List_Orotate(_1674915, hAPP(c_Nat_OSuc, _1674917)), _1674919) = hAPP(c_List_Orotate1(_1674915), hAPP(c_List_Orotate(_1674915, _1674917), _1674919)))], (22931 ^ _781404) ^ [_1191417, _1191419] : [class_Int_Onumber__ring(_1191417), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191417), _1191419), hAPP(c_Int_Onumber__class_Onumber__of(_1191417), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191417), _1191419), _1191419))], (34771 ^ _781404) ^ [_1427352, _1427354] : [class_Rings_Osemiring__1(_1427352), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1427352), _1427354) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1427352, hAPP(hAPP(c_COMBC(_1427352, _1427352, _1427352), c_Groups_Oplus__class_Oplus(_1427352)), c_Groups_Oone__class_Oone(_1427352)), _1427354, c_Groups_Ozero__class_Ozero(_1427352)))], (52676 ^ _781404) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (19470 ^ _781404) ^ [_1127613] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1127613)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1127613))))], (42589 ^ _781404) ^ [_1625588, _1625590, _1625592, _1625594] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1625588)), hAPP(hAPP(c_List_Olist_OCons(_1625588), _1625590), _1625592)), c_List_Olists(_1625588, _1625594))), 42592 ^ _781404 : [(42595 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1625588)), _1625592), c_List_Olists(_1625588, _1625594))))], (42593 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625588), _1625590), _1625594)))]]], (48813 ^ _781404) ^ [_1764620, _1764622, _1764624] : [c_List_Oall__interval__nat(_1764620, _1764622, _1764624), -(c_List_Olist__all(tc_Nat_Onat, _1764620, c_List_Oupt(_1764622, _1764624)))], (48038 ^ _781404) ^ [_1747770, _1747772, _1747774] : [hBOOL(hAPP(hAPP(c_member(_1747770), _1747772), hAPP(c_List_Oset(_1747770), _1747774))), -(c_List_Oinsert(_1747770, _1747772, _1747774) = _1747774)], (2224 ^ _781404) ^ [_813720, _813722, _813724, _813726] : [-(c_Nitpick_Onat__lcm(_813726, _813722) = c_Nitpick_Onat__lcm(_813724, _813720)), _813726 = _813724, _813722 = _813720], (38387 ^ _781404) ^ [_1509660, _1509662, _1509664, _1509666] : [c_Wellfounded_Omax__extp(_1509660, _1509662, _1509664, _1509666), 38390 ^ _781404 : [(38393 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1509660), _1509666)))], (38395 ^ _781404) ^ [] : [_1509666 = c_Orderings_Obot__class_Obot(tc_fun(_1509660, tc_HOL_Obool))], (38397 ^ _781404) ^ [_1509876] : [hBOOL(hAPP(hAPP(c_member(_1509660), _1509876), _1509664)), 38401 ^ _781404 : [(38404 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1509662, _1509876), 38400 ^ [_1509660, _1509662, _1509664, _1509666, _1509876])))], (38402 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1509660), 38400 ^ [_1509660, _1509662, _1509664, _1509666, _1509876]), _1509666)))]]], (38391 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1509660), _1509664)))]]], (43376 ^ _781404) ^ [_1646002, _1646004] : [43378 ^ _781404 : [(43382 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43380 ^ [_1646002, _1646004]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646002)), _1646004))))], (43384 ^ _781404) ^ [] : [43377 ^ [_1646002, _1646004] = 43380 ^ [_1646002, _1646004]], (43386 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1646002), _1646004), 43377 ^ [_1646002, _1646004]) = hAPP(hAPP(c_List_Onth(_1646002), _1646004), 43380 ^ [_1646002, _1646004]))], (43379 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43377 ^ [_1646002, _1646004]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646002)), _1646004))))]], -(hBOOL(hAPP(c_List_Odistinct(_1646002), _1646004)))], (19207 ^ _781404) ^ [_1122990] : [19209 ^ _781404 : [(19212 ^ _781404) ^ [] : [hBOOL(hAPP(_1122990, 19208 ^ [_1122990]))], (19210 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19208 ^ [_1122990])))]], 19213 ^ _781404 : [(19214 ^ _781404) ^ [_1123117] : [-(hBOOL(hAPP(_1122990, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123117))))]]], (18691 ^ _781404) ^ [_1114794] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1114794) = _1114794)], (4550 ^ _781404) ^ [_850503, _850505, _850507, _850509] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850509, _850505) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850507, _850503)), _850509 = _850507, _850505 = _850503], (5835 ^ _781404) ^ [_873944, _873946, _873948] : [_873944 = _873946, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873948, tc_HOL_Obool)), _873946), _873944)))], (21039 ^ _781404) ^ [_1155068, _1155070, _1155072] : [21040 ^ _781404 : [(21043 ^ _781404) ^ [] : [_1155070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21041 ^ _781404) ^ [] : [_1155068 = _1155072]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155068), _1155070) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155072), _1155070))], (7888 ^ _781404) ^ [_911987, _911989, _911991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911987, tc_HOL_Obool)), _911989), _911991)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911987, tc_HOL_Obool)), _911989), _911991) = _911989)], (14293 ^ _781404) ^ [_1031132, _1031134, _1031136] : [hBOOL(hAPP(_1031132, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031134), _1031136))), 14296 ^ _781404 : [(14303 ^ _781404) ^ [_1031317] : [_1031134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031136), _1031317), -(hBOOL(hAPP(_1031132, _1031317)))], (14297 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1031134), _1031136)), -(hBOOL(hAPP(_1031132, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (35533 ^ _781404) ^ [_1444484, _1444486] : [-(c_Divides_Odivmod__int(_1444484, _1444486) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1444484), _1444486)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1444484, _1444486)))], (45736 ^ _781404) ^ [_1697565, _1697567, _1697569, _1697571, _1697573] : [c_List_Opartition(_1697565, _1697567, _1697569) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1697565), tc_List_Olist(_1697565)), _1697571), _1697573), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1697565, tc_HOL_Obool)), hAPP(c_List_Oset(_1697565), _1697571)), hAPP(c_List_Oset(_1697565), _1697573)) = hAPP(c_List_Oset(_1697565), _1697569))], (48268 ^ _781404) ^ [_1753304, _1753306] : [class_Orderings_Olinorder(_1753304), hBOOL(hAPP(c_Finite__Set_Ofinite(_1753304), _1753306)), 48276 ^ _781404 : [(48279 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1753304, 48275 ^ [_1753304, _1753306]))], (48281 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1753304), 48275 ^ [_1753304, _1753306])))], (48283 ^ _781404) ^ [_1753630] : [-(_1753630 = 48275 ^ [_1753304, _1753306]), hAPP(c_List_Oset(_1753304), _1753630) = _1753306, c_List_Olinorder__class_Osorted(_1753304, _1753630), hBOOL(hAPP(c_List_Odistinct(_1753304), _1753630))], (48277 ^ _781404) ^ [] : [-(hAPP(c_List_Oset(_1753304), 48275 ^ [_1753304, _1753306]) = _1753306)]]], (33976 ^ _781404) ^ [_1404829, _1404831] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1404829), _1404831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1404829)), _1404831)))], (35280 ^ _781404) ^ [_1438603, _1438605, _1438607, _1438609, _1438611, _1438613, _1438615] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1438603, tc_fun(_1438605, tc_fun(_1438607, tc_HOL_Obool))), _1438609), _1438611), _1438613), _1438615)), 35283 ^ _781404 : [(35284 ^ _781404) ^ [_1438731] : [hBOOL(hAPP(hAPP(c_member(_1438603), _1438731), _1438609)), -(hBOOL(hAPP(hAPP(hAPP(_1438611, _1438731), _1438613), _1438615)))]]], (49231 ^ _781404) ^ [_1773727, _1773729, _1773731] : [-(_1773727 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1773729), c_List_Oreplicate(_1773729, _1773727, _1773731)) = hAPP(hAPP(c_Set_Oinsert(_1773729), _1773731), c_Orderings_Obot__class_Obot(tc_fun(_1773729, tc_HOL_Obool))))], (30156 ^ _781404) ^ [_1322571, _1322573, _1322575, _1322577, _1322579] : [class_Groups_Ocomm__monoid__mult(_1322571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322573), _1322575)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322573), _1322577)), 30170 ^ _781404 : [(30173 ^ _781404) ^ [] : [hAPP(_1322579, 30169 ^ [_1322571, _1322573, _1322575, _1322577, _1322579]) = c_Groups_Oone__class_Oone(_1322571)], (30171 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322573), 30169 ^ [_1322571, _1322573, _1322575, _1322577, _1322579]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322573, tc_HOL_Obool)), _1322575), _1322577))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1322573, _1322571), _1322579), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322573, tc_HOL_Obool)), _1322575), _1322577)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322571), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1322573, _1322571), _1322579), _1322575)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1322573, _1322571), _1322579), _1322577)))], (12660 ^ _781404) ^ [_1000279, _1000281, _1000283, _1000285] : [hBOOL(hAPP(hAPP(c_member(_1000279), _1000281), c_SetInterval_Oord_OatMost(_1000279, _1000283, _1000285))), -(hBOOL(hAPP(hAPP(_1000283, _1000281), _1000285)))], (38975 ^ _781404) ^ [_1526070, _1526072] : [hAPP(c_Set_OCollect(_1526070), _1526072) = c_Orderings_Obot__class_Obot(tc_fun(_1526070, tc_HOL_Obool)), 38978 ^ _781404 : [(38979 ^ _781404) ^ [_1526155] : [hBOOL(hAPP(_1526072, _1526155))]]], (38837 ^ _781404) ^ [_1522083, _1522085, _1522087, _1522089] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1522083), _1522085)), 38843 ^ _781404 : [(38846 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1522087), hAPP(_1522089, 38842 ^ [_1522083, _1522085, _1522087, _1522089])))], (38844 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1522083), 38842 ^ [_1522083, _1522085, _1522087, _1522089]), _1522085)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1522083, _1522087)), hAPP(hAPP(c_Product__Type_OSigma(_1522083, _1522087), _1522085), _1522089))))], (38187 ^ _781404) ^ [_1505292, _1505294, _1505296, _1505298, _1505300] : [c_Relation_Orefl__on(_1505292, _1505294, _1505296), c_Relation_Orefl__on(_1505292, _1505298, _1505300), -(c_Relation_Orefl__on(_1505292, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1505292, tc_HOL_Obool)), _1505294), _1505298), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1505292, _1505292), tc_HOL_Obool)), _1505296), _1505300)))], (37954 ^ _781404) ^ [_1498876, _1498878, _1498880, _1498882] : [c_Equiv__Relations_Oequivp(_1498876, _1498878), hBOOL(hAPP(hAPP(_1498878, _1498880), _1498882)), -(hBOOL(hAPP(hAPP(_1498878, _1498882), _1498880)))], (33139 ^ _781404) ^ [_1379742, _1379744, _1379746] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1379742), _1379744), _1379746) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1379742), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1379742, tc_Int_Oint), _1379744), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1379746))), class_Groups_Ocomm__monoid__add(_1379742), class_Groups_Ocomm__monoid__mult(_1379742)], (31396 ^ _781404) ^ [_1346137, _1346139, _1346141] : [class_Orderings_Olinorder(_1346137), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346137), _1346139)), -(_1346141 = c_Orderings_Obot__class_Obot(tc_fun(_1346137, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1346137, tc_HOL_Obool)), _1346141), _1346139)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346137), c_Big__Operators_Olinorder__class_OMin(_1346137, _1346141)), c_Big__Operators_Olinorder__class_OMin(_1346137, _1346139)) = c_Big__Operators_Olinorder__class_OMin(_1346137, _1346139))], (45605 ^ _781404) ^ [_1694948, _1694950, _1694952, _1694954] : [class_Groups_Ocomm__monoid__add(_1694948), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1694948), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1694948), _1694950), c_List_Oupto(_1694952, _1694954))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1694948), _1694950), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1694952, _1694954))))], (28907 ^ _781404) ^ [_1298915, _1298917, _1298919, _1298921] : [class_Fields_Olinordered__field__inverse__zero(_1298915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298915), _1298917), _1298919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298915), _1298921), c_Groups_Ozero__class_Ozero(_1298915))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298915), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298915), _1298919), _1298921)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298915), _1298917), _1298921))))], (15615 ^ _781404) ^ [_1057744, _1057746] : [class_Complete__Lattice_Ocomplete__lattice(_1057744), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057744), _1057746)), -(_1057746 = c_Orderings_Obot__class_Obot(tc_fun(_1057744, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1057744, _1057746) = c_Complete__Lattice_OSup__class_OSup(_1057744, _1057746))], (23842 ^ _781404) ^ [_1209320, _1209322, _1209324] : [class_Divides_Osemiring__div(_1209320), -(_1209322 = c_Groups_Ozero__class_Ozero(_1209320)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209320), _1209324), _1209322)), _1209322) = _1209324)], (31372 ^ _781404) ^ [_1345738, _1345740, _1345742] : [class_Orderings_Olinorder(_1345738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345738), _1345740)), -(c_Big__Operators_Olattice_OInf__fin(_1345738, c_Orderings_Oord__class_Omin(_1345738), hAPP(hAPP(c_Set_Oinsert(_1345738), _1345742), _1345740)) = hAPP(hAPP(c_Finite__Set_Ofold(_1345738, _1345738, c_Orderings_Oord__class_Omin(_1345738)), _1345742), _1345740))], (44020 ^ _781404) ^ [_1659874, _1659876, _1659878] : [-(hAPP(c_List_Oset(_1659874), hAPP(hAPP(c_List_Oappend(_1659874), _1659876), _1659878)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1659874, tc_HOL_Obool)), hAPP(c_List_Oset(_1659874), _1659876)), hAPP(c_List_Oset(_1659874), _1659878)))], (44537 ^ _781404) ^ [_1672336, _1672338, _1672340, _1672342, _1672344] : [-(hAPP(hAPP(c_List_Ozip(_1672336, _1672338), _1672340), hAPP(hAPP(c_List_Oappend(_1672338), _1672342), _1672344)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1672336, _1672338)), hAPP(hAPP(c_List_Ozip(_1672336, _1672338), hAPP(hAPP(c_List_Otake(_1672336), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672338)), _1672342)), _1672340)), _1672342)), hAPP(hAPP(c_List_Ozip(_1672336, _1672338), hAPP(hAPP(c_List_Odrop(_1672336), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672338)), _1672342)), _1672340)), _1672344)))], (50654 ^ _781404) ^ [_1805130, _1805132, _1805134, _1805136, _1805138] : [c_Fun_Oinj__on(_1805130, _1805132, _1805134, c_Orderings_Otop__class_Otop(tc_fun(_1805130, tc_HOL_Obool))), 50660 ^ _781404 : [(50663 ^ _781404) ^ [] : [hBOOL(hAPP(_1805136, hAPP(c_Hilbert__Choice_Oinv__into(_1805130, _1805132, c_Orderings_Otop__class_Otop(tc_fun(_1805130, tc_HOL_Obool)), _1805134), 50659 ^ [_1805130, _1805132, _1805134, _1805136, _1805138])))], (50661 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805132), 50659 ^ [_1805130, _1805132, _1805134, _1805136, _1805138]), hAPP(c_Set_Oimage(_1805130, _1805132, _1805134), c_Orderings_Otop__class_Otop(tc_fun(_1805130, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1805136, _1805138)))], (18253 ^ _781404) ^ [_1106634, _1106636, _1106638, _1106640] : [class_Rings_Olinordered__semidom(_1106634), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1106636), _1106638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106634), c_Groups_Oone__class_Oone(_1106634)), _1106640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106634), hAPP(hAPP(c_Power_Opower__class_Opower(_1106634), _1106640), _1106636)), hAPP(hAPP(c_Power_Opower__class_Opower(_1106634), _1106640), _1106638))))], (15693 ^ _781404) ^ [_1058979, _1058981, _1058983] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1058979), _1058981)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058979), _1058983)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1058979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1058979, tc_HOL_Obool)), _1058981), _1058983))), hAPP(c_Finite__Set_Ocard(_1058979), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1058979, tc_HOL_Obool)), _1058981), _1058983))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1058979), _1058981)), hAPP(c_Finite__Set_Ocard(_1058979), _1058983)))], (15451 ^ _781404) ^ [_1054793, _1054795] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1054793, _1054795)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1054795), _1054793))], (37214 ^ _781404) ^ [_1479585, _1479587, _1479589, _1479591] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1479585), _1479587)), 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)), _1479585), _1479589)), 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)), _1479587), _1479591)), 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)), _1479587), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1479589), _1479591))), c_FunDef_Omin__weak)))], (8435 ^ _781404) ^ [_923684, _923686, _923688] : [8437 ^ _781404 : [(8443 ^ _781404) ^ [] : [-(8436 ^ [_923684, _923686, _923688] = 8439 ^ [_923684, _923686, _923688])], (8441 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_923684), 8439 ^ [_923684, _923686, _923688]), _923688)))], (8438 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_923684), 8436 ^ [_923684, _923686, _923688]), _923686)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923684, tc_HOL_Obool)), _923686), _923688) = c_Orderings_Obot__class_Obot(tc_fun(_923684, tc_HOL_Obool)))], (25357 ^ _781404) ^ [_1234760, _1234762, _1234764, _1234766] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1234760, _1234762, _1234764), _1234766), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1234762)], (50979 ^ _781404) ^ [_1811970, _1811972, _1811974] : [c_Fun_Obij__betw(_1811970, _1811972, _1811974, c_Orderings_Otop__class_Otop(tc_fun(_1811970, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1811972, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1811970, _1811972, _1811974, c_Orderings_Otop__class_Otop(tc_fun(_1811970, tc_HOL_Obool))))], (5262 ^ _781404) ^ [_861725, _861727, _861729, _861731] : [-(c_Transitive__Closure_Ortrancl(_861731, _861727) = c_Transitive__Closure_Ortrancl(_861729, _861725)), _861731 = _861729, _861727 = _861725], (46243 ^ _781404) ^ [_1709489, _1709491] : [c_List_Oremdups(_1709489, _1709491) = _1709491, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709489)), c_List_Oremdups(_1709489, _1709491)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709489)), _1709491))], (2268 ^ _781404) ^ [_814428, _814430, _814432, _814434] : [-(c_Orderings_Oord_Omax(_814434, _814430) = c_Orderings_Oord_Omax(_814432, _814428)), _814434 = _814432, _814430 = _814428], (42597 ^ _781404) ^ [_1625769, _1625771, _1625773, _1625775] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1625769)), hAPP(hAPP(c_List_Olist_OCons(_1625769), _1625771), _1625773)), c_List_Olists(_1625769, _1625775)))), hBOOL(hAPP(hAPP(c_member(_1625769), _1625771), _1625775)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1625769)), _1625773), c_List_Olists(_1625769, _1625775)))], (19472 ^ _781404) ^ [_1127648, _1127650] : [class_Rings_Oring__1(_1127648), -(hBOOL(hAPP(hAPP(c_member(_1127648), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127648), _1127650)), c_Int_Oring__1__class_OInts(_1127648))))], (52400 ^ _781404) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (36977 ^ _781404) ^ [_1474570, _1474572, _1474574, _1474576, _1474578, _1474580] : [c_Finite__Set_Ofolding__idem(_1474570, _1474572, _1474574, _1474576), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474570), _1474578)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474570), _1474580)), -(hAPP(_1474576, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474570, tc_HOL_Obool)), _1474578), _1474580)) = hAPP(c_Fun_Ocomp(_1474572, _1474572, _1474572, hAPP(_1474576, _1474578)), hAPP(_1474576, _1474580)))], (2910 ^ _781404) ^ [_824559, _824561, _824563, _824565] : [-(c_Nitpick_Oint__lcm(_824565, _824561) = c_Nitpick_Oint__lcm(_824563, _824559)), _824565 = _824563, _824561 = _824559], (1266 ^ _781404) ^ [_800269, _800271] : [-(class_Rings_Olinordered__idom(_800269)), _800271 = _800269, class_Rings_Olinordered__idom(_800271)], (30538 ^ _781404) ^ [_1330283, _1330285, _1330287, _1330289, _1330291, _1330293, _1330295] : [hBOOL(hAPP(hAPP(c_member(_1330283), _1330285), _1330287)), c_Nitpick_Ofold__graph_H(_1330283, _1330289, _1330291, _1330293, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330283, tc_HOL_Obool)), _1330287), hAPP(hAPP(c_Set_Oinsert(_1330283), _1330285), c_Orderings_Obot__class_Obot(tc_fun(_1330283, tc_HOL_Obool)))), _1330295), -(c_Nitpick_Ofold__graph_H(_1330283, _1330289, _1330291, _1330293, _1330287, hAPP(hAPP(_1330291, _1330285), _1330295)))], (49788 ^ _781404) ^ [_1786540, _1786542, _1786544] : [c_Relation_Otrans(_1786540, _1786542), c_Relation_Otrans(_1786540, _1786544), -(c_Relation_Otrans(_1786540, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1786540, _1786540), tc_HOL_Obool)), _1786542), _1786544)))], (46554 ^ _781404) ^ [_1716683, _1716685, _1716687] : [-(c_List_Opartition(_1716683, _1716685, _1716687) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716683), tc_List_Olist(_1716683)), hAPP(c_List_Ofilter(_1716683, _1716685), _1716687)), hAPP(c_List_Ofilter(_1716683, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1716683, c_fNot), _1716685)), _1716687)))], (39872 ^ _781404) ^ [_1556460, _1556462, _1556464] : [c_Wellfounded_Owf(_1556460, _1556462), hBOOL(hAPP(hAPP(c_member(tc_prod(_1556460, _1556460)), hAPP(hAPP(c_Product__Type_OPair(_1556460, _1556460), _1556464), _1556464)), _1556462))], (31914 ^ _781404) ^ [_1355855] : [class_Orderings_Olinorder(_1355855), -(c_Finite__Set_Ofun__left__comm__idem(_1355855, _1355855, c_Orderings_Oord__class_Omax(_1355855)))], (41986 ^ _781404) ^ [_1607112, _1607114, _1607116, _1607118, _1607120] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607112, _1607112)), hAPP(hAPP(c_Product__Type_OPair(_1607112, _1607112), _1607114), _1607116)), c_Transitive__Closure_Ortrancl(_1607112, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1607112, _1607112), tc_HOL_Obool)), _1607118), _1607120)))), 41992 ^ _781404 : [(41998 ^ _781404) ^ [] : [41994 ^ [_1607112, _1607114, _1607116, _1607118, _1607120] = 41991 ^ [_1607112, _1607114, _1607116, _1607118, _1607120]], (41996 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607112, _1607112)), hAPP(hAPP(c_Product__Type_OPair(_1607112, _1607112), 41994 ^ [_1607112, _1607114, _1607116, _1607118, _1607120]), 41991 ^ [_1607112, _1607114, _1607116, _1607118, _1607120])), _1607120)))], (41993 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607112, _1607112)), hAPP(hAPP(c_Product__Type_OPair(_1607112, _1607112), 41991 ^ [_1607112, _1607114, _1607116, _1607118, _1607120]), _1607116)), c_Transitive__Closure_Ortrancl(_1607112, _1607118))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607112, _1607112)), hAPP(hAPP(c_Product__Type_OPair(_1607112, _1607112), _1607114), _1607116)), c_Transitive__Closure_Ortrancl(_1607112, _1607118))))], (33382 ^ _781404) ^ [_1386320, _1386322, _1386324, _1386326, _1386328, _1386330] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1386322, _1386324)), hAPP(hAPP(c_Product__Type_OPair(_1386322, _1386324), _1386328), _1386330)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1386320, tc_fun(tc_prod(_1386322, _1386324), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1386320, tc_HOL_Obool))), _1386326))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1386320, tc_fun(_1386322, tc_fun(_1386324, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1386320, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1386322, _1386324), tc_HOL_Obool), tc_fun(_1386322, tc_fun(_1386324, tc_HOL_Obool)), _1386320), hAPP(c_COMBC(_1386322, tc_fun(tc_prod(_1386322, _1386324), tc_HOL_Obool), tc_fun(_1386324, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1386324, tc_fun(tc_fun(tc_prod(_1386322, _1386324), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1386322, _1386324), tc_HOL_Obool), tc_fun(_1386324, tc_HOL_Obool)), _1386322), c_COMBC(_1386324, tc_fun(tc_prod(_1386322, _1386324), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1386324, tc_prod(_1386322, _1386324)), tc_fun(_1386324, tc_fun(tc_fun(tc_prod(_1386322, _1386324), tc_HOL_Obool), tc_HOL_Obool)), _1386322), hAPP(c_COMBB(tc_prod(_1386322, _1386324), tc_fun(tc_fun(tc_prod(_1386322, _1386324), tc_HOL_Obool), tc_HOL_Obool), _1386324), c_member(tc_prod(_1386322, _1386324)))), c_Product__Type_OPair(_1386322, _1386324))))), _1386326)), _1386328), _1386330)))], (37680 ^ _781404) ^ [_1492499, _1492501, _1492503, _1492505, _1492507] : [c_Equiv__Relations_Oequiv(_1492499, _1492501, _1492503), hBOOL(hAPP(hAPP(c_member(tc_fun(_1492499, tc_HOL_Obool)), _1492505), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1492499), _1492501), _1492503))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1492499, tc_HOL_Obool)), _1492507), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1492499), _1492501), _1492503))), -(_1492505 = _1492507), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1492499, tc_HOL_Obool)), _1492505), _1492507) = c_Orderings_Obot__class_Obot(tc_fun(_1492499, tc_HOL_Obool)))], (8285 ^ _781404) ^ [_921024, _921026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921024, tc_HOL_Obool)), _921026), c_Orderings_Obot__class_Obot(tc_fun(_921024, tc_HOL_Obool)))), -(_921026 = c_Orderings_Obot__class_Obot(tc_fun(_921024, tc_HOL_Obool)))], (7127 ^ _781404) ^ [_896849, _896851, _896853, _896855] : [class_Lattices_Osemilattice__sup(_896849), 7130 ^ _781404 : [(7139 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896849), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896849), _896851), _896853)), _896855))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896849), _896851), _896855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896849), _896853), _896855))], (7131 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896849), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896849), _896851), _896853)), _896855)), 7134 ^ _781404 : [(7137 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896849), _896853), _896855)))], (7135 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896849), _896851), _896855)))]]]]], (50439 ^ _781404) ^ [_1800039, _1800041] : [c_Equiv__Relations_Opart__equivp(_1800039, _1800041), 50443 ^ _781404 : [(50448 ^ _781404) ^ [] : [-(c_Predicate_Otransp(_1800039, _1800041))], (50446 ^ _781404) ^ [] : [-(c_Predicate_Osymp(_1800039, _1800041))], (50444 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1800041, 50442 ^ [_1800039, _1800041]), 50442 ^ [_1800039, _1800041])))]]], (41187 ^ _781404) ^ [_1587517, _1587519, _1587521, _1587523, _1587525] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587517, _1587517)), hAPP(hAPP(c_Product__Type_OPair(_1587517, _1587517), _1587519), _1587521)), c_Transitive__Closure_Ortrancl(_1587517, _1587523))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587517, _1587517)), hAPP(hAPP(c_Product__Type_OPair(_1587517, _1587517), _1587521), _1587525)), c_Transitive__Closure_Ortrancl(_1587517, _1587523))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587517, _1587517)), hAPP(hAPP(c_Product__Type_OPair(_1587517, _1587517), _1587519), _1587525)), c_Transitive__Closure_Ortrancl(_1587517, _1587523))))], (15389 ^ _781404) ^ [_1053765] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1053765)) = _1053765)], (15347 ^ _781404) ^ [_1052863, _1052865, _1052867, _1052869, _1052871] : [class_Groups_Ocomm__monoid__add(_1052863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052865), _1052867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1052865, tc_HOL_Obool)), _1052869), _1052867)), 15361 ^ _781404 : [(15364 ^ _781404) ^ [] : [hAPP(_1052871, 15360 ^ [_1052863, _1052865, _1052867, _1052869, _1052871]) = c_Groups_Ozero__class_Ozero(_1052863)], (15362 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1052865), 15360 ^ [_1052863, _1052865, _1052867, _1052869, _1052871]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1052865, tc_HOL_Obool)), _1052867), _1052869))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1052865, _1052863), _1052871), _1052869) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1052865, _1052863), _1052871), _1052867))], (21307 ^ _781404) ^ [_1160014, _1160016, _1160018] : [class_Rings_Oordered__cancel__semiring(_1160014), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160014), _1160016), _1160018)), c_Groups_Ozero__class_Ozero(_1160014)))), 21312 ^ _781404 : [(21319 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160014), _1160016), c_Groups_Ozero__class_Ozero(_1160014))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160014), c_Groups_Ozero__class_Ozero(_1160014)), _1160018))], (21313 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160014), c_Groups_Ozero__class_Ozero(_1160014)), _1160016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160014), _1160018), c_Groups_Ozero__class_Ozero(_1160014)))]]], (3526 ^ _781404) ^ [_834111, _834113] : [_834113 = _834111, -(c_List_Otranspose__rel(_834113) = c_List_Otranspose__rel(_834111))], (10557 ^ _781404) ^ [_960999, _961001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960999), hAPP(c_Nat_OSuc, _961001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960999), _961001))), -(_960999 = _961001)], (17521 ^ _781404) ^ [_1093837] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093837), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1093837)], (33111 ^ _781404) ^ [_1378928, _1378930] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1378928)), _1378930) = 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), _1378928)), _1378930))], (11967 ^ _781404) ^ [_986478, _986480, _986482, _986484] : [11968 ^ _781404 : [(11971 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_986478), _986480), _986484))], (11969 ^ _781404) ^ [] : [_986480 = _986482]], -(hBOOL(hAPP(hAPP(c_member(_986478), _986480), hAPP(hAPP(c_Set_Oinsert(_986478), _986482), _986484))))], (21845 ^ _781404) ^ [_1169928, _1169930, _1169932, _1169934] : [class_Rings_Olinordered__comm__semiring__strict(_1169928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169928), _1169930), _1169932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169928), c_Groups_Ozero__class_Ozero(_1169928)), _1169934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169928), _1169934), _1169930)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169928), _1169934), _1169932))))], (17206 ^ _781404) ^ [_1088062, _1088064, _1088066] : [class_Int_Onumber__ring(_1088062), -(hAPP(c_Int_Onumber__class_Onumber__of(_1088062), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1088064), _1088066)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088062), hAPP(c_Int_Onumber__class_Onumber__of(_1088062), _1088064)), hAPP(c_Int_Onumber__class_Onumber__of(_1088062), _1088066)))], (52404 ^ _781404) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (45317 ^ _781404) ^ [_1688882, _1688884, _1688886, _1688888] : [-(_1688882 = c_List_Olist_ONil(_1688884)), -(hAPP(c_List_Ohd(_1688886), hAPP(hAPP(c_List_Omap(_1688884, _1688886), _1688888), _1688882)) = hAPP(_1688888, hAPP(c_List_Ohd(_1688884), _1688882)))], (166 ^ _781404) ^ [_784023, _784025, _784027, _784029, _784031, _784033, _784035, _784037, _784039, _784041] : [-(c_Big__Operators_Ocomm__monoid__big(_784039, _784035, _784031, _784027, _784023)), c_Big__Operators_Ocomm__monoid__big(_784041, _784037, _784033, _784029, _784025), _784041 = _784039, _784037 = _784035, _784033 = _784031, _784029 = _784027, _784025 = _784023], (43825 ^ _781404) ^ [_1655432, _1655434, _1655436, _1655438, _1655440] : [hAPP(hAPP(c_List_Oappend(_1655432), _1655434), hAPP(hAPP(c_List_Olist_OCons(_1655432), _1655436), c_List_Olist_ONil(_1655432))) = hAPP(hAPP(c_List_Oappend(_1655432), _1655438), hAPP(hAPP(c_List_Olist_OCons(_1655432), _1655440), c_List_Olist_ONil(_1655432))), 43828 ^ _781404 : [(43831 ^ _781404) ^ [] : [-(_1655436 = _1655440)], (43829 ^ _781404) ^ [] : [-(_1655434 = _1655438)]]], (29209 ^ _781404) ^ [_1304096, _1304098, _1304100] : [class_Fields_Olinordered__field(_1304096), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304096), _1304098), c_Groups_Ozero__class_Ozero(_1304096))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304096), c_Groups_Ozero__class_Ozero(_1304096)), _1304100)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304096), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304096), _1304098), _1304100)), c_Groups_Ozero__class_Ozero(_1304096))))], (27339 ^ _781404) ^ [_1269717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1269717)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1269717 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7621 ^ _781404) ^ [_906536, _906538, _906540, _906542, _906544] : [hAPP(c_Set_Oimage(_906536, _906538, _906540), _906542) = _906544, -(hAPP(c_Set_Oimage(tc_fun(_906536, tc_HOL_Obool), tc_fun(_906538, tc_HOL_Obool), c_Set_Oimage(_906536, _906538, _906540)), hAPP(c_Set_OPow(_906536), _906542)) = hAPP(c_Set_OPow(_906538), _906544))], (15437 ^ _781404) ^ [_1054547] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1054547)) = hAPP(c_Nat_OSuc, _1054547))], (17513 ^ _781404) ^ [_1093688, _1093690, _1093692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093688), _1093690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093688), _1093692)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093690), _1093692))))], (1064 ^ _781404) ^ [_797358, _797360, _797362, _797364] : [-(c_Equiv__Relations_Oequivp(_797362, _797358)), c_Equiv__Relations_Oequivp(_797364, _797360), _797364 = _797362, _797360 = _797358], (4342 ^ _781404) ^ [_847149, _847151, _847153, _847155, _847157, _847159] : [-(c_List_Oreplicate(_847159, _847155, _847151) = c_List_Oreplicate(_847157, _847153, _847149)), _847159 = _847157, _847155 = _847153, _847151 = _847149], (25301 ^ _781404) ^ [_1233988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233988), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1233988)), c_Int_OMin)))], (49394 ^ _781404) ^ [_1777286, _1777288, _1777290] : [hBOOL(hAPP(hAPP(c_member(_1777286), _1777288), hAPP(c_List_Oset(_1777286), _1777290))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1777286), _1777290), _1777288)))], (16348 ^ _781404) ^ [_1071797, _1071799] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071797), hAPP(c_Nat_OSuc, _1071799)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071797), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1071799))], (43358 ^ _781404) ^ [_1645542, _1645544] : [hBOOL(hAPP(c_List_Odistinct(_1645542), _1645544)), 43361 ^ _781404 : [(43362 ^ _781404) ^ [_1645674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645674), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645542)), _1645544))), 43365 ^ _781404 : [(43366 ^ _781404) ^ [_1645801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645801), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645542)), _1645544))), -(_1645674 = _1645801), hAPP(hAPP(c_List_Onth(_1645542), _1645544), _1645674) = hAPP(hAPP(c_List_Onth(_1645542), _1645544), _1645801)]]]]], (3948 ^ _781404) ^ [_840832, _840834, _840836, _840838, _840840, _840842, _840844, _840846] : [-(c_New__DSequence_Oneg__decr__bind(_840846, _840842, _840838, _840834) = c_New__DSequence_Oneg__decr__bind(_840844, _840840, _840836, _840832)), _840846 = _840844, _840842 = _840840, _840838 = _840836, _840834 = _840832], (23083 ^ _781404) ^ [_1194646, _1194648, _1194650] : [23084 ^ _781404 : [(23087 ^ _781404) ^ [] : [_1194648 = _1194650], (23085 ^ _781404) ^ [] : [_1194646 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194646), _1194648) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194646), _1194650))], (41197 ^ _781404) ^ [_1587790, _1587792, _1587794, _1587796, _1587798] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587790, _1587790)), hAPP(hAPP(c_Product__Type_OPair(_1587790, _1587790), _1587792), _1587794)), c_Transitive__Closure_Ortrancl(_1587790, _1587796))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587790, _1587790)), hAPP(hAPP(c_Product__Type_OPair(_1587790, _1587790), _1587794), _1587798)), _1587796)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587790, _1587790)), hAPP(hAPP(c_Product__Type_OPair(_1587790, _1587790), _1587792), _1587798)), c_Transitive__Closure_Ortrancl(_1587790, _1587796))))], (40425 ^ _781404) ^ [_1568869, _1568871, _1568873, _1568875, _1568877, _1568879] : [40428 ^ _781404 : [(40431 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1568875), _1568877), hAPP(hAPP(_1568879, 40426 ^ [_1568869, _1568871, _1568873, _1568875, _1568877, _1568879]), 40427 ^ [_1568869, _1568871, _1568873, _1568875, _1568877, _1568879])))], (40429 ^ _781404) ^ [] : [-(_1568869 = hAPP(hAPP(c_Product__Type_OPair(_1568871, _1568873), 40426 ^ [_1568869, _1568871, _1568873, _1568875, _1568877, _1568879]), 40427 ^ [_1568869, _1568871, _1568873, _1568875, _1568877, _1568879]))]], -(hBOOL(hAPP(hAPP(c_member(_1568875), _1568877), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1568871, _1568873, tc_fun(_1568875, tc_HOL_Obool)), _1568879), _1568869))))], (6403 ^ _781404) ^ [_883211] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883211), _883211)))], (26745 ^ _781404) ^ [_1258427, _1258429, _1258431, _1258433] : [class_Groups_Ocomm__monoid__add(_1258427), hBOOL(hAPP(c_Finite__Set_Ofinite(_1258429), _1258431)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1258429, _1258427), _1258433), _1258431) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1258427, _1258429, c_Groups_Oplus__class_Oplus(_1258427)), _1258433), c_Groups_Ozero__class_Ozero(_1258427)), _1258431))], (45315 ^ _781404) ^ [_1688812, _1688814, _1688816, _1688818, _1688820] : [-(hAPP(hAPP(c_List_Omap(_1688812, _1688814), _1688816), hAPP(hAPP(c_List_Oappend(_1688812), _1688818), _1688820)) = hAPP(hAPP(c_List_Oappend(_1688814), hAPP(hAPP(c_List_Omap(_1688812, _1688814), _1688816), _1688818)), hAPP(hAPP(c_List_Omap(_1688812, _1688814), _1688816), _1688820)))], (52320 ^ _781404) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (44415 ^ _781404) ^ [_1669307, _1669309, _1669311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669307)), _1669311)), _1669309)), -(hAPP(hAPP(c_List_Odrop(_1669307), _1669309), _1669311) = c_List_Olist_ONil(_1669307))], (50728 ^ _781404) ^ [_1806933, _1806935, _1806937, _1806939] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1806933, _1806935, _1806937, _1806939, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1806935)) = _1806937)], (24814 ^ _781404) ^ [_1226294] : [hBOOL(hAPP(_1226294, 24815 ^ [_1226294])), 24818 ^ _781404 : [(24819 ^ _781404) ^ [_1226388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226388)), -(hBOOL(hAPP(_1226294, hAPP(c_Int_Onat, _1226388))))]]], (24642 ^ _781404) ^ [_1223409, _1223411] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223409, _1223411) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223409), _1223411)), _1223411)))], (36534 ^ _781404) ^ [_1464284, _1464286, _1464288, _1464290, _1464292, _1464294, _1464296] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1464284, _1464286, _1464288), hAPP(c_Fun_Ocomp(_1464290, tc_fun(_1464286, _1464288), _1464284, _1464292), _1464294)), _1464296) = hAPP(hAPP(_1464292, hAPP(_1464294, hAPP(c_Product__Type_Ofst(_1464284, _1464286), _1464296))), hAPP(c_Product__Type_Osnd(_1464284, _1464286), _1464296)))], (4264 ^ _781404) ^ [_846000, _846002, _846004, _846006] : [-(c_List_Olast(_846006, _846002) = c_List_Olast(_846004, _846000)), _846006 = _846004, _846002 = _846000], (49173 ^ _781404) ^ [_1772650, _1772652] : [-(c_List_Oconcat(_1772650, c_List_Oreplicate(tc_List_Olist(_1772650), _1772652, c_List_Olist_ONil(_1772650))) = c_List_Olist_ONil(_1772650))], (33343 ^ _781404) ^ [_1385003, _1385005, _1385007, _1385009, _1385011, _1385013] : [-(hAPP(c_Set_Oimage(_1385003, _1385005, _1385007), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385009, tc_fun(_1385003, tc_HOL_Obool)), _1385011), _1385013)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385009, tc_fun(_1385005, tc_HOL_Obool)), _1385011), hAPP(hAPP(c_COMBB(tc_fun(_1385003, tc_HOL_Obool), tc_fun(_1385005, tc_HOL_Obool), _1385009), c_Set_Oimage(_1385003, _1385005, _1385007)), _1385013)))], (914 ^ _781404) ^ [_795133, _795135, _795137, _795139] : [-(c_Relation_Otrans(_795137, _795133)), c_Relation_Otrans(_795139, _795135), _795139 = _795137, _795135 = _795133], (49602 ^ _781404) ^ [_1782176, _1782178, _1782180] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1782176, _1782178, _1782180, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1782178)], (26509 ^ _781404) ^ [_1254039] : [c_Nat__Transfer_Ois__nat(_1254039), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254039)))], (33279 ^ _781404) ^ [_1383313, _1383315] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383313, tc_fun(_1383313, tc_HOL_Obool)), _1383315), hAPP(hAPP(c_COMBC(_1383313, tc_fun(_1383313, tc_HOL_Obool), tc_fun(_1383313, tc_HOL_Obool)), c_Set_Oinsert(_1383313)), c_Orderings_Obot__class_Obot(tc_fun(_1383313, tc_HOL_Obool)))) = _1383315)], (28643 ^ _781404) ^ [_1293983, _1293985] : [class_Fields_Olinordered__field__inverse__zero(_1293983), class_Int_Onumber__ring(_1293983), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293983), c_Groups_Ozero__class_Ozero(_1293983)), _1293985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293983), c_Groups_Ozero__class_Ozero(_1293983)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293983), _1293985), hAPP(c_Int_Onumber__class_Onumber__of(_1293983), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (3176 ^ _781404) ^ [_828684, _828686] : [_828686 = _828684, -(c_List_Orotate1(_828686) = c_List_Orotate1(_828684))], (13357 ^ _781404) ^ [_1013557, _1013559, _1013561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013559), _1013561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013557), _1013559)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013557), _1013561))))], (42141 ^ _781404) ^ [_1611617, _1611619] : [-(c_Nitpick_Ouminus__frac(_1611617, _1611619) = c_Nitpick_OAbs__Frac(_1611617, 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(_1611617), _1611619))), hAPP(c_Nitpick_Odenom(_1611617), _1611619))))], (11667 ^ _781404) ^ [_981154, _981156, _981158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981154), _981156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981154), _981158)), _981156)))], (34659 ^ _781404) ^ [_1424785, _1424787, _1424789, _1424791] : [class_Complete__Lattice_Ocomplete__lattice(_1424785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424787), _1424789)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1424787, _1424785), _1424789), _1424791) = hAPP(hAPP(c_Finite__Set_Ofold(_1424787, _1424785, hAPP(hAPP(c_COMBB(_1424785, tc_fun(_1424785, _1424785), _1424787), c_Lattices_Osemilattice__sup__class_Osup(_1424785)), _1424791)), c_Orderings_Obot__class_Obot(_1424785)), _1424789))], (19029 ^ _781404) ^ [_1120150, _1120152] : [c_Int_OBit1(_1120150) = c_Int_OBit1(_1120152), -(_1120150 = _1120152)], (25105 ^ _781404) ^ [_1230802, _1230804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1230802)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1230802), _1230804)), _1230802) = _1230804)], (41642 ^ _781404) ^ [_1598763, _1598765, _1598767] : [c_Relation_Orefl__on(_1598763, _1598765, _1598767), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598763, _1598763), tc_HOL_Obool)), _1598767), hAPP(hAPP(c_Relation_Orel__comp(_1598763, _1598763, _1598763), hAPP(c_Relation_Oconverse(_1598763, _1598763), _1598767)), _1598767))))], (8572 ^ _781404) ^ [_925956, _925958] : [class_Lattices_Obounded__lattice__bot(_925956), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925956), c_Orderings_Obot__class_Obot(_925956)), _925958) = c_Orderings_Obot__class_Obot(_925956))], (44641 ^ _781404) ^ [_1674376, _1674378, _1674380] : [hAPP(c_List_Orotate(_1674376, _1674378), _1674380) = c_List_Olist_ONil(_1674376), -(_1674380 = c_List_Olist_ONil(_1674376))], (22955 ^ _781404) ^ [_1191865] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1191865), 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), _1191865), _1191865))], (41267 ^ _781404) ^ [_1589530, _1589532, _1589534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1589530, _1589530), tc_HOL_Obool)), c_Relation_OId(_1589530)), _1589532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1589530, _1589530), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1589530, _1589530, _1589530), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1589530, _1589530), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1589530, _1589534)), _1589532)), _1589534)), _1589532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1589530, _1589530), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1589530, _1589534)), _1589532)))], (49303 ^ _781404) ^ [_1775184, _1775186] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1775184), _1775186))), 49306 ^ _781404 : [(49313 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1775184), _1775186))), -(c_Lazy__Sequence_Osmall__lazy_H(_1775184, _1775186) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1775186), c_Lazy__Sequence_Osmall__lazy_H(_1775184, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1775186), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (49307 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1775184), _1775186)), -(c_Lazy__Sequence_Osmall__lazy_H(_1775184, _1775186) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (51594 ^ _781404) ^ [_1826382, _1826384, _1826386] : [class_Rings_Ocomm__semiring__1(_1826382), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826382), _1826384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826382), _1826384), _1826386))))], (308 ^ _781404) ^ [_786176, _786178] : [-(class_Fields_Ofield(_786176)), _786178 = _786176, class_Fields_Ofield(_786178)], (12806 ^ _781404) ^ [_1003353, _1003355, _1003357, _1003359, _1003361, _1003363] : [-(hBOOL(hAPP(hAPP(c_member(_1003353), _1003355), _1003357))), -(hAPP(c_Set_Oimage(_1003353, _1003359, c_Fun_Ofun__upd(_1003353, _1003359, _1003361, _1003355, _1003363)), _1003357) = hAPP(c_Set_Oimage(_1003353, _1003359, _1003361), _1003357))], (46619 ^ _781404) ^ [_1718163, _1718165, _1718167, _1718169] : [hBOOL(hAPP(hAPP(c_member(_1718163), _1718165), hAPP(c_List_Oset(_1718163), _1718167))), -(hBOOL(hAPP(_1718169, _1718165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718163)), hAPP(c_List_Ofilter(_1718163, _1718169), _1718167))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718163)), _1718167))))], (36670 ^ _781404) ^ [_1466857, _1466859, _1466861, _1466863] : [c_Fun_Oinj__on(_1466857, _1466859, _1466861, c_Orderings_Otop__class_Otop(tc_fun(_1466857, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466857, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1466857, _1466859, _1466861), hAPP(hAPP(c_Set_Oinsert(_1466859), _1466863), c_Orderings_Obot__class_Obot(tc_fun(_1466859, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1466857), c_HOL_OThe(_1466857, hAPP(hAPP(c_COMBC(_1466857, _1466859, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1466859, tc_fun(_1466859, tc_HOL_Obool), _1466857), c_fequal), _1466861)), _1466863))), c_Orderings_Obot__class_Obot(tc_fun(_1466857, tc_HOL_Obool))))))], (26349 ^ _781404) ^ [_1251421, _1251423] : [c_Nat__Transfer_Ois__nat(_1251421), c_Nat__Transfer_Ois__nat(_1251423), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1251421, _1251423)))], (31736 ^ _781404) ^ [_1352556, _1352558] : [class_Groups_Olinordered__ab__group__add(_1352556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352556), _1352558)), -(_1352558 = c_Orderings_Obot__class_Obot(tc_fun(_1352556, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1352556), c_Big__Operators_Olinorder__class_OMax(_1352556, _1352558)) = c_Big__Operators_Olinorder__class_OMin(_1352556, hAPP(c_Set_Oimage(_1352556, _1352556, c_Groups_Ouminus__class_Ouminus(_1352556)), _1352558)))], (31560 ^ _781404) ^ [_1349046, _1349048, _1349050] : [class_Orderings_Olinorder(_1349046), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349046), _1349048)), 31567 ^ _781404 : [(31574 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349046, tc_HOL_Obool)), _1349048), hAPP(hAPP(c_Set_Oinsert(_1349046), _1349050), c_Orderings_Obot__class_Obot(tc_fun(_1349046, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1349046, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1349046, hAPP(hAPP(c_Set_Oinsert(_1349046), _1349050), _1349048)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349046), _1349050), c_Big__Operators_Olinorder__class_OMin(_1349046, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349046, tc_HOL_Obool)), _1349048), hAPP(hAPP(c_Set_Oinsert(_1349046), _1349050), c_Orderings_Obot__class_Obot(tc_fun(_1349046, tc_HOL_Obool)))))))], (31568 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349046, tc_HOL_Obool)), _1349048), hAPP(hAPP(c_Set_Oinsert(_1349046), _1349050), c_Orderings_Obot__class_Obot(tc_fun(_1349046, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1349046, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1349046, hAPP(hAPP(c_Set_Oinsert(_1349046), _1349050), _1349048)) = _1349050)]]], (13301 ^ _781404) ^ [_1012463, _1012465] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1012463)), _1012465) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012463), hAPP(c_Nat_OSuc, _1012465)))], (11111 ^ _781404) ^ [_970033, _970035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _970033)), _970035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970033), _970035)))], (37485 ^ _781404) ^ [_1487414, _1487416, _1487418, _1487420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1487414), _1487420)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1487418), _1487416))), -(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), _1487414), _1487416)), 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), _1487418), _1487420)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (19536 ^ _781404) ^ [_1128759] : [class_Int_Onumber__ring(_1128759), -(c_Groups_Oone__class_Oone(_1128759) = hAPP(c_Int_Onumber__class_Onumber__of(_1128759), c_Int_OBit1(c_Int_OPls)))], (41207 ^ _781404) ^ [_1588057, _1588059, _1588061, _1588063, _1588065] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588057, _1588057)), hAPP(hAPP(c_Product__Type_OPair(_1588057, _1588057), _1588059), _1588061)), _1588063)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588057, _1588057)), hAPP(hAPP(c_Product__Type_OPair(_1588057, _1588057), _1588061), _1588065)), c_Transitive__Closure_Ortrancl(_1588057, _1588063))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588057, _1588057)), hAPP(hAPP(c_Product__Type_OPair(_1588057, _1588057), _1588059), _1588065)), c_Transitive__Closure_Ortrancl(_1588057, _1588063))))], (21093 ^ _781404) ^ [_1155910, _1155912, _1155914] : [class_Rings_Oring(_1155910), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1155910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155910), _1155912), _1155914)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155910), hAPP(c_Groups_Ouminus__class_Ouminus(_1155910), _1155912)), _1155914))], (51992 ^ _781404) ^ [_1833430, _1833432, _1833434] : [class_Divides_Osemiring__div(_1833430), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833430), _1833432), _1833434)), -(c_Divides_Odiv__class_Omod(_1833430, _1833434, _1833432) = c_Groups_Ozero__class_Ozero(_1833430))], (18731 ^ _781404) ^ [_1115362] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115362), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1115362), c_Int_OPls)))], (30121 ^ _781404) ^ [_1321750, _1321752, _1321754, _1321756, _1321758] : [class_Groups_Ocomm__monoid__mult(_1321750), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321752), _1321754)), hBOOL(hAPP(hAPP(c_member(_1321752), _1321756), _1321754)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1321752, _1321750), _1321758), _1321754) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321750), hAPP(_1321758, _1321756)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1321752, _1321750), _1321758), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321752, tc_HOL_Obool)), _1321754), hAPP(hAPP(c_Set_Oinsert(_1321752), _1321756), c_Orderings_Obot__class_Obot(tc_fun(_1321752, tc_HOL_Obool)))))))], (9685 ^ _781404) ^ [_946932, _946934, _946936] : [class_Orderings_Olinorder(_946932), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946932), _946934), _946936))), -(_946934 = _946936), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946932), _946936), _946934)))], (5556 ^ _781404) ^ [_866380, _866382] : [_866382 = _866380, -(c_Groups_Oone__class_Oone(_866382) = c_Groups_Oone__class_Oone(_866380))], (33498 ^ _781404) ^ [_1390582, _1390584, _1390586, _1390588] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1390582, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390584, tc_fun(_1390582, tc_HOL_Obool)), _1390586), _1390588)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390584, tc_fun(_1390582, tc_HOL_Obool)), _1390586), hAPP(hAPP(c_COMBB(tc_fun(_1390582, tc_HOL_Obool), tc_fun(_1390582, tc_HOL_Obool), _1390584), c_Groups_Ouminus__class_Ouminus(tc_fun(_1390582, tc_HOL_Obool))), _1390588)))], (41221 ^ _781404) ^ [_1588392, _1588394] : [-(c_Transitive__Closure_Ortrancl(_1588392, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1588392, _1588392), tc_HOL_Obool)), _1588394), c_Relation_OId(_1588392))) = c_Transitive__Closure_Ortrancl(_1588392, _1588394))], (35159 ^ _781404) ^ [_1436387, _1436389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436387), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1436389, _1436387) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1436389), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1436387)))], (18045 ^ _781404) ^ [_1103093, _1103095] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1103093), c_Groups_Ozero__class_Ozero(_1103093)), hAPP(c_Nat_OSuc, _1103095)) = c_Groups_Ozero__class_Ozero(_1103093)), class_Power_Opower(_1103093), class_Rings_Osemiring__0(_1103093)], (16282 ^ _781404) ^ [_1070814, _1070816] : [class_Groups_Oone(_1070814), 16285 ^ _781404 : [(16292 ^ _781404) ^ [] : [_1070816 = c_Groups_Oone__class_Oone(_1070814), -(c_Groups_Oone__class_Oone(_1070814) = _1070816)], (16286 ^ _781404) ^ [] : [c_Groups_Oone__class_Oone(_1070814) = _1070816, -(_1070816 = c_Groups_Oone__class_Oone(_1070814))]]], (7828 ^ _781404) ^ [_910591, _910593, _910595, _910597] : [class_Lattices_Odistrib__lattice(_910591), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_910591), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910591), _910593), _910595)), _910597) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910591), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_910591), _910593), _910597)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_910591), _910595), _910597)))], (43046 ^ _781404) ^ [_1638777, _1638779] : [class_Groups_Ocomm__monoid__add(_1638777), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1638777), _1638779) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1638777), hAPP(c_List_Onth(_1638777), _1638779)), 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(_1638777)), _1638779))))], (35792 ^ _781404) ^ [_1449680, _1449682] : [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), _1449680), _1449682))), 35795 ^ _781404 : [(35804 ^ _781404) ^ [] : [-(c_Divides_OnegDivAlg(_1449680, _1449682) = hAPP(c_Divides_Oadjust(_1449682), c_Divides_OnegDivAlg(_1449680, 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)))), _1449682)))), -(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), _1449680), _1449682)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1449682), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35796 ^ _781404) ^ [] : [35797 ^ _781404 : [(35800 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1449682), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35798 ^ _781404) ^ [] : [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), _1449680), _1449682)))]], -(c_Divides_OnegDivAlg(_1449680, _1449682) = 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), _1449680), _1449682)))]]], (10095 ^ _781404) ^ [_953503, _953505, _953507] : [class_Orderings_Oorder(_953503), -(_953505 = _953507), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953503), _953507), _953505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953503), _953507), _953505)))], (46692 ^ _781404) ^ [_1720681, _1720683, _1720685, _1720687, _1720689, _1720691] : [-(c_List_Ofoldr(_1720681, _1720683, _1720685, hAPP(hAPP(c_List_Oappend(_1720681), _1720687), _1720689), _1720691) = c_List_Ofoldr(_1720681, _1720683, _1720685, _1720687, c_List_Ofoldr(_1720681, _1720683, _1720685, _1720689, _1720691)))], (41606 ^ _781404) ^ [_1597603, _1597605, _1597607, _1597609] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597603, _1597603)), hAPP(hAPP(c_Product__Type_OPair(_1597603, _1597603), _1597605), _1597607)), c_Transitive__Closure_Ortrancl(_1597603, _1597609))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597603, _1597603)), hAPP(hAPP(c_Product__Type_OPair(_1597603, _1597603), _1597607), _1597605)), c_Transitive__Closure_Ortrancl(_1597603, hAPP(c_Relation_Oconverse(_1597603, _1597603), _1597609)))))], (10655 ^ _781404) ^ [_962482, _962484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962482)), hAPP(c_Nat_OSuc, _962484))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962482), _962484)))], (46724 ^ _781404) ^ [_1721624, _1721626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1721624), _1721626)), -(c_List_Oupt(_1721624, hAPP(c_Nat_OSuc, _1721626)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1721624, _1721626)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1721626), c_List_Olist_ONil(tc_Nat_Onat))))], (49400 ^ _781404) ^ [_1777399, _1777401, _1777403] : [hBOOL(hAPP(hAPP(c_List_Omember(_1777399), _1777403), _1777401)), -(hBOOL(hAPP(hAPP(c_member(_1777399), _1777401), hAPP(c_List_Oset(_1777399), _1777403))))], (4674 ^ _781404) ^ [_852481, _852483] : [_852483 = _852481, -(c_DSequence_Ounion(_852483) = c_DSequence_Ounion(_852481))], (25961 ^ _781404) ^ [_1245334] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245334, 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, _1245334, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25365 ^ _781404) ^ [_1234939] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234939))), -(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), _1234939)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (39133 ^ _781404) ^ [_1529613, _1529615, _1529617, _1529619] : [-(hAPP(c_Set_OCollect(_1529613), hAPP(hAPP(c_COMBB(tc_fun(_1529615, tc_HOL_Obool), tc_HOL_Obool, _1529613), c_HOL_OAll(_1529615)), hAPP(hAPP(c_COMBB(tc_fun(_1529615, tc_HOL_Obool), tc_fun(_1529615, tc_HOL_Obool), _1529613), hAPP(c_COMBS(_1529615, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529615), c_fimplies), hAPP(hAPP(c_COMBC(_1529615, tc_fun(_1529615, tc_HOL_Obool), tc_HOL_Obool), c_member(_1529615)), _1529617)))), _1529619))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1529615, tc_fun(_1529613, tc_HOL_Obool)), _1529617), hAPP(hAPP(c_COMBB(tc_fun(_1529613, tc_HOL_Obool), tc_fun(_1529613, tc_HOL_Obool), _1529615), c_Set_OCollect(_1529613)), hAPP(c_COMBC(_1529613, _1529615, tc_HOL_Obool), _1529619))))], (3128 ^ _781404) ^ [_827936, _827938, _827940, _827942] : [-(c_List_Olistset(_827942, _827938) = c_List_Olistset(_827940, _827936)), _827942 = _827940, _827938 = _827936], (49349 ^ _781404) ^ [_1776308, _1776310, _1776312, _1776314, _1776316, _1776318] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1776308, _1776310, _1776312, _1776314, c_Lazy__Sequence_Olazy__sequence_OInsert(_1776310, _1776316, _1776318)) = hAPP(hAPP(_1776314, _1776316), _1776318))], (37512 ^ _781404) ^ [_1488026] : [-(hAPP(c_Relation_OField(_1488026), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1488026, _1488026), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1488026, tc_HOL_Obool)))], (18923 ^ _781404) ^ [_1118453, _1118455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118453), _1118455)), -(c_Nat__Transfer_Otsub(_1118455, _1118453) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1118455), _1118453))], (10295 ^ _781404) ^ [_956498, _956500, _956502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956498), _956500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956498), _956502)), 10302 ^ _781404 : [(10309 ^ _781404) ^ [] : [_956500 = _956502, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956500), _956498) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956502), _956498))], (10303 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956500), _956498) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956502), _956498), -(_956500 = _956502)]]], (52390 ^ _781404) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (45664 ^ _781404) ^ [_1696366, _1696368] : [hAPP(c_Code__Numeral_Onat__of, _1696366) = hAPP(c_Code__Numeral_Onat__of, _1696368), -(_1696366 = _1696368)], (16609 ^ _781404) ^ [_1076935, _1076937] : [-(hBOOL(hAPP(_1076935, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1076935, _1076937)), 16617 ^ _781404 : [(16620 ^ _781404) ^ [_1077173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077173), 16616 ^ [_1076935, _1076937])), hBOOL(hAPP(_1076935, _1077173))], (16626 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1076935, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 16616 ^ [_1076935, _1076937]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (16618 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16616 ^ [_1076935, _1076937]), _1076937)))]]], (332 ^ _781404) ^ [_786494, _786496] : [-(c_Nat__Transfer_Ois__nat(_786494)), _786496 = _786494, c_Nat__Transfer_Ois__nat(_786496)], (33229 ^ _781404) ^ [_1381928] : [-(c_Fun_Oinj__on(_1381928, tc_fun(_1381928, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1381928, tc_fun(_1381928, tc_HOL_Obool), tc_fun(_1381928, tc_HOL_Obool)), c_Set_Oinsert(_1381928)), c_Orderings_Obot__class_Obot(tc_fun(_1381928, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1381928, tc_HOL_Obool))))], (11325 ^ _781404) ^ [_974114, _974116, _974118, _974120] : [-(_974114 = c_Orderings_Obot__class_Obot(tc_fun(_974116, tc_HOL_Obool))), 11328 ^ _781404 : [(11329 ^ _781404) ^ [] : [-(hAPP(c_Set_Oimage(_974118, _974116, 11336 ^ [_974114, _974116, _974118, _974120]), _974120) = _974114), 11330 ^ _781404 : [(11331 ^ _781404) ^ [_974255] : [c_Fun_Oinj__on(_974116, _974118, _974255, _974114), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974118, tc_HOL_Obool)), hAPP(c_Set_Oimage(_974116, _974118, _974255), _974114)), _974120))]]], (11340 ^ _781404) ^ [] : [11341 ^ _781404 : [(11342 ^ _781404) ^ [_974447] : [hAPP(c_Set_Oimage(_974118, _974116, _974447), _974120) = _974114]], 11344 ^ _781404 : [(11347 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974118, tc_HOL_Obool)), hAPP(c_Set_Oimage(_974116, _974118, 11343 ^ [_974114, _974116, _974118, _974120]), _974114)), _974120)))], (11345 ^ _781404) ^ [] : [-(c_Fun_Oinj__on(_974116, _974118, 11343 ^ [_974114, _974116, _974118, _974120], _974114))]]]]], (25355 ^ _781404) ^ [_1234727] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1234727)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1234727)))], (45611 ^ _781404) ^ [_1695091, _1695093, _1695095, _1695097] : [class_Groups_Ocomm__monoid__add(_1695091), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1695091), _1695093), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1695095, _1695097))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1695091), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1695091), _1695093), c_List_Oupto(_1695095, _1695097))))], (8668 ^ _781404) ^ [_927570, _927572, _927574] : [class_Orderings_Oorder(_927570), 8671 ^ _781404 : [(8678 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927570), _927572), _927574))), -(c_SetInterval_Oord__class_OatLeastAtMost(_927570, _927572, _927574) = c_Orderings_Obot__class_Obot(tc_fun(_927570, tc_HOL_Obool)))], (8672 ^ _781404) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_927570, _927572, _927574) = c_Orderings_Obot__class_Obot(tc_fun(_927570, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927570), _927572), _927574))]]], (19643 ^ _781404) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28893 ^ _781404) ^ [_1298646, _1298648, _1298650, _1298652] : [class_Fields_Olinordered__field__inverse__zero(_1298646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298646), _1298648), _1298650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298646), c_Groups_Ozero__class_Ozero(_1298646)), _1298652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298646), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298646), _1298648), _1298652)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298646), _1298650), _1298652))))], (26755 ^ _781404) ^ [_1258622, _1258624, _1258626, _1258628] : [class_Groups_Ocomm__monoid__add(_1258622), 26758 ^ _781404 : [(26765 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1258624), _1258626))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1258624, _1258622), _1258628), _1258626) = c_Groups_Ozero__class_Ozero(_1258622))], (26759 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1258624), _1258626)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1258624, _1258622), _1258628), _1258626) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1258622, _1258624, c_Groups_Oplus__class_Oplus(_1258622)), _1258628), c_Groups_Ozero__class_Ozero(_1258622)), _1258626))]]], (23611 ^ _781404) ^ [_1205482, _1205484] : [class_Divides_Osemiring__div(_1205482), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1205482), _1205484), c_Groups_Ozero__class_Ozero(_1205482)) = c_Groups_Ozero__class_Ozero(_1205482))], (34519 ^ _781404) ^ [_1421376, _1421378, _1421380, _1421382, _1421384] : [class_Complete__Lattice_Ocomplete__lattice(_1421376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421378), _1421380)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1421376), _1421382), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1421378, _1421376), _1421380), _1421384)) = hAPP(hAPP(c_Finite__Set_Ofold(_1421378, _1421376, hAPP(hAPP(c_COMBB(_1421376, tc_fun(_1421376, _1421376), _1421378), c_Lattices_Osemilattice__inf__class_Oinf(_1421376)), _1421384)), _1421382), _1421380))], (36213 ^ _781404) ^ [_1457387, _1457389, _1457391, _1457393] : [-(hAPP(c_Product__Type_Osnd(_1457387, _1457389), hAPP(hAPP(c_Product__Type_OPair(_1457387, _1457389), _1457391), _1457393)) = _1457393)], (41059 ^ _781404) ^ [_1583597, _1583599] : [-(hAPP(c_Relation_ORange(_1583597, _1583597), c_Transitive__Closure_Otrancl(_1583597, _1583599)) = hAPP(c_Relation_ORange(_1583597, _1583597), _1583599))], (40118 ^ _781404) ^ [_1561874, _1561876, _1561878, _1561880] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1561874, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1561874, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1561874, _1561876), _1561878)), hAPP(c_Relation_ODomain(_1561874, _1561876), _1561880))), hAPP(c_Relation_ODomain(_1561874, _1561876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1561874, _1561876), tc_HOL_Obool)), _1561878), _1561880)))))], (26313 ^ _781404) ^ [_1250934, _1250936] : [class_Int_Onumber__ring(_1250934), -(hAPP(c_Int_Onumber__class_Onumber__of(_1250934), _1250936) = hAPP(c_Int_Oring__1__class_Oof__int(_1250934), _1250936))], (7840 ^ _781404) ^ [_910909, _910911, _910913, _910915] : [class_Lattices_Odistrib__lattice(_910909), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_910909), _910911), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910909), _910913), _910915)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910909), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_910909), _910911), _910913)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_910909), _910911), _910915)))], (14827 ^ _781404) ^ [_1041612, _1041614, _1041616] : [class_Rings_Ocomm__ring__1(_1041612), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041612), _1041614), _1041616) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041612), _1041614), hAPP(c_Groups_Ouminus__class_Ouminus(_1041612), _1041616)))], (52688 ^ _781404) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (41948 ^ _781404) ^ [_1606200] : [-(c_Nat_Ofunpow(_1606200) = c_Nat_Ocompow(_1606200, _1606200))], (25875 ^ _781404) ^ [_1243841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243841)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1243841)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1243841)))], (16678 ^ _781404) ^ [_1078198, _1078200] : [class_Int_Oring__char__0(_1078198), hBOOL(hAPP(hAPP(c_member(_1078198), _1078200), c_Int_Oring__1__class_OInts(_1078198))), 16685 ^ _781404 : [(16692 ^ _781404) ^ [] : [_1078200 = c_Groups_Ozero__class_Ozero(_1078198), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078198), _1078200), _1078200) = c_Groups_Ozero__class_Ozero(_1078198))], (16686 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078198), _1078200), _1078200) = c_Groups_Ozero__class_Ozero(_1078198), -(_1078200 = c_Groups_Ozero__class_Ozero(_1078198))]]], (1316 ^ _781404) ^ [_800894, _800896] : [-(class_Divides_Oring__div(_800894)), _800896 = _800894, class_Divides_Oring__div(_800896)], (20893 ^ _781404) ^ [_1152339, _1152341, _1152343] : [class_Rings_Ono__zero__divisors(_1152339), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152339), _1152341), _1152343) = c_Groups_Ozero__class_Ozero(_1152339), -(_1152341 = c_Groups_Ozero__class_Ozero(_1152339)), -(_1152343 = c_Groups_Ozero__class_Ozero(_1152339))], (40005 ^ _781404) ^ [_1559111, _1559113, _1559115, _1559117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559111, _1559113), tc_HOL_Obool)), _1559115), _1559117)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1559111, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1559111, _1559113), _1559115)), hAPP(c_Relation_ODomain(_1559111, _1559113), _1559117))))], (31212 ^ _781404) ^ [_1343084, _1343086] : [class_Orderings_Olinorder(_1343084), -(c_Big__Operators_Olinorder__class_OMin(_1343084, hAPP(hAPP(c_Set_Oinsert(_1343084), _1343086), c_Orderings_Obot__class_Obot(tc_fun(_1343084, tc_HOL_Obool)))) = _1343086)], (23355 ^ _781404) ^ [_1200030, _1200032, _1200034, _1200036] : [class_Divides_Osemiring__div(_1200030), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200030), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200030), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200030), _1200032), _1200034)), _1200034)), c_Divides_Odiv__class_Omod(_1200030, _1200032, _1200034))), _1200036) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200030), _1200032), _1200036))], (17531 ^ _781404) ^ [_1094037, _1094039] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094037), _1094039)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094037)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094039)))], (43615 ^ _781404) ^ [_1650648, _1650650, _1650652, _1650654] : [-(_1650648 = _1650650), 43618 ^ _781404 : [(43625 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1650652), _1650648), hAPP(c_List_Oset(_1650652), _1650654))), -(hBOOL(hAPP(hAPP(c_member(_1650652), _1650648), hAPP(c_List_Oset(_1650652), c_List_Oremove1(_1650652, _1650650, _1650654)))))], (43619 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1650652), _1650648), hAPP(c_List_Oset(_1650652), c_List_Oremove1(_1650652, _1650650, _1650654)))), -(hBOOL(hAPP(hAPP(c_member(_1650652), _1650648), hAPP(c_List_Oset(_1650652), _1650654))))]]], (36110 ^ _781404) ^ [_1455245, _1455247, _1455249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455245, tc_fun(_1455245, tc_HOL_Obool))), _1455247), _1455249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455245, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1455245, _1455249)), c_Wellfounded_Oaccp(_1455245, _1455247))))], (7701 ^ _781404) ^ [_908062, _908064, _908066, _908068] : [class_Lattices_Osemilattice__inf(_908062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908062), _908064), _908066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908062), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_908062), _908064), _908068)), _908066)))], (22037 ^ _781404) ^ [_1174005, _1174007] : [class_Rings_Oring__1__no__zero__divisors(_1174005), 22040 ^ _781404 : [(22041 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174005), _1174007), _1174007) = c_Groups_Oone__class_Oone(_1174005), -(_1174007 = c_Groups_Oone__class_Oone(_1174005)), -(_1174007 = hAPP(c_Groups_Ouminus__class_Ouminus(_1174005), c_Groups_Oone__class_Oone(_1174005)))], (22051 ^ _781404) ^ [] : [22052 ^ _781404 : [(22055 ^ _781404) ^ [] : [_1174007 = hAPP(c_Groups_Ouminus__class_Ouminus(_1174005), c_Groups_Oone__class_Oone(_1174005))], (22053 ^ _781404) ^ [] : [_1174007 = c_Groups_Oone__class_Oone(_1174005)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174005), _1174007), _1174007) = c_Groups_Oone__class_Oone(_1174005))]]], (30980 ^ _781404) ^ [_1338468, _1338470, _1338472] : [class_Orderings_Olinorder(_1338468), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338468), _1338470)), hBOOL(hAPP(hAPP(c_member(_1338468), _1338472), _1338470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338468), hAPP(c_Finite__Set_Ofold1(_1338468, c_Orderings_Oord__class_Omin(_1338468)), _1338470)), _1338472)))], (52488 ^ _781404) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (46674 ^ _781404) ^ [_1720066, _1720068] : [-(c_Random_Oselect__weight(_1720066, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1720066), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1720066, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1720066, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1720066)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1720068)) = c_Random_Oselect__weight(_1720066, _1720068))], (43509 ^ _781404) ^ [_1648817, _1648819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1648817), _1648819)), -(c_List_Oupto(_1648819, _1648817) = c_List_Olist_ONil(tc_Int_Oint))], (16188 ^ _781404) ^ [_1068808, _1068810, _1068812] : [hAPP(c_Finite__Set_Ocard(_1068808), _1068810) = hAPP(c_Nat_OSuc, _1068812), 16193 ^ _781404 : [(16196 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1068808), 16191 ^ [_1068808, _1068810, _1068812]), 16192 ^ [_1068808, _1068810, _1068812]))], (16198 ^ _781404) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1068808), 16192 ^ [_1068808, _1068810, _1068812]) = _1068812)], (16200 ^ _781404) ^ [] : [_1068812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(16192 ^ [_1068808, _1068810, _1068812] = c_Orderings_Obot__class_Obot(tc_fun(_1068808, tc_HOL_Obool)))], (16194 ^ _781404) ^ [] : [-(_1068810 = hAPP(hAPP(c_Set_Oinsert(_1068808), 16191 ^ [_1068808, _1068810, _1068812]), 16192 ^ [_1068808, _1068810, _1068812]))]]], (21177 ^ _781404) ^ [_1157632, _1157634, _1157636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157632), _1157634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157636), _1157632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157636), _1157634))))], (42284 ^ _781404) ^ [_1616202, _1616204, _1616206, _1616208, _1616210, _1616212] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616202), tc_List_Olist(_1616202))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616202), tc_List_Olist(_1616202)), hAPP(hAPP(c_List_Olist_OCons(_1616202), _1616204), _1616206)), hAPP(hAPP(c_List_Olist_OCons(_1616202), _1616208), _1616210))), c_List_Olexord(_1616202, _1616212))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616202, _1616202)), hAPP(hAPP(c_Product__Type_OPair(_1616202, _1616202), _1616204), _1616208)), _1616212))), 42291 ^ _781404 : [(42294 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616202), tc_List_Olist(_1616202))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616202), tc_List_Olist(_1616202)), _1616206), _1616210)), c_List_Olexord(_1616202, _1616212))))], (42292 ^ _781404) ^ [] : [-(_1616204 = _1616208)]]], (6072 ^ _781404) ^ [_877749, _877751, _877753, _877755] : [class_Orderings_Oord(_877749), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877749), hAPP(_877751, 6077 ^ [_877749, _877751, _877753, _877755])), hAPP(_877753, 6077 ^ [_877749, _877751, _877753, _877755]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877755, _877749)), _877751), _877753)))], (7960 ^ _781404) ^ [_913973, _913975] : [class_Lattices_Obounded__lattice__top(_913973), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913973), _913975), c_Orderings_Otop__class_Otop(_913973)) = c_Orderings_Otop__class_Otop(_913973))], (46532 ^ _781404) ^ [_1716328, _1716330, _1716332, _1716334] : [-(hBOOL(hAPP(_1716328, _1716330))), -(c_List_Oremove1(_1716332, _1716330, hAPP(c_List_Ofilter(_1716332, _1716328), _1716334)) = hAPP(c_List_Ofilter(_1716332, _1716328), _1716334))], (46489 ^ _781404) ^ [_1715244, _1715246] : [-(c_List_Oconcat(_1715244, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715244), tc_List_Olist(_1715244)), c_List_Olist_Olist__case(tc_List_Olist(_1715244), _1715244, c_List_Olist_ONil(_1715244), hAPP(hAPP(c_COMBB(tc_List_Olist(_1715244), tc_fun(tc_List_Olist(_1715244), tc_List_Olist(_1715244)), _1715244), c_COMBK(tc_List_Olist(_1715244), tc_List_Olist(_1715244))), hAPP(hAPP(c_COMBC(_1715244, tc_List_Olist(_1715244), tc_List_Olist(_1715244)), c_List_Olist_OCons(_1715244)), c_List_Olist_ONil(_1715244))))), _1715246)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715244), _1715244), c_List_Ohd(_1715244)), hAPP(c_List_Ofilter(tc_List_Olist(_1715244), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1715244)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1715244), tc_List_Olist(_1715244), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1715244)))), _1715246)))], (23709 ^ _781404) ^ [_1207235, _1207237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1207235), 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)), _1207237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1207235), _1207237)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39856 ^ _781404) ^ [_1556212, _1556214, _1556216] : [c_Wellfounded_Owf(_1556212, _1556214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1556212, _1556212), tc_HOL_Obool)), _1556216), _1556214)), -(c_Wellfounded_Owf(_1556212, _1556216))], (33861 ^ _781404) ^ [_1401066, _1401068, _1401070, _1401072] : [class_Rings_Oring__1(_1401066), -(hAPP(c_Int_Oring__1__class_Oof__int(_1401066), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1401068, tc_Int_Oint), _1401070), _1401072)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1401068, _1401066), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1401066, _1401068), c_Int_Oring__1__class_Oof__int(_1401066)), _1401070)), _1401072))], (50045 ^ _781404) ^ [_1792850, _1792852] : [c_Relation_Oantisym(_1792850, hAPP(c_Relation_Oconverse(_1792850, _1792850), _1792852)), -(c_Relation_Oantisym(_1792850, _1792852))], (12911 ^ _781404) ^ [_1005505, _1005507, _1005509, _1005511, _1005513] : [c_Fun_Ofun__upd(_1005505, _1005507, _1005509, _1005511, _1005513) = _1005509, -(hAPP(_1005509, _1005511) = _1005513)], (46333 ^ _781404) ^ [_1711109, _1711111, _1711113] : [-(hAPP(c_List_Oset(_1711109), hAPP(c_List_OremoveAll(_1711109, _1711111), _1711113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1711109, tc_HOL_Obool)), hAPP(c_List_Oset(_1711109), _1711113)), hAPP(hAPP(c_Set_Oinsert(_1711109), _1711111), c_Orderings_Obot__class_Obot(tc_fun(_1711109, tc_HOL_Obool)))))], (13217 ^ _781404) ^ [_1010926, _1010928, _1010930, _1010932] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1010926), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010926), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010926), _1010928), _1010930)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010926), _1010932), _1010930))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010926), _1010928), _1010932)))], (506 ^ _781404) ^ [_789029, _789031] : [-(class_Rings_Oinverse(_789029)), _789031 = _789029, class_Rings_Oinverse(_789031)], (39682 ^ _781404) ^ [_1550460, _1550462, _1550464, _1550466] : [-(hAPP(c_Relation_ORange(_1550460, _1550462), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1550460, _1550462), tc_HOL_Obool)), _1550464), _1550466)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1550462, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1550460, _1550462), _1550464)), hAPP(c_Relation_ORange(_1550460, _1550462), _1550466)))], (41463 ^ _781404) ^ [_1594168, _1594170] : [-(c_Relation_Oirrefl(_1594168, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1594168, _1594168), tc_HOL_Obool)), _1594170), c_Relation_OId(_1594168))))], (36711 ^ _781404) ^ [_1468176, _1468178] : [-(c_Divides_Odivmod__nat(_1468176, _1468178) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1468176, _1468178)))], (47720 ^ _781404) ^ [_1741124, _1741126, _1741128, _1741130, _1741132] : [-(hBOOL(hAPP(_1741124, _1741126))), -(c_List_OtakeWhile(_1741128, _1741124, hAPP(hAPP(c_List_Oappend(_1741128), _1741130), hAPP(hAPP(c_List_Olist_OCons(_1741128), _1741126), _1741132))) = c_List_OtakeWhile(_1741128, _1741124, _1741130))], (52304 ^ _781404) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (25275 ^ _781404) ^ [_1233568] : [class_Int_Onumber__ring(_1233568), -(hAPP(c_Int_Onumber__class_Onumber__of(_1233568), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1233568), c_Groups_Oone__class_Oone(_1233568)))], (33633 ^ _781404) ^ [_1394639, _1394641, _1394643, _1394645] : [class_Groups_Ouminus(_1394639), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1394641, _1394639)), _1394643), _1394645) = hAPP(c_Groups_Ouminus__class_Ouminus(_1394639), hAPP(_1394643, _1394645)))], (33353 ^ _781404) ^ [_1385354, _1385356, _1385358, _1385360] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385354, tc_fun(_1385356, tc_HOL_Obool)), _1385358), _1385360) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1385356, tc_HOL_Obool), hAPP(c_Set_Oimage(_1385354, tc_fun(_1385356, tc_HOL_Obool), _1385360), _1385358)))], (11099 ^ _781404) ^ [_969812, _969814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969812), _969814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969812)), _969814)))], (5062 ^ _781404) ^ [_858619, _858621, _858623, _858625] : [-(c_Quickcheck_Obeyond(_858625, _858621) = c_Quickcheck_Obeyond(_858623, _858619)), _858625 = _858623, _858621 = _858619], (13261 ^ _781404) ^ [_1011772, _1011774, _1011776] : [class_Groups_Ogroup__add(_1011772), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1011772), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011772), _1011774), _1011776)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011772), hAPP(c_Groups_Ouminus__class_Ouminus(_1011772), _1011776)), hAPP(c_Groups_Ouminus__class_Ouminus(_1011772), _1011774)))], (22095 ^ _781404) ^ [_1174892, _1174894, _1174896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174892), _1174894)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174892), _1174896))), 22098 ^ _781404 : [(22101 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174894), _1174896)))], (22099 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174892)))]]], (6639 ^ _781404) ^ [_887611] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_887611, tc_HOL_Obool) = c_Set_OBall(_887611))], (27431 ^ _781404) ^ [_1271218, _1271220] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1271218), hAPP(hAPP(c_Power_Opower__class_Opower(_1271218), hAPP(c_Int_Onumber__class_Onumber__of(_1271218), c_Int_OMin)), _1271220)) = c_Groups_Oone__class_Oone(_1271218)), class_Int_Onumber__ring(_1271218), class_Rings_Olinordered__idom(_1271218)], (38824 ^ _781404) ^ [_1521746, _1521748, _1521750, _1521752] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521746), _1521748)), 38830 ^ _781404 : [(38833 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521750), hAPP(_1521752, 38829 ^ [_1521746, _1521748, _1521750, _1521752])))], (38831 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1521746), 38829 ^ [_1521746, _1521748, _1521750, _1521752]), _1521748)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1521746, _1521750)), hAPP(hAPP(c_Product__Type_OSigma(_1521746, _1521750), _1521748), _1521752)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1521746, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1521750, tc_HOL_Obool), tc_Nat_Onat, _1521746), c_Finite__Set_Ocard(_1521750)), _1521752)), _1521748))], (17945 ^ _781404) ^ [_1101434, _1101436, _1101438] : [class_Rings_Oring__1__no__zero__divisors(_1101434), -(_1101436 = c_Groups_Ozero__class_Ozero(_1101434)), hAPP(hAPP(c_Power_Opower__class_Opower(_1101434), _1101436), _1101438) = c_Groups_Ozero__class_Ozero(_1101434)], (2214 ^ _781404) ^ [_813571, _813573, _813575, _813577] : [-(c_Random_Oinc__shift(_813577, _813573) = c_Random_Oinc__shift(_813575, _813571)), _813577 = _813575, _813573 = _813571], (2062 ^ _781404) ^ [_811221, _811223, _811225, _811227, _811229, _811231] : [-(c_SetInterval_Oord_OgreaterThan(_811231, _811227, _811223) = c_SetInterval_Oord_OgreaterThan(_811229, _811225, _811221)), _811231 = _811229, _811227 = _811225, _811223 = _811221], (37473 ^ _781404) ^ [_1487001, _1487003, _1487005, _1487007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1487001), _1487007)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1487005), _1487003))), -(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), _1487001), _1487003)), 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), _1487005), _1487007)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (46335 ^ _781404) ^ [_1711176, _1711178] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711176)), c_List_Oremdups(_1711176, c_List_Oconcat(_1711176, _1711178))) = hAPP(c_Finite__Set_Ocard(_1711176), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1711176), tc_fun(_1711176, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1711176)), _1711178)), c_List_Oset(_1711176))))], (33388 ^ _781404) ^ [_1386836, _1386838, _1386840, _1386842, _1386844, _1386846] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386836, tc_fun(_1386838, tc_fun(_1386840, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1386836, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1386838, _1386840), tc_HOL_Obool), tc_fun(_1386838, tc_fun(_1386840, tc_HOL_Obool)), _1386836), hAPP(c_COMBC(_1386838, tc_fun(tc_prod(_1386838, _1386840), tc_HOL_Obool), tc_fun(_1386840, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1386840, tc_fun(tc_fun(tc_prod(_1386838, _1386840), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1386838, _1386840), tc_HOL_Obool), tc_fun(_1386840, tc_HOL_Obool)), _1386838), c_COMBC(_1386840, tc_fun(tc_prod(_1386838, _1386840), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1386840, tc_prod(_1386838, _1386840)), tc_fun(_1386840, tc_fun(tc_fun(tc_prod(_1386838, _1386840), tc_HOL_Obool), tc_HOL_Obool)), _1386838), hAPP(c_COMBB(tc_prod(_1386838, _1386840), tc_fun(tc_fun(tc_prod(_1386838, _1386840), tc_HOL_Obool), tc_HOL_Obool), _1386840), c_member(tc_prod(_1386838, _1386840)))), c_Product__Type_OPair(_1386838, _1386840))))), _1386842)), _1386844), _1386846)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1386838, _1386840)), hAPP(hAPP(c_Product__Type_OPair(_1386838, _1386840), _1386844), _1386846)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386836, tc_fun(tc_prod(_1386838, _1386840), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1386836, tc_HOL_Obool))), _1386842))))], (45988 ^ _781404) ^ [_1703909, _1703911, _1703913, _1703915, _1703917, _1703919] : [c_List_Olist__all2(_1703909, _1703911, _1703913, _1703915, _1703917), -(c_List_Olist__all2(_1703909, _1703911, _1703913, hAPP(hAPP(c_List_Otake(_1703909), _1703919), _1703915), hAPP(hAPP(c_List_Otake(_1703911), _1703919), _1703917)))], (49533 ^ _781404) ^ [_1780650] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1780650)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1780650)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38584 ^ _781404) ^ [_1514906, _1514908, _1514910, _1514912, _1514914] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1514906, _1514908), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1514906, tc_HOL_Obool)), _1514910), _1514912)), hAPP(c_COMBK(tc_fun(_1514908, tc_HOL_Obool), _1514906), _1514914)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1514906, _1514908), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1514906, _1514908), _1514910), hAPP(c_COMBK(tc_fun(_1514908, tc_HOL_Obool), _1514906), _1514914))), hAPP(hAPP(c_Product__Type_OSigma(_1514906, _1514908), _1514912), hAPP(c_COMBK(tc_fun(_1514908, tc_HOL_Obool), _1514906), _1514914))))], (12734 ^ _781404) ^ [_1001771, _1001773, _1001775, _1001777, _1001779] : [-(hBOOL(hAPP(hAPP(c_member(_1001771), _1001773), c_SetInterval_Oord_OgreaterThanLessThan(_1001771, _1001775, _1001777, _1001779)))), hBOOL(hAPP(hAPP(_1001775, _1001777), _1001773)), hBOOL(hAPP(hAPP(_1001775, _1001773), _1001779))], (36804 ^ _781404) ^ [_1470203] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1470203) = _1470203)], (52646 ^ _781404) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (8235 ^ _781404) ^ [] : [-(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)))], (44234 ^ _781404) ^ [_1664478, _1664480, _1664482, _1664484] : [-(c_List_Osublist(_1664478, hAPP(hAPP(c_List_Oappend(_1664478), _1664480), _1664482), _1664484) = hAPP(hAPP(c_List_Oappend(_1664478), c_List_Osublist(_1664478, _1664480, _1664484)), c_List_Osublist(_1664478, _1664482, 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(_1664478)), _1664480)))), _1664484)))))], (41889 ^ _781404) ^ [_1604554, _1604556, _1604558, _1604560] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604554, _1604554), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1604556), _1604558)), _1604560) = hAPP(hAPP(c_Relation_Orel__comp(_1604554, _1604554, _1604554), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604554, _1604554), tc_HOL_Obool), _1604556), _1604560)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604554, _1604554), tc_HOL_Obool), _1604558), _1604560)))], (50061 ^ _781404) ^ [_1793082, _1793084, _1793086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1793082, _1793082), tc_HOL_Obool)), _1793084), _1793086)), c_Relation_Oantisym(_1793082, _1793086), -(c_Relation_Oantisym(_1793082, _1793084))], (30566 ^ _781404) ^ [_1330848] : [class_Orderings_Olinorder(_1330848), -(c_Finite__Set_Ofun__left__comm__idem(_1330848, _1330848, c_Orderings_Oord__class_Omin(_1330848)))], (49269 ^ _781404) ^ [_1774624, _1774626, _1774628, _1774630, _1774632] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1774624, _1774626, _1774628) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1774624, _1774630, _1774632), 49272 ^ _781404 : [(49275 ^ _781404) ^ [] : [-(_1774628 = _1774632)], (49273 ^ _781404) ^ [] : [-(_1774626 = _1774630)]]], (19557 ^ _781404) ^ [_1129136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1129136)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129136), c_Int_OPls)))], (9867 ^ _781404) ^ [_949966, _949968, _949970, _949972, _949974] : [c_Fun_Oinj__on(_949966, _949968, _949970, _949972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949966, tc_HOL_Obool)), _949974), _949972)), -(c_Fun_Oinj__on(_949966, _949968, _949970, _949974))], (49931 ^ _781404) ^ [_1790937, _1790939] : [c_Equiv__Relations_Oequivp(_1790937, _1790939), 49934 ^ _781404 : [(49939 ^ _781404) ^ [] : [-(c_Predicate_Otransp(_1790937, _1790939))], (49937 ^ _781404) ^ [] : [-(c_Predicate_Osymp(_1790937, _1790939))], (49935 ^ _781404) ^ [] : [-(c_Predicate_Oreflp(_1790937, _1790939))]]], (39057 ^ _781404) ^ [_1527731, _1527733, _1527735] : [-(hAPP(hAPP(c_Set_Oinsert(_1527731), _1527733), _1527735) = hAPP(c_Set_OCollect(_1527731), hAPP(hAPP(c_COMBS(_1527731, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527731), c_fdisj), hAPP(hAPP(c_COMBC(_1527731, _1527731, tc_HOL_Obool), c_fequal), _1527733))), hAPP(hAPP(c_COMBC(_1527731, tc_fun(_1527731, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527731)), _1527735))))], (21167 ^ _781404) ^ [_1157435] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157435), _1157435))))], (44673 ^ _781404) ^ [_1674962, _1674964, _1674966] : [-(hAPP(c_List_Otl(_1674962), hAPP(hAPP(c_List_Oappend(_1674962), _1674964), _1674966)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1674962), _1674962, hAPP(c_List_Otl(_1674962), _1674966), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1674962), tc_List_Olist(_1674962)), _1674962), hAPP(hAPP(c_COMBC(tc_List_Olist(_1674962), tc_List_Olist(_1674962), tc_List_Olist(_1674962)), c_List_Oappend(_1674962)), _1674966))), _1674964))], (51966 ^ _781404) ^ [_1832933, _1832935] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832933), _1832935)), -(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)))), _1832935, _1832933) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (31087 ^ _781404) ^ [_1340383, _1340385, _1340387] : [class_Orderings_Olinorder(_1340383), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340383), _1340385)), -(_1340385 = c_Orderings_Obot__class_Obot(tc_fun(_1340383, tc_HOL_Obool))), 31098 ^ _781404 : [(31099 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340383), _1340387), hAPP(c_Finite__Set_Ofold1(_1340383, c_Orderings_Oord__class_Omin(_1340383)), _1340385))), 31102 ^ _781404 : [(31103 ^ _781404) ^ [_1340676] : [hBOOL(hAPP(hAPP(c_member(_1340383), _1340676), _1340385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340383), _1340387), _1340676)))]]], (31109 ^ _781404) ^ [] : [31111 ^ _781404 : [(31114 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340383), _1340387), 31110 ^ [_1340383, _1340385, _1340387]))], (31112 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1340383), 31110 ^ [_1340383, _1340385, _1340387]), _1340385)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340383), _1340387), hAPP(c_Finite__Set_Ofold1(_1340383, c_Orderings_Oord__class_Omin(_1340383)), _1340385))))]]], (12370 ^ _781404) ^ [_994599, _994601, _994603, _994605] : [-(hBOOL(hAPP(hAPP(c_member(_994599), _994601), _994603))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994599, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_994599), _994601), _994605)), _994603) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994599, tc_HOL_Obool)), _994605), _994603))], (2256 ^ _781404) ^ [_814258, _814260] : [_814260 = _814258, -(c_SetInterval_Oord__class_OatLeast(_814260) = c_SetInterval_Oord__class_OatLeast(_814258))], (49360 ^ _781404) ^ [_1776643, _1776645, _1776647] : [hBOOL(hAPP(hAPP(c_List_Omember(_1776643), _1776645), _1776647)), -(hBOOL(hAPP(hAPP(c_member(_1776643), _1776647), hAPP(c_List_Oset(_1776643), _1776645))))], (7948 ^ _781404) ^ [_913683, _913685, _913687, _913689, _913691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913683, tc_HOL_Obool)), hAPP(c_Set_Oimage(_913685, _913683, _913687), _913689)), _913691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_913683, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_913685, tc_HOL_Obool), tc_fun(_913683, tc_HOL_Obool), c_Set_Oimage(_913685, _913683, _913687)), hAPP(c_Set_OPow(_913685), _913689))), hAPP(c_Set_OPow(_913683), _913691))))], (43112 ^ _781404) ^ [_1640064, _1640066, _1640068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1640064), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1640066))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1640066), _1640064), _1640068)) = 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), _1640066)), _1640068)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1640066), _1640064)))], (15513 ^ _781404) ^ [_1055946, _1055948, _1055950, _1055952] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055946), _1055948)), 15516 ^ _781404 : [(15523 ^ _781404) ^ [] : [hAPP(c_Finite__Set_Ocard(_1055950), hAPP(c_Set_Oimage(_1055946, _1055950, _1055952), _1055948)) = hAPP(c_Finite__Set_Ocard(_1055946), _1055948), -(c_Fun_Oinj__on(_1055946, _1055950, _1055952, _1055948))], (15517 ^ _781404) ^ [] : [c_Fun_Oinj__on(_1055946, _1055950, _1055952, _1055948), -(hAPP(c_Finite__Set_Ocard(_1055950), hAPP(c_Set_Oimage(_1055946, _1055950, _1055952), _1055948)) = hAPP(c_Finite__Set_Ocard(_1055946), _1055948))]]], (13373 ^ _781404) ^ [_1013889, _1013891, _1013893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013889), _1013891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013889), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013893), _1013891))))], (30860 ^ _781404) ^ [_1336149, _1336151, _1336153, _1336155] : [class_Orderings_Olinorder(_1336149), 30863 ^ _781404 : [(30872 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336149), _1336151), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1336149), _1336153), _1336155)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336149), _1336151), _1336153)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336149), _1336151), _1336155))], (30864 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336149), _1336151), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1336149), _1336153), _1336155))), 30867 ^ _781404 : [(30870 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336149), _1336151), _1336155)))], (30868 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336149), _1336151), _1336153)))]]]]], (39381 ^ _781404) ^ [_1539481, _1539483, _1539485] : [class_Lattices_Odistrib__lattice(_1539481), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539481), _1539483)), -(_1539483 = c_Orderings_Obot__class_Obot(tc_fun(_1539481, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1539481), _1539485), c_Big__Operators_Olattice__class_OSup__fin(_1539481, _1539483)) = c_Big__Operators_Olattice__class_OSup__fin(_1539481, hAPP(c_Set_OCollect(_1539481), hAPP(hAPP(c_COMBB(tc_fun(_1539481, tc_HOL_Obool), tc_HOL_Obool, _1539481), c_HOL_OEx(_1539481)), hAPP(hAPP(c_COMBC(_1539481, tc_fun(_1539481, tc_HOL_Obool), tc_fun(_1539481, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1539481, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1539481, tc_HOL_Obool), tc_fun(_1539481, tc_HOL_Obool)), _1539481), c_COMBS(_1539481, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1539481, tc_HOL_Obool), tc_fun(_1539481, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1539481), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539481), c_fconj)), hAPP(hAPP(c_COMBC(_1539481, tc_fun(_1539481, _1539481), tc_fun(_1539481, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1539481, tc_HOL_Obool), tc_fun(tc_fun(_1539481, _1539481), tc_fun(_1539481, tc_HOL_Obool)), _1539481), c_COMBB(_1539481, tc_HOL_Obool, _1539481)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1539481), _1539485))))), hAPP(hAPP(c_COMBC(_1539481, tc_fun(_1539481, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539481)), _1539483))))))], (46586 ^ _781404) ^ [_1717385, _1717387, _1717389] : [46588 ^ _781404 : [(46591 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1717387, 46587 ^ [_1717385, _1717387, _1717389])))], (46589 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1717385), 46587 ^ [_1717385, _1717387, _1717389]), hAPP(c_List_Oset(_1717385), _1717389))))]], -(hAPP(c_List_Ofilter(_1717385, _1717387), _1717389) = c_List_Olist_ONil(_1717385))], (10855 ^ _781404) ^ [_965701, _965703, _965705, _965707, _965709] : [class_Orderings_Oorder(_965701), class_Orderings_Oorder(_965703), c_Orderings_Oorder__class_Ostrict__mono(_965703, _965701, _965705), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965703), _965707), _965709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965701), hAPP(_965705, _965707)), hAPP(_965705, _965709))))], (46880 ^ _781404) ^ [_1724418, _1724420, _1724422, _1724424] : [class_Groups_Ocomm__monoid__add(_1724418), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1724418), _1724420), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1724422, _1724424))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1724418), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1724418), _1724420), c_List_Oupt(_1724422, _1724424))))], (46337 ^ _781404) ^ [_1711242, _1711244] : [class_Orderings_Olinorder(_1711242), -(c_List_Olinorder__class_Osorted__list__of__set(_1711242, hAPP(c_List_Oset(_1711242), _1711244)) = c_List_Olinorder__class_Osort__key(_1711242, _1711242, c_COMBI(_1711242), c_List_Oremdups(_1711242, _1711244)))], (1806 ^ _781404) ^ [_807019, _807021] : [-(class_Rings_Ozero__neq__one(_807019)), _807021 = _807019, class_Rings_Ozero__neq__one(_807021)], (44148 ^ _781404) ^ [_1662385, _1662387, _1662389, _1662391] : [-(hBOOL(hAPP(hAPP(c_member(_1662385), _1662387), hAPP(c_List_Oset(_1662385), _1662389)))), -(c_List_Oremove1(_1662385, _1662387, hAPP(hAPP(c_List_Oappend(_1662385), _1662389), _1662391)) = hAPP(hAPP(c_List_Oappend(_1662385), _1662389), c_List_Oremove1(_1662385, _1662387, _1662391)))], (26119 ^ _781404) ^ [_1247925] : [c_Code__Numeral_OSuc__code__numeral(_1247925) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (46385 ^ _781404) ^ [_1712124, _1712126] : [c_List_Olist_ONil(_1712124) = c_List_Oconcat(_1712124, _1712126), 46388 ^ _781404 : [(46389 ^ _781404) ^ [_1712215] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712124)), _1712215), hAPP(c_List_Oset(tc_List_Olist(_1712124)), _1712126))), -(_1712215 = c_List_Olist_ONil(_1712124))]]], (47792 ^ _781404) ^ [_1742528] : [c_List_Onat__list(_1742528), -(c_List_Oembed__list(c_List_Oreturn__list(_1742528)) = _1742528)], (41165 ^ _781404) ^ [_1587026, _1587028, _1587030, _1587032] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587026, _1587026)), hAPP(hAPP(c_Product__Type_OPair(_1587026, _1587026), _1587028), _1587030)), c_Transitive__Closure_Otrancl(_1587026, _1587032))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587026, _1587026)), hAPP(hAPP(c_Product__Type_OPair(_1587026, _1587026), _1587028), _1587030)), c_Transitive__Closure_Ortrancl(_1587026, _1587032))))], (17357 ^ _781404) ^ [_1091017, _1091019] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091017)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091019)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1091017), _1091019)))], (20787 ^ _781404) ^ [_1150404, _1150406, _1150408, _1150410] : [class_Rings_Ocomm__semiring__1(_1150404), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150404), _1150406), _1150408)), _1150410) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150404), _1150406), _1150410)), _1150408))], (49513 ^ _781404) ^ [_1780152, _1780154, _1780156, _1780158, _1780160, _1780162, _1780164] : [49515 ^ _781404 : [(49518 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1780156, 49514 ^ [_1780152, _1780154, _1780156, _1780158, _1780160, _1780162, _1780164]), _1780158), _1780160))], (49516 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1780152), 49514 ^ [_1780152, _1780154, _1780156, _1780158, _1780160, _1780162, _1780164]), _1780154)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1780152, tc_fun(_1780162, tc_fun(_1780164, tc_HOL_Obool))), _1780154), _1780156), _1780158), _1780160)))], (43539 ^ _781404) ^ [_1649286, _1649288] : [-(c_List_Osublist(_1649286, c_List_Olist_ONil(_1649286), _1649288) = c_List_Olist_ONil(_1649286))], (12266 ^ _781404) ^ [_992338, _992340, _992342] : [class_Groups_Ocomm__monoid__add(_992338), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_992340, _992338), _992342), c_Orderings_Obot__class_Obot(tc_fun(_992340, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_992338))], (29393 ^ _781404) ^ [_1307610, _1307612, _1307614, _1307616] : [class_Fields_Olinordered__field(_1307610), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307610), c_Groups_Ozero__class_Ozero(_1307610)), _1307612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307610), _1307614), _1307612)), _1307616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307610), _1307614), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307610), _1307616), _1307612))))], (49854 ^ _781404) ^ [_1787999, _1788001, _1788003, _1788005] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1787999, tc_fun(_1788001, tc_HOL_Obool)), _1788003), _1788005) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1788001, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1788001, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1787999, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1788001, tc_HOL_Obool)), c_HOL_OEx(_1787999)), hAPP(hAPP(c_COMBB(tc_fun(_1787999, tc_HOL_Obool), tc_fun(_1787999, tc_HOL_Obool), tc_fun(_1788001, tc_HOL_Obool)), hAPP(c_COMBS(_1787999, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1787999), c_fconj), hAPP(hAPP(c_COMBC(_1787999, tc_fun(_1787999, tc_HOL_Obool), tc_HOL_Obool), c_member(_1787999)), _1788003)))), hAPP(hAPP(c_COMBC(tc_fun(_1788001, tc_HOL_Obool), tc_fun(_1787999, tc_fun(_1788001, tc_HOL_Obool)), tc_fun(_1787999, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1788001, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1787999, tc_fun(_1788001, tc_HOL_Obool)), tc_fun(_1787999, tc_HOL_Obool)), tc_fun(_1788001, tc_HOL_Obool)), c_COMBB(tc_fun(_1788001, tc_HOL_Obool), tc_HOL_Obool, _1787999)), c_fequal)), _1788005))))))], (17224 ^ _781404) ^ [_1088449, _1088451] : [class_Int_Onumber__ring(_1088449), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1088449), hAPP(c_Int_Onumber__class_Onumber__of(_1088449), _1088451)) = hAPP(c_Int_Onumber__class_Onumber__of(_1088449), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1088451)))], (9887 ^ _781404) ^ [_950302, _950304, _950306, _950308, _950310] : [c_Fun_Oinj__on(_950302, _950304, _950306, c_Orderings_Otop__class_Otop(tc_fun(_950302, tc_HOL_Obool))), 9890 ^ _781404 : [(9897 ^ _781404) ^ [] : [_950308 = _950310, -(hAPP(_950306, _950308) = hAPP(_950306, _950310))], (9891 ^ _781404) ^ [] : [hAPP(_950306, _950308) = hAPP(_950306, _950310), -(_950308 = _950310)]]], (44757 ^ _781404) ^ [_1676784, _1676786] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1676784), _1676786) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1676784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44763 ^ _781404 : [(44766 ^ _781404) ^ [] : [44762 ^ [_1676784, _1676786] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44764 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 44762 ^ [_1676784, _1676786]), hAPP(c_List_Oset(tc_Nat_Onat), _1676786))))]]], (31908 ^ _781404) ^ [_1355696, _1355698, _1355700, _1355702] : [class_Orderings_Olinorder(_1355696), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355696), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355696), _1355698), _1355700)), _1355702) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355696), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355696), _1355698), _1355702)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355696), _1355700), _1355702)))], (22697 ^ _781404) ^ [_1187134, _1187136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1187134)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1187136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1187134), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1187134), _1187136))))], (17933 ^ _781404) ^ [_1101261, _1101263] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1101261), _1101263))))], (13303 ^ _781404) ^ [_1012506, _1012508] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1012506)), _1012508) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012506), _1012508)))], (42839 ^ _781404) ^ [_1632114, _1632116, _1632118] : [42841 ^ _781404 : [(42844 ^ _781404) ^ [] : [hBOOL(hAPP(_1632118, hAPP(hAPP(c_List_Onth(_1632114), _1632116), 42840 ^ [_1632114, _1632116, _1632118])))], (42842 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42840 ^ [_1632114, _1632116, _1632118]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632114)), _1632116))))]], 42845 ^ _781404 : [(42846 ^ _781404) ^ [_1632316] : [hBOOL(hAPP(hAPP(c_member(_1632114), _1632316), hAPP(c_List_Oset(_1632114), _1632116))), -(hBOOL(hAPP(_1632118, _1632316)))]]], (20811 ^ _781404) ^ [_1150976, _1150978, _1150980] : [class_Rings_Ocomm__semiring__1(_1150976), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150976), _1150978), _1150980) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150976), _1150980), _1150978))], (12234 ^ _781404) ^ [_991761, _991763, _991765] : [hBOOL(hAPP(hAPP(c_member(_991761), _991763), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_991761, tc_HOL_Obool)), _991765))), hBOOL(hAPP(hAPP(c_member(_991761), _991763), _991765))], (3846 ^ _781404) ^ [_839155, _839157] : [_839157 = _839155, -(c_New__DSequence_Opos__not__seq(_839157) = c_New__DSequence_Opos__not__seq(_839155))], (25887 ^ _781404) ^ [_1244085] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1244085)), 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, _1244085, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (25327 ^ _781404) ^ [_1234366, _1234368] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234366), _1234368) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 25328 ^ _781404 : [(25335 ^ _781404) ^ [] : [_1234366 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1234368 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (25329 ^ _781404) ^ [] : [_1234366 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1234368 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (8608 ^ _781404) ^ [_926521, _926523] : [class_Groups_Oordered__ab__group__add(_926521), 8611 ^ _781404 : [(8618 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926521), c_Groups_Ozero__class_Ozero(_926521)), _926523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926521), hAPP(c_Groups_Ouminus__class_Ouminus(_926521), _926523)), c_Groups_Ozero__class_Ozero(_926521))))], (8612 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926521), hAPP(c_Groups_Ouminus__class_Ouminus(_926521), _926523)), c_Groups_Ozero__class_Ozero(_926521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926521), c_Groups_Ozero__class_Ozero(_926521)), _926523)))]]], (41381 ^ _781404) ^ [_1592286] : [-(hAPP(c_Relation_ORange(_1592286, _1592286), c_Relation_OId(_1592286)) = c_Orderings_Otop__class_Otop(tc_fun(_1592286, tc_HOL_Obool)))], (25451 ^ _781404) ^ [_1236456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1236456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236456)))], (9781 ^ _781404) ^ [_948459, _948461, _948463, _948465, _948467] : [c_Fun_Oinj__on(_948459, _948461, _948463, _948465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_948459, tc_HOL_Obool)), _948467), _948465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_948461, tc_HOL_Obool)), hAPP(c_Set_Oimage(_948459, _948461, _948463), _948467)), hAPP(c_Set_Oimage(_948459, _948461, _948463), _948465))))], (14751 ^ _781404) ^ [_1040222, _1040224, _1040226, _1040228] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040222), hAPP(c_Set_Oimage(_1040224, _1040222, _1040226), _1040228))), c_Fun_Oinj__on(_1040224, _1040222, _1040226, _1040228), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040224), _1040228)))], (41730 ^ _781404) ^ [_1600510, _1600512, _1600514, _1600516, _1600518, _1600520] : [c_Relation_Osingle__valued(_1600510, _1600512, _1600514), hBOOL(hAPP(hAPP(c_member(tc_prod(_1600510, _1600512)), hAPP(hAPP(c_Product__Type_OPair(_1600510, _1600512), _1600516), _1600518)), _1600514)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1600510, _1600512)), hAPP(hAPP(c_Product__Type_OPair(_1600510, _1600512), _1600516), _1600520)), _1600514)), -(_1600518 = _1600520)], (14033 ^ _781404) ^ [_1026188, _1026190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026188), _1026190)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026188), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026190), _1026188)) = _1026190)], (51456 ^ _781404) ^ [_1823549, _1823551, _1823553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1823549)), 51459 ^ _781404 : [(51466 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823551), _1823553)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823549), _1823551)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823549), _1823553))))], (51460 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823549), _1823551)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823549), _1823553))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823551), _1823553)))]]], (4032 ^ _781404) ^ [_842324, _842326, _842328, _842330, _842332, _842334, _842336, _842338] : [-(c_New__Random__Sequence_Opos__empty(_842338, _842334, _842330, _842326) = c_New__Random__Sequence_Opos__empty(_842336, _842332, _842328, _842324)), _842338 = _842336, _842334 = _842332, _842330 = _842328, _842326 = _842324], (34193 ^ _781404) ^ [_1411359, _1411361, _1411363, _1411365] : [hBOOL(hAPP(hAPP(c_member(_1411359), _1411365), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411359, tc_HOL_Obool)), _1411361), _1411363))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411359, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1411359, tc_fun(_1411359, tc_HOL_Obool), tc_HOL_Obool), c_member(_1411359)), _1411361)), hAPP(hAPP(c_COMBC(_1411359, tc_fun(_1411359, tc_HOL_Obool), tc_HOL_Obool), c_member(_1411359)), _1411363)), _1411365)))], (50493 ^ _781404) ^ [_1801326, _1801328, _1801330, _1801332, _1801334] : [c_Fun_Oinj__on(_1801326, _1801328, _1801330, _1801332), hBOOL(hAPP(hAPP(c_member(_1801326), _1801334), _1801332)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1801326, _1801328, _1801332, _1801330), hAPP(_1801330, _1801334)) = _1801334)], (16434 ^ _781404) ^ [_1073363, _1073365, _1073367, _1073369] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1073363), _1073365)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073367), _1073369)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1073363, _1073367)), c_Sum__Type_OPlus(_1073363, _1073367, _1073365, _1073369))))], (1336 ^ _781404) ^ [_801144, _801146] : [-(class_Int_Oring__char__0(_801144)), _801146 = _801144, class_Int_Oring__char__0(_801146)], (22771 ^ _781404) ^ [_1188481, _1188483, _1188485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188481), _1188483)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188481), _1188485))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1188483), _1188485)))], (36737 ^ _781404) ^ [_1468756, _1468758, _1468760, _1468762, _1468764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1468756, _1468758)), hAPP(_1468756, _1468760))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1468762, _1468762)), hAPP(hAPP(c_Product__Type_OPair(_1468762, _1468762), _1468758), _1468760)), _1468764)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1468762, _1468762)), hAPP(hAPP(c_Product__Type_OPair(_1468762, _1468762), _1468758), _1468760)), c_Wellfounded_Omlex__prod(_1468762, _1468756, _1468764))))], (47738 ^ _781404) ^ [_1741392, _1741394] : [-(c_List_OtakeWhile(_1741392, _1741394, c_List_Olist_ONil(_1741392)) = c_List_Olist_ONil(_1741392))], (30630 ^ _781404) ^ [_1331919, _1331921, _1331923, _1331925] : [class_Orderings_Olinorder(_1331919), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331919), _1331921), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331919), _1331923), _1331925)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331919), _1331923), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331919), _1331921), _1331925)))], (41532 ^ _781404) ^ [_1595748, _1595750, _1595752] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1595750, _1595748)), _1595752)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1595748, _1595750)), hAPP(c_Relation_Oconverse(_1595750, _1595748), _1595752))))], (39274 ^ _781404) ^ [_1535225, _1535227] : [-(hAPP(c_Set_OPow(_1535225), _1535227) = hAPP(c_Set_OCollect(tc_fun(_1535225, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1535225, tc_HOL_Obool), tc_fun(_1535225, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1535225, tc_HOL_Obool))), _1535227)))], (9865 ^ _781404) ^ [_949941] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _949941))], (41333 ^ _781404) ^ [_1591176, _1591178, _1591180, _1591182] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591176, _1591176)), hAPP(hAPP(c_Product__Type_OPair(_1591176, _1591176), _1591178), _1591180)), c_Transitive__Closure_Ortrancl(_1591176, _1591182))), -(_1591178 = _1591180), 41340 ^ _781404 : [(41343 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591176, _1591176)), hAPP(hAPP(c_Product__Type_OPair(_1591176, _1591176), _1591178), _1591180)), c_Transitive__Closure_Otrancl(_1591176, _1591182))))], (41341 ^ _781404) ^ [] : [_1591178 = _1591180]]], (4316 ^ _781404) ^ [_846766, _846768] : [_846768 = _846766, -(c_List_Oappend(_846768) = c_List_Oappend(_846766))], (7954 ^ _781404) ^ [_913880, _913882] : [class_Orderings_Otop(_913880), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913880), _913882), c_Orderings_Otop__class_Otop(_913880))))], (36225 ^ _781404) ^ [_1457597, _1457599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1457597), 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)), _1457599)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1457597, _1457599) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1457597, _1457599)))], (46111 ^ _781404) ^ [_1706530, _1706532, _1706534, _1706536] : [hBOOL(hAPP(c_List_Odistinct(_1706530), _1706532)), hBOOL(hAPP(c_List_Odistinct(_1706534), _1706536)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1706530, _1706534)), c_Enum_Oproduct(_1706530, _1706534, _1706532, _1706536))))], (7639 ^ _781404) ^ [_906998, _907000, _907002] : [class_Lattices_Olattice(_906998), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906998), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_906998), _907000), _907002)), _907000)))], (16280 ^ _781404) ^ [] : [-(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))], (2444 ^ _781404) ^ [_817242, _817244] : [_817244 = _817242, -(c_Int_OBit0(_817244) = c_Int_OBit0(_817242))], (11863 ^ _781404) ^ [_984445, _984447, _984449, _984451, _984453] : [hBOOL(hAPP(hAPP(c_member(_984445), hAPP(_984447, _984449)), _984451)), -(hBOOL(hAPP(hAPP(c_member(_984453), _984449), hAPP(c_Set_Ovimage(_984453, _984445, _984447), _984451))))], (25407 ^ _781404) ^ [_1235585, _1235587, _1235589] : [hBOOL(hAPP(_1235585, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235587), _1235589))), 25410 ^ _781404 : [(25417 ^ _781404) ^ [] : [-(_1235589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25420 ^ _781404 : [(25421 ^ _781404) ^ [_1235837, _1235839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235837), _1235589)), _1235587 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235589), _1235839)), _1235837), -(hBOOL(hAPP(_1235585, _1235839)))]]], (25411 ^ _781404) ^ [] : [_1235589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1235585, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (51916 ^ _781404) ^ [_1832040, _1832042] : [51917 ^ _781404 : [(51920 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832042), _1832040))], (51918 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832040), _1832042)))]], -(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)))), _1832040, _1832042))], (26943 ^ _781404) ^ [_1262410, _1262412] : [class_Groups_Oordered__ab__group__add__abs(_1262410), 26946 ^ _781404 : [(26953 ^ _781404) ^ [] : [_1262412 = c_Groups_Ozero__class_Ozero(_1262410), -(hAPP(c_Groups_Oabs__class_Oabs(_1262410), _1262412) = c_Groups_Ozero__class_Ozero(_1262410))], (26947 ^ _781404) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1262410), _1262412) = c_Groups_Ozero__class_Ozero(_1262410), -(_1262412 = c_Groups_Ozero__class_Ozero(_1262410))]]], (8768 ^ _781404) ^ [_929248, _929250] : [class_Complete__Lattice_Ocomplete__lattice(_929248), -(c_Complete__Lattice_OInf__class_OInf(_929248, hAPP(hAPP(c_Set_Oinsert(_929248), _929250), c_Orderings_Obot__class_Obot(tc_fun(_929248, tc_HOL_Obool)))) = _929250)], (5578 ^ _781404) ^ [_866699, _866701] : [_866701 = _866699, -(tc_Option_Ooption(_866701) = tc_Option_Ooption(_866699))], (45365 ^ _781404) ^ [_1689963, _1689965, _1689967, _1689969, _1689971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689963), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689965)), _1689967))), -(hAPP(hAPP(c_List_Onth(_1689969), hAPP(hAPP(c_List_Omap(_1689965, _1689969), _1689971), _1689967)), _1689963) = hAPP(_1689971, hAPP(hAPP(c_List_Onth(_1689965), _1689967), _1689963)))], (2438 ^ _781404) ^ [_817157, _817159] : [_817159 = _817157, -(c_Divides_Oadjust(_817159) = c_Divides_Oadjust(_817157))], (44735 ^ _781404) ^ [_1676335, _1676337, _1676339, _1676341, _1676343, _1676345] : [-(hAPP(c_List_Ofoldl(_1676335, _1676337, _1676339, _1676341), hAPP(hAPP(c_List_Olist_OCons(_1676337), _1676343), _1676345)) = hAPP(c_List_Ofoldl(_1676335, _1676337, _1676339, hAPP(hAPP(_1676339, _1676341), _1676343)), _1676345))], (48510 ^ _781404) ^ [_1758675, _1758677, _1758679] : [-(c_List_Olist__ex(_1758675, _1758677, _1758679)), 48511 ^ _781404 : [(48512 ^ _781404) ^ [_1758740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1758740), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758675)), _1758679))), hBOOL(hAPP(_1758677, hAPP(hAPP(c_List_Onth(_1758675), _1758679), _1758740)))]]], (34169 ^ _781404) ^ [_1409646, _1409648, _1409650, _1409652, _1409654, _1409656] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409646, tc_fun(_1409648, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1409646, tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_fun(_1409648, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409648, tc_fun(tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_fun(_1409648, tc_HOL_Obool)), _1409646), c_COMBC(_1409648, tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409648, tc_prod(_1409646, _1409648)), tc_fun(_1409648, tc_fun(tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_HOL_Obool)), _1409646), hAPP(c_COMBB(tc_prod(_1409646, _1409648), tc_fun(tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_HOL_Obool), _1409648), c_member(tc_prod(_1409646, _1409648)))), c_Product__Type_OPair(_1409646, _1409648)))), _1409650)), hAPP(hAPP(c_COMBC(_1409646, tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_fun(_1409648, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409648, tc_fun(tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_fun(_1409648, tc_HOL_Obool)), _1409646), c_COMBC(_1409648, tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409648, tc_prod(_1409646, _1409648)), tc_fun(_1409648, tc_fun(tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_HOL_Obool)), _1409646), hAPP(c_COMBB(tc_prod(_1409646, _1409648), tc_fun(tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool), tc_HOL_Obool), _1409648), c_member(tc_prod(_1409646, _1409648)))), c_Product__Type_OPair(_1409646, _1409648)))), _1409652)), _1409654), _1409656)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1409646, _1409648)), hAPP(hAPP(c_Product__Type_OPair(_1409646, _1409648), _1409654), _1409656)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1409646, _1409648), tc_HOL_Obool)), _1409650), _1409652))))], (44222 ^ _781404) ^ [_1664206, _1664208, _1664210, _1664212, _1664214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1664206), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664208)), _1664210))), -(hAPP(hAPP(c_List_Olist__update(_1664208, hAPP(hAPP(c_List_Oappend(_1664208), _1664210), _1664212)), _1664206), _1664214) = hAPP(hAPP(c_List_Oappend(_1664208), hAPP(hAPP(c_List_Olist__update(_1664208, _1664210), _1664206), _1664214)), _1664212))], (24532 ^ _781404) ^ [_1221503, _1221505, _1221507, _1221509] : [_1221503 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1221505), _1221507)), _1221509), -(_1221505 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1221503, _1221505) = _1221509), 24539 ^ _781404 : [(24542 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221509)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1221509), _1221505))], (24540 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221505)))]], 24547 ^ _781404 : [(24550 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1221505), _1221509)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1221509), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24548 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221505))]]], (23497 ^ _781404) ^ [_1203151, _1203153, _1203155] : [class_Divides_Osemiring__div(_1203151), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1203151), c_Divides_Odiv__class_Omod(_1203151, _1203153, _1203155)), _1203155) = c_Groups_Ozero__class_Ozero(_1203151))], (41520 ^ _781404) ^ [_1595460, _1595462] : [-(hAPP(c_Relation_OField(_1595460), hAPP(c_Relation_Oconverse(_1595460, _1595460), _1595462)) = hAPP(c_Relation_OField(_1595460), _1595462))], (52734 ^ _781404) ^ [_1842268, _1842270, _1842272, _1842274, _1842276, _1842278] : [-(hAPP(hAPP(hAPP(c_COMBS(_1842268, _1842270, _1842272), _1842274), _1842276), _1842278) = hAPP(hAPP(_1842274, _1842278), hAPP(_1842276, _1842278)))], (42932 ^ _781404) ^ [_1634509, _1634511, _1634513] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1634509), _1634511)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1634509)), hAPP(c_Set_OCollect(tc_List_Olist(_1634509)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1634509), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1634509)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1634509), tc_fun(_1634509, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1634509, tc_HOL_Obool), tc_fun(tc_fun(_1634509, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1634509)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1634509, tc_HOL_Obool))), c_List_Oset(_1634509))), _1634511))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1634509), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1634509)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1634509)))), _1634513))))))], (46965 ^ _781404) ^ [_1726196, _1726198] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1726196, _1726198)))], (41946 ^ _781404) ^ [_1606129, _1606131] : [-(c_Transitive__Closure_Ortrancl(_1606129, _1606131) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1606129, _1606129), 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(_1606129, _1606129), tc_HOL_Obool), tc_fun(tc_prod(_1606129, _1606129), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1606129, _1606129), tc_HOL_Obool)), _1606131)))], (4638 ^ _781404) ^ [_851879, _851881, _851883, _851885, _851887, _851889, _851891, _851893] : [-(c_Product__Type_Oscomp(_851893, _851889, _851885, _851881) = c_Product__Type_Oscomp(_851891, _851887, _851883, _851879)), _851893 = _851891, _851889 = _851887, _851885 = _851883, _851881 = _851879], (13734 ^ _781404) ^ [_1020894, _1020896, _1020898, _1020900, _1020902] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1020894), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020894), _1020896), _1020898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020894), _1020900), _1020902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020894), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020894), _1020896), _1020900)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020894), _1020898), _1020902))))], (33434 ^ _781404) ^ [_1388976, _1388978, _1388980, _1388982, _1388984] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388976, tc_HOL_Obool)), _1388978), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388980, tc_fun(_1388976, tc_HOL_Obool)), _1388982), _1388984)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388980, tc_fun(_1388976, tc_HOL_Obool)), _1388982), hAPP(hAPP(c_COMBB(tc_fun(_1388976, tc_HOL_Obool), tc_fun(_1388976, tc_HOL_Obool), _1388980), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388976, tc_HOL_Obool)), _1388978)), _1388984)))], (45712 ^ _781404) ^ [_1697169] : [-(c_Code__Numeral_OSuc__code__numeral(_1697169) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1697169))))], (45970 ^ _781404) ^ [_1703541, _1703543, _1703545, _1703547, _1703549, _1703551, _1703553] : [c_List_Olist__all2(_1703541, _1703543, _1703545, hAPP(hAPP(c_List_Olist_OCons(_1703541), _1703547), _1703549), hAPP(hAPP(c_List_Olist_OCons(_1703543), _1703551), _1703553)), 45973 ^ _781404 : [(45976 ^ _781404) ^ [] : [-(c_List_Olist__all2(_1703541, _1703543, _1703545, _1703549, _1703553))], (45974 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1703545, _1703547), _1703551)))]]], (23295 ^ _781404) ^ [_1198812, _1198814, _1198816, _1198818, _1198820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198812), _1198814)), 23298 ^ _781404 : [(23305 ^ _781404) ^ [] : [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), _1198814), _1198812)), _1198816)), _1198818) = _1198820, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198814), _1198816)), _1198818) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198812), _1198816)), _1198820))], (23299 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198814), _1198816)), _1198818) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198812), _1198816)), _1198820), -(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), _1198814), _1198812)), _1198816)), _1198818) = _1198820)]]], (49721 ^ _781404) ^ [_1785068, _1785070] : [c_Relation_Otrans(_1785068, _1785070), -(c_Relation_Otrans(tc_List_Olist(_1785068), c_List_Olistrel(_1785068, _1785070)))], (52700 ^ _781404) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (30240 ^ _781404) ^ [_1324463, _1324465, _1324467] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1324463), _1324465)), 30246 ^ _781404 : [(30249 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1324467, 30245 ^ [_1324463, _1324465, _1324467])))], (30247 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1324463), 30245 ^ [_1324463, _1324465, _1324467]), _1324465)))]], -(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(_1324463, tc_Nat_Onat), _1324467), _1324465))))], (40495 ^ _781404) ^ [_1570406, _1570408, _1570410, _1570412, _1570414, _1570416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1570406, tc_HOL_Obool)), _1570408), _1570410)), 40501 ^ _781404 : [(40504 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1570412, tc_HOL_Obool)), hAPP(_1570414, 40500 ^ [_1570406, _1570408, _1570410, _1570412, _1570414, _1570416])), hAPP(_1570416, 40500 ^ [_1570406, _1570408, _1570410, _1570412, _1570414, _1570416])))], (40502 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1570406), 40500 ^ [_1570406, _1570408, _1570410, _1570412, _1570414, _1570416]), _1570408)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570406, _1570412), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1570406, _1570412), _1570408), _1570414)), hAPP(hAPP(c_Product__Type_OSigma(_1570406, _1570412), _1570410), _1570416))))], (17527 ^ _781404) ^ [_1093935, _1093937, _1093939] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093935), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093937), _1093939)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093935), _1093939)))], (30994 ^ _781404) ^ [_1338705, _1338707, _1338709] : [class_Orderings_Olinorder(_1338705), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338705), _1338707)), -(_1338707 = c_Orderings_Obot__class_Obot(tc_fun(_1338705, tc_HOL_Obool))), 31005 ^ _781404 : [(31006 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338705), _1338709), hAPP(c_Finite__Set_Ofold1(_1338705, c_Orderings_Oord__class_Omin(_1338705)), _1338707))), 31009 ^ _781404 : [(31010 ^ _781404) ^ [_1338998] : [hBOOL(hAPP(hAPP(c_member(_1338705), _1338998), _1338707)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338705), _1338709), _1338998)))]]], (31016 ^ _781404) ^ [] : [31018 ^ _781404 : [(31021 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338705), _1338709), 31017 ^ [_1338705, _1338707, _1338709]))], (31019 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1338705), 31017 ^ [_1338705, _1338707, _1338709]), _1338707)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338705), _1338709), hAPP(c_Finite__Set_Ofold1(_1338705, c_Orderings_Oord__class_Omin(_1338705)), _1338707))))]]], (7942 ^ _781404) ^ [_913521, _913523] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913521, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_913521, tc_HOL_Obool))), _913523) = c_Orderings_Otop__class_Otop(tc_fun(_913521, tc_HOL_Obool)))], (18929 ^ _781404) ^ [_1118558, _1118560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1118558)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1118560)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118558)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118560), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1118558))))], (7645 ^ _781404) ^ [_907105, _907107, _907109] : [class_Lattices_Osemilattice__inf(_907105), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907105), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_907105), _907107), _907109)), _907107)))], (48704 ^ _781404) ^ [_1762550, _1762552] : [-(c_FunDef_Ois__measure(_1762550, _1762552))], (9140 ^ _781404) ^ [_936735, _936737, _936739, _936741] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936735, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936735, tc_HOL_Obool)), _936737), _936739)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936735, tc_HOL_Obool)), _936741), _936739)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936735, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936735, tc_HOL_Obool)), _936737), _936739)), _936741))], (47881 ^ _781404) ^ [_1744341, _1744343, _1744345, _1744347, _1744349] : [-(c_List_OdropWhile(_1744341, _1744343, hAPP(hAPP(c_List_Omap(_1744345, _1744341), _1744347), _1744349)) = hAPP(hAPP(c_List_Omap(_1744345, _1744341), _1744347), c_List_OdropWhile(_1744345, hAPP(c_Fun_Ocomp(_1744341, tc_HOL_Obool, _1744345, _1744343), _1744347), _1744349)))], (8291 ^ _781404) ^ [_921137, _921139] : [_921139 = c_Orderings_Obot__class_Obot(tc_fun(_921137, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921137, tc_HOL_Obool)), _921139), c_Orderings_Obot__class_Obot(tc_fun(_921137, tc_HOL_Obool)))))], (13866 ^ _781404) ^ [_1023226, _1023228, _1023230] : [class_Groups_Ogroup__add(_1023226), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1023226), _1023228), hAPP(c_Groups_Ouminus__class_Ouminus(_1023226), _1023230)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023226), _1023228), _1023230))], (32016 ^ _781404) ^ [_1357794, _1357796, _1357798, _1357800] : [class_Orderings_Olinorder(_1357794), 32019 ^ _781404 : [(32020 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357794), _1357796), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357794), _1357798), _1357800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357794), _1357796), _1357798))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357794), _1357796), _1357800)))], (32030 ^ _781404) ^ [] : [32031 ^ _781404 : [(32034 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357794), _1357796), _1357800))], (32032 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357794), _1357796), _1357798))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357794), _1357796), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357794), _1357798), _1357800))))]]], (48044 ^ _781404) ^ [_1747875, _1747877, _1747879] : [-(hBOOL(hAPP(hAPP(c_member(_1747875), _1747877), hAPP(c_List_Oset(_1747875), _1747879)))), -(c_List_Oinsert(_1747875, _1747877, _1747879) = hAPP(hAPP(c_List_Olist_OCons(_1747875), _1747877), _1747879))], (19311 ^ _781404) ^ [_1124869, _1124871] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124869)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124871)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1124869), _1124871)))], (42238 ^ _781404) ^ [_1614487, _1614489, _1614491, _1614493, _1614495, _1614497] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614487), tc_List_Olist(_1614487))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614487), tc_List_Olist(_1614487)), hAPP(hAPP(c_List_Olist_OCons(_1614487), _1614489), _1614491)), hAPP(hAPP(c_List_Olist_OCons(_1614487), _1614493), _1614495))), c_List_Olex(_1614487, _1614497))), 42243 ^ _781404 : [(42246 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614487)), _1614491) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614487)), _1614495))], (42244 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614487, _1614487)), hAPP(hAPP(c_Product__Type_OPair(_1614487, _1614487), _1614489), _1614493)), _1614497)))]], 42247 ^ _781404 : [(42250 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614487), tc_List_Olist(_1614487))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614487), tc_List_Olist(_1614487)), _1614491), _1614495)), c_List_Olex(_1614487, _1614497))))], (42248 ^ _781404) ^ [] : [-(_1614489 = _1614493)]]], (6309 ^ _781404) ^ [_881729, _881731, _881733] : [c_Hoare__Mirabelle_Otriple__valid(_881729, hAPP(c_Nat_OSuc, _881731), _881733), -(c_Hoare__Mirabelle_Otriple__valid(_881729, _881731, _881733))], (40369 ^ _781404) ^ [_1567529, _1567531] : [40371 ^ _781404 : [(40374 ^ _781404) ^ [] : [hBOOL(hAPP(_1567529, hAPP(c_Int_OAbs__Integ, 40370 ^ [_1567529, _1567531])))], (40372 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40370 ^ [_1567529, _1567531]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1567529, _1567531)))], (50913 ^ _781404) ^ [_1810718, _1810720, _1810722] : [c_Fun_Oinj__on(_1810718, _1810720, _1810722, c_Orderings_Otop__class_Otop(tc_fun(_1810718, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1810718, _1810720, _1810722), c_Orderings_Otop__class_Otop(tc_fun(_1810718, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1810720, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1810718, _1810720, _1810722, c_Orderings_Otop__class_Otop(tc_fun(_1810718, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1810720, tc_HOL_Obool))))], (33713 ^ _781404) ^ [_1396428, _1396430, _1396432, _1396434] : [class_Complete__Lattice_Ocomplete__lattice(_1396428), -(_1396430 = c_Orderings_Obot__class_Obot(tc_fun(_1396432, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396432, _1396428), _1396430), hAPP(c_COMBK(_1396428, _1396432), _1396434)) = _1396434)], (28419 ^ _781404) ^ [_1289617, _1289619, _1289621, _1289623] : [class_Fields_Olinordered__field__inverse__zero(_1289617), class_Int_Onumber(_1289617), 28426 ^ _781404 : [(28427 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289617), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289617), _1289619), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621))), _1289623)), 28430 ^ _781404 : [(28437 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289617), c_Groups_Ozero__class_Ozero(_1289617)), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621)))), 28440 ^ _781404 : [(28447 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289617), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621)), c_Groups_Ozero__class_Ozero(_1289617)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289617), c_Groups_Ozero__class_Ozero(_1289617)), _1289623)))], (28441 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289617), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621)), c_Groups_Ozero__class_Ozero(_1289617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289617), _1289623), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621))), _1289619)))]]], (28431 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289617), c_Groups_Ozero__class_Ozero(_1289617)), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289617), _1289619), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289617), _1289623), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621)))))]]], (28453 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289617), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289617), _1289619), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621))), _1289623))), 28456 ^ _781404 : [(28459 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289617), _1289619), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289617), _1289623), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621))))], (28457 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289617), c_Groups_Ozero__class_Ozero(_1289617)), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621))))]], 28460 ^ _781404 : [(28463 ^ _781404) ^ [] : [28464 ^ _781404 : [(28467 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289617), _1289623), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621))), _1289619))], (28465 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289617), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621)), c_Groups_Ozero__class_Ozero(_1289617))))]], 28468 ^ _781404 : [(28471 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289617), c_Groups_Ozero__class_Ozero(_1289617)), _1289623))], (28469 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289617), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621)), c_Groups_Ozero__class_Ozero(_1289617)))]]], (28461 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289617), c_Groups_Ozero__class_Ozero(_1289617)), hAPP(c_Int_Onumber__class_Onumber__of(_1289617), _1289621)))]]]]], (42129 ^ _781404) ^ [_1611378, _1611380, _1611382] : [-(c_Nitpick_Oof__frac(_1611380, _1611378, _1611382) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1611378), hAPP(c_Int_Oring__1__class_Oof__int(_1611378), hAPP(c_Nitpick_Onum(_1611380), _1611382))), hAPP(c_Int_Oring__1__class_Oof__int(_1611378), hAPP(c_Nitpick_Odenom(_1611380), _1611382)))), class_Rings_Oinverse(_1611378), class_Rings_Oring__1(_1611378)], (41034 ^ _781404) ^ [_1583084, _1583086] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583084, _1583084)), hAPP(hAPP(c_Product__Type_OPair(_1583084, _1583084), 41035 ^ [_1583084, _1583086]), 41035 ^ [_1583084, _1583086])), c_Transitive__Closure_Otrancl(_1583084, _1583086)))), -(c_Wellfounded_Oacyclic(_1583084, _1583086))], (23787 ^ _781404) ^ [_1208471, _1208473] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208471, _1208473) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1208471 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1208473), 23790 ^ [_1208471, _1208473]))], (48629 ^ _781404) ^ [_1760950, _1760952, _1760954] : [48630 ^ _781404 : [(48631 ^ _781404) ^ [_1761027, _1761029] : [_1760954 = hAPP(hAPP(c_List_Oappend(_1760950), _1761029), hAPP(hAPP(c_List_Olist_OCons(_1760950), _1760952), _1761027))]], -(hBOOL(hAPP(hAPP(c_member(_1760950), _1760952), hAPP(c_List_Oset(_1760950), _1760954))))], (23543 ^ _781404) ^ [_1203962, _1203964, _1203966, _1203968] : [class_Divides_Osemiring__div(_1203962), -(c_Divides_Odiv__class_Omod(_1203962, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1203962), _1203964), _1203966), _1203968) = c_Divides_Odiv__class_Omod(_1203962, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1203962), _1203964), c_Divides_Odiv__class_Omod(_1203962, _1203966, _1203968)), _1203968))], (48591 ^ _781404) ^ [_1760358, _1760360, _1760362, _1760364] : [c_List_Olist__ex(_1760358, _1760360, hAPP(hAPP(c_List_Olist_OCons(_1760358), _1760362), _1760364)), -(hBOOL(hAPP(_1760360, _1760362))), -(c_List_Olist__ex(_1760358, _1760360, _1760364))], (46526 ^ _781404) ^ [_1716137, _1716139, _1716141] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716137)), hAPP(c_List_Ofilter(_1716137, _1716139), _1716141))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716137)), _1716141))))], (12979 ^ _781404) ^ [_1006599, _1006601, _1006603, _1006605] : [class_Groups_Ocancel__semigroup__add(_1006599), 12982 ^ _781404 : [(12989 ^ _781404) ^ [] : [_1006601 = _1006605, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006599), _1006601), _1006603) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006599), _1006605), _1006603))], (12983 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006599), _1006601), _1006603) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006599), _1006605), _1006603), -(_1006601 = _1006605)]]], (40273 ^ _781404) ^ [_1565670, _1565672] : [c_Wellfounded_Owf(_1565670, _1565672), -(c_Wellfounded_OwfP(_1565670, hAPP(hAPP(c_COMBC(_1565670, tc_fun(tc_prod(_1565670, _1565670), tc_HOL_Obool), tc_fun(_1565670, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565670, tc_fun(tc_fun(tc_prod(_1565670, _1565670), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1565670, _1565670), tc_HOL_Obool), tc_fun(_1565670, tc_HOL_Obool)), _1565670), c_COMBC(_1565670, tc_fun(tc_prod(_1565670, _1565670), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565670, tc_prod(_1565670, _1565670)), tc_fun(_1565670, tc_fun(tc_fun(tc_prod(_1565670, _1565670), tc_HOL_Obool), tc_HOL_Obool)), _1565670), hAPP(c_COMBB(tc_prod(_1565670, _1565670), tc_fun(tc_fun(tc_prod(_1565670, _1565670), tc_HOL_Obool), tc_HOL_Obool), _1565670), c_member(tc_prod(_1565670, _1565670)))), c_Product__Type_OPair(_1565670, _1565670)))), _1565672)))], (19167 ^ _781404) ^ [_1122453, _1122455] : [class_Rings_Osemiring__1(_1122453), 19170 ^ _781404 : [(19177 ^ _781404) ^ [] : [_1122455 = c_Groups_Ozero__class_Ozero(_1122453), -(c_Int_Oiszero(_1122453, _1122455))], (19171 ^ _781404) ^ [] : [c_Int_Oiszero(_1122453, _1122455), -(_1122455 = c_Groups_Ozero__class_Ozero(_1122453))]]], (9226 ^ _781404) ^ [_938917, _938919, _938921] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938917, tc_HOL_Obool)), _938919), _938921) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938917, tc_HOL_Obool)), _938919), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938917, tc_HOL_Obool)), _938921)))], (5530 ^ _781404) ^ [_865989, _865991] : [_865991 = _865989, -(c_Divides_Odiv__class_Odiv(_865991) = c_Divides_Odiv__class_Odiv(_865989))], (44276 ^ _781404) ^ [_1665815, _1665817, _1665819, _1665821, _1665823, _1665825] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665815), tc_List_Olist(_1665815))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665815), tc_List_Olist(_1665815)), hAPP(hAPP(c_List_Oappend(_1665815), _1665817), hAPP(hAPP(c_List_Olist_OCons(_1665815), _1665819), c_List_Olist_ONil(_1665815)))), hAPP(hAPP(c_List_Oappend(_1665815), _1665821), hAPP(hAPP(c_List_Olist_OCons(_1665815), _1665823), c_List_Olist_ONil(_1665815))))), c_List_Olistrel1(_1665815, _1665825)))), 44277 ^ _781404 : [(44284 ^ _781404) ^ [] : [_1665817 = _1665821, hBOOL(hAPP(hAPP(c_member(tc_prod(_1665815, _1665815)), hAPP(hAPP(c_Product__Type_OPair(_1665815, _1665815), _1665819), _1665823)), _1665825))], (44278 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665815), tc_List_Olist(_1665815))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665815), tc_List_Olist(_1665815)), _1665817), _1665821)), c_List_Olistrel1(_1665815, _1665825))), _1665819 = _1665823]]], (33131 ^ _781404) ^ [_1379483, _1379485] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1379483, 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(_1379483, tc_HOL_Obool)), tc_fun(_1379483, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1379483, tc_HOL_Obool)), tc_fun(_1379483, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1379483, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1379485)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1379483, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1379485))], (5196 ^ _781404) ^ [_860676, _860678, _860680, _860682, _860684, _860686, _860688, _860690] : [-(c_Product__Type_Ocurry(_860690, _860686, _860682, _860678) = c_Product__Type_Ocurry(_860688, _860684, _860680, _860676)), _860690 = _860688, _860686 = _860684, _860682 = _860680, _860678 = _860676], (42127 ^ _781404) ^ [_1611307, _1611309, _1611311] : [-(c_Nitpick_Otimes__frac(_1611307, _1611309, _1611311) = hAPP(hAPP(c_Nitpick_Ofrac(_1611307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1611307), _1611309)), hAPP(c_Nitpick_Onum(_1611307), _1611311))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1611307), _1611309)), hAPP(c_Nitpick_Odenom(_1611307), _1611311))))], (43613 ^ _781404) ^ [_1650609, _1650611, _1650613] : [-(hAPP(hAPP(c_List_Olist__update(_1650609, c_List_Olist_ONil(_1650609)), _1650611), _1650613) = c_List_Olist_ONil(_1650609))], (31218 ^ _781404) ^ [_1343191, _1343193, _1343195] : [class_Orderings_Olinorder(_1343191), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343191), _1343193)), hBOOL(hAPP(hAPP(c_member(_1343191), _1343195), _1343193)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1343191), _1343195), c_Big__Operators_Olattice_OInf__fin(_1343191, c_Orderings_Oord__class_Omin(_1343191), _1343193)) = c_Big__Operators_Olattice_OInf__fin(_1343191, c_Orderings_Oord__class_Omin(_1343191), _1343193))], (52678 ^ _781404) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (32636 ^ _781404) ^ [_1369357, _1369359, _1369361] : [class_Orderings_Olinorder(_1369357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369357), _1369359)), hBOOL(hAPP(hAPP(c_member(_1369357), _1369361), _1369359)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1369357), _1369361), c_Big__Operators_Olattice_OSup__fin(_1369357, c_Orderings_Oord__class_Omax(_1369357), _1369359)) = c_Big__Operators_Olattice_OSup__fin(_1369357, c_Orderings_Oord__class_Omax(_1369357), _1369359))], (19665 ^ _781404) ^ [_1130938] : [class_Int_Onumber__ring(_1130938), -(c_Int_Oiszero(_1130938, hAPP(c_Int_Onumber__class_Onumber__of(_1130938), c_Int_OPls)))], (46955 ^ _781404) ^ [_1726049, _1726051, _1726053] : [class_Orderings_Olinorder(_1726049), c_List_Olinorder__class_Osorted(_1726049, _1726051), -(c_List_Olinorder__class_Osorted(_1726049, hAPP(hAPP(c_List_Odrop(_1726049), _1726053), _1726051)))], (52512 ^ _781404) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (29421 ^ _781404) ^ [_1308148, _1308150, _1308152, _1308154] : [class_Fields_Olinordered__field(_1308148), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308148), c_Groups_Ozero__class_Ozero(_1308148)), _1308150)), 29428 ^ _781404 : [(29435 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308148), _1308152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308148), _1308154), _1308150))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308148), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308148), _1308152), _1308150)), _1308154)))], (29429 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308148), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308148), _1308152), _1308150)), _1308154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308148), _1308152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308148), _1308154), _1308150))))]]], (8130 ^ _781404) ^ [_917725, _917727] : [class_Orderings_Olinorder(_917725), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917725, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_917725), _917727)), hAPP(hAPP(c_Set_Oinsert(_917725), _917727), c_Orderings_Obot__class_Obot(tc_fun(_917725, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_917725), _917727))], (37194 ^ _781404) ^ [_1479167, _1479169, _1479171, _1479173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1479167), _1479169)), -(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), _1479167), _1479171)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1479169), _1479173))), c_FunDef_Opair__leq)))], (52748 ^ _781404) ^ [] : [hBOOL(c_fFalse)], (39135 ^ _781404) ^ [_1529747, _1529749, _1529751] : [-(hAPP(c_Set_OCollect(_1529747), hAPP(hAPP(c_COMBS(_1529747, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529747), c_fimplies), _1529749)), _1529751)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1529747, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1529747, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1529747), _1529749))), hAPP(c_Set_OCollect(_1529747), _1529751)))], (43757 ^ _781404) ^ [_1653411, _1653413, _1653415] : [-(_1653411 = c_List_Olist_ONil(_1653413)), -(hBOOL(hAPP(hAPP(c_member(_1653413), hAPP(c_Product__Type_Ofst(_1653413, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1653413, _1653411), _1653415))), hAPP(c_List_Oset(_1653413), _1653411))))], (37670 ^ _781404) ^ [_1492292, _1492294, _1492296, _1492298] : [c_Equiv__Relations_Oequiv(_1492292, _1492294, _1492296), hBOOL(hAPP(hAPP(c_member(_1492292), _1492298), _1492294)), -(hBOOL(hAPP(hAPP(c_member(_1492292), _1492298), hAPP(c_Relation_OImage(_1492292, _1492292, _1492296), hAPP(hAPP(c_Set_Oinsert(_1492292), _1492298), c_Orderings_Obot__class_Obot(tc_fun(_1492292, tc_HOL_Obool)))))))], (31314 ^ _781404) ^ [_1344733, _1344735, _1344737] : [class_Orderings_Olinorder(_1344733), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344733), _1344735)), -(_1344737 = c_Orderings_Obot__class_Obot(tc_fun(_1344733, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1344733, tc_HOL_Obool)), _1344737), _1344735)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1344733), c_Big__Operators_Olattice_OInf__fin(_1344733, c_Orderings_Oord__class_Omin(_1344733), _1344737)), c_Big__Operators_Olattice_OInf__fin(_1344733, c_Orderings_Oord__class_Omin(_1344733), _1344735)) = c_Big__Operators_Olattice_OInf__fin(_1344733, c_Orderings_Oord__class_Omin(_1344733), _1344735))], (36562 ^ _781404) ^ [_1464804, _1464806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1464804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1464806), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1464804), _1464806) = 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), _1464804), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1464806)))))], (35746 ^ _781404) ^ [_1448594, _1448596, _1448598, _1448600] : [-(hAPP(c_Nat_Onat_Onat__rec(_1448594, _1448596, _1448598), hAPP(c_Nat_OSuc, _1448600)) = hAPP(hAPP(_1448598, _1448600), hAPP(c_Nat_Onat_Onat__rec(_1448594, _1448596, _1448598), _1448600)))], (50588 ^ _781404) ^ [_1803531, _1803533, _1803535] : [hAPP(c_Set_Oimage(_1803531, _1803533, _1803535), c_Orderings_Otop__class_Otop(tc_fun(_1803531, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1803533, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1803533, _1803531, c_Hilbert__Choice_Oinv__into(_1803531, _1803533, c_Orderings_Otop__class_Otop(tc_fun(_1803531, tc_HOL_Obool)), _1803535), c_Orderings_Otop__class_Otop(tc_fun(_1803533, tc_HOL_Obool))))], (38 ^ _781404) ^ [_781933, _781935, _781937, _781939, _781941, _781943] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_781941, _781937, _781933)), c_Hoare__Mirabelle_Ohoare__derivs(_781943, _781939, _781935), _781943 = _781941, _781939 = _781937, _781935 = _781933], (33432 ^ _781404) ^ [_1388867, _1388869, _1388871, _1388873, _1388875] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388867, tc_fun(_1388869, tc_HOL_Obool)), _1388871), hAPP(hAPP(c_COMBC(_1388867, tc_fun(_1388869, tc_HOL_Obool), tc_fun(_1388869, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1388869, tc_HOL_Obool), tc_fun(tc_fun(_1388869, tc_HOL_Obool), tc_fun(_1388869, tc_HOL_Obool)), _1388867), c_Groups_Ominus__class_Ominus(tc_fun(_1388869, tc_HOL_Obool))), _1388873)), _1388875)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1388869, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388867, tc_fun(_1388869, tc_HOL_Obool)), _1388871), _1388873)), _1388875))], (52286 ^ _781404) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (41277 ^ _781404) ^ [_1589805, _1589807] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589805, _1589805, _1589805), c_Transitive__Closure_Ortrancl(_1589805, _1589807)), c_Transitive__Closure_Ortrancl(_1589805, _1589807)) = c_Transitive__Closure_Ortrancl(_1589805, _1589807))], (25031 ^ _781404) ^ [_1229609] : [-(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)), _1229609)) = _1229609)], (30612 ^ _781404) ^ [_1331560, _1331562, _1331564] : [class_Orderings_Olinorder(_1331560), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331560), _1331562), _1331564) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331560), _1331564), _1331562))], (5762 ^ _781404) ^ [_872595, _872597, _872599, _872601] : [class_Orderings_Oord(_872595), 5765 ^ _781404 : [(5772 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872595), hAPP(_872599, 5773 ^ [_872595, _872597, _872599, _872601])), hAPP(_872601, 5773 ^ [_872595, _872597, _872599, _872601]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872597, _872595)), _872599), _872601)))], (5766 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872597, _872595)), _872599), _872601)), 5769 ^ _781404 : [(5770 ^ _781404) ^ [_872752] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872595), hAPP(_872599, _872752)), hAPP(_872601, _872752))))]]]]], (10315 ^ _781404) ^ [_956821, _956823, _956825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956821), _956823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956821), _956825)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956823), _956821)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956825), _956821)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956823), _956825))], (41911 ^ _781404) ^ [_1605188, _1605190, _1605192, _1605194, _1605196, _1605198] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605188, _1605188)), hAPP(hAPP(c_Product__Type_OPair(_1605188, _1605188), _1605190), _1605192)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605188, _1605188), tc_HOL_Obool), _1605194), _1605196))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1605188, _1605188)), hAPP(hAPP(c_Product__Type_OPair(_1605188, _1605188), _1605192), _1605198)), _1605196)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605188, _1605188)), hAPP(hAPP(c_Product__Type_OPair(_1605188, _1605188), _1605190), _1605198)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605188, _1605188), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1605194)), _1605196))))], (34839 ^ _781404) ^ [_1429005, _1429007, _1429009, _1429011, _1429013, _1429015, _1429017, _1429019] : [class_Groups_Ocomm__monoid__mult(_1429005), c_Fun_Oinj__on(_1429007, _1429009, _1429011, _1429013), _1429015 = hAPP(c_Set_Oimage(_1429007, _1429009, _1429011), _1429013), _1429017 = hAPP(c_Fun_Ocomp(_1429009, _1429005, _1429007, _1429019), _1429011), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1429009, _1429005), _1429019), _1429015) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1429007, _1429005), _1429017), _1429013))], (12744 ^ _781404) ^ [_1001985, _1001987, _1001989, _1001991, _1001993, _1001995] : [hBOOL(hAPP(hAPP(c_member(_1001985), _1001987), c_SetInterval_Oord_OatLeastLessThan(_1001985, _1001989, _1001991, _1001993, _1001995))), 12747 ^ _781404 : [(12750 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1001991, _1001987), _1001995)))], (12748 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1001989, _1001993), _1001987)))]]], (36062 ^ _781404) ^ [_1454264, _1454266, _1454268] : [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), _1454264), _1454266))), -(hBOOL(hAPP(hAPP(_1454268, _1454264), _1454266))), 36069 ^ _781404 : [(36072 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1454268, 36067 ^ [_1454264, _1454266, _1454268]), 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)))), 36068 ^ [_1454264, _1454266, _1454268])))), -(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), 36067 ^ [_1454264, _1454266, _1454268]), 36068 ^ [_1454264, _1454266, _1454268])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 36068 ^ [_1454264, _1454266, _1454268]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36082 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1454268, 36067 ^ [_1454264, _1454266, _1454268]), 36068 ^ [_1454264, _1454266, _1454268]))], (36070 ^ _781404) ^ [] : [-(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), 36067 ^ [_1454264, _1454266, _1454268]), 36068 ^ [_1454264, _1454266, _1454268]))))]]], (35852 ^ _781404) ^ [_1450864, _1450866, _1450868, _1450870, _1450872, _1450874] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450864, _1450866), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1450868), _1450870))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450864, _1450866), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1450872), _1450874))), -(_1450866 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1450868 = _1450872)], (25672 ^ _781404) ^ [_1240154, _1240156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240156)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1240154), _1240156)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1240154)), hAPP(c_Int_Onat, _1240156)))], (51245 ^ _781404) ^ [_1817327, _1817329, _1817331] : [hBOOL(hAPP(hAPP(c_member(_1817327), _1817329), c_Quotient_ORespects(_1817327, _1817331))), -(hBOOL(hAPP(hAPP(_1817331, _1817329), _1817329)))], (12240 ^ _781404) ^ [_991879, _991881, _991883] : [-(hBOOL(hAPP(hAPP(c_member(_991879), _991881), _991883))), -(hBOOL(hAPP(hAPP(c_member(_991879), _991881), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_991879, tc_HOL_Obool)), _991883))))], (13987 ^ _781404) ^ [_1025279, _1025281] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025279), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025279), _1025281)))))], (20907 ^ _781404) ^ [_1152511, _1152513] : [class_Rings_Ocomm__semiring__1(_1152511), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152511), _1152513), c_Groups_Ozero__class_Ozero(_1152511)) = c_Groups_Ozero__class_Ozero(_1152511))], (40980 ^ _781404) ^ [_1581719, _1581721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581719), _1581721)), -(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), _1581719), _1581721)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (30670 ^ _781404) ^ [_1332817, _1332819, _1332821] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1332817), _1332819)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1332821), _1332819)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1332817), _1332821)), _1332819))], (11365 ^ _781404) ^ [_974864, _974866, _974868, _974870, _974872] : [c_Fun_Oinj__on(_974864, _974866, _974868, hAPP(hAPP(c_Set_Oinsert(_974864), _974870), _974872)), 11368 ^ _781404 : [(11371 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_974866), hAPP(_974868, _974870)), hAPP(c_Set_Oimage(_974864, _974866, _974868), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974864, tc_HOL_Obool)), _974872), hAPP(hAPP(c_Set_Oinsert(_974864), _974870), c_Orderings_Obot__class_Obot(tc_fun(_974864, tc_HOL_Obool)))))))], (11369 ^ _781404) ^ [] : [-(c_Fun_Oinj__on(_974864, _974866, _974868, _974872))]]], (35640 ^ _781404) ^ [_1446610, _1446612, _1446614, _1446616, _1446618, _1446620, _1446622] : [-(hAPP(c_Product__Type_Oapsnd(_1446610, _1446612, _1446614, _1446616), hAPP(c_Product__Type_Oapsnd(_1446618, _1446610, _1446614, _1446620), _1446622)) = hAPP(c_Product__Type_Oapsnd(_1446618, _1446612, _1446614, hAPP(c_Fun_Ocomp(_1446610, _1446612, _1446618, _1446616), _1446620)), _1446622))], (49640 ^ _781404) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (41413 ^ _781404) ^ [_1592887, _1592889, _1592891, _1592893] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592887, _1592887)), hAPP(hAPP(c_Product__Type_OPair(_1592887, _1592887), _1592889), _1592891)), c_Transitive__Closure_Ortrancl(_1592887, _1592893))), hBOOL(hAPP(hAPP(c_member(_1592887), _1592891), c_Wellfounded_Oacc(_1592887, _1592893))), -(hBOOL(hAPP(hAPP(c_member(_1592887), _1592889), c_Wellfounded_Oacc(_1592887, _1592893))))], (21489 ^ _781404) ^ [_1163467, _1163469, _1163471] : [class_Rings_Oordered__cancel__semiring(_1163467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163467), c_Groups_Ozero__class_Ozero(_1163467)), _1163469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163467), _1163471), c_Groups_Ozero__class_Ozero(_1163467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163467), _1163471), _1163469)), c_Groups_Ozero__class_Ozero(_1163467))))], (35708 ^ _781404) ^ [_1447675, _1447677, _1447679, _1447681, _1447683] : [-(hAPP(c_Nat_Onat_Onat__rec(_1447675, _1447677, _1447679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1447681)), _1447683)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1447675), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1447681))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1447675, _1447675), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1447675, tc_fun(_1447675, _1447675)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1447675, tc_fun(_1447675, _1447675)), tc_Int_Oint), c_If(_1447675)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1447675, _1447677, _1447679), _1447683))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1447675, _1447675), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1447675, _1447675), tc_Int_Oint), _1447679), 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)), _1447683))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1447675, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1447675, _1447677, _1447679)), 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)), _1447683))))))], (35085 ^ _781404) ^ [_1434812, _1434814, _1434816, _1434818, _1434820, _1434822, _1434824] : [c_Fun_Oinj__on(_1434812, _1434814, _1434816, hAPP(c_Set_Oimage(_1434818, _1434812, _1434820), _1434822)), c_Fun_Oinj__on(_1434818, _1434812, _1434820, _1434822), hBOOL(hAPP(hAPP(c_member(_1434814), _1434824), hAPP(c_Set_Oimage(_1434812, _1434814, _1434816), hAPP(c_Set_Oimage(_1434818, _1434812, _1434820), _1434822)))), -(hAPP(c_Fun_Othe__inv__into(_1434818, _1434814, _1434822, hAPP(c_Fun_Ocomp(_1434812, _1434814, _1434818, _1434816), _1434820)), _1434824) = hAPP(hAPP(c_Fun_Ocomp(_1434812, _1434818, _1434814, c_Fun_Othe__inv__into(_1434818, _1434812, _1434822, _1434820)), c_Fun_Othe__inv__into(_1434812, _1434814, hAPP(c_Set_Oimage(_1434818, _1434812, _1434820), _1434822), _1434816)), _1434824))], (22865 ^ _781404) ^ [_1190264, _1190266, _1190268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190264), _1190266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1190268)), -(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), _1190268)), _1190264)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1190268)), _1190266))))], (24598 ^ _781404) ^ [_1222653, _1222655] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222653))), -(c_SMT_Oz3div(_1222655, _1222653) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222655), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1222653))))], (18369 ^ _781404) ^ [_1108796, _1108798, _1108800, _1108802, _1108804, _1108806] : [c_Finite__Set_Ofun__left__comm(_1108796, _1108798, _1108800), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108796), _1108802)), -(hBOOL(hAPP(hAPP(c_member(_1108796), _1108804), _1108802))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1108796, _1108798, _1108800), _1108806), hAPP(hAPP(c_Set_Oinsert(_1108796), _1108804), _1108802)) = hAPP(hAPP(_1108800, _1108804), hAPP(hAPP(c_Finite__Set_Ofold(_1108796, _1108798, _1108800), _1108806), _1108802)))], (45395 ^ _781404) ^ [_1690561, _1690563] : [class_Groups_Oordered__ab__group__add__abs(_1690561), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1690561), hAPP(c_Groups_Oabs__class_Oabs(_1690561), hAPP(c_List_Omonoid__add__class_Olistsum(_1690561), _1690563))), hAPP(c_List_Omonoid__add__class_Olistsum(_1690561), hAPP(hAPP(c_List_Omap(_1690561, _1690561), c_Groups_Oabs__class_Oabs(_1690561)), _1690563)))))], (23257 ^ _781404) ^ [_1197859, _1197861, _1197863, _1197865, _1197867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1197859), _1197861)), 23260 ^ _781404 : [(23267 ^ _781404) ^ [] : [_1197865 = 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), _1197861), _1197859)), _1197863)), _1197867), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197859), _1197863)), _1197865) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197861), _1197863)), _1197867))], (23261 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197859), _1197863)), _1197865) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197861), _1197863)), _1197867), -(_1197865 = 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), _1197861), _1197859)), _1197863)), _1197867))]]], (26993 ^ _781404) ^ [_1263226, _1263228, _1263230, _1263232, _1263234, _1263236] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1263226, _1263228, _1263230, _1263232, _1263234), _1263236)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1263226), _1263234)))], (19067 ^ _781404) ^ [_1120699, _1120701] : [class_Rings_Osemiring__1(_1120699), -(hBOOL(hAPP(hAPP(c_member(_1120699), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1120699), _1120701)), c_Nat_Osemiring__1__class_ONats(_1120699))))], (41526 ^ _781404) ^ [_1595633, _1595635, _1595637] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1595633, _1595635)), hAPP(c_Relation_Oconverse(_1595635, _1595633), _1595637))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1595635, _1595633)), _1595637)))], (46702 ^ _781404) ^ [_1720920, _1720922, _1720924] : [class_Groups_Omonoid__add(_1720920), -(hAPP(c_List_Ofoldl(_1720920, _1720920, c_Groups_Oplus__class_Oplus(_1720920), _1720922), _1720924) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1720920), _1720922), c_List_Ofoldr(_1720920, _1720920, c_Groups_Oplus__class_Oplus(_1720920), _1720924, c_Groups_Ozero__class_Ozero(_1720920))))], (39463 ^ _781404) ^ [_1543428] : [-(c_Int_Oint__ge__less__than(_1543428) = 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), _1543428)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (52410 ^ _781404) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (6207 ^ _781404) ^ [_880199, _880201, _880203, _880205] : [c_Hoare__Mirabelle_Ohoare__derivs(_880199, _880201, _880203), c_Hoare__Mirabelle_Ohoare__derivs(_880199, _880205, _880201), -(c_Hoare__Mirabelle_Ohoare__derivs(_880199, _880205, _880203))], (6909 ^ _781404) ^ [_892368, _892370, _892372, _892374] : [class_Lattices_Osemilattice__sup(_892368), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892368), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892368), _892370), _892372)), _892374) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892368), _892370), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892368), _892372), _892374)))], (34871 ^ _781404) ^ [_1429606, _1429608, _1429610] : [class_Fields_Ofield(_1429606), -(_1429608 = c_Groups_Oone__class_Oone(_1429606)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429606), hAPP(c_Power_Opower__class_Opower(_1429606), _1429608)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1429610)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1429606), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1429606), hAPP(hAPP(c_Power_Opower__class_Opower(_1429606), _1429608), _1429610)), c_Groups_Oone__class_Oone(_1429606))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1429606), _1429608), c_Groups_Oone__class_Oone(_1429606))))], (7607 ^ _781404) ^ [_906250, _906252, _906254, _906256] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_906250, tc_HOL_Obool)), _906252), _906254), _906256)), -(hBOOL(hAPP(_906254, _906256)))], (19871 ^ _781404) ^ [_1134386, _1134388, _1134390] : [class_Int_Onumber__ring(_1134386), 19874 ^ _781404 : [(19881 ^ _781404) ^ [] : [c_Int_Oiszero(_1134386, hAPP(c_Int_Onumber__class_Onumber__of(_1134386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1134388), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1134390)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1134386), _1134388) = hAPP(c_Int_Onumber__class_Onumber__of(_1134386), _1134390))], (19875 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1134386), _1134388) = hAPP(c_Int_Onumber__class_Onumber__of(_1134386), _1134390), -(c_Int_Oiszero(_1134386, hAPP(c_Int_Onumber__class_Onumber__of(_1134386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1134388), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1134390)))))]]], (41586 ^ _781404) ^ [_1597205, _1597207] : [-(c_Transitive__Closure_Otrancl(_1597205, hAPP(c_Relation_Oconverse(_1597205, _1597205), _1597207)) = hAPP(c_Relation_Oconverse(_1597205, _1597205), c_Transitive__Closure_Otrancl(_1597205, _1597207)))], (7864 ^ _781404) ^ [_911421, _911423, _911425] : [class_Groups_Oordered__ab__group__add(_911421), -(hAPP(c_Set_Oimage(_911421, _911421, c_Groups_Ouminus__class_Ouminus(_911421)), c_SetInterval_Oord__class_OgreaterThanAtMost(_911421, _911423, _911425)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_911421, hAPP(c_Groups_Ouminus__class_Ouminus(_911421), _911425)), hAPP(c_Groups_Ouminus__class_Ouminus(_911421), _911423)))], (43515 ^ _781404) ^ [_1648928, _1648930, _1648932] : [hAPP(hAPP(c_List_Otake(_1648928), _1648930), _1648932) = c_List_Olist_ONil(_1648928), -(_1648930 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1648932 = c_List_Olist_ONil(_1648928))], (30300 ^ _781404) ^ [_1325581] : [class_Lattices_Osemilattice__inf(_1325581), -(c_Finite__Set_Ofun__left__comm__idem(_1325581, _1325581, c_Lattices_Osemilattice__inf__class_Oinf(_1325581)))], (39131 ^ _781404) ^ [_1529541, _1529543, _1529545, _1529547] : [-(hAPP(c_Set_Ovimage(_1529541, _1529543, _1529545), _1529547) = hAPP(c_Set_OCollect(_1529541), hAPP(hAPP(c_COMBC(_1529541, tc_fun(_1529543, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1529543, tc_fun(tc_fun(_1529543, tc_HOL_Obool), tc_HOL_Obool), _1529541), c_member(_1529543)), _1529545)), _1529547)))], (19512 ^ _781404) ^ [_1128335, _1128337] : [class_Int_Onumber__ring(_1128335), -(hAPP(c_Int_Onumber__class_Onumber__of(_1128335), c_Int_OBit1(_1128337)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128335), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128335), c_Groups_Oone__class_Oone(_1128335)), hAPP(c_Int_Onumber__class_Onumber__of(_1128335), _1128337))), hAPP(c_Int_Onumber__class_Onumber__of(_1128335), _1128337)))], (6939 ^ _781404) ^ [_893045, _893047, _893049, _893051] : [hBOOL(hAPP(_893045, _893047)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_893049, tc_HOL_Obool)), _893045), _893051), _893047)))], (40230 ^ _781404) ^ [_1564750] : [-(c_Wellfounded_OwfP(_1564750, hAPP(c_COMBK(tc_fun(_1564750, tc_HOL_Obool), _1564750), hAPP(c_COMBK(tc_HOL_Obool, _1564750), c_fFalse))))], (32336 ^ _781404) ^ [_1363691, _1363693, _1363695, _1363697, _1363699] : [class_Orderings_Olinorder(_1363691), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1363691, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1363691, _1363693, _1363695)), c_SetInterval_Oord__class_OatLeastAtMost(_1363691, _1363697, _1363699)) = c_SetInterval_Oord__class_OatLeastAtMost(_1363691, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363691), _1363693), _1363697), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1363691), _1363695), _1363699)))], (7795 ^ _781404) ^ [_909758, _909760, _909762, _909764, _909766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909758, tc_HOL_Obool)), _909760), hAPP(c_Set_Oimage(_909762, _909758, _909764), _909766))), 7799 ^ _781404 : [(7802 ^ _781404) ^ [] : [-(_909760 = hAPP(c_Set_Oimage(_909762, _909758, _909764), 7798 ^ [_909758, _909760, _909762, _909764, _909766]))], (7800 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909762, tc_HOL_Obool)), 7798 ^ [_909758, _909760, _909762, _909764, _909766]), _909766)))]]], (24774 ^ _781404) ^ [_1225655] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1225655, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14392 ^ _781404) ^ [_1033156, _1033158, _1033160, _1033162, _1033164, _1033166] : [c_Fun_Oinj__on(_1033156, _1033158, _1033160, _1033162), -(hBOOL(hAPP(hAPP(c_member(_1033158), _1033164), hAPP(c_Set_Oimage(_1033156, _1033158, _1033160), _1033162)))), -(c_Fun_Oinj__on(_1033156, _1033158, c_Fun_Ofun__upd(_1033156, _1033158, _1033160, _1033166, _1033164), _1033162))], (33655 ^ _781404) ^ [_1395041, _1395043, _1395045, _1395047] : [class_Groups_Oab__group__add(_1395041), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1395043, _1395041), hAPP(hAPP(c_COMBB(_1395041, _1395041, _1395043), c_Groups_Ouminus__class_Ouminus(_1395041)), _1395045)), _1395047) = hAPP(c_Groups_Ouminus__class_Ouminus(_1395041), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1395043, _1395041), _1395045), _1395047)))], (46886 ^ _781404) ^ [_1724561, _1724563, _1724565, _1724567, _1724569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724561), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1724563), _1724565))), -(hAPP(hAPP(c_List_Onth(_1724567), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1724567), _1724569), c_List_Oupt(_1724565, _1724563))), _1724561) = hAPP(_1724569, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1724565), _1724561)))], (41568 ^ _781404) ^ [_1596627, _1596629, _1596631, _1596633, _1596635] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596627, _1596629)), hAPP(hAPP(c_Product__Type_OPair(_1596627, _1596629), _1596631), _1596633)), _1596635)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596629, _1596627)), hAPP(hAPP(c_Product__Type_OPair(_1596629, _1596627), _1596633), _1596631)), hAPP(c_Relation_Oconverse(_1596627, _1596629), _1596635))))], (9248 ^ _781404) ^ [_939363, _939365] : [class_Orderings_Oorder(_939363), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939363, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_939363), _939365), c_Orderings_Obot__class_Obot(tc_fun(_939363, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_939363), _939365)) = hAPP(hAPP(c_Set_Oinsert(_939363), _939365), c_Orderings_Obot__class_Obot(tc_fun(_939363, tc_HOL_Obool))))], (23832 ^ _781404) ^ [_1209192, _1209194, _1209196] : [class_Divides_Osemiring__div(_1209192), -(_1209194 = c_Groups_Ozero__class_Ozero(_1209192)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209192), _1209194), _1209196)), _1209194) = _1209196)], (23597 ^ _781404) ^ [_1205151, _1205153, _1205155] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1205151), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1205153, _1205155)), _1205155) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1205151), _1205153), _1205155))], (22859 ^ _781404) ^ [_1190125, _1190127] : [class_Int_Onumber__ring(_1190125), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190125), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190125), c_Groups_Oone__class_Oone(_1190125)), c_Groups_Oone__class_Oone(_1190125))), hAPP(c_Int_Onumber__class_Onumber__of(_1190125), _1190127)) = hAPP(c_Int_Onumber__class_Onumber__of(_1190125), c_Int_OBit0(_1190127)))], (44337 ^ _781404) ^ [_1667590, _1667592] : [hBOOL(hAPP(c_List_Odistinct(_1667590), hAPP(c_List_Orotate1(_1667590), _1667592))), -(hBOOL(hAPP(c_List_Odistinct(_1667590), _1667592)))], (8449 ^ _781404) ^ [_923891, _923893] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923891, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_923891, tc_HOL_Obool))), _923893) = c_Orderings_Obot__class_Obot(tc_fun(_923891, tc_HOL_Obool)))], (28171 ^ _781404) ^ [_1284786, _1284788, _1284790, _1284792] : [class_Fields_Olinordered__field__inverse__zero(_1284786), class_Int_Onumber(_1284786), 28178 ^ _781404 : [(28179 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), _1284788), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284786), _1284790), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792)))), 28182 ^ _781404 : [(28189 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), c_Groups_Ozero__class_Ozero(_1284786)), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792)))), 28192 ^ _781404 : [(28199 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792)), c_Groups_Ozero__class_Ozero(_1284786)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), _1284788), c_Groups_Ozero__class_Ozero(_1284786))))], (28193 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792)), c_Groups_Ozero__class_Ozero(_1284786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), _1284790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284786), _1284788), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792)))))]]], (28183 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), c_Groups_Ozero__class_Ozero(_1284786)), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284786), _1284788), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792))), _1284790)))]]], (28205 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), _1284788), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284786), _1284790), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792))))), 28208 ^ _781404 : [(28211 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284786), _1284788), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792))), _1284790))], (28209 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), c_Groups_Ozero__class_Ozero(_1284786)), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792))))]], 28212 ^ _781404 : [(28215 ^ _781404) ^ [] : [28216 ^ _781404 : [(28219 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), _1284790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284786), _1284788), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792))))], (28217 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792)), c_Groups_Ozero__class_Ozero(_1284786))))]], 28220 ^ _781404 : [(28223 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), _1284788), c_Groups_Ozero__class_Ozero(_1284786)))], (28221 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792)), c_Groups_Ozero__class_Ozero(_1284786)))]]], (28213 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284786), c_Groups_Ozero__class_Ozero(_1284786)), hAPP(c_Int_Onumber__class_Onumber__of(_1284786), _1284792)))]]]]], (36858 ^ _781404) ^ [_1471103, _1471105, _1471107, _1471109, _1471111, _1471113, _1471115] : [c_Finite__Set_Ofolding__image(_1471103, _1471105, _1471107, _1471109, _1471111), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471105), _1471113)), -(hAPP(hAPP(_1471111, _1471115), _1471113) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1471103, _1471105, _1471107), _1471115), _1471109), _1471113))], (25215 ^ _781404) ^ [_1232621, _1232623] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232621) = _1232623, 25218 ^ _781404 : [(25221 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232623)))], (25219 ^ _781404) ^ [] : [-(_1232621 = hAPP(c_Int_Onat, _1232623))]]], (42758 ^ _781404) ^ [_1630142, _1630144, _1630146] : [-(hAPP(c_List_Oset(_1630142), c_List_Osublist(_1630142, _1630144, _1630146)) = hAPP(c_Set_OCollect(_1630142), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1630142), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1630142, 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)), _1630142), 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)), _1630142), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1630142, tc_fun(tc_Nat_Onat, _1630142), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630142, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1630142), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1630142), c_COMBB(_1630142, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1630142), _1630144))))), 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(_1630142)), _1630144)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1630146))))))], (45728 ^ _781404) ^ [_1697476] : [-(_1697476 = 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, _1697476)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1697476))))], (41580 ^ _781404) ^ [_1596969, _1596971, _1596973, _1596975] : [-(hAPP(c_Relation_Oconverse(_1596969, _1596971), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1596969, _1596971), tc_HOL_Obool)), _1596973), _1596975)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1596971, _1596969), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1596969, _1596971), _1596973)), hAPP(c_Relation_Oconverse(_1596969, _1596971), _1596975)))], (11893 ^ _781404) ^ [_985026, _985028, _985030, _985032, _985034] : [hBOOL(hAPP(hAPP(c_member(_985026), _985028), hAPP(c_Set_Ovimage(_985026, _985030, _985032), hAPP(hAPP(c_Set_Oinsert(_985030), _985034), c_Orderings_Obot__class_Obot(tc_fun(_985030, tc_HOL_Obool)))))), -(hAPP(_985032, _985028) = _985034)], (1100 ^ _781404) ^ [_797904, _797906, _797908, _797910, _797912, _797914, _797916, _797918, _797920, _797922, _797924, _797926] : [-(c_Equiv__Relations_Ocongruent2(_797924, _797920, _797916, _797912, _797908, _797904)), c_Equiv__Relations_Ocongruent2(_797926, _797922, _797918, _797914, _797910, _797906), _797926 = _797924, _797922 = _797920, _797918 = _797916, _797914 = _797912, _797910 = _797908, _797906 = _797904], (12346 ^ _781404) ^ [_994013, _994015, _994017, _994019, _994021] : [hBOOL(hAPP(hAPP(c_member(_994013), _994015), _994017)), -(hAPP(hAPP(c_Set_Oinsert(_994019), hAPP(_994021, _994015)), hAPP(c_Set_Oimage(_994013, _994019, _994021), _994017)) = hAPP(c_Set_Oimage(_994013, _994019, _994021), _994017))], (7449 ^ _781404) ^ [_903023, _903025] : [class_Lattices_Osemilattice__inf(_903023), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903023), _903025), _903025) = _903025)], (52350 ^ _781404) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (27167 ^ _781404) ^ [_1266411, _1266413, _1266415] : [class_Rings_Olinordered__idom(_1266411), 27170 ^ _781404 : [(27179 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266411), hAPP(c_Groups_Oabs__class_Oabs(_1266411), _1266413)), _1266415))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266411), _1266413), _1266415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266411), hAPP(c_Groups_Ouminus__class_Ouminus(_1266411), _1266413)), _1266415))], (27171 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266411), hAPP(c_Groups_Oabs__class_Oabs(_1266411), _1266413)), _1266415)), 27174 ^ _781404 : [(27177 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266411), hAPP(c_Groups_Ouminus__class_Ouminus(_1266411), _1266413)), _1266415)))], (27175 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266411), _1266413), _1266415)))]]]]], (10055 ^ _781404) ^ [_952928, _952930, _952932] : [class_Orderings_Olinorder(_952928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952928), _952930), _952932)), 10062 ^ _781404 : [(10069 ^ _781404) ^ [] : [_952930 = _952932, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952928), _952930), _952932))], (10063 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952928), _952930), _952932))), -(_952930 = _952932)]]], (46201 ^ _781404) ^ [_1708672, _1708674, _1708676, _1708678, _1708680] : [c_Fun_Oinj__on(_1708672, _1708674, _1708676, hAPP(hAPP(c_Set_Oinsert(_1708672), _1708678), hAPP(c_List_Oset(_1708672), _1708680))), -(hAPP(hAPP(c_List_Omap(_1708672, _1708674), _1708676), hAPP(c_List_OremoveAll(_1708672, _1708678), _1708680)) = hAPP(c_List_OremoveAll(_1708674, hAPP(_1708676, _1708678)), hAPP(hAPP(c_List_Omap(_1708672, _1708674), _1708676), _1708680)))], (52472 ^ _781404) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (29267 ^ _781404) ^ [_1305197, _1305199, _1305201, _1305203, _1305205] : [class_Fields_Olinordered__field(_1305197), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305197), c_Groups_Ozero__class_Ozero(_1305197)), _1305199)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305197), _1305199), _1305201)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305197), c_Groups_Ozero__class_Ozero(_1305197)), _1305203)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305197), _1305203), _1305205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305197), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305197), _1305199), _1305205)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305197), _1305201), _1305203))))], (24440 ^ _781404) ^ [_1219749, _1219751, _1219753] : [-(hBOOL(hAPP(_1219749, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1219751, _1219753)))), 24443 ^ _781404 : [(24446 ^ _781404) ^ [] : [hBOOL(hAPP(_1219749, _1219751))], (24444 ^ _781404) ^ [] : [-(_1219753 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 24449 ^ _781404 : [(24450 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219753)))], (24456 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24452 ^ [_1219749, _1219751, _1219753]), _1219753)))], (24460 ^ _781404) ^ [] : [hBOOL(hAPP(_1219749, 24452 ^ [_1219749, _1219751, _1219753]))], (24458 ^ _781404) ^ [] : [-(_1219751 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219753), 24451 ^ [_1219749, _1219751, _1219753])), 24452 ^ [_1219749, _1219751, _1219753]))], (24454 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24452 ^ [_1219749, _1219751, _1219753])))]], 24461 ^ _781404 : [(24462 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1219753), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24468 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24464 ^ [_1219749, _1219751, _1219753]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24472 ^ _781404) ^ [] : [hBOOL(hAPP(_1219749, 24464 ^ [_1219749, _1219751, _1219753]))], (24470 ^ _781404) ^ [] : [-(_1219751 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219753), 24463 ^ [_1219749, _1219751, _1219753])), 24464 ^ [_1219749, _1219751, _1219753]))], (24466 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1219753), 24464 ^ [_1219749, _1219751, _1219753])))]]], (4284 ^ _781404) ^ [_846298, _846300] : [_846300 = _846298, -(c_Orderings_Oord__class_Omin(_846300) = c_Orderings_Oord__class_Omin(_846298))], (20281 ^ _781404) ^ [_1141376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141376)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1141376))], (5340 ^ _781404) ^ [_862920, _862922, _862924, _862926, _862928, _862930, _862932, _862934, _862936, _862938] : [-(c_New__DSequence_Opos__map(_862938, _862934, _862930, _862926, _862922) = c_New__DSequence_Opos__map(_862936, _862932, _862928, _862924, _862920)), _862938 = _862936, _862934 = _862932, _862930 = _862928, _862926 = _862924, _862922 = _862920], (39315 ^ _781404) ^ [_1536883] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1536883) = 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), _1536883), c_Int_Onat)))))], (49989 ^ _781404) ^ [_1791733, _1791735, _1791737, _1791739] : [c_Wellfounded_Omax__extp(_1791733, _1791735, _1791737, _1791739), 49992 ^ _781404 : [(49995 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1791733), _1791739)))], (49997 ^ _781404) ^ [] : [_1791739 = c_Orderings_Obot__class_Obot(tc_fun(_1791733, tc_HOL_Obool))], (49999 ^ _781404) ^ [_1791949] : [hBOOL(hAPP(hAPP(c_member(_1791733), _1791949), _1791737)), 50003 ^ _781404 : [(50006 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1791735, _1791949), 50002 ^ [_1791733, _1791735, _1791737, _1791739, _1791949])))], (50004 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791733), 50002 ^ [_1791733, _1791735, _1791737, _1791739, _1791949]), _1791739)))]]], (49993 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1791733), _1791737)))]]], (6522 ^ _781404) ^ [_885351, _885353] : [class_Orderings_Olinorder(_885351), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_885351, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_885351), _885353)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_885351), _885353))], (46139 ^ _781404) ^ [_1707343, _1707345] : [-(c_Enum_Oenum__the(_1707343, _1707345) = c_HOL_OThe(_1707343, _1707345))], (33514 ^ _781404) ^ [_1391173, _1391175] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1391173, tc_HOL_Obool), _1391175) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1391173, tc_HOL_Obool), tc_fun(_1391173, tc_HOL_Obool)), _1391175), c_COMBI(tc_fun(_1391173, tc_HOL_Obool))))], (43525 ^ _781404) ^ [_1649040, _1649042, _1649044] : [43526 ^ _781404 : [(43529 ^ _781404) ^ [] : [_1649044 = c_List_Olist_ONil(_1649040)], (43527 ^ _781404) ^ [] : [_1649042 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1649040), _1649042), _1649044) = c_List_Olist_ONil(_1649040))], (13183 ^ _781404) ^ [_1010265, _1010267, _1010269, _1010271] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1010265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010265), _1010267), _1010269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010265), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010265), _1010267), _1010271)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010265), _1010269), _1010271))))], (3676 ^ _781404) ^ [_836472, _836474, _836476, _836478, _836480, _836482, _836484, _836486, _836488, _836490] : [-(c_List_Ofoldr(_836490, _836486, _836482, _836478, _836474) = c_List_Ofoldr(_836488, _836484, _836480, _836476, _836472)), _836490 = _836488, _836486 = _836484, _836482 = _836480, _836478 = _836476, _836474 = _836472], (9118 ^ _781404) ^ [_936069, _936071, _936073, _936075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936069, tc_HOL_Obool)), _936071), _936073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936069, tc_HOL_Obool)), _936073), _936075)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936069, tc_HOL_Obool)), _936073), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936069, tc_HOL_Obool)), _936075), _936071)) = _936071)], (31978 ^ _781404) ^ [_1356926, _1356928, _1356930, _1356932] : [class_Orderings_Olinorder(_1356926), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356926), _1356928), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356926), _1356930), _1356932)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356926), _1356930), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356926), _1356928), _1356932)))], (29787 ^ _781404) ^ [_1315027, _1315029, _1315031, _1315033, _1315035] : [class_Fields_Ofield(_1315027), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315029), _1315031)), -(hAPP(_1315033, _1315035) = c_Groups_Ozero__class_Ozero(_1315027)), 29798 ^ _781404 : [(29805 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1315029), _1315035), _1315031))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315029, _1315027), _1315033), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315029, tc_HOL_Obool)), _1315031), hAPP(hAPP(c_Set_Oinsert(_1315029), _1315035), c_Orderings_Obot__class_Obot(tc_fun(_1315029, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315029, _1315027), _1315033), _1315031))], (29799 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1315029), _1315035), _1315031)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315029, _1315027), _1315033), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315029, tc_HOL_Obool)), _1315031), hAPP(hAPP(c_Set_Oinsert(_1315029), _1315035), c_Orderings_Obot__class_Obot(tc_fun(_1315029, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315027), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315029, _1315027), _1315033), _1315031)), hAPP(_1315033, _1315035)))]]], (49606 ^ _781404) ^ [_1782257, _1782259, _1782261, _1782263] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1782257), _1782259), _1782261), _1782263) = 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(_1782257)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1782257), _1782259)))], (2076 ^ _781404) ^ [_811442, _811444, _811446, _811448, _811450, _811452, _811454, _811456] : [-(c_Sum__Type_OPlus(_811456, _811452, _811448, _811444) = c_Sum__Type_OPlus(_811454, _811450, _811446, _811442)), _811456 = _811454, _811452 = _811450, _811448 = _811446, _811444 = _811442], (25309 ^ _781404) ^ [_1234116] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1234116)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1234116)))], (4234 ^ _781404) ^ [_845575, _845577] : [_845577 = _845575, -(c_List_Otl(_845577) = c_List_Otl(_845575))], (2410 ^ _781404) ^ [_816707, _816709, _816711, _816713, _816715, _816717, _816719, _816721] : [-(c_Nitpick_Opair__box_OPairBox(_816721, _816717, _816713, _816709) = c_Nitpick_Opair__box_OPairBox(_816719, _816715, _816711, _816707)), _816721 = _816719, _816717 = _816715, _816713 = _816711, _816709 = _816707], (8864 ^ _781404) ^ [_931145, _931147, _931149, _931151] : [class_Orderings_Oorder(_931145), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931145, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_931145, _931147), _931149)), c_SetInterval_Oord__class_OatLeastAtMost(_931145, _931149, _931151)) = c_Orderings_Obot__class_Obot(tc_fun(_931145, tc_HOL_Obool)))], (2316 ^ _781404) ^ [_815176, _815178, _815180, _815182] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_815182, _815178) = c_Code__Numeral_Odiv__mod__code__numeral(_815180, _815176)), _815182 = _815180, _815178 = _815176], (10523 ^ _781404) ^ [_960542, _960544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960542), _960544)), _960544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11919 ^ _781404) ^ [_985697, _985699, _985701, _985703, _985705] : [-(hAPP(c_Set_Ovimage(_985697, _985699, _985701), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985699, tc_HOL_Obool)), _985703), _985705)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985697, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_985697, _985699, _985701), _985703)), hAPP(c_Set_Ovimage(_985697, _985699, _985701), _985705)))], (43124 ^ _781404) ^ [_1640378, _1640380, _1640382, _1640384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640378)), _1640380)), _1640382)), -(hAPP(hAPP(c_List_Olist__update(_1640378, _1640380), _1640382), _1640384) = _1640380)], (6405 ^ _781404) ^ [_883235, _883237] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883235), _883237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883237), _883235)))], (52280 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (2734 ^ _781404) ^ [_821839, _821841, _821843, _821845] : [-(c_Wellfounded_Omin__ext(_821845, _821841) = c_Wellfounded_Omin__ext(_821843, _821839)), _821845 = _821843, _821841 = _821839], (33817 ^ _781404) ^ [] : [-(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)))], (23599 ^ _781404) ^ [_1205202, _1205204, _1205206] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1205202), _1205204), _1205206) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1205202), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1205204, _1205206)), _1205206))], (48417 ^ _781404) ^ [_1756940, _1756942] : [class_Enum_Oenum(_1756940), 48420 ^ _781404 : [(48427 ^ _781404) ^ [] : [hBOOL(hAPP(_1756942, 48428 ^ [_1756940, _1756942])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1756940), _1756942)))], (48421 ^ _781404) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1756940), _1756942)), 48424 ^ _781404 : [(48425 ^ _781404) ^ [_1757066] : [-(hBOOL(hAPP(_1756942, _1757066)))]]]]], (22573 ^ _781404) ^ [_1184164, _1184166, _1184168] : [class_Rings_Olinordered__idom(_1184164), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184164), c_Groups_Ozero__class_Ozero(_1184164)), _1184166)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184164), c_Groups_Ozero__class_Ozero(_1184164)), _1184168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184164), _1184168), c_Groups_Oone__class_Oone(_1184164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184164), _1184166), _1184168)), _1184166)))], (11237 ^ _781404) ^ [_972058, _972060] : [11239 ^ _781404 : [(11242 ^ _781404) ^ [] : [hBOOL(hAPP(_972060, 11238 ^ [_972058, _972060]))], (11240 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 11238 ^ [_972058, _972060]), _972058)))]], 11243 ^ _781404 : [(11244 ^ _781404) ^ [_972208] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _972208), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972058))), -(hBOOL(hAPP(_972060, _972208)))]]], (45938 ^ _781404) ^ [_1702890, _1702892, _1702894, _1702896, _1702898, _1702900, _1702902] : [c_List_Olist__all2(_1702890, _1702892, _1702894, _1702896, _1702898), c_List_Olist__all2(_1702890, _1702892, _1702894, _1702900, _1702902), -(c_List_Olist__all2(_1702890, _1702892, _1702894, hAPP(hAPP(c_List_Oappend(_1702890), _1702896), _1702900), hAPP(hAPP(c_List_Oappend(_1702892), _1702898), _1702902)))], (11123 ^ _781404) ^ [_970252, _970254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970252), hAPP(c_Nat_OSuc, _970254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970252), _970254)))], (29039 ^ _781404) ^ [_1301332, _1301334, _1301336] : [class_Fields_Olinordered__field__inverse__zero(_1301332), 29042 ^ _781404 : [(29057 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301332), c_Groups_Ozero__class_Ozero(_1301332)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301332), _1301334), _1301336)))), 29058 ^ _781404 : [(29065 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301332), _1301334), c_Groups_Ozero__class_Ozero(_1301332))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301332), _1301336), c_Groups_Ozero__class_Ozero(_1301332)))], (29059 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301332), c_Groups_Ozero__class_Ozero(_1301332)), _1301334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301332), c_Groups_Ozero__class_Ozero(_1301332)), _1301336))]]], (29043 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301332), c_Groups_Ozero__class_Ozero(_1301332)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301332), _1301334), _1301336))), 29048 ^ _781404 : [(29051 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301332), c_Groups_Ozero__class_Ozero(_1301332)), _1301336)))], (29049 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301332), c_Groups_Ozero__class_Ozero(_1301332)), _1301334)))]], 29052 ^ _781404 : [(29055 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301332), _1301336), c_Groups_Ozero__class_Ozero(_1301332))))], (29053 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301332), _1301334), c_Groups_Ozero__class_Ozero(_1301332))))]]]]], (7820 ^ _781404) ^ [_910358, _910360, _910362, _910364, _910366] : [-(hAPP(c_Set_Oimage(_910358, _910360, _910362), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910358, tc_HOL_Obool)), _910364), _910366)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910360, tc_HOL_Obool)), hAPP(c_Set_Oimage(_910358, _910360, _910362), _910364)), hAPP(c_Set_Oimage(_910358, _910360, _910362), _910366)))], (2692 ^ _781404) ^ [_821152, _821154, _821156, _821158, _821160, _821162, _821164, _821166] : [-(c_Product__Type_Oapfst(_821166, _821162, _821158, _821154) = c_Product__Type_Oapfst(_821164, _821160, _821156, _821152)), _821166 = _821164, _821162 = _821160, _821158 = _821156, _821154 = _821152], (43579 ^ _781404) ^ [_1649983, _1649985] : [_1649985 = c_List_Olist_ONil(_1649983), -(hAPP(c_List_Oset(_1649983), _1649985) = c_Orderings_Obot__class_Obot(tc_fun(_1649983, tc_HOL_Obool)))], (25055 ^ _781404) ^ [_1229949, _1229951] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1229949)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1229949)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1229951)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1229949)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1229951))))], (25185 ^ _781404) ^ [_1232129, _1232131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232131)), 25192 ^ _781404 : [(25199 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232129), _1232131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1232129)), hAPP(c_Int_Onat, _1232131))))], (25193 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1232129)), hAPP(c_Int_Onat, _1232131))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232129), _1232131)))]]], (33546 ^ _781404) ^ [_1392052, _1392054, _1392056, _1392058] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392052, tc_fun(_1392054, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1392052, tc_HOL_Obool), _1392056)), _1392058) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1392052, tc_HOL_Obool), tc_fun(_1392054, tc_HOL_Obool)), _1392056), hAPP(hAPP(c_COMBC(tc_fun(_1392052, tc_HOL_Obool), tc_fun(_1392052, tc_fun(_1392054, tc_HOL_Obool)), tc_fun(_1392054, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392052, tc_fun(_1392054, tc_HOL_Obool))), _1392058)))], (16410 ^ _781404) ^ [_1072995, _1072997] : [_1072995 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1072995), _1072997) = _1072997)], (32712 ^ _781404) ^ [_1370667, _1370669, _1370671] : [class_Orderings_Olinorder(_1370667), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370667), _1370669)), -(_1370669 = c_Orderings_Obot__class_Obot(tc_fun(_1370667, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370667), _1370671)), -(_1370671 = c_Orderings_Obot__class_Obot(tc_fun(_1370667, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1370667, c_Orderings_Oord__class_Omax(_1370667), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1370667, tc_HOL_Obool)), _1370669), _1370671)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1370667), c_Big__Operators_Olattice_OSup__fin(_1370667, c_Orderings_Oord__class_Omax(_1370667), _1370669)), c_Big__Operators_Olattice_OSup__fin(_1370667, c_Orderings_Oord__class_Omax(_1370667), _1370671)))], (45012 ^ _781404) ^ [_1682085, _1682087, _1682089, _1682091] : [-(_1682085 = c_List_Olist_ONil(_1682087)), 45015 ^ _781404 : [(45022 ^ _781404) ^ [] : [-(_1682089 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682087)), _1682085)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1682087, hAPP(hAPP(c_List_Olist__update(_1682087, _1682085), _1682089), _1682091)) = c_List_Olast(_1682087, _1682085))], (45016 ^ _781404) ^ [] : [_1682089 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682087)), _1682085)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1682087, hAPP(hAPP(c_List_Olist__update(_1682087, _1682085), _1682089), _1682091)) = _1682091)]]], (33867 ^ _781404) ^ [_1401215, _1401217, _1401219, _1401221, _1401223] : [class_Fields_Ofield(_1401215), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1401215), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1401217, _1401215), _1401219), _1401221)), _1401223) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1401217, _1401215), hAPP(hAPP(c_COMBC(_1401217, _1401215, _1401215), hAPP(hAPP(c_COMBB(_1401215, tc_fun(_1401215, _1401215), _1401217), c_Rings_Oinverse__class_Odivide(_1401215)), _1401219)), _1401223)), _1401221))], (38219 ^ _781404) ^ [_1505908, _1505910, _1505912, _1505914, _1505916] : [c_Relation_Orefl__on(_1505908, _1505910, _1505912), hBOOL(hAPP(hAPP(c_member(tc_prod(_1505908, _1505908)), hAPP(hAPP(c_Product__Type_OPair(_1505908, _1505908), _1505914), _1505916)), _1505912)), -(hBOOL(hAPP(hAPP(c_member(_1505908), _1505914), _1505910)))], (2366 ^ _781404) ^ [_815929, _815931, _815933, _815935, _815937, _815939, _815941, _815943, _815945, _815947] : [-(c_Nitpick_Opair__box_Opair__box__case(_815947, _815943, _815939, _815935, _815931) = c_Nitpick_Opair__box_Opair__box__case(_815945, _815941, _815937, _815933, _815929)), _815947 = _815945, _815943 = _815941, _815939 = _815937, _815935 = _815933, _815931 = _815929], (17669 ^ _781404) ^ [_1096339, _1096341, _1096343, _1096345] : [class_Lattices_Osemilattice__inf(_1096339), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096339), _1096341)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1096339, _1096339, c_Lattices_Osemilattice__inf__class_Oinf(_1096339)), _1096343), hAPP(hAPP(c_Set_Oinsert(_1096339), _1096345), _1096341)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096339), _1096345), hAPP(hAPP(c_Finite__Set_Ofold(_1096339, _1096339, c_Lattices_Osemilattice__inf__class_Oinf(_1096339)), _1096343), _1096341)))], (6359 ^ _781404) ^ [_882531, _882533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882531), _882533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882531), hAPP(c_Nat_OSuc, _882533))))], (9056 ^ _781404) ^ [_934952, _934954] : [class_Groups_Ogroup__add(_934952), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_934952), _934954), _934954) = c_Groups_Ozero__class_Ozero(_934952))], (37441 ^ _781404) ^ [_1486108] : [-(c_Wellfounded_Omeasure(_1486108) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1486108), c_Wellfounded_Oless__than))], (20431 ^ _781404) ^ [_1143874, _1143876] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143874) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143876)), 20434 ^ _781404 : [(20437 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143876)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20435 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143874))))]], 20438 ^ _781404 : [(20441 ^ _781404) ^ [] : [20442 ^ _781404 : [(20445 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143874) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (20443 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143876))))]], 20446 ^ _781404 : [(20449 ^ _781404) ^ [] : [_1143874 = _1143876], (20447 ^ _781404) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143876)))]]], (20439 ^ _781404) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143874)))]]], (4384 ^ _781404) ^ [_847844, _847846, _847848, _847850, _847852, _847854, _847856, _847858] : [-(c_Lazy__Sequence_Oproduct(_847858, _847854, _847850, _847846) = c_Lazy__Sequence_Oproduct(_847856, _847852, _847848, _847844)), _847858 = _847856, _847854 = _847852, _847850 = _847848, _847846 = _847844], (12037 ^ _781404) ^ [_987800, _987802, _987804, _987806, _987808] : [hBOOL(hAPP(hAPP(c_member(_987800), _987802), hAPP(c_Set_Oimage(_987804, _987800, _987806), _987808))), 12041 ^ _781404 : [(12044 ^ _781404) ^ [] : [-(_987802 = hAPP(_987806, 12040 ^ [_987800, _987802, _987804, _987806, _987808]))], (12042 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_987804), 12040 ^ [_987800, _987802, _987804, _987806, _987808]), _987808)))]]], (49504 ^ _781404) ^ [_1779926, _1779928, _1779930, _1779932, _1779934, _1779936, _1779938] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1779926, tc_fun(_1779928, tc_fun(_1779930, tc_HOL_Obool))), _1779932), _1779934), _1779936), _1779938)), 49508 ^ _781404 : [(49511 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1779934, 49507 ^ [_1779926, _1779928, _1779930, _1779932, _1779934, _1779936, _1779938]), _1779936), _1779938)))], (49509 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779926), 49507 ^ [_1779926, _1779928, _1779930, _1779932, _1779934, _1779936, _1779938]), _1779932)))]]], (33193 ^ _781404) ^ [_1381018, _1381020, _1381022, _1381024, _1381026] : [class_Groups_Ocomm__monoid__mult(_1381018), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381020), _1381022)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381020, _1381018), hAPP(hAPP(c_COMBS(_1381020, _1381018, _1381018), hAPP(hAPP(c_COMBB(_1381018, tc_fun(_1381018, _1381018), _1381020), c_Groups_Otimes__class_Otimes(_1381018)), _1381024)), _1381026)), _1381022) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381018), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381020, _1381018), _1381024), _1381022)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381020, _1381018), _1381026), _1381022)))], (13979 ^ _781404) ^ [_1025120, _1025122] : [13980 ^ _781404 : [(13981 ^ _781404) ^ [_1025173] : [_1025122 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025120), _1025173))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025120), _1025122)))], (4590 ^ _781404) ^ [_851107, _851109, _851111, _851113] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_851113, _851109) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_851111, _851107)), _851113 = _851111, _851109 = _851107], (8138 ^ _781404) ^ [_917926] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _917926)) = 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), _917926))))], (41171 ^ _781404) ^ [_1587195, _1587197] : [-(c_Transitive__Closure_Otrancl(_1587195, _1587197) = hAPP(hAPP(c_Relation_Orel__comp(_1587195, _1587195, _1587195), _1587197), c_Transitive__Closure_Ortrancl(_1587195, _1587197)))], (298 ^ _781404) ^ [_786051, _786053] : [-(class_Fields_Ofield__inverse__zero(_786051)), _786053 = _786051, class_Fields_Ofield__inverse__zero(_786053)], (32066 ^ _781404) ^ [_1358613, _1358615, _1358617, _1358619] : [class_Orderings_Olinorder(_1358613), 32069 ^ _781404 : [(32078 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358613), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358613), _1358615), _1358617)), _1358619))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358613), _1358615), _1358619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358613), _1358617), _1358619))], (32070 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358613), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358613), _1358615), _1358617)), _1358619)), 32073 ^ _781404 : [(32076 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358613), _1358617), _1358619)))], (32074 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358613), _1358615), _1358619)))]]]]], (51446 ^ _781404) ^ [_1823368, _1823370, _1823372] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823368), _1823370)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823368), _1823372))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1823368)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823370), _1823372)))], (19336 ^ _781404) ^ [_1125364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1125364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1125364))))], (34343 ^ _781404) ^ [_1416991, _1416993, _1416995] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1416991, tc_Nat_Onat), _1416993), _1416995) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1416991, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1416991), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1416993)), _1416995)))], (16020 ^ _781404) ^ [_1065312, _1065314, _1065316] : [class_Lattices_Olattice(_1065312), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065312), _1065314)), 16027 ^ _781404 : [(16034 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065312, tc_HOL_Obool)), _1065314), hAPP(hAPP(c_Set_Oinsert(_1065312), _1065316), c_Orderings_Obot__class_Obot(tc_fun(_1065312, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1065312, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1065312, hAPP(hAPP(c_Set_Oinsert(_1065312), _1065316), _1065314)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065312), _1065316), c_Big__Operators_Olattice__class_OSup__fin(_1065312, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065312, tc_HOL_Obool)), _1065314), hAPP(hAPP(c_Set_Oinsert(_1065312), _1065316), c_Orderings_Obot__class_Obot(tc_fun(_1065312, tc_HOL_Obool)))))))], (16028 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065312, tc_HOL_Obool)), _1065314), hAPP(hAPP(c_Set_Oinsert(_1065312), _1065316), c_Orderings_Obot__class_Obot(tc_fun(_1065312, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1065312, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1065312, hAPP(hAPP(c_Set_Oinsert(_1065312), _1065316), _1065314)) = _1065316)]]], (33500 ^ _781404) ^ [_1390664, _1390666, _1390668, _1390670, _1390672, _1390674] : [-(hAPP(c_Set_Ovimage(_1390664, _1390666, _1390668), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390670, tc_fun(_1390666, tc_HOL_Obool)), _1390672), _1390674)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390670, tc_fun(_1390664, tc_HOL_Obool)), _1390672), hAPP(hAPP(c_COMBB(tc_fun(_1390666, tc_HOL_Obool), tc_fun(_1390664, tc_HOL_Obool), _1390670), c_Set_Ovimage(_1390664, _1390666, _1390668)), _1390674)))], (11917 ^ _781404) ^ [_985623, _985625, _985627, _985629, _985631] : [-(hAPP(c_Set_Ovimage(_985623, _985625, _985627), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_985625, tc_HOL_Obool)), _985629), _985631)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_985623, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_985623, _985625, _985627), _985629)), hAPP(c_Set_Ovimage(_985623, _985625, _985627), _985631)))], (32290 ^ _781404) ^ [_1362788, _1362790, _1362792] : [class_Groups_Olinordered__ab__group__add(_1362788), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1362788), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1362788), _1362790), _1362792)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362788), hAPP(c_Groups_Ouminus__class_Ouminus(_1362788), _1362790)), hAPP(c_Groups_Ouminus__class_Ouminus(_1362788), _1362792)))], (39282 ^ _781404) ^ [_1535645, _1535647, _1535649, _1535651] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1535645), hAPP(c_Set_OCollect(_1535645), _1535647))), 39285 ^ _781404 : [(39286 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1535649), hAPP(c_Set_OCollect(_1535649), hAPP(hAPP(c_COMBB(tc_fun(_1535645, tc_HOL_Obool), tc_HOL_Obool, _1535649), c_HOL_OEx(_1535645)), hAPP(hAPP(c_COMBB(tc_fun(_1535645, tc_HOL_Obool), tc_fun(_1535645, tc_HOL_Obool), _1535649), hAPP(c_COMBS(_1535645, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535645), c_fconj), _1535647))), _1535651))))), 39289 ^ _781404 : [(39290 ^ _781404) ^ [_1535928] : [hBOOL(hAPP(_1535647, _1535928)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1535649), hAPP(c_Set_OCollect(_1535649), hAPP(hAPP(c_COMBC(_1535649, _1535645, tc_HOL_Obool), _1535651), _1535928)))))]]], (39296 ^ _781404) ^ [] : [39298 ^ _781404 : [(39301 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1535649), hAPP(c_Set_OCollect(_1535649), hAPP(hAPP(c_COMBC(_1535649, _1535645, tc_HOL_Obool), _1535651), 39297 ^ [_1535645, _1535647, _1535649, _1535651]))))], (39299 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1535647, 39297 ^ [_1535645, _1535647, _1535649, _1535651])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1535649), hAPP(c_Set_OCollect(_1535649), hAPP(hAPP(c_COMBB(tc_fun(_1535645, tc_HOL_Obool), tc_HOL_Obool, _1535649), c_HOL_OEx(_1535645)), hAPP(hAPP(c_COMBB(tc_fun(_1535645, tc_HOL_Obool), tc_fun(_1535645, tc_HOL_Obool), _1535649), hAPP(c_COMBS(_1535645, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535645), c_fconj), _1535647))), _1535651))))))]]], (33518 ^ _781404) ^ [_1391274, _1391276, _1391278, _1391280, _1391282, _1391284, _1391286] : [-(hAPP(c_Fun_Ocomp(_1391274, _1391276, _1391278, _1391280), hAPP(c_Fun_Ocomp(_1391282, _1391274, _1391278, _1391284), _1391286)) = hAPP(c_Fun_Ocomp(_1391282, _1391276, _1391278, hAPP(c_Fun_Ocomp(_1391274, _1391276, _1391282, _1391280), _1391284)), _1391286))], (25758 ^ _781404) ^ [_1241700, _1241702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241700)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241702)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1241700)), hAPP(c_Int_Onat, _1241702)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1241700, _1241702)))], (30930 ^ _781404) ^ [_1337429, _1337431, _1337433, _1337435] : [class_Orderings_Olinorder(_1337429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337429), _1337431)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1337429, _1337429, c_Orderings_Oord__class_Omin(_1337429)), _1337433), hAPP(hAPP(c_Set_Oinsert(_1337429), _1337435), _1337431)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1337429), _1337435), hAPP(hAPP(c_Finite__Set_Ofold(_1337429, _1337429, c_Orderings_Oord__class_Omin(_1337429)), _1337433), _1337431)))], (30702 ^ _781404) ^ [_1333376, _1333378, _1333380] : [class_Orderings_Olinorder(_1333376), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333376), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333376), _1333378), _1333380)), _1333380)))], (49225 ^ _781404) ^ [_1773626, _1773628, _1773630] : [_1773626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1773628), c_List_Oreplicate(_1773628, _1773626, _1773630)) = c_Orderings_Obot__class_Obot(tc_fun(_1773628, tc_HOL_Obool)))], (36725 ^ _781404) ^ [_1468520, _1468522, _1468524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468520, tc_HOL_Obool)), _1468522), hAPP(hAPP(c_Set_Oinsert(_1468520), _1468524), c_Orderings_Obot__class_Obot(tc_fun(_1468520, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1468520, _1468524, _1468522) = _1468524)], (30672 ^ _781404) ^ [_1332874, _1332876] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1332874)), hAPP(c_Nat_OSuc, _1332876)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1332874), _1332876)))], (51027 ^ _781404) ^ [_1812798, _1812800, _1812802, _1812804] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1812798), _1812800)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1812802), _1812804)), 51034 ^ _781404 : [(51041 ^ _781404) ^ [] : [hAPP(c_Finite__Set_Ocard(_1812798), _1812800) = hAPP(c_Finite__Set_Ocard(_1812802), _1812804), -(c_Fun_Obij__betw(_1812798, _1812802, 51044 ^ [_1812798, _1812800, _1812802, _1812804], _1812800, _1812804))], (51035 ^ _781404) ^ [] : [51036 ^ _781404 : [(51037 ^ _781404) ^ [_1812987] : [c_Fun_Obij__betw(_1812798, _1812802, _1812987, _1812800, _1812804)]], -(hAPP(c_Finite__Set_Ocard(_1812798), _1812800) = hAPP(c_Finite__Set_Ocard(_1812802), _1812804))]]], (37234 ^ _781404) ^ [_1479961] : [-(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)), _1479961), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (9128 ^ _781404) ^ [_936290, _936292, _936294] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_936290, tc_HOL_Obool)), _936292), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936290, tc_HOL_Obool)), _936294), _936292)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_936290, tc_HOL_Obool)), _936292), _936294))], (10545 ^ _781404) ^ [_960833, _960835] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960833), _960835))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960835), hAPP(c_Nat_OSuc, _960833))))], (27035 ^ _781404) ^ [_1263936, _1263938] : [class_Groups_Oordered__ab__group__add__abs(_1263936), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263936), c_Groups_Ozero__class_Ozero(_1263936)), _1263938)), -(hAPP(c_Groups_Oabs__class_Oabs(_1263936), _1263938) = _1263938)], (45658 ^ _781404) ^ [_1696260, _1696262] : [_1696260 = _1696262, -(hAPP(c_Code__Numeral_Onat__of, _1696260) = hAPP(c_Code__Numeral_Onat__of, _1696262))], (13433 ^ _781404) ^ [_1015046, _1015048, _1015050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015048), _1015050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015046), _1015048)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015046), _1015050))))], (46730 ^ _781404) ^ [_1721747, _1721749] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1721747), _1721749))), -(c_List_Oupt(_1721747, hAPP(c_Nat_OSuc, _1721749)) = c_List_Olist_ONil(tc_Nat_Onat))], (8846 ^ _781404) ^ [_930694, _930696, _930698] : [class_Complete__Lattice_Ocomplete__lattice(_930694), -(c_Complete__Lattice_OInf__class_OInf(_930694, hAPP(hAPP(c_Set_Oinsert(_930694), _930696), hAPP(hAPP(c_Set_Oinsert(_930694), _930698), c_Orderings_Obot__class_Obot(tc_fun(_930694, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930694), _930696), _930698))], (22479 ^ _781404) ^ [_1182402, _1182404, _1182406, _1182408] : [class_Rings_Olinordered__ring__strict(_1182402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182402), c_Groups_Ozero__class_Ozero(_1182402)), _1182404)), 22486 ^ _781404 : [(22493 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182402), _1182406), _1182408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182402), _1182404), _1182406)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182402), _1182404), _1182408))))], (22487 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182402), _1182404), _1182406)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182402), _1182404), _1182408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182402), _1182406), _1182408)))]]], (8784 ^ _781404) ^ [_929602, _929604, _929606] : [class_Orderings_Oorder(_929602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929602), _929604), _929606)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_929602, _929606, _929604) = c_Orderings_Obot__class_Obot(tc_fun(_929602, tc_HOL_Obool)))], (30103 ^ _781404) ^ [_1321355, _1321357, _1321359, _1321361, _1321363] : [class_Groups_Ocomm__monoid__mult(_1321355), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321357), _1321359)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321357), _1321361)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321357, tc_HOL_Obool)), _1321359), _1321361) = c_Orderings_Obot__class_Obot(tc_fun(_1321357, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1321357, _1321355), _1321363), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321357, tc_HOL_Obool)), _1321359), _1321361)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321355), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1321357, _1321355), _1321363), _1321359)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1321357, _1321355), _1321363), _1321361)))], (44403 ^ _781404) ^ [_1669047, _1669049, _1669051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669047)), _1669049)), _1669051)), -(hAPP(hAPP(c_List_Odrop(_1669047), _1669051), _1669049) = c_List_Olist_ONil(_1669047))], (27469 ^ _781404) ^ [_1271870, _1271872, _1271874] : [class_Lattices_Osemilattice__inf(_1271870), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271870), _1271872)), hBOOL(hAPP(hAPP(c_member(_1271870), _1271874), _1271872)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271870), hAPP(c_Finite__Set_Ofold1(_1271870, c_Lattices_Osemilattice__inf__class_Oinf(_1271870)), _1271872)), _1271874)))], (10123 ^ _781404) ^ [_953935, _953937, _953939] : [class_Orderings_Olinorder(_953935), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953935), _953937), _953939))), 10130 ^ _781404 : [(10137 ^ _781404) ^ [] : [_953937 = _953939, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953935), _953937), _953939)))], (10131 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953935), _953937), _953939)), -(_953937 = _953939)]]], (27805 ^ _781404) ^ [_1278865, _1278867, _1278869, _1278871] : [class_Rings_Odivision__ring(_1278865), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278865), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278865), _1278867), _1278869)), _1278871) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278865), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278865), _1278867), _1278871)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278865), _1278869), _1278871)))], (8900 ^ _781404) ^ [_931919, _931921, _931923] : [class_Orderings_Oorder(_931919), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931919, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_931919), _931921)), c_SetInterval_Oord__class_OgreaterThanAtMost(_931919, _931921, _931923)) = c_Orderings_Obot__class_Obot(tc_fun(_931919, tc_HOL_Obool)))], (21227 ^ _781404) ^ [_1158734, _1158736] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1158734)), _1158736) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158734), _1158736)))], (248 ^ _781404) ^ [_785256, _785258] : [-(class_Fields_Olinordered__field__inverse__zero(_785256)), _785258 = _785256, class_Fields_Olinordered__field__inverse__zero(_785258)], (43741 ^ _781404) ^ [_1653161, _1653163] : [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), _1653161), _1653163))), 43744 ^ _781404 : [(43751 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1653161), _1653163))), -(c_List_Oupto(_1653161, _1653163) = c_List_Olist_ONil(tc_Int_Oint))], (43745 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1653161), _1653163)), -(c_List_Oupto(_1653161, _1653163) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1653161), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1653161), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1653163)))]]], (7107 ^ _781404) ^ [_896491, _896493, _896495, _896497] : [class_Lattices_Osemilattice__sup(_896491), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896491), _896493), _896495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896491), _896493), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896491), _896497), _896495))))], (14234 ^ _781404) ^ [_1030001, _1030003, _1030005] : [class_Groups_Oordered__comm__monoid__add(_1030001), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030001), c_Groups_Ozero__class_Ozero(_1030001)), _1030003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030001), c_Groups_Ozero__class_Ozero(_1030001)), _1030005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030001), c_Groups_Ozero__class_Ozero(_1030001)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030001), _1030003), _1030005))))], (24686 ^ _781404) ^ [_1224270] : [c_Int_OMin = c_Int_OBit1(_1224270), -(c_Int_OMin = _1224270)], (52504 ^ _781404) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (11179 ^ _781404) ^ [_971125, _971127, _971129] : [class_Orderings_Oorder(_971125), 11182 ^ _781404 : [(11189 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971125), _971127), _971129))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_971125, _971127, _971129) = c_Orderings_Obot__class_Obot(tc_fun(_971125, tc_HOL_Obool)))], (11183 ^ _781404) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_971125, _971127, _971129) = c_Orderings_Obot__class_Obot(tc_fun(_971125, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971125), _971127), _971129))]]], (18597 ^ _781404) ^ [_1113134, _1113136, _1113138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1113134)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1113136), _1113138)), 18604 ^ _781404 : [(18605 ^ _781404) ^ [_1113330] : [18607 ^ _781404 : [(18613 ^ _781404) ^ [] : [-(_1113330 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 18609 ^ [_1113134, _1113136, _1113138, _1113330]), 18606 ^ [_1113134, _1113136, _1113138, _1113330]))], (18611 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18609 ^ [_1113134, _1113136, _1113138, _1113330]), _1113138)))], (18608 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18606 ^ [_1113134, _1113136, _1113138, _1113330]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1113134))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113330), _1113136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1113330), _1113134)), _1113136)))]]], (19697 ^ _781404) ^ [_1131478] : [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), _1131478))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1131478)))], (33355 ^ _781404) ^ [_1385429, _1385431, _1385433] : [hBOOL(hAPP(c_Predicate_OPowp(_1385429, _1385431), _1385433)), 33358 ^ _781404 : [(33359 ^ _781404) ^ [_1385513] : [hBOOL(hAPP(hAPP(c_member(_1385429), _1385513), _1385433)), -(hBOOL(hAPP(_1385431, _1385513)))]]], (35203 ^ _781404) ^ [_1437060, _1437062] : [35204 ^ _781404 : [(35207 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1437062), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35205 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437060), _1437062))]], -(c_Divides_OposDivAlg(_1437060, _1437062) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437060))], (52652 ^ _781404) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (20405 ^ _781404) ^ [_1143489, _1143491] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143489) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143491), 20408 ^ _781404 : [(20415 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143489)))), 20418 ^ _781404 : [(20425 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143491)))), -(_1143489 = _1143491)], (20419 ^ _781404) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143491))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143489) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (20409 ^ _781404) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143491)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (15659 ^ _781404) ^ [_1058382, _1058384, _1058386] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1058382), _1058384)), -(hBOOL(hAPP(hAPP(c_member(_1058382), _1058386), _1058384))), -(hAPP(c_Finite__Set_Ocard(_1058382), hAPP(hAPP(c_Set_Oinsert(_1058382), _1058386), _1058384)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1058382), _1058384)))], (17847 ^ _781404) ^ [_1099651, _1099653, _1099655, _1099657] : [class_Rings_Olinordered__semidom(_1099651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099651), c_Groups_Oone__class_Oone(_1099651)), _1099653)), 17854 ^ _781404 : [(17861 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1099655), _1099657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099651), hAPP(hAPP(c_Power_Opower__class_Opower(_1099651), _1099653), _1099655)), hAPP(hAPP(c_Power_Opower__class_Opower(_1099651), _1099653), _1099657))))], (17855 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099651), hAPP(hAPP(c_Power_Opower__class_Opower(_1099651), _1099653), _1099655)), hAPP(hAPP(c_Power_Opower__class_Opower(_1099651), _1099653), _1099657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1099655), _1099657)))]]], (38239 ^ _781404) ^ [] : [-(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))], (33347 ^ _781404) ^ [_1385164, _1385166, _1385168, _1385170] : [-(hAPP(c_Set_Oimage(_1385164, _1385166, _1385168), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1385164, tc_HOL_Obool), _1385170)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1385164, tc_HOL_Obool), tc_fun(_1385166, tc_HOL_Obool)), _1385170), c_Set_Oimage(_1385164, _1385166, _1385168)))], (36245 ^ _781404) ^ [_1457917] : [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), _1457917))), -(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), _1457917)) = 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), _1457917))))], (22121 ^ _781404) ^ [_1175391, _1175393, _1175395] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175391), _1175393)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175395), _1175393)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1175391), _1175395))], (49161 ^ _781404) ^ [_1772487, _1772489, _1772491, _1772493] : [hBOOL(hAPP(_1772487, _1772489)), -(hAPP(c_List_Ofilter(_1772491, _1772487), c_List_Oreplicate(_1772491, _1772493, _1772489)) = c_List_Oreplicate(_1772491, _1772493, _1772489))], (47079 ^ _781404) ^ [_1727935, _1727937, _1727939] : [class_Orderings_Olinorder(_1727935), c_List_Olinorder__class_Osorted(_1727935, _1727937), hBOOL(hAPP(c_List_Odistinct(_1727935), _1727937)), c_List_Olinorder__class_Osorted(_1727935, _1727939), hBOOL(hAPP(c_List_Odistinct(_1727935), _1727939)), hAPP(c_List_Oset(_1727935), _1727937) = hAPP(c_List_Oset(_1727935), _1727939), -(_1727937 = _1727939)], (47240 ^ _781404) ^ [_1730940, _1730942, _1730944, _1730946, _1730948, _1730950] : [class_Orderings_Olinorder(_1730940), c_List_Olinorder__class_Osorted(_1730940, hAPP(hAPP(c_List_Omap(_1730942, _1730940), _1730944), _1730946)), hBOOL(hAPP(_1730948, _1730950)), -(hAPP(c_List_Ofilter(_1730942, _1730948), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1730942, _1730940, _1730944), _1730950), _1730946)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1730942, _1730940, _1730944), _1730950), hAPP(c_List_Ofilter(_1730942, _1730948), _1730946)))], (40066 ^ _781404) ^ [_1560428, _1560430, _1560432, _1560434] : [40067 ^ _781404 : [(40068 ^ _781404) ^ [_1560503] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560428, _1560432)), hAPP(hAPP(c_Product__Type_OPair(_1560428, _1560432), _1560430), _1560503)), _1560434))]], -(hBOOL(hAPP(hAPP(c_member(_1560428), _1560430), hAPP(c_Relation_ODomain(_1560428, _1560432), _1560434))))], (4258 ^ _781404) ^ [_845915, _845917] : [_845917 = _845915, -(c_List_Ohd(_845917) = c_List_Ohd(_845915))], (32284 ^ _781404) ^ [_1362649, _1362651, _1362653] : [class_Groups_Olinordered__ab__group__add(_1362649), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1362649), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362649), _1362651), _1362653)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1362649), hAPP(c_Groups_Ouminus__class_Ouminus(_1362649), _1362651)), hAPP(c_Groups_Ouminus__class_Ouminus(_1362649), _1362653)))], (24018 ^ _781404) ^ [_1212348, _1212350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212348)), 24021 ^ _781404 : [(24030 ^ _781404) ^ [] : [-(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), _1212348), _1212350)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212350), _1212348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212350))], (24022 ^ _781404) ^ [] : [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), _1212348), _1212350))), 24025 ^ _781404 : [(24028 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212350)))], (24026 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212350), _1212348)))]]]]], (7423 ^ _781404) ^ [_902597, _902599, _902601, _902603] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_902597, tc_HOL_Obool)), _902599), _902601), _902603)), 7426 ^ _781404 : [(7429 ^ _781404) ^ [] : [-(hBOOL(hAPP(_902601, _902603)))], (7427 ^ _781404) ^ [] : [-(hBOOL(hAPP(_902599, _902603)))]]], (25395 ^ _781404) ^ [_1235376, _1235378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235378), _1235376))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235378), _1235376) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1235378), _1235376)), _1235376)))], (44539 ^ _781404) ^ [_1672443, _1672445, _1672447, _1672449, _1672451] : [-(hAPP(hAPP(c_List_Ozip(_1672443, _1672445), hAPP(hAPP(c_List_Oappend(_1672443), _1672447), _1672449)), _1672451) = hAPP(hAPP(c_List_Oappend(tc_prod(_1672443, _1672445)), hAPP(hAPP(c_List_Ozip(_1672443, _1672445), _1672447), hAPP(hAPP(c_List_Otake(_1672445), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672443)), _1672447)), _1672451))), hAPP(hAPP(c_List_Ozip(_1672443, _1672445), _1672449), hAPP(hAPP(c_List_Odrop(_1672445), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672443)), _1672447)), _1672451))))], (33582 ^ _781404) ^ [_1393045, _1393047, _1393049, _1393051, _1393053] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393045, tc_fun(_1393047, tc_HOL_Obool)), _1393049), _1393051), _1393053)), 33586 ^ _781404 : [(33589 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1393051, 33585 ^ [_1393045, _1393047, _1393049, _1393051, _1393053]), _1393053)))], (33587 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1393045), 33585 ^ [_1393045, _1393047, _1393049, _1393051, _1393053]), _1393049)))]]], (44547 ^ _781404) ^ [_1672739, _1672741, _1672743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672739), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672741)), _1672743))), -(hAPP(hAPP(c_List_Oappend(_1672741), hAPP(hAPP(c_List_Otake(_1672741), _1672739), _1672743)), hAPP(hAPP(c_List_Olist_OCons(_1672741), hAPP(c_List_Ohd(_1672741), hAPP(hAPP(c_List_Odrop(_1672741), _1672739), _1672743))), c_List_Olist_ONil(_1672741))) = hAPP(hAPP(c_List_Otake(_1672741), hAPP(c_Nat_OSuc, _1672739)), _1672743))], (52742 ^ _781404) ^ [_1842412, _1842414] : [_1842412 = _1842414, -(hBOOL(hAPP(hAPP(c_fequal, _1842412), _1842414)))], (7884 ^ _781404) ^ [_911891, _911893, _911895] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911891, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911891, tc_HOL_Obool)), _911893), _911895)), _911893)))], (12536 ^ _781404) ^ [_997731, _997733, _997735] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_997731, tc_HOL_Obool)), _997733), _997735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997731, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_997731, tc_HOL_Obool), _997735)), _997733)))], (8882 ^ _781404) ^ [_931534, _931536, _931538, _931540] : [class_Orderings_Oorder(_931534), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931534, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_931534, _931536, _931538)), c_SetInterval_Oord__class_OgreaterThanAtMost(_931534, _931538, _931540)) = c_Orderings_Obot__class_Obot(tc_fun(_931534, tc_HOL_Obool)))], (44355 ^ _781404) ^ [_1667905, _1667907, _1667909] : [-(hAPP(hAPP(c_List_Odrop(_1667905), _1667907), c_List_Obutlast(_1667905, _1667909)) = c_List_Obutlast(_1667905, hAPP(hAPP(c_List_Odrop(_1667905), _1667907), _1667909)))], (42316 ^ _781404) ^ [_1617174, _1617176, _1617178, _1617180] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617174), tc_List_Olist(_1617174))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617174), tc_List_Olist(_1617174)), _1617176), _1617178)), c_List_Olex(_1617174, _1617180)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617174), tc_List_Olist(_1617174))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617174), tc_List_Olist(_1617174)), _1617176), _1617178)), c_List_Olexord(_1617174, _1617180))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617174)), _1617176) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617174)), _1617178)], (13844 ^ _781404) ^ [_1022855, _1022857] : [class_Groups_Ogroup__add(_1022855), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022855), hAPP(c_Groups_Ouminus__class_Ouminus(_1022855), _1022857)), _1022857) = c_Groups_Ozero__class_Ozero(_1022855))], (23531 ^ _781404) ^ [_1203744, _1203746, _1203748] : [class_Divides_Osemiring__div(_1203744), -(c_Divides_Odiv__class_Omod(_1203744, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1203744), _1203746), _1203748), _1203748) = c_Divides_Odiv__class_Omod(_1203744, _1203746, _1203748))], (45309 ^ _781404) ^ [_1688636, _1688638, _1688640, _1688642] : [-(hAPP(hAPP(c_List_Omap(_1688636, _1688638), _1688640), c_List_Obutlast(_1688636, _1688642)) = c_List_Obutlast(_1688638, hAPP(hAPP(c_List_Omap(_1688636, _1688638), _1688640), _1688642)))], (52142 ^ _781404) ^ [_1835993] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835993), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1835993 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (33522 ^ _781404) ^ [_1391391, _1391393, _1391395, _1391397, _1391399, _1391401, _1391403, _1391405, _1391407] : [hAPP(c_Fun_Ocomp(_1391391, _1391393, _1391395, _1391397), _1391399) = hAPP(c_Fun_Ocomp(_1391401, _1391393, _1391395, _1391403), _1391405), -(hAPP(_1391397, hAPP(_1391399, _1391407)) = hAPP(_1391403, hAPP(_1391405, _1391407)))], (23806 ^ _781404) ^ [_1208777, _1208779] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208777, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1208779)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208777, _1208779) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (44250 ^ _781404) ^ [_1664936, _1664938, _1664940, _1664942, _1664944, _1664946, _1664948] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1664936, _1664936)), hAPP(hAPP(c_Product__Type_OPair(_1664936, _1664936), _1664938), _1664940)), _1664942)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664936), tc_List_Olist(_1664936))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664936), tc_List_Olist(_1664936)), hAPP(hAPP(c_List_Oappend(_1664936), _1664944), hAPP(hAPP(c_List_Olist_OCons(_1664936), _1664938), _1664946))), hAPP(hAPP(c_List_Oappend(_1664936), _1664944), hAPP(hAPP(c_List_Olist_OCons(_1664936), _1664940), _1664948)))), c_List_Olexord(_1664936, _1664942))))], (23852 ^ _781404) ^ [_1209448, _1209450, _1209452, _1209454] : [class_Divides_Osemiring__div(_1209448), 23855 ^ _781404 : [(23862 ^ _781404) ^ [] : [-(_1209450 = c_Groups_Ozero__class_Ozero(_1209448)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209448), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209448), _1209450), _1209452)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209448), _1209450), _1209454)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209448), _1209452), _1209454))], (23856 ^ _781404) ^ [] : [_1209450 = c_Groups_Ozero__class_Ozero(_1209448), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209448), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209448), _1209450), _1209452)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209448), _1209450), _1209454)) = c_Groups_Ozero__class_Ozero(_1209448))]]], (5851 ^ _781404) ^ [_874208, _874210, _874212] : [class_Orderings_Olinorder(_874208), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874208), _874210), _874212))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874208), _874212), _874210)))], (30636 ^ _781404) ^ [_1332062, _1332064, _1332066, _1332068] : [class_Orderings_Olinorder(_1332062), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332062), _1332064), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332062), _1332066), _1332068)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332062), _1332066), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332062), _1332064), _1332068)))], (46576 ^ _781404) ^ [_1717180, _1717182, _1717184] : [hAPP(c_List_Ofilter(_1717180, _1717182), _1717184) = c_List_Olist_ONil(_1717180), 46579 ^ _781404 : [(46580 ^ _781404) ^ [_1717277] : [hBOOL(hAPP(hAPP(c_member(_1717180), _1717277), hAPP(c_List_Oset(_1717180), _1717184))), hBOOL(hAPP(_1717182, _1717277))]]], (10499 ^ _781404) ^ [_960183, _960185, _960187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960183, tc_HOL_Obool)), _960185), _960187)), 10502 ^ _781404 : [(10505 ^ _781404) ^ [] : [_960185 = _960187], (10503 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960183, tc_HOL_Obool)), _960185), _960187)))]]], (32734 ^ _781404) ^ [_1371034, _1371036, _1371038] : [class_Orderings_Olinorder(_1371034), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371034), _1371036)), -(c_Big__Operators_Olattice_OSup__fin(_1371034, c_Orderings_Oord__class_Omax(_1371034), hAPP(hAPP(c_Set_Oinsert(_1371034), _1371038), _1371036)) = hAPP(hAPP(c_Finite__Set_Ofold(_1371034, _1371034, c_Orderings_Oord__class_Omax(_1371034)), _1371038), _1371036))], (34463 ^ _781404) ^ [_1420022, _1420024, _1420026, _1420028] : [class_Rings_Osemiring__1(_1420022), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1420024, _1420022), hAPP(c_COMBK(_1420022, _1420024), _1420026)), _1420028) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420022), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1420022), hAPP(c_Finite__Set_Ocard(_1420024), _1420028))), _1420026))], (30960 ^ _781404) ^ [_1338058, _1338060, _1338062, _1338064] : [class_Orderings_Olinorder(_1338058), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338058, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1338058), _1338060)), c_SetInterval_Oord__class_OatLeastAtMost(_1338058, _1338062, _1338064)) = c_SetInterval_Oord__class_OatLeastAtMost(_1338058, _1338062, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338058), _1338060), _1338064)))], (14446 ^ _781404) ^ [_1034332, _1034334, _1034336, _1034338] : [class_Groups_Ocomm__monoid__add(_1034332), 14449 ^ _781404 : [(14456 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034334), _1034336))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1034332), _1034338), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1034336), hAPP(c_Nat_OSuc, _1034334))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034332), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1034332), _1034338), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1034336), _1034334))), hAPP(_1034338, _1034334)))], (14450 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034334), _1034336)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1034332), _1034338), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1034336), hAPP(c_Nat_OSuc, _1034334))) = c_Groups_Ozero__class_Ozero(_1034332))]]], (41383 ^ _781404) ^ [_1592322] : [-(c_Relation_Orefl__on(_1592322, c_Orderings_Otop__class_Otop(tc_fun(_1592322, tc_HOL_Obool)), c_Relation_OId(_1592322)))], (36496 ^ _781404) ^ [_1463428, _1463430, _1463432, _1463434, _1463436] : [-(hAPP(c_Product__Type_Ofst(_1463428, _1463430), hAPP(c_Product__Type_Oapsnd(_1463432, _1463430, _1463428, _1463434), _1463436)) = hAPP(c_Product__Type_Ofst(_1463428, _1463432), _1463436))], (13249 ^ _781404) ^ [_1011534, _1011536, _1011538] : [class_Groups_Ogroup__add(_1011534), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011534), hAPP(c_Groups_Ouminus__class_Ouminus(_1011534), _1011536)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011534), _1011536), _1011538)) = _1011538)], (24198 ^ _781404) ^ [_1215355, _1215357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215355), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215357), _1215355)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215355, _1215357) = _1215355)], (29441 ^ _781404) ^ [_1308529, _1308531, _1308533, _1308535] : [class_Fields_Olinordered__field(_1308529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308529), c_Groups_Ozero__class_Ozero(_1308529)), _1308531)), 29448 ^ _781404 : [(29455 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308529), _1308533), _1308531)), _1308535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308529), _1308533), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308529), _1308535), _1308531))))], (29449 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308529), _1308533), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308529), _1308535), _1308531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308529), _1308533), _1308531)), _1308535)))]]], (24714 ^ _781404) ^ [_1224662, _1224664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224662)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1224662), _1224664)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1224662)), hAPP(c_Int_Onat, _1224664)))], (48788 ^ _781404) ^ [_1764145, _1764147, _1764149] : [c_List_Olist__all(_1764145, _1764147, _1764149), 48791 ^ _781404 : [(48792 ^ _781404) ^ [_1764226] : [hBOOL(hAPP(hAPP(c_member(_1764145), _1764226), hAPP(c_List_Oset(_1764145), _1764149))), -(hBOOL(hAPP(_1764147, _1764226)))]]], (41556 ^ _781404) ^ [_1596287, _1596289, _1596291, _1596293, _1596295] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596287, _1596289)), hAPP(hAPP(c_Product__Type_OPair(_1596287, _1596289), _1596291), _1596293)), hAPP(c_Relation_Oconverse(_1596289, _1596287), _1596295))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596289, _1596287)), hAPP(hAPP(c_Product__Type_OPair(_1596289, _1596287), _1596293), _1596291)), _1596295)))], (1326 ^ _781404) ^ [_801019, _801021] : [-(class_Rings_Ocomm__ring(_801019)), _801021 = _801019, class_Rings_Ocomm__ring(_801021)], (49057 ^ _781404) ^ [_1770606, _1770608, _1770610] : [-(hAPP(c_List_Orev(_1770606), c_List_Oreplicate(_1770606, _1770608, _1770610)) = c_List_Oreplicate(_1770606, _1770608, _1770610))], (12917 ^ _781404) ^ [_1005602, _1005604, _1005606, _1005608, _1005610] : [hAPP(_1005606, _1005608) = _1005610, -(c_Fun_Ofun__upd(_1005602, _1005604, _1005606, _1005608, _1005610) = _1005606)], (4718 ^ _781404) ^ [_853173, _853175] : [_853175 = _853173, -(c_DSequence_Osingle(_853175) = c_DSequence_Osingle(_853173))], (14661 ^ _781404) ^ [_1038462] : [class_Finite__Set_Ofinite(_1038462), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038462), c_Orderings_Otop__class_Otop(tc_fun(_1038462, tc_HOL_Obool)))))], (6117 ^ _781404) ^ [_878552, _878554, _878556, _878558] : [c_Hoare__Mirabelle_Ohoare__derivs(_878552, _878554, _878556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_878552), tc_HOL_Obool)), _878558), _878556)), -(c_Hoare__Mirabelle_Ohoare__derivs(_878552, _878554, _878558))], (22287 ^ _781404) ^ [_1178715, _1178717, _1178719, _1178721] : [class_Rings_Olinordered__semiring__strict(_1178715), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178715), _1178717), _1178719)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178715), _1178717), _1178721))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178715), c_Groups_Ozero__class_Ozero(_1178715)), _1178717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178715), _1178719), _1178721)))], (15909 ^ _781404) ^ [_1063219, _1063221, _1063223, _1063225, _1063227] : [c_Fun_Oinj__on(_1063219, _1063221, _1063223, _1063225), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1063221, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1063219, _1063221, _1063223), _1063225)), _1063227)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063221), _1063227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1063219), _1063225)), hAPP(c_Finite__Set_Ocard(_1063221), _1063227))))], (18075 ^ _781404) ^ [_1103587, _1103589] : [class_Power_Opower(_1103587), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1103587), _1103589), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1103587))], (36703 ^ _781404) ^ [_1467842, _1467844, _1467846, _1467848] : [-(c_HOL_OThe(tc_prod(_1467842, _1467844), hAPP(c_Product__Type_Oprod_Oprod__case(_1467842, _1467844, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1467842, tc_fun(_1467844, tc_HOL_Obool), tc_fun(_1467844, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1467844, tc_HOL_Obool), tc_fun(_1467844, tc_HOL_Obool)), _1467842), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1467844)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1467842), c_fconj), hAPP(c_fequal, _1467846)))), hAPP(c_fequal, _1467848)))) = hAPP(hAPP(c_Product__Type_OPair(_1467842, _1467844), _1467846), _1467848))], (46295 ^ _781404) ^ [_1710416, _1710418, _1710420] : [hBOOL(hAPP(c_List_Odistinct(_1710416), _1710418)), -(c_List_Oremove1(_1710416, _1710420, c_List_Oremdups(_1710416, _1710418)) = c_List_Oremdups(_1710416, c_List_Oremove1(_1710416, _1710420, _1710418)))], (22223 ^ _781404) ^ [_1177458, _1177460, _1177462, _1177464] : [class_Rings_Ocomm__semiring__1(_1177458), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177458), hAPP(hAPP(c_Power_Opower__class_Opower(_1177458), _1177460), _1177462)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177458), _1177460), _1177464)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1177458), _1177460), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1177462), _1177464)))], (35480 ^ _781404) ^ [_1443383, _1443385, _1443387, _1443389, _1443391] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1443383, _1443385, tc_HOL_Obool), _1443387), hAPP(hAPP(c_Product__Type_OPair(_1443383, _1443385), _1443389), _1443391))), -(hBOOL(hAPP(hAPP(_1443387, _1443389), _1443391)))], (7461 ^ _781404) ^ [_903223, _903225, _903227] : [class_Lattices_Olattice(_903223), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903223), _903225), _903227) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903223), _903227), _903225))], (36967 ^ _781404) ^ [_1474341, _1474343, _1474345] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1474341, tc_HOL_Obool), tc_fun(_1474341, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1474341, tc_HOL_Obool), tc_fun(_1474341, tc_HOL_Obool)), _1474343), _1474345)), c_Wellfounded_Ofinite__psubset(_1474341)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1474341, tc_HOL_Obool)), _1474343), _1474345)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474341), _1474345))], (43611 ^ _781404) ^ [_1650569, _1650571, _1650573] : [-(hAPP(hAPP(c_List_Olist__update(_1650569, c_List_Olist_ONil(_1650569)), _1650571), _1650573) = c_List_Olist_ONil(_1650569))], (36030 ^ _781404) ^ [_1453772, _1453774] : [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), _1453772), _1453774))), 36033 ^ _781404 : [(36040 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453774), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36043 ^ _781404 : [(36052 ^ _781404) ^ [] : [-(c_Nitpick_Onorm__frac(_1453772, _1453774) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1453772), _1453774)), 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), _1453772))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1453774)))), -(_1453772 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1453774 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36044 ^ _781404) ^ [] : [36045 ^ _781404 : [(36048 ^ _781404) ^ [] : [_1453774 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36046 ^ _781404) ^ [] : [_1453772 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1453772, _1453774) = 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)))]]], (36034 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453774), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1453772, _1453774) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1453772), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1453774)))]]], (20739 ^ _781404) ^ [_1149161, _1149163] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149161)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149163)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1149161), _1149163)))], (15368 ^ _781404) ^ [_1053314, _1053316, _1053318, _1053320, _1053322] : [class_Groups_Ocomm__monoid__add(_1053314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053316), _1053318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1053316, tc_HOL_Obool)), _1053320), _1053318)), 15382 ^ _781404 : [(15385 ^ _781404) ^ [] : [hAPP(_1053322, 15381 ^ [_1053314, _1053316, _1053318, _1053320, _1053322]) = c_Groups_Ozero__class_Ozero(_1053314)], (15383 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1053316), 15381 ^ [_1053314, _1053316, _1053318, _1053320, _1053322]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053316, tc_HOL_Obool)), _1053318), _1053320))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1053316, _1053314), _1053322), _1053318) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1053316, _1053314), _1053322), _1053320))], (32396 ^ _781404) ^ [_1365049, _1365051, _1365053] : [class_Orderings_Olinorder(_1365049), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365049), _1365051)), -(_1365051 = c_Orderings_Obot__class_Obot(tc_fun(_1365049, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1365049, hAPP(hAPP(c_Set_Oinsert(_1365049), _1365053), _1365051)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365049), _1365053), c_Big__Operators_Olinorder__class_OMax(_1365049, _1365051)))], (45881 ^ _781404) ^ [_1701249, _1701251, _1701253, _1701255, _1701257] : [-(c_Enum_Oproduct(_1701249, _1701251, hAPP(hAPP(c_List_Olist_OCons(_1701249), _1701253), _1701255), _1701257) = hAPP(hAPP(c_List_Oappend(tc_prod(_1701249, _1701251)), hAPP(hAPP(c_List_Omap(_1701251, tc_prod(_1701249, _1701251)), hAPP(c_Product__Type_OPair(_1701249, _1701251), _1701253)), _1701257)), c_Enum_Oproduct(_1701249, _1701251, _1701255, _1701257)))], (12872 ^ _781404) ^ [_1004743, _1004745, _1004747, _1004749] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1004743, tc_Nat_Onat), _1004745), _1004747) = hAPP(c_Nat_OSuc, _1004749), 12876 ^ _781404 : [(12879 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1004745, 12875 ^ [_1004743, _1004745, _1004747, _1004749]))))], (12877 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1004743), 12875 ^ [_1004743, _1004745, _1004747, _1004749]), _1004747)))]]], (52466 ^ _781404) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (51122 ^ _781404) ^ [_1814809, _1814811] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1814809), _1814811)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1814809, 51125 ^ [_1814809, _1814811], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1814809), _1814811)), _1814811))], (36991 ^ _781404) ^ [_1474851, _1474853, _1474855, _1474857, _1474859, _1474861, _1474863] : [c_Finite__Set_Ofolding__idem(_1474851, _1474853, _1474855, _1474857), -(hAPP(c_Fun_Ocomp(_1474853, _1474853, _1474859, hAPP(_1474855, _1474861)), hAPP(c_Fun_Ocomp(_1474853, _1474853, _1474859, hAPP(_1474855, _1474861)), _1474863)) = hAPP(c_Fun_Ocomp(_1474853, _1474853, _1474859, hAPP(_1474855, _1474861)), _1474863))], (20559 ^ _781404) ^ [_1146120, _1146122, _1146124] : [class_Rings_Olinordered__semidom(_1146120), hAPP(hAPP(c_Power_Opower__class_Opower(_1146120), _1146122), 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(_1146120), _1146124), 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(_1146120), c_Groups_Ozero__class_Ozero(_1146120)), _1146122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146120), c_Groups_Ozero__class_Ozero(_1146120)), _1146124)), -(_1146122 = _1146124)], (43138 ^ _781404) ^ [_1640608, _1640610, _1640612, _1640614] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640608)), hAPP(hAPP(c_List_Olist__update(_1640608, _1640610), _1640612), _1640614)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640608)), _1640610))], (2476 ^ _781404) ^ [_817710, _817712, _817714, _817716] : [-(c_Divides_OnegDivAlg(_817716, _817712) = c_Divides_OnegDivAlg(_817714, _817710)), _817716 = _817714, _817712 = _817710], (44040 ^ _781404) ^ [_1660266, _1660268, _1660270] : [hAPP(hAPP(c_List_Oappend(_1660266), _1660268), _1660270) = _1660268, -(_1660270 = c_List_Olist_ONil(_1660266))], (36908 ^ _781404) ^ [_1472601, _1472603, _1472605, _1472607, _1472609, _1472611, _1472613, _1472615] : [c_Fun_Oinj__on(_1472601, _1472603, _1472605, _1472607), 36914 ^ _781404 : [(36917 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472601, tc_HOL_Obool)), hAPP(_1472613, 36913 ^ [_1472601, _1472603, _1472605, _1472607, _1472609, _1472611, _1472613, _1472615])), _1472607))], (36915 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472609), 36913 ^ [_1472601, _1472603, _1472605, _1472607, _1472609, _1472611, _1472613, _1472615]), _1472611)))]], hBOOL(hAPP(hAPP(c_member(_1472609), _1472615), _1472611)), -(hAPP(c_Set_Oimage(_1472601, _1472603, _1472605), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1472609, tc_fun(_1472601, tc_HOL_Obool)), _1472611), _1472613)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1472609, tc_fun(_1472603, tc_HOL_Obool)), _1472611), hAPP(hAPP(c_COMBB(tc_fun(_1472601, tc_HOL_Obool), tc_fun(_1472603, tc_HOL_Obool), _1472609), c_Set_Oimage(_1472601, _1472603, _1472605)), _1472613)))], (39973 ^ _781404) ^ [_1558282, _1558284] : [hAPP(hAPP(c_Relation_Orel__comp(_1558282, _1558282, _1558282), _1558284), _1558284) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1558282, _1558282), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1558282, _1558284))], (29811 ^ _781404) ^ [_1315568, _1315570, _1315572] : [class_Fields_Olinordered__field__inverse__zero(_1315568), 29817 ^ _781404 : [(29822 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315568), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315568), 29816 ^ [_1315568, _1315570, _1315572]), _1315570)), _1315572))], (29820 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315568), 29816 ^ [_1315568, _1315570, _1315572]), c_Groups_Oone__class_Oone(_1315568))))], (29818 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315568), c_Groups_Ozero__class_Ozero(_1315568)), 29816 ^ [_1315568, _1315570, _1315572])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315568), _1315570), _1315572)))], (31025 ^ _781404) ^ [_1339283, _1339285, _1339287] : [class_Orderings_Olinorder(_1339283), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339283), _1339285)), -(_1339285 = c_Orderings_Obot__class_Obot(tc_fun(_1339283, tc_HOL_Obool))), 31036 ^ _781404 : [(31046 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339283), hAPP(c_Finite__Set_Ofold1(_1339283, c_Orderings_Oord__class_Omin(_1339283)), _1339285)), _1339287))), 31047 ^ _781404 : [(31048 ^ _781404) ^ [_1339672] : [hBOOL(hAPP(hAPP(c_member(_1339283), _1339672), _1339285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339283), _1339672), _1339287))]]], (31037 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339283), hAPP(c_Finite__Set_Ofold1(_1339283, c_Orderings_Oord__class_Omin(_1339283)), _1339285)), _1339287)), 31041 ^ _781404 : [(31044 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339283), 31040 ^ [_1339283, _1339285, _1339287]), _1339287)))], (31042 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339283), 31040 ^ [_1339283, _1339285, _1339287]), _1339285)))]]]]], (8794 ^ _781404) ^ [_929765] : [class_Complete__Lattice_Ocomplete__lattice(_929765), -(c_Complete__Lattice_OInf__class_OInf(_929765, c_Orderings_Obot__class_Obot(tc_fun(_929765, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_929765))], (44317 ^ _781404) ^ [_1667007, _1667009] : [-(hAPP(c_List_Orotate1(_1667007), _1667009) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1667007), _1667007, c_List_Olist_ONil(_1667007), hAPP(hAPP(c_COMBB(tc_List_Olist(_1667007), tc_fun(tc_List_Olist(_1667007), tc_List_Olist(_1667007)), _1667007), hAPP(c_COMBC(tc_List_Olist(_1667007), tc_List_Olist(_1667007), tc_List_Olist(_1667007)), c_List_Oappend(_1667007))), hAPP(hAPP(c_COMBC(_1667007, tc_List_Olist(_1667007), tc_List_Olist(_1667007)), c_List_Olist_OCons(_1667007)), c_List_Olist_ONil(_1667007)))), _1667009))], (52764 ^ _781404) ^ [_1842654, _1842656] : [hBOOL(_1842654), hBOOL(_1842656), -(hBOOL(hAPP(hAPP(c_fconj, _1842654), _1842656)))], (20239 ^ _781404) ^ [_1140761, _1140763] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1140761)), c_Int_OBit1(_1140763)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140761), _1140763)))], (52524 ^ _781404) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (50779 ^ _781404) ^ [_1807874, _1807876, _1807878, _1807880, _1807882] : [c_Fun_Obij__betw(_1807874, _1807876, _1807878, _1807880, _1807882), -(c_Fun_Obij__betw(_1807876, _1807874, c_Hilbert__Choice_Oinv__into(_1807874, _1807876, _1807880, _1807878), _1807882, _1807880))], (39717 ^ _781404) ^ [_1551635, _1551637, _1551639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1551635, _1551635), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1551635, _1551635, _1551635), _1551637), _1551639)), _1551637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1551635, tc_HOL_Obool), tc_fun(_1551635, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1551635, tc_HOL_Obool), tc_fun(_1551635, tc_HOL_Obool), tc_fun(_1551635, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1551635, _1551637)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1551635, tc_HOL_Obool), tc_fun(_1551635, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1551635, _1551639)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1551635, tc_HOL_Obool), tc_fun(_1551635, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1551635, tc_HOL_Obool), tc_fun(_1551635, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1551635, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1551635, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1551635, tc_HOL_Obool), tc_fun(_1551635, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1551635, _1551637))))], (37555 ^ _781404) ^ [_1489214, _1489216, _1489218] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1489214), _1489216), _1489218) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1489214, tc_HOL_Obool), tc_HOL_Obool)), -(_1489216 = c_Orderings_Obot__class_Obot(tc_fun(_1489214, tc_HOL_Obool)))], (37463 ^ _781404) ^ [_1486697, _1486699] : [-(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), _1486697), _1486699)), 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), _1486697), _1486699))], (26325 ^ _781404) ^ [_1251108, _1251110] : [c_Nat__Transfer_Ois__nat(_1251108), c_Nat__Transfer_Ois__nat(_1251110), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1251108), _1251110)))], (15557 ^ _781404) ^ [_1056775, _1056777, _1056779] : [class_Lattices_Olattice(_1056775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056775), _1056777)), hBOOL(hAPP(hAPP(c_member(_1056775), _1056779), _1056777)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1056775), _1056779), c_Big__Operators_Olattice__class_OInf__fin(_1056775, _1056777)) = _1056779)], (50606 ^ _781404) ^ [_1803964, _1803966, _1803968] : [c_Fun_Oinj__on(_1803964, _1803966, _1803968, c_Orderings_Otop__class_Otop(tc_fun(_1803964, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1803966, _1803964, c_Hilbert__Choice_Oinv__into(_1803964, _1803966, c_Orderings_Otop__class_Otop(tc_fun(_1803964, tc_HOL_Obool)), _1803968)), c_Orderings_Otop__class_Otop(tc_fun(_1803966, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1803964, tc_HOL_Obool)))], (43481 ^ _781404) ^ [_1648366, _1648368, _1648370] : [_1648366 = c_List_Olist_ONil(_1648368), -(c_List_Obutlast(_1648368, hAPP(hAPP(c_List_Olist_OCons(_1648368), _1648370), _1648366)) = c_List_Olist_ONil(_1648368))], (39165 ^ _781404) ^ [_1531119, _1531121, _1531123, _1531125, _1531127] : [class_Groups_Ocomm__monoid__add(_1531119), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531121), _1531123)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1531121, _1531119), _1531125), hAPP(c_Set_OCollect(_1531121), hAPP(hAPP(c_COMBS(_1531121, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1531121), c_fconj), hAPP(hAPP(c_COMBC(_1531121, tc_fun(_1531121, tc_HOL_Obool), tc_HOL_Obool), c_member(_1531121)), _1531123))), hAPP(hAPP(c_COMBC(_1531121, tc_fun(_1531121, tc_HOL_Obool), tc_HOL_Obool), c_member(_1531121)), _1531127)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1531121, _1531119), hAPP(hAPP(c_COMBC(_1531121, _1531119, _1531119), hAPP(hAPP(c_COMBS(_1531121, _1531119, tc_fun(_1531119, _1531119)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1531119, tc_fun(_1531119, _1531119)), _1531121), c_If(_1531119)), hAPP(hAPP(c_COMBC(_1531121, tc_fun(_1531121, tc_HOL_Obool), tc_HOL_Obool), c_member(_1531121)), _1531127))), _1531125)), c_Groups_Ozero__class_Ozero(_1531119))), _1531123))], (39331 ^ _781404) ^ [_1537410, _1537412, _1537414] : [class_Groups_Olinordered__ab__semigroup__add(_1537410), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537410), _1537412)), -(_1537412 = c_Orderings_Obot__class_Obot(tc_fun(_1537410, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1537410), _1537414), c_Big__Operators_Olinorder__class_OMin(_1537410, _1537412)) = c_Big__Operators_Olinorder__class_OMin(_1537410, hAPP(c_Set_OCollect(_1537410), hAPP(hAPP(c_COMBB(tc_fun(_1537410, tc_HOL_Obool), tc_HOL_Obool, _1537410), c_HOL_OEx(_1537410)), hAPP(hAPP(c_COMBC(_1537410, tc_fun(_1537410, tc_HOL_Obool), tc_fun(_1537410, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1537410, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1537410, tc_HOL_Obool), tc_fun(_1537410, tc_HOL_Obool)), _1537410), c_COMBS(_1537410, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1537410, tc_HOL_Obool), tc_fun(_1537410, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1537410), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1537410), c_fconj)), hAPP(hAPP(c_COMBC(_1537410, tc_fun(_1537410, _1537410), tc_fun(_1537410, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1537410, tc_HOL_Obool), tc_fun(tc_fun(_1537410, _1537410), tc_fun(_1537410, tc_HOL_Obool)), _1537410), c_COMBB(_1537410, tc_HOL_Obool, _1537410)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1537410), _1537414))))), hAPP(hAPP(c_COMBC(_1537410, tc_fun(_1537410, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537410)), _1537412))))))], (4190 ^ _781404) ^ [_844899, _844901] : [_844901 = _844899, -(c_New__Random__Sequence_Opos__single(_844901) = c_New__Random__Sequence_Opos__single(_844899))], (52220 ^ _781404) ^ [_1837019, _1837021] : [class_Lattices_Olattice(_1837019), -(class_Lattices_Olattice(tc_fun(_1837021, _1837019)))], (48676 ^ _781404) ^ [_1762113, _1762115] : [-(c_List_Olist__all(_1762113, _1762115, c_List_Olist_ONil(_1762113)))], (34291 ^ _781404) ^ [_1415744, _1415746, _1415748, _1415750, _1415752] : [_1415744 = c_Orderings_Obot__class_Obot(tc_fun(_1415746, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415746, tc_fun(_1415748, tc_HOL_Obool)), _1415744), hAPP(hAPP(c_COMBC(_1415746, tc_fun(_1415748, tc_HOL_Obool), tc_fun(_1415748, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1415748, tc_HOL_Obool), tc_fun(tc_fun(_1415748, tc_HOL_Obool), tc_fun(_1415748, tc_HOL_Obool)), _1415746), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415748, tc_HOL_Obool))), _1415750)), _1415752)) = c_Orderings_Obot__class_Obot(tc_fun(_1415748, tc_HOL_Obool)))], (19905 ^ _781404) ^ [] : [-(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)))], (11915 ^ _781404) ^ [_985549, _985551, _985553, _985555, _985557] : [-(hAPP(c_Set_Ovimage(_985549, _985551, _985553), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_985551, tc_HOL_Obool)), _985555), _985557)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_985549, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_985549, _985551, _985553), _985555)), hAPP(c_Set_Ovimage(_985549, _985551, _985553), _985557)))], (34699 ^ _781404) ^ [_1425645, _1425647, _1425649, _1425651, _1425653, _1425655] : [hBOOL(hAPP(hAPP(c_member(_1425645), _1425647), _1425649)), 34702 ^ _781404 : [(34709 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425645), _1425651), _1425649))), -(hAPP(c_Set_Ovimage(_1425653, _1425645, hAPP(hAPP(c_COMBC(_1425653, _1425645, _1425645), hAPP(hAPP(c_COMBC(_1425653, _1425645, tc_fun(_1425645, _1425645)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1425645, tc_fun(_1425645, _1425645)), _1425653), c_If(_1425645)), hAPP(hAPP(c_COMBC(_1425653, tc_fun(_1425653, tc_HOL_Obool), tc_HOL_Obool), c_member(_1425653)), _1425655))), _1425647)), _1425651)), _1425649) = _1425655)], (34703 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1425645), _1425651), _1425649)), -(hAPP(c_Set_Ovimage(_1425653, _1425645, hAPP(hAPP(c_COMBC(_1425653, _1425645, _1425645), hAPP(hAPP(c_COMBC(_1425653, _1425645, tc_fun(_1425645, _1425645)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1425645, tc_fun(_1425645, _1425645)), _1425653), c_If(_1425645)), hAPP(hAPP(c_COMBC(_1425653, tc_fun(_1425653, tc_HOL_Obool), tc_HOL_Obool), c_member(_1425653)), _1425655))), _1425647)), _1425651)), _1425649) = c_Orderings_Otop__class_Otop(tc_fun(_1425653, tc_HOL_Obool)))]]], (40602 ^ _781404) ^ [_1573087, _1573089, _1573091] : [class_Complete__Lattice_Ocomplete__lattice(_1573087), _1573089 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1573087, _1573091), c_Orderings_Oorder__class_Omono(_1573087, _1573087, _1573091), -(_1573089 = hAPP(_1573091, _1573089))], (42465 ^ _781404) ^ [_1621807, _1621809] : [-(c_List_Olistrel(_1621807, c_Transitive__Closure_Ortrancl(_1621807, _1621809)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1621807), c_List_Olistrel1(_1621807, _1621809)))], (26503 ^ _781404) ^ [_1253902, _1253904, _1253906] : [class_Rings_Oring__1(_1253902), -(hAPP(c_Int_Oring__1__class_Oof__int(_1253902), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1253904), _1253906)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1253902), hAPP(c_Int_Oring__1__class_Oof__int(_1253902), _1253904)), _1253906))], (4154 ^ _781404) ^ [_844297, _844299, _844301, _844303, _844305, _844307, _844309, _844311] : [-(c_New__Random__Sequence_Opos__map(_844311, _844307, _844303, _844299) = c_New__Random__Sequence_Opos__map(_844309, _844305, _844301, _844297)), _844311 = _844309, _844307 = _844305, _844303 = _844301, _844299 = _844297], (26925 ^ _781404) ^ [_1261985, _1261987] : [class_Rings_Olinordered__idom(_1261985), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1261985), hAPP(c_Groups_Oabs__class_Oabs(_1261985), _1261987)), hAPP(c_Groups_Oabs__class_Oabs(_1261985), _1261987)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1261985), _1261987), _1261987))], (1816 ^ _781404) ^ [_807144, _807146] : [-(class_Orderings_Opreorder(_807144)), _807146 = _807144, class_Orderings_Opreorder(_807146)], (40261 ^ _781404) ^ [_1565261, _1565263] : [c_Wellfounded_Owf(_1565261, _1565263), -(c_Wellfounded_OwfP(_1565261, c_FunDef_Oin__rel(_1565261, _1565261, _1565263)))], (48971 ^ _781404) ^ [_1768266, _1768268, _1768270] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1768266, _1768266, hAPP(hAPP(c_COMBB(tc_fun(_1768266, tc_HOL_Obool), tc_fun(_1768266, tc_HOL_Obool), _1768266), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1768266), c_fNot)), c_fequal)), _1768268), _1768270)), _1768268 = _1768270], (27560 ^ _781404) ^ [_1273529, _1273531] : [class_Rings_Olinordered__idom(_1273529), -(hAPP(c_Groups_Oabs__class_Oabs(_1273529), hAPP(hAPP(c_Power_Opower__class_Opower(_1273529), _1273531), 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(_1273529), _1273531), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (51924 ^ _781404) ^ [_1832203, _1832205] : [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)))), _1832203, _1832205) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832203), _1832205)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832205), _1832203)))], (42738 ^ _781404) ^ [_1629481, _1629483, _1629485, _1629487] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629481), tc_List_Olist(_1629481))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629481), tc_List_Olist(_1629481)), _1629483), _1629485)), c_List_Olexord(_1629481, _1629487)))), 42739 ^ _781404 : [(42746 ^ _781404) ^ [_1629788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1629788), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629481)), _1629483)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629481)), _1629485)))), hAPP(hAPP(c_List_Otake(_1629481), _1629788), _1629483) = hAPP(hAPP(c_List_Otake(_1629481), _1629788), _1629485), hBOOL(hAPP(hAPP(c_member(tc_prod(_1629481, _1629481)), hAPP(hAPP(c_Product__Type_OPair(_1629481, _1629481), hAPP(hAPP(c_List_Onth(_1629481), _1629483), _1629788)), hAPP(hAPP(c_List_Onth(_1629481), _1629485), _1629788))), _1629487))], (42740 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629481)), _1629483)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629481)), _1629485))), hAPP(hAPP(c_List_Otake(_1629481), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629481)), _1629483)), _1629485) = _1629483]]], (288 ^ _781404) ^ [_785926, _785928] : [-(class_Fields_Olinordered__field(_785926)), _785928 = _785926, class_Fields_Olinordered__field(_785928)], (23986 ^ _781404) ^ [_1211857, _1211859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211857)), 23989 ^ _781404 : [(23996 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211859)), -(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), _1211859), _1211857))))], (23990 ^ _781404) ^ [] : [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), _1211859), _1211857))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211859)))]]], (27636 ^ _781404) ^ [_1274989, _1274991, _1274993, _1274995, _1274997] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1274989, _1274989, _1274991, _1274993, _1274995), _1274997)), -(hBOOL(hAPP(hAPP(c_member(_1274989), _1274993), _1274995))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1274989, _1274991, hAPP(hAPP(c_Set_Oinsert(_1274989), _1274993), _1274995)), _1274997)))], (52510 ^ _781404) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (7822 ^ _781404) ^ [_910432, _910434, _910436, _910438] : [class_Lattices_Odistrib__lattice(_910432), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910432), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_910432), _910434), _910436)), _910438) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_910432), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910432), _910434), _910438)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910432), _910436), _910438)))], (26919 ^ _781404) ^ [_1261856, _1261858, _1261860] : [class_Groups_Oordered__ab__group__add__abs(_1261856), -(hAPP(c_Groups_Oabs__class_Oabs(_1261856), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1261856), _1261858), _1261860)) = hAPP(c_Groups_Oabs__class_Oabs(_1261856), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1261856), _1261860), _1261858)))], (46058 ^ _781404) ^ [_1705256, _1705258, _1705260, _1705262, _1705264] : [c_List_Olist__all2(_1705256, _1705258, _1705260, _1705262, _1705264), 46061 ^ _781404 : [(46064 ^ _781404) ^ [_1705419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1705419), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705256)), _1705262))), -(hBOOL(hAPP(hAPP(_1705260, hAPP(hAPP(c_List_Onth(_1705256), _1705262), _1705419)), hAPP(hAPP(c_List_Onth(_1705258), _1705264), _1705419))))], (46062 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705256)), _1705262) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705258)), _1705264))]]], (34231 ^ _781404) ^ [_1412544, _1412546, _1412548, _1412550, _1412552, _1412554, _1412556] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412544, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412546, tc_fun(_1412544, tc_HOL_Obool)), _1412548), _1412550)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412552, tc_fun(_1412544, tc_HOL_Obool)), _1412554), _1412556)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412546, tc_fun(_1412544, tc_HOL_Obool)), _1412548), hAPP(hAPP(c_COMBB(tc_fun(_1412552, tc_fun(_1412544, tc_HOL_Obool)), tc_fun(_1412544, tc_HOL_Obool), _1412546), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412552, tc_fun(_1412544, tc_HOL_Obool)), _1412554)), hAPP(hAPP(c_COMBC(_1412546, tc_fun(_1412552, tc_fun(_1412544, tc_HOL_Obool)), tc_fun(_1412552, tc_fun(_1412544, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1412544, tc_HOL_Obool), tc_fun(_1412544, tc_HOL_Obool)), tc_fun(tc_fun(_1412552, tc_fun(_1412544, tc_HOL_Obool)), tc_fun(_1412552, tc_fun(_1412544, tc_HOL_Obool))), _1412546), c_COMBB(tc_fun(_1412544, tc_HOL_Obool), tc_fun(_1412544, tc_HOL_Obool), _1412552)), hAPP(hAPP(c_COMBB(tc_fun(_1412544, tc_HOL_Obool), tc_fun(tc_fun(_1412544, tc_HOL_Obool), tc_fun(_1412544, tc_HOL_Obool)), _1412546), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412544, tc_HOL_Obool))), _1412550))), _1412556))))], (45090 ^ _781404) ^ [_1683186, _1683188, _1683190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683186), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683188)), _1683190))), -(c_List_Olast(_1683188, hAPP(hAPP(c_List_Odrop(_1683188), _1683186), _1683190)) = c_List_Olast(_1683188, _1683190))], (51399 ^ _781404) ^ [_1822425] : [-(c_Lazy__Sequence_Oflat(_1822425, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1822425))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1822425))], (49297 ^ _781404) ^ [_1775122, _1775124] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1775122), _1775124))), -(c_Lazy__Sequence_Osmall__lazy_H(_1775122, _1775124) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1775124), c_Lazy__Sequence_Osmall__lazy_H(_1775122, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1775124), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (17723 ^ _781404) ^ [_1097392, _1097394, _1097396, _1097398] : [class_Lattices_Osemilattice__inf(_1097392), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097392), _1097394)), hBOOL(hAPP(hAPP(c_member(_1097392), _1097396), _1097394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097392), hAPP(hAPP(c_Finite__Set_Ofold(_1097392, _1097392, c_Lattices_Osemilattice__inf__class_Oinf(_1097392)), _1097398), _1097394)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1097392), _1097396), _1097398))))], (25087 ^ _781404) ^ [] : [-(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))))], (17867 ^ _781404) ^ [_1100026, _1100028, _1100030, _1100032] : [class_Rings_Olinordered__semidom(_1100026), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100026), c_Groups_Oone__class_Oone(_1100026)), _1100028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100026), hAPP(hAPP(c_Power_Opower__class_Opower(_1100026), _1100028), _1100030)), hAPP(hAPP(c_Power_Opower__class_Opower(_1100026), _1100028), _1100032))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1100030), _1100032)))], (7004 ^ _781404) ^ [_894483, _894485, _894487, _894489] : [7018 ^ _781404 : [(7021 ^ _781404) ^ [] : [-(hBOOL(hAPP(_894489, 7017 ^ [_894483, _894485, _894487, _894489])))], (7019 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894483), 7017 ^ [_894483, _894485, _894487, _894489]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894483, tc_HOL_Obool)), _894485), _894487))))]], 7005 ^ _781404 : [(7012 ^ _781404) ^ [_894692] : [hBOOL(hAPP(hAPP(c_member(_894483), _894692), _894487)), hBOOL(hAPP(_894489, _894692))], (7006 ^ _781404) ^ [_894596] : [hBOOL(hAPP(hAPP(c_member(_894483), _894596), _894485)), hBOOL(hAPP(_894489, _894596))]]], (41506 ^ _781404) ^ [_1595236] : [-(hAPP(c_Relation_Oconverse(_1595236, _1595236), c_Relation_OId(_1595236)) = c_Relation_OId(_1595236))], (39209 ^ _781404) ^ [_1532889, _1532891] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1532889))), -(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)), _1532889))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1532891)))) = 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)), _1532889))), 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, _1532891))))))], (15337 ^ _781404) ^ [_1052703, _1052705] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1052703, _1052705)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1052703, _1052705), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1052705), c_Orderings_Otop__class_Otop(tc_fun(_1052705, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052703), c_Orderings_Otop__class_Otop(tc_fun(_1052703, tc_HOL_Obool)))))], (23323 ^ _781404) ^ [_1199321, _1199323] : [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), _1199321))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1199323)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1199321))) = 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), _1199323), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1199321)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36705 ^ _781404) ^ [_1467948, _1467950, _1467952] : [-(c_HOL_OThe(tc_prod(_1467948, _1467950), _1467952) = c_HOL_OThe(tc_prod(_1467948, _1467950), hAPP(c_Product__Type_Oprod_Oprod__case(_1467948, _1467950, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1467950, tc_prod(_1467948, _1467950)), tc_fun(_1467950, tc_HOL_Obool), _1467948), hAPP(c_COMBB(tc_prod(_1467948, _1467950), tc_HOL_Obool, _1467950), _1467952)), c_Product__Type_OPair(_1467948, _1467950)))))], (41279 ^ _781404) ^ [_1589849, _1589851] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589849, _1589849, _1589849), _1589851), c_Transitive__Closure_Ortrancl(_1589849, _1589851)) = hAPP(hAPP(c_Relation_Orel__comp(_1589849, _1589849, _1589849), c_Transitive__Closure_Ortrancl(_1589849, _1589851)), _1589851))], (41758 ^ _781404) ^ [_1601185, _1601187, _1601189] : [41761 ^ _781404 : [(41767 ^ _781404) ^ [] : [41760 ^ [_1601185, _1601187, _1601189] = 41763 ^ [_1601185, _1601187, _1601189]], (41765 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601185, _1601187)), hAPP(hAPP(c_Product__Type_OPair(_1601185, _1601187), 41759 ^ [_1601185, _1601187, _1601189]), 41763 ^ [_1601185, _1601187, _1601189])), _1601189)))], (41762 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601185, _1601187)), hAPP(hAPP(c_Product__Type_OPair(_1601185, _1601187), 41759 ^ [_1601185, _1601187, _1601189]), 41760 ^ [_1601185, _1601187, _1601189])), _1601189)))]], -(c_Relation_Osingle__valued(_1601185, _1601187, _1601189))], (39604 ^ _781404) ^ [_1548147, _1548149, _1548151, _1548153, _1548155] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548147, _1548149)), hAPP(hAPP(c_Product__Type_OPair(_1548147, _1548149), _1548151), _1548153)), _1548155)), -(hBOOL(hAPP(hAPP(c_member(_1548149), _1548153), hAPP(c_Relation_ORange(_1548147, _1548149), _1548155))))], (21225 ^ _781404) ^ [_1158677, _1158679, _1158681] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1158677), _1158679)), _1158681) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158677), _1158681)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158679), _1158681)))], (7984 ^ _781404) ^ [_914517, _914519, _914521] : [class_Lattices_Oboolean__algebra(_914517), -(hAPP(c_Groups_Ouminus__class_Ouminus(_914517), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_914517), _914519), _914521)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914517), hAPP(c_Groups_Ouminus__class_Ouminus(_914517), _914519)), hAPP(c_Groups_Ouminus__class_Ouminus(_914517), _914521)))], (39658 ^ _781404) ^ [_1549807, _1549809] : [-(hAPP(c_Relation_ORange(_1549807, _1549809), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549807, _1549809), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1549809, tc_HOL_Obool)))], (46595 ^ _781404) ^ [_1717502, _1717504, _1717506, _1717508, _1717510] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717502)), hAPP(c_List_Ofilter(_1717502, _1717504), hAPP(hAPP(c_List_Omap(_1717506, _1717502), _1717508), _1717510))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717506)), hAPP(c_List_Ofilter(_1717506, hAPP(c_Fun_Ocomp(_1717502, tc_HOL_Obool, _1717506, _1717504), _1717508)), _1717510)))], (19603 ^ _781404) ^ [_1129886, _1129888] : [class_Int_Onumber__ring(_1129886), 19606 ^ _781404 : [(19613 ^ _781404) ^ [] : [c_Int_Oiszero(_1129886, hAPP(c_Int_Onumber__class_Onumber__of(_1129886), 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), _1129888)))), -(c_Groups_Oone__class_Oone(_1129886) = hAPP(c_Int_Onumber__class_Onumber__of(_1129886), _1129888))], (19607 ^ _781404) ^ [] : [c_Groups_Oone__class_Oone(_1129886) = hAPP(c_Int_Onumber__class_Onumber__of(_1129886), _1129888), -(c_Int_Oiszero(_1129886, hAPP(c_Int_Onumber__class_Onumber__of(_1129886), 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), _1129888)))))]]], (23773 ^ _781404) ^ [_1208199, _1208201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1208199), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1208199), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208201, _1208199))))], (30696 ^ _781404) ^ [_1333269, _1333271, _1333273] : [class_Orderings_Olinorder(_1333269), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333269), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333269), _1333271), _1333273)), _1333271)))], (18935 ^ _781404) ^ [_1118685, _1118687] : [class_Int_Onumber__ring(_1118685), 18938 ^ _781404 : [(18945 ^ _781404) ^ [] : [c_Int_Oiszero(_1118685, hAPP(c_Int_Onumber__class_Onumber__of(_1118685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1118687)))), -(c_Groups_Ozero__class_Ozero(_1118685) = hAPP(c_Int_Onumber__class_Onumber__of(_1118685), _1118687))], (18939 ^ _781404) ^ [] : [c_Groups_Ozero__class_Ozero(_1118685) = hAPP(c_Int_Onumber__class_Onumber__of(_1118685), _1118687), -(c_Int_Oiszero(_1118685, hAPP(c_Int_Onumber__class_Onumber__of(_1118685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1118687)))))]]], (12556 ^ _781404) ^ [_998185, _998187] : [hAPP(_998185, 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), _998185), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _998187)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _998185), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _998187)))], (11319 ^ _781404) ^ [_973940, _973942, _973944, _973946] : [c_Fun_Oinj__on(_973940, _973942, _973944, c_Orderings_Otop__class_Otop(tc_fun(_973940, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973942, tc_HOL_Obool)), hAPP(c_Set_Oimage(_973940, _973942, _973944), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973940, tc_HOL_Obool)), _973946))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973942, tc_HOL_Obool)), hAPP(c_Set_Oimage(_973940, _973942, _973944), _973946)))))], (14015 ^ _781404) ^ [_1025821, _1025823, _1025825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025821), _1025823)), _1025825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025821), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025825), _1025823))))], (41724 ^ _781404) ^ [_1600413, _1600415, _1600417] : [c_Relation_Ototal__on(_1600413, _1600415, _1600417), -(c_Relation_Ototal__on(_1600413, _1600415, hAPP(c_Relation_Oconverse(_1600413, _1600413), _1600417)))], (23812 ^ _781404) ^ [_1208868, _1208870, _1208872, _1208874] : [class_Divides_Osemiring__div(_1208868), -(_1208870 = c_Groups_Ozero__class_Ozero(_1208868)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208868), _1208870), _1208872)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208868), _1208870), _1208874)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208868), _1208872), _1208874))], (17445 ^ _781404) ^ [_1092562, _1092564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092562), _1092564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1092562), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1092564)))], (52696 ^ _781404) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (6843 ^ _781404) ^ [_891055, _891057] : [class_Lattices_Osemilattice__sup(_891055), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891055), _891057), _891057) = _891057)], (5398 ^ _781404) ^ [_863865, _863867] : [_863867 = _863865, -(c_Groups_Otimes__class_Otimes(_863867) = c_Groups_Otimes__class_Otimes(_863865))], (5252 ^ _781404) ^ [_861576, _861578, _861580, _861582] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_861582, _861578) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_861580, _861576)), _861582 = _861580, _861578 = _861576], (21139 ^ _781404) ^ [_1156745, _1156747, _1156749] : [_1156747 = _1156749, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1156745)), _1156747) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1156745)), _1156749))], (15545 ^ _781404) ^ [_1056543, _1056545, _1056547] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1056543), _1056545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1056543, tc_HOL_Obool)), _1056547), _1056545)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1056543), _1056547)), hAPP(c_Finite__Set_Ocard(_1056543), _1056545))))], (10013 ^ _781404) ^ [_952408, _952410, _952412] : [class_Orderings_Oorder(_952408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952408), _952410), _952412)), -(_952412 = _952410), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952408), _952410), _952412)))], (34731 ^ _781404) ^ [_1426650, _1426652] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1426650)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1426652)), hAPP(c_Int_Onat, _1426650)) = hAPP(c_Int_Onat, _1426652))], (17256 ^ _781404) ^ [_1089062, _1089064, _1089066, _1089068] : [class_Int_Onumber__ring(_1089062), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089062), hAPP(c_Int_Onumber__class_Onumber__of(_1089062), _1089064)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1089062), hAPP(c_Int_Onumber__class_Onumber__of(_1089062), _1089066)), _1089068)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1089062), hAPP(c_Int_Onumber__class_Onumber__of(_1089062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1089064), _1089066))), _1089068))], (5484 ^ _781404) ^ [_865260, _865262, _865264, _865266, _865268, _865270, _865272, _865274, _865276, _865278] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_865278, _865274, _865270, _865266, _865262) = c_SetInterval_Oord_OgreaterThanAtMost(_865276, _865272, _865268, _865264, _865260)), _865278 = _865276, _865274 = _865272, _865270 = _865268, _865266 = _865264, _865262 = _865260], (24114 ^ _781404) ^ [_1213901, _1213903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213901), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213903), _1213901)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213901), _1213903) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48621 ^ _781404) ^ [_1760791, _1760793, _1760795] : [hBOOL(hAPP(hAPP(c_member(_1760791), _1760793), hAPP(c_List_Oset(_1760791), _1760795))), -(_1760795 = hAPP(hAPP(c_List_Oappend(_1760791), 48624 ^ [_1760791, _1760793, _1760795]), hAPP(hAPP(c_List_Olist_OCons(_1760791), _1760793), 48625 ^ [_1760791, _1760793, _1760795])))], (1536 ^ _781404) ^ [_803644, _803646] : [-(class_Lazy__Sequence_Osmall__lazy(_803644)), _803646 = _803644, class_Lazy__Sequence_Osmall__lazy(_803646)], (23575 ^ _781404) ^ [_1204728, _1204730, _1204732, _1204734, _1204736, _1204738] : [class_Divides_Osemiring__div(_1204728), c_Divides_Odiv__class_Omod(_1204728, _1204730, _1204732) = c_Divides_Odiv__class_Omod(_1204728, _1204734, _1204732), c_Divides_Odiv__class_Omod(_1204728, _1204736, _1204732) = c_Divides_Odiv__class_Omod(_1204728, _1204738, _1204732), -(c_Divides_Odiv__class_Omod(_1204728, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204728), _1204730), _1204736), _1204732) = c_Divides_Odiv__class_Omod(_1204728, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204728), _1204734), _1204738), _1204732))], (37102 ^ _781404) ^ [_1477279, _1477281, _1477283, _1477285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1477279), _1477281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1477283), _1477285)), -(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), _1477279), _1477283)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1477281), _1477285))), c_FunDef_Opair__less)))], (18819 ^ _781404) ^ [_1116800, _1116802] : [class_Int_Onumber__ring(_1116800), class_Rings_Olinordered__idom(_1116800), 18826 ^ _781404 : [(18833 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1116802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116800), c_Groups_Ozero__class_Ozero(_1116800)), hAPP(c_Int_Onumber__class_Onumber__of(_1116800), _1116802))))], (18827 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116800), c_Groups_Ozero__class_Ozero(_1116800)), hAPP(c_Int_Onumber__class_Onumber__of(_1116800), _1116802))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1116802)))]]], (41323 ^ _781404) ^ [_1590909, _1590911, _1590913, _1590915, _1590917] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590909, _1590909)), hAPP(hAPP(c_Product__Type_OPair(_1590909, _1590909), _1590911), _1590913)), c_Transitive__Closure_Ortrancl(_1590909, _1590915))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590909, _1590909)), hAPP(hAPP(c_Product__Type_OPair(_1590909, _1590909), _1590913), _1590917)), _1590915)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590909, _1590909)), hAPP(hAPP(c_Product__Type_OPair(_1590909, _1590909), _1590911), _1590917)), c_Transitive__Closure_Otrancl(_1590909, _1590915))))], (13267 ^ _781404) ^ [_1011911, _1011913, _1011915] : [class_Groups_Oab__group__add(_1011911), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1011911), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011911), _1011913), _1011915)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011911), hAPP(c_Groups_Ouminus__class_Ouminus(_1011911), _1011913)), hAPP(c_Groups_Ouminus__class_Ouminus(_1011911), _1011915)))], (48927 ^ _781404) ^ [_1767001, _1767003, _1767005, _1767007] : [-(c_New__Random__Sequence_Opos__empty(_1767001, _1767003, _1767005, _1767007) = c_New__DSequence_Opos__empty(_1767001))], (7870 ^ _781404) ^ [_911556, _911558, _911560] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911556, tc_HOL_Obool)), _911558), hAPP(hAPP(c_Set_Oinsert(_911556), _911560), _911558))))], (48246 ^ _781404) ^ [_1752728, _1752730, _1752732, _1752734] : [48248 ^ _781404 : [(48251 ^ _781404) ^ [] : [hBOOL(hAPP(_1752732, 48247 ^ [_1752728, _1752730, _1752732, _1752734]))], (48249 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752728), 48247 ^ [_1752728, _1752730, _1752732, _1752734]), hAPP(c_List_Oset(_1752728), _1752730))))]], -(c_List_OdropWhile(_1752728, _1752732, hAPP(hAPP(c_List_Oappend(_1752728), _1752730), _1752734)) = c_List_OdropWhile(_1752728, _1752732, _1752734))], (52530 ^ _781404) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (43240 ^ _781404) ^ [_1642920, _1642922] : [-(c_List_Obutlast(_1642920, _1642922) = hAPP(hAPP(c_List_Otake(_1642920), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642920)), _1642922)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1642922))], (17709 ^ _781404) ^ [_1097125, _1097127, _1097129, _1097131] : [class_Lattices_Osemilattice__sup(_1097125), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097125), _1097127)), hBOOL(hAPP(hAPP(c_member(_1097125), _1097129), _1097127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097125), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1097125), _1097129), _1097131)), hAPP(hAPP(c_Finite__Set_Ofold(_1097125, _1097125, c_Lattices_Osemilattice__sup__class_Osup(_1097125)), _1097131), _1097127))))], (15883 ^ _781404) ^ [_1062578, _1062580, _1062582] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062578), _1062580)), -(hAPP(c_Finite__Set_Ocard(_1062578), hAPP(hAPP(c_Set_Oinsert(_1062578), _1062582), _1062580)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1062578), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1062578, tc_HOL_Obool)), _1062580), hAPP(hAPP(c_Set_Oinsert(_1062578), _1062582), c_Orderings_Obot__class_Obot(tc_fun(_1062578, tc_HOL_Obool)))))))], (50487 ^ _781404) ^ [_1801199, _1801201, _1801203, _1801205] : [c_Fun_Oinj__on(_1801199, _1801201, _1801203, c_Orderings_Otop__class_Otop(tc_fun(_1801199, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1801199, _1801201, c_Orderings_Otop__class_Otop(tc_fun(_1801199, tc_HOL_Obool)), _1801203), hAPP(_1801203, _1801205)) = _1801205)], (47563 ^ _781404) ^ [_1737745, _1737747, _1737749, _1737751] : [_1737747 = hAPP(hAPP(c_List_Oappend(_1737745), hAPP(c_List_Orev(_1737745), _1737751)), hAPP(hAPP(c_List_Olist_OCons(_1737745), _1737749), c_List_Olist_ONil(_1737745))), -(hAPP(c_List_Orev(_1737745), _1737747) = hAPP(hAPP(c_List_Olist_OCons(_1737745), _1737749), _1737751))], (12204 ^ _781404) ^ [_991180, _991182, _991184, _991186, _991188, _991190] : [c_Fun_Oinj__on(_991180, _991182, _991184, _991186), hAPP(_991184, _991188) = hAPP(_991184, _991190), hBOOL(hAPP(hAPP(c_member(_991180), _991188), _991186)), hBOOL(hAPP(hAPP(c_member(_991180), _991190), _991186)), -(_991188 = _991190)], (47557 ^ _781404) ^ [_1737596, _1737598, _1737600, _1737602] : [hAPP(c_List_Orev(_1737596), _1737598) = hAPP(hAPP(c_List_Olist_OCons(_1737596), _1737600), _1737602), -(_1737598 = hAPP(hAPP(c_List_Oappend(_1737596), hAPP(c_List_Orev(_1737596), _1737602)), hAPP(hAPP(c_List_Olist_OCons(_1737596), _1737600), c_List_Olist_ONil(_1737596))))], (30756 ^ _781404) ^ [_1334298, _1334300, _1334302, _1334304] : [class_Orderings_Olinorder(_1334298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334298), _1334300), _1334302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334298), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334298), _1334304), _1334300)), _1334302)))], (8778 ^ _781404) ^ [_929453, _929455, _929457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_929453, tc_HOL_Obool), tc_HOL_Obool)), _929455), _929457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929453, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_929453, tc_HOL_Obool), _929455)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_929453, tc_HOL_Obool), _929457))))], (44331 ^ _781404) ^ [_1667444, _1667446, _1667448, _1667450, _1667452] : [hAPP(hAPP(c_List_Odrop(_1667444), _1667446), _1667448) = hAPP(hAPP(c_List_Olist_OCons(_1667444), _1667450), _1667452), -(hAPP(hAPP(c_List_Onth(_1667444), _1667448), _1667446) = _1667450)], (35616 ^ _781404) ^ [_1446110, _1446112] : [_1446110 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1446110, _1446112) = 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)))], (10345 ^ _781404) ^ [_957387, _957389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957387, tc_HOL_Obool)), _957389), c_Orderings_Obot__class_Obot(tc_fun(_957387, tc_HOL_Obool))))], (33502 ^ _781404) ^ [_1390748, _1390750, _1390752, _1390754] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1390748, tc_HOL_Obool), tc_fun(_1390750, tc_HOL_Obool)), _1390752), hAPP(hAPP(c_COMBC(tc_fun(_1390748, tc_HOL_Obool), tc_fun(_1390748, tc_fun(_1390750, tc_HOL_Obool)), tc_fun(_1390750, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390748, tc_fun(_1390750, tc_HOL_Obool))), _1390754)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390748, tc_fun(_1390750, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1390748, tc_HOL_Obool), _1390752)), _1390754))], (20 ^ _781404) ^ [_781664, _781666, _781668, _781670, _781672, _781674] : [-(c_Hoare__Mirabelle_Ohoare__valids(_781672, _781668, _781664)), c_Hoare__Mirabelle_Ohoare__valids(_781674, _781670, _781666), _781674 = _781672, _781670 = _781668, _781666 = _781664], (15056 ^ _781404) ^ [_1046868, _1046870, _1046872, _1046874, _1046876, _1046878, _1046880, _1046882] : [c_Finite__Set_Ofolding__image__simple(_1046868, _1046870, _1046872, _1046874, _1046876, _1046878), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046870), _1046880)), -(hBOOL(hAPP(hAPP(c_member(_1046870), _1046882), _1046880))), -(hAPP(_1046878, hAPP(hAPP(c_Set_Oinsert(_1046870), _1046882), _1046880)) = hAPP(hAPP(_1046872, hAPP(_1046876, _1046882)), hAPP(_1046878, _1046880)))], (37449 ^ _781404) ^ [] : [-(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))))))], (16316 ^ _781404) ^ [_1071291] : [class_Rings_Olinordered__semidom(_1071291), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071291), c_Groups_Ozero__class_Ozero(_1071291)), c_Groups_Oone__class_Oone(_1071291))))], (43487 ^ _781404) ^ [_1648469, _1648471, _1648473] : [-(_1648469 = c_List_Olist_ONil(_1648471)), -(c_List_Obutlast(_1648471, hAPP(hAPP(c_List_Olist_OCons(_1648471), _1648473), _1648469)) = hAPP(hAPP(c_List_Olist_OCons(_1648471), _1648473), c_List_Obutlast(_1648471, _1648469)))], (15014 ^ _781404) ^ [_1045895, _1045897, _1045899, _1045901, _1045903] : [class_Rings_Ocomm__semiring__1(_1045895), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045895), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045895), _1045897), _1045899)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045895), _1045901), _1045903)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045895), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045895), _1045897), _1045901)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045895), _1045899), _1045903)))], (20805 ^ _781404) ^ [_1150833, _1150835, _1150837, _1150839] : [class_Rings_Ocomm__semiring__1(_1150833), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150833), _1150835), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150833), _1150837), _1150839)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150833), _1150837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150833), _1150835), _1150839)))], (9224 ^ _781404) ^ [_938852, _938854, _938856] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938852, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938852, tc_HOL_Obool)), _938854), _938856)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938852, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938852, tc_HOL_Obool)), _938854)), _938856))], (36717 ^ _781404) ^ [_1468331, _1468333] : [-(c_Set_Othe__elem(_1468331, _1468333) = c_HOL_OThe(_1468331, hAPP(hAPP(c_COMBB(tc_fun(_1468331, tc_HOL_Obool), tc_HOL_Obool, _1468331), hAPP(c_fequal, _1468333)), hAPP(hAPP(c_COMBC(_1468331, tc_fun(_1468331, tc_HOL_Obool), tc_fun(_1468331, tc_HOL_Obool)), c_Set_Oinsert(_1468331)), c_Orderings_Obot__class_Obot(tc_fun(_1468331, tc_HOL_Obool))))))], (52636 ^ _781404) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (24616 ^ _781404) ^ [_1222856, _1222858] : [class_Rings_Osemiring__1(_1222856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222858)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1222856), 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)))), _1222858))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1222856), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1222856), hAPP(c_Int_Onat, _1222858))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1222856), hAPP(c_Int_Onat, _1222858))))], (39878 ^ _781404) ^ [_1556578, _1556580, _1556582, _1556584] : [c_Wellfounded_Owf(_1556578, _1556580), hBOOL(hAPP(hAPP(c_member(tc_prod(_1556578, _1556578)), hAPP(hAPP(c_Product__Type_OPair(_1556578, _1556578), _1556582), _1556584)), _1556580)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1556578, _1556578)), hAPP(hAPP(c_Product__Type_OPair(_1556578, _1556578), _1556584), _1556582)), _1556580))], (25145 ^ _781404) ^ [_1231454, _1231456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231454)), 25148 ^ _781404 : [(25155 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231456), _1231454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1231456)), hAPP(c_Int_Onat, _1231454))))], (25149 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1231456)), hAPP(c_Int_Onat, _1231454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231456), _1231454)))]]], (23457 ^ _781404) ^ [_1202433, _1202435, _1202437, _1202439] : [class_Divides_Osemiring__div(_1202433), -(c_Divides_Odiv__class_Omod(_1202433, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202433), c_Divides_Odiv__class_Omod(_1202433, _1202435, _1202437)), _1202439), _1202437) = c_Divides_Odiv__class_Omod(_1202433, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202433), _1202435), _1202439), _1202437))], (50985 ^ _781404) ^ [_1812089, _1812091, _1812093, _1812095, _1812097] : [c_Fun_Obij__betw(_1812089, _1812091, _1812093, _1812095, _1812097), -(hAPP(c_Finite__Set_Ocard(_1812089), _1812095) = hAPP(c_Finite__Set_Ocard(_1812091), _1812097))], (47499 ^ _781404) ^ [_1736417, _1736419, _1736421, _1736423, _1736425] : [c_List_Olist__all2(_1736417, _1736419, _1736421, _1736423, hAPP(c_List_Orev(_1736419), _1736425)), -(c_List_Olist__all2(_1736417, _1736419, _1736421, hAPP(c_List_Orev(_1736417), _1736423), _1736425))], (43547 ^ _781404) ^ [_1649428, _1649430] : [-(c_List_Olistrelp(_1649428, _1649430, c_List_Olist_ONil(_1649428), c_List_Olist_ONil(_1649428)))], (42087 ^ _781404) ^ [_1610145, _1610147, _1610149, _1610151, _1610153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610145, tc_HOL_Obool)), _1610147), _1610149)), 42093 ^ _781404 : [(42098 ^ _781404) ^ [] : [hBOOL(hAPP(_1610153, 42092 ^ [_1610145, _1610147, _1610149, _1610151, _1610153]))], (42096 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1610151, 42092 ^ [_1610145, _1610147, _1610149, _1610151, _1610153])))], (42094 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1610145), 42092 ^ [_1610145, _1610147, _1610149, _1610151, _1610153]), _1610147)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610145, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610145, tc_HOL_Obool)), _1610147), hAPP(c_Set_OCollect(_1610145), _1610151))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610145, tc_HOL_Obool)), _1610149), hAPP(c_Set_OCollect(_1610145), _1610153)))))], (44577 ^ _781404) ^ [_1673361, _1673363, _1673365] : [-(_1673361 = c_List_Olist_ONil(_1673363)), -(hAPP(c_List_Ohd(_1673363), hAPP(hAPP(c_List_Oappend(_1673363), _1673361), _1673365)) = hAPP(c_List_Ohd(_1673363), _1673361))], (9142 ^ _781404) ^ [_936819, _936821, _936823] : [class_Groups_Oordered__ab__group__add(_936819), 9145 ^ _781404 : [(9152 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_936819), _936821), _936823)), c_Groups_Ozero__class_Ozero(_936819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936819), _936821), _936823)))], (9146 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936819), _936821), _936823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_936819), _936821), _936823)), c_Groups_Ozero__class_Ozero(_936819))))]]], (41161 ^ _781404) ^ [_1586931, _1586933, _1586935] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586931, _1586931)), hAPP(hAPP(c_Product__Type_OPair(_1586931, _1586931), _1586933), _1586933)), c_Transitive__Closure_Ortrancl(_1586931, _1586935))))], (11940 ^ _781404) ^ [_986071, _986073] : [-(_986073 = c_Orderings_Obot__class_Obot(tc_fun(_986071, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_986071), 11943 ^ [_986071, _986073]), _986073)))], (10517 ^ _781404) ^ [_960506] : [-(_960506 = 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)), _960506)))], (37238 ^ _781404) ^ [] : [-(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)))))], (3532 ^ _781404) ^ [_834196, _834198, _834200, _834202, _834204, _834206] : [-(c_List_Osublist(_834206, _834202, _834198) = c_List_Osublist(_834204, _834200, _834196)), _834206 = _834204, _834202 = _834200, _834198 = _834196], (37599 ^ _781404) ^ [_1490489, _1490491, _1490493, _1490495] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1490489, _1490489)), hAPP(hAPP(c_Product__Type_OPair(_1490489, _1490489), _1490491), _1490493)), c_Relation_OId__on(_1490489, _1490495))), 37602 ^ _781404 : [(37605 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490489), _1490491), _1490495)))], (37603 ^ _781404) ^ [] : [-(_1490491 = _1490493)]]], (35527 ^ _781404) ^ [_1444359, _1444361, _1444363, _1444365, _1444367, _1444369] : [_1444359 = _1444361, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1444363, _1444365, _1444367), _1444369), _1444359) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1444363, _1444365, _1444367), _1444369), _1444361))], (41858 ^ _781404) ^ [_1603787, _1603789, _1603791] : [c_Wellfounded_Owf(_1603787, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603787, _1603787), tc_HOL_Obool), _1603789), _1603791)), -(c_Wellfounded_Owf(_1603787, _1603791))], (32088 ^ _781404) ^ [_1358993, _1358995, _1358997, _1358999] : [class_Orderings_Olinorder(_1358993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358993), _1358995), _1358997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358993), _1358995), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358993), _1358997), _1358999))))], (2388 ^ _781404) ^ [_816318, _816320, _816322, _816324, _816326, _816328, _816330, _816332, _816334, _816336] : [-(c_Nitpick_Opair__box_Opair__box__rec(_816336, _816332, _816328, _816324, _816320) = c_Nitpick_Opair__box_Opair__box__rec(_816334, _816330, _816326, _816322, _816318)), _816336 = _816334, _816332 = _816330, _816328 = _816326, _816324 = _816322, _816320 = _816318], (1032 ^ _781404) ^ [_796896, _796898, _796900, _796902, _796904, _796906] : [-(c_Relation_Orefl__on(_796904, _796900, _796896)), c_Relation_Orefl__on(_796906, _796902, _796898), _796906 = _796904, _796902 = _796900, _796898 = _796896], (52334 ^ _781404) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (47483 ^ _781404) ^ [_1736012, _1736014, _1736016] : [-(hAPP(c_List_Orev(_1736012), hAPP(c_List_Ofilter(_1736012, _1736014), _1736016)) = hAPP(c_List_Ofilter(_1736012, _1736014), hAPP(c_List_Orev(_1736012), _1736016)))], (52346 ^ _781404) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (35606 ^ _781404) ^ [_1445890, _1445892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1445890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1445890), _1445892)), -(c_Divides_Odivmod__nat(_1445892, _1445890) = 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), _1445892), _1445890)), _1445890))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1445892), _1445890), _1445890)))], (44327 ^ _781404) ^ [_1667345, _1667347, _1667349] : [-(hAPP(hAPP(c_List_Odrop(_1667345), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1667345), _1667347), _1667349)) = _1667349)], (3166 ^ _781404) ^ [_828535, _828537, _828539, _828541] : [-(c_Nat_Ocompow(_828541, _828537) = c_Nat_Ocompow(_828539, _828535)), _828541 = _828539, _828537 = _828535], (5945 ^ _781404) ^ [_875658, _875660, _875662, _875664] : [class_Orderings_Oorder(_875658), _875660 = _875662, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875658), _875664), _875662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875658), _875664), _875660)))], (45716 ^ _781404) ^ [_1697249] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1697249), 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, _1697249)) = _1697249)], (52698 ^ _781404) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (7195 ^ _781404) ^ [_898092, _898094, _898096, _898098, _898100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898092, tc_HOL_Obool)), _898094), _898096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898092, tc_HOL_Obool)), _898098), _898100)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898092, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898092, tc_HOL_Obool)), _898094), _898098)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898092, tc_HOL_Obool)), _898096), _898100))))], (24985 ^ _781404) ^ [_1228964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228964), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1228964)), c_Int_OMin)))], (6737 ^ _781404) ^ [_889299, _889301, _889303] : [class_Groups_Oordered__ab__group__add(_889299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889299), _889301), _889303)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889299), hAPP(c_Groups_Ouminus__class_Ouminus(_889299), _889303)), hAPP(c_Groups_Ouminus__class_Ouminus(_889299), _889301))))], (49157 ^ _781404) ^ [_1772356, _1772358, _1772360, _1772362] : [-(hAPP(hAPP(c_List_Oappend(_1772356), c_List_Oreplicate(_1772356, _1772358, _1772360)), c_List_Oreplicate(_1772356, _1772362, _1772360)) = hAPP(hAPP(c_List_Oappend(_1772356), c_List_Oreplicate(_1772356, _1772362, _1772360)), c_List_Oreplicate(_1772356, _1772358, _1772360)))], (8038 ^ _781404) ^ [_915869, _915871] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915869, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_915869, tc_HOL_Obool)), _915871)), _915871) = c_Orderings_Otop__class_Otop(tc_fun(_915869, tc_HOL_Obool)))], (35015 ^ _781404) ^ [_1433278, _1433280, _1433282, _1433284, _1433286] : [class_Groups_Ocomm__monoid__add(_1433278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433280), _1433282)), c_Fun_Oinj__on(_1433280, _1433280, _1433284, _1433282), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1433280, _1433278), _1433286), hAPP(c_Set_Oimage(_1433280, _1433280, _1433284), _1433282)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1433280, _1433278), hAPP(c_Fun_Ocomp(_1433280, _1433278, _1433280, _1433286), _1433284)), _1433282))], (46129 ^ _781404) ^ [_1706927, _1706929, _1706931] : [-(c_Enum_Osublists(_1706927, hAPP(hAPP(c_List_Olist_OCons(_1706927), _1706929), _1706931)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1706927)), tc_List_Olist(tc_List_Olist(_1706927))), c_Enum_Osublists(_1706927, _1706931)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1706927)), tc_List_Olist(tc_List_Olist(_1706927)), tc_List_Olist(tc_List_Olist(_1706927))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1706927)), tc_fun(tc_List_Olist(tc_List_Olist(_1706927)), tc_List_Olist(tc_List_Olist(_1706927))), tc_List_Olist(tc_List_Olist(_1706927))), c_List_Oappend(tc_List_Olist(_1706927))), hAPP(c_List_Omap(tc_List_Olist(_1706927), tc_List_Olist(_1706927)), hAPP(c_List_Olist_OCons(_1706927), _1706929)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1706927))))))], (26164 ^ _781404) ^ [_1248589] : [-(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)), _1248589)))], (22021 ^ _781404) ^ [_1173647, _1173649, _1173651, _1173653] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173647), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1173647), _1173649), _1173651)), hAPP(c_Int_Onumber__class_Onumber__of(_1173647), _1173653)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1173647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173647), _1173649), hAPP(c_Int_Onumber__class_Onumber__of(_1173647), _1173653))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173647), _1173651), hAPP(c_Int_Onumber__class_Onumber__of(_1173647), _1173653)))), class_Int_Onumber(_1173647), class_Rings_Oring(_1173647)], (9641 ^ _781404) ^ [_946392, _946394, _946396] : [class_Orderings_Oorder(_946392), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946392), _946394), _946396)), _946394 = _946396], (45407 ^ _781404) ^ [_1690867, _1690869, _1690871, _1690873] : [c_Fun_Oinj__on(_1690867, _1690869, _1690871, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1690867, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1690867), tc_fun(_1690867, tc_HOL_Obool), c_List_Oset(_1690867)), _1690873))), -(c_Fun_Oinj__on(tc_List_Olist(_1690867), tc_List_Olist(_1690869), hAPP(c_List_Omap(_1690867, _1690869), _1690871), _1690873))], (30660 ^ _781404) ^ [_1332582, _1332584, _1332586, _1332588] : [-(c_Nitpick_Ofold__graph_H(_1332582, _1332584, _1332586, _1332588, c_Orderings_Obot__class_Obot(tc_fun(_1332582, tc_HOL_Obool)), _1332588))], (11693 ^ _781404) ^ [_981649, _981651, _981653, _981655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_981649, tc_HOL_Obool)), _981651), _981653)), hBOOL(hAPP(hAPP(c_member(_981649), _981655), _981651)), -(hBOOL(hAPP(hAPP(c_member(_981649), _981655), _981653)))], (11815 ^ _781404) ^ [_983627, _983629, _983631, _983633] : [_983627 = _983629, 11818 ^ _781404 : [(11825 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_983631), _983633), _983629)), -(hBOOL(hAPP(hAPP(c_member(_983631), _983633), _983627)))], (11819 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_983631), _983633), _983627)), -(hBOOL(hAPP(hAPP(c_member(_983631), _983633), _983629)))]]], (46036 ^ _781404) ^ [_1704759, _1704761, _1704763] : [-(c_Enum_Oproduct(_1704759, _1704761, c_List_Olist_ONil(_1704759), _1704763) = c_List_Olist_ONil(tc_prod(_1704759, _1704761)))], (44511 ^ _781404) ^ [_1671723, _1671725, _1671727, _1671729] : [-(hAPP(c_List_Orotate1(_1671725), hAPP(hAPP(c_List_Olist_OCons(_1671725), _1671727), _1671729)) = hAPP(hAPP(c_List_Oappend(_1671725), _1671729), hAPP(hAPP(c_List_Olist_OCons(_1671725), _1671727), c_List_Olist_ONil(_1671725))))], (17899 ^ _781404) ^ [_1100630, _1100632, _1100634, _1100636] : [class_Rings_Olinordered__semidom(_1100630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100632), _1100634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100630), c_Groups_Ozero__class_Ozero(_1100630)), _1100636)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100630), _1100636), c_Groups_Oone__class_Oone(_1100630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100630), hAPP(hAPP(c_Power_Opower__class_Opower(_1100630), _1100636), _1100634)), hAPP(hAPP(c_Power_Opower__class_Opower(_1100630), _1100636), _1100632))))], (1836 ^ _781404) ^ [_807394, _807396] : [-(class_Groups_Omonoid__mult(_807394)), _807396 = _807394, class_Groups_Omonoid__mult(_807396)], (24638 ^ _781404) ^ [_1223273, _1223275, _1223277] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223273), _1223275)), _1223277) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223273), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223275), _1223277))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223273), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223275, _1223277))), _1223277)))], (11605 ^ _781404) ^ [_979955, _979957, _979959, _979961] : [hBOOL(hAPP(hAPP(c_member(_979955), _979957), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979955, tc_HOL_Obool)), _979959), _979961))), 11608 ^ _781404 : [(11611 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_979955), _979957), _979961))], (11609 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_979955), _979957), _979959)))]]], (33603 ^ _781404) ^ [_1393576, _1393578, _1393580, _1393582, _1393584, _1393586] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393576, tc_fun(_1393578, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393580, tc_fun(_1393576, tc_HOL_Obool)), _1393582), _1393584)), _1393586) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393580, tc_fun(_1393578, tc_HOL_Obool)), _1393582), hAPP(hAPP(c_COMBC(_1393580, tc_fun(_1393576, tc_fun(_1393578, tc_HOL_Obool)), tc_fun(_1393578, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393576, tc_HOL_Obool), tc_fun(tc_fun(_1393576, tc_fun(_1393578, tc_HOL_Obool)), tc_fun(_1393578, tc_HOL_Obool)), _1393580), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393576, tc_fun(_1393578, tc_HOL_Obool))), _1393584)), _1393586)))], (34485 ^ _781404) ^ [_1420653] : [class_Orderings_Olinorder(_1420653), -(c_Orderings_Oord_Omax(_1420653, hAPP(c_COMBC(_1420653, _1420653, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1420653))) = c_Orderings_Oord__class_Omin(_1420653))], (49351 ^ _781404) ^ [_1776357, _1776359, _1776361, _1776363, _1776365] : [49353 ^ _781404 : [(49356 ^ _781404) ^ [] : [c_Relation_Orefl__on(_1776361, hAPP(_1776363, 49352 ^ [_1776357, _1776359, _1776361, _1776363, _1776365]), hAPP(_1776365, 49352 ^ [_1776357, _1776359, _1776361, _1776363, _1776365]))], (49354 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776357), 49352 ^ [_1776357, _1776359, _1776361, _1776363, _1776365]), _1776359)))]], -(c_Relation_Orefl__on(_1776361, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1776357, tc_fun(_1776361, tc_HOL_Obool)), _1776359), _1776363), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1776357, tc_fun(tc_prod(_1776361, _1776361), tc_HOL_Obool)), _1776359), _1776365)))], (14777 ^ _781404) ^ [_1040671, _1040673] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1040671, _1040673)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1040671, _1040673), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040673), c_Orderings_Otop__class_Otop(tc_fun(_1040673, tc_HOL_Obool)))))], (24668 ^ _781404) ^ [_1223981, _1223983] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223981, _1223983)), _1223981)))], (4680 ^ _781404) ^ [_852566, _852568, _852570, _852572, _852574, _852576, _852578, _852580] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_852580, _852576, _852572, _852568) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_852578, _852574, _852570, _852566)), _852580 = _852578, _852576 = _852574, _852572 = _852570, _852568 = _852566], (39532 ^ _781404) ^ [_1546225, _1546227] : [-(hAPP(c_Set_Ovimage(_1546225, _1546225, c_Fun_Oid(_1546225)), _1546227) = _1546227)], (39590 ^ _781404) ^ [_1547337, _1547339, _1547341, _1547343, _1547345] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1547337, _1547339, _1547341), _1547343), _1547345) = hAPP(c_Set_OCollect(tc_prod(_1547337, _1547341)), hAPP(c_Product__Type_Oprod_Oprod__case(_1547337, _1547341, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1547341, tc_fun(_1547339, tc_HOL_Obool)), tc_fun(_1547341, tc_HOL_Obool), _1547337), hAPP(c_COMBB(tc_fun(_1547339, tc_HOL_Obool), tc_HOL_Obool, _1547341), c_HOL_OEx(_1547339))), hAPP(hAPP(c_COMBC(_1547337, tc_fun(_1547341, tc_fun(_1547339, tc_HOL_Obool)), tc_fun(_1547341, tc_fun(_1547339, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1547339, tc_HOL_Obool), tc_fun(_1547339, tc_HOL_Obool)), tc_fun(tc_fun(_1547341, tc_fun(_1547339, tc_HOL_Obool)), tc_fun(_1547341, tc_fun(_1547339, tc_HOL_Obool))), _1547337), c_COMBB(tc_fun(_1547339, tc_HOL_Obool), tc_fun(_1547339, tc_HOL_Obool), _1547341)), hAPP(hAPP(c_COMBB(tc_fun(_1547339, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1547339, tc_HOL_Obool), tc_fun(_1547339, tc_HOL_Obool)), _1547337), c_COMBS(_1547339, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547339, tc_HOL_Obool), tc_fun(_1547339, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1547337), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547339), c_fconj)), hAPP(hAPP(c_COMBC(_1547337, tc_fun(tc_prod(_1547337, _1547339), tc_HOL_Obool), tc_fun(_1547339, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547339, tc_fun(tc_fun(tc_prod(_1547337, _1547339), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1547337, _1547339), tc_HOL_Obool), tc_fun(_1547339, tc_HOL_Obool)), _1547337), c_COMBC(_1547339, tc_fun(tc_prod(_1547337, _1547339), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547339, tc_prod(_1547337, _1547339)), tc_fun(_1547339, tc_fun(tc_fun(tc_prod(_1547337, _1547339), tc_HOL_Obool), tc_HOL_Obool)), _1547337), hAPP(c_COMBB(tc_prod(_1547337, _1547339), tc_fun(tc_fun(tc_prod(_1547337, _1547339), tc_HOL_Obool), tc_HOL_Obool), _1547339), c_member(tc_prod(_1547337, _1547339)))), c_Product__Type_OPair(_1547337, _1547339)))), _1547343))))), hAPP(hAPP(c_COMBC(_1547341, tc_fun(tc_prod(_1547339, _1547341), tc_HOL_Obool), tc_fun(_1547339, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547339, tc_fun(tc_fun(tc_prod(_1547339, _1547341), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1547339, _1547341), tc_HOL_Obool), tc_fun(_1547339, tc_HOL_Obool)), _1547341), c_COMBC(_1547339, tc_fun(tc_prod(_1547339, _1547341), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547339, tc_prod(_1547339, _1547341)), tc_fun(_1547339, tc_fun(tc_fun(tc_prod(_1547339, _1547341), tc_HOL_Obool), tc_HOL_Obool)), _1547341), hAPP(c_COMBB(tc_prod(_1547339, _1547341), tc_fun(tc_fun(tc_prod(_1547339, _1547341), tc_HOL_Obool), tc_HOL_Obool), _1547339), c_member(tc_prod(_1547339, _1547341)))), hAPP(c_COMBC(_1547339, _1547341, tc_prod(_1547339, _1547341)), c_Product__Type_OPair(_1547339, _1547341))))), _1547345))))))], (21679 ^ _781404) ^ [_1166843, _1166845, _1166847, _1166849] : [class_Rings_Olinordered__ring__strict(_1166843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166843), c_Groups_Ozero__class_Ozero(_1166843)), _1166845)), 21686 ^ _781404 : [(21693 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166843), _1166847), _1166849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166843), _1166845), _1166847)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166843), _1166845), _1166849))))], (21687 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166843), _1166845), _1166847)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166843), _1166845), _1166849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166843), _1166847), _1166849)))]]], (46528 ^ _781404) ^ [_1716189, _1716191, _1716193] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716189)), hAPP(c_List_Ofilter(_1716189, _1716191), _1716193))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716189)), hAPP(c_List_Ofilter(_1716189, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1716189), c_fNot), _1716191)), _1716193))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716189)), _1716193))], (28859 ^ _781404) ^ [_1298056, _1298058, _1298060] : [class_Fields_Olinordered__field__inverse__zero(_1298056), 28862 ^ _781404 : [(28877 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298056), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298056), _1298058), _1298060)), c_Groups_Ozero__class_Ozero(_1298056)))), 28878 ^ _781404 : [(28885 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298056), _1298058), c_Groups_Ozero__class_Ozero(_1298056))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298056), c_Groups_Ozero__class_Ozero(_1298056)), _1298060))], (28879 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298056), c_Groups_Ozero__class_Ozero(_1298056)), _1298058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298056), _1298060), c_Groups_Ozero__class_Ozero(_1298056)))]]], (28863 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298056), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298056), _1298058), _1298060)), c_Groups_Ozero__class_Ozero(_1298056))), 28868 ^ _781404 : [(28871 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298056), _1298060), c_Groups_Ozero__class_Ozero(_1298056))))], (28869 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298056), c_Groups_Ozero__class_Ozero(_1298056)), _1298058)))]], 28872 ^ _781404 : [(28875 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298056), c_Groups_Ozero__class_Ozero(_1298056)), _1298060)))], (28873 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298056), _1298058), c_Groups_Ozero__class_Ozero(_1298056))))]]]]], (49979 ^ _781404) ^ [_1791581, _1791583] : [c_Equiv__Relations_Oequivp(_1791581, _1791583), 49982 ^ _781404 : [(49987 ^ _781404) ^ [] : [-(c_Predicate_Otransp(_1791581, _1791583))], (49985 ^ _781404) ^ [] : [-(c_Predicate_Osymp(_1791581, _1791583))], (49983 ^ _781404) ^ [] : [-(c_Predicate_Oreflp(_1791581, _1791583))]]], (5917 ^ _781404) ^ [_875220, _875222, _875224, _875226] : [class_Orderings_Oorder(_875220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875220), _875222), _875224)), _875222 = _875226, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875220), _875226), _875224)))], (17529 ^ _781404) ^ [_1093986, _1093988, _1093990] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093986), _1093988)), _1093990) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093986), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093988), _1093990)))], (17457 ^ _781404) ^ [_1092791, _1092793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092791), _1092793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1092791), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1092793)))], (33311 ^ _781404) ^ [_1384181, _1384183, _1384185, _1384187, _1384189] : [-(_1384181 = c_Orderings_Obot__class_Obot(tc_fun(_1384183, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384185, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384183, tc_fun(_1384185, tc_HOL_Obool)), _1384181), _1384187)), _1384189) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384183, tc_fun(_1384185, tc_HOL_Obool)), _1384181), hAPP(hAPP(c_COMBC(_1384183, tc_fun(_1384185, tc_HOL_Obool), tc_fun(_1384185, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1384185, tc_HOL_Obool), tc_fun(tc_fun(_1384185, tc_HOL_Obool), tc_fun(_1384185, tc_HOL_Obool)), _1384183), c_Groups_Ominus__class_Ominus(tc_fun(_1384185, tc_HOL_Obool))), _1384187)), _1384189)))], (38654 ^ _781404) ^ [_1516877, _1516879, _1516881, _1516883] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1516877, _1516879)), hAPP(hAPP(c_Product__Type_OSigma(_1516877, _1516879), _1516881), hAPP(c_COMBK(tc_fun(_1516879, tc_HOL_Obool), _1516877), _1516883)))), -(_1516883 = c_Orderings_Obot__class_Obot(tc_fun(_1516879, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1516877), _1516881)))], (20371 ^ _781404) ^ [_1142971, _1142973] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1142971)), c_Int_OBit1(_1142973)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1142971)), _1142973)))], (2976 ^ _781404) ^ [_825554, _825556, _825558, _825560] : [-(c_Nitpick_OAbs__Frac(_825560, _825556) = c_Nitpick_OAbs__Frac(_825558, _825554)), _825560 = _825558, _825556 = _825554], (36753 ^ _781404) ^ [_1469154, _1469156, _1469158, _1469160] : [class_Orderings_Oorder(_1469154), class_Orderings_Oorder(_1469156), c_Orderings_Oorder__class_Omono(_1469156, _1469154, _1469158), -(c_Orderings_Oord__class_OLeast(_1469154, hAPP(hAPP(c_COMBC(_1469154, tc_fun(_1469154, tc_HOL_Obool), tc_HOL_Obool), c_member(_1469154)), hAPP(c_Set_Oimage(_1469156, _1469154, _1469158), _1469160))) = hAPP(_1469158, c_Orderings_Oord__class_OLeast(_1469156, hAPP(hAPP(c_COMBC(_1469156, tc_fun(_1469156, tc_HOL_Obool), tc_HOL_Obool), c_member(_1469156)), _1469160)))), 36766 ^ _781404 : [(36767 ^ _781404) ^ [_1469438] : [hBOOL(hAPP(hAPP(c_member(_1469156), _1469438), _1469160)), 36771 ^ _781404 : [(36774 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1469156), _1469438), 36770 ^ [_1469154, _1469156, _1469158, _1469160, _1469438]))], (36772 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1469156), 36770 ^ [_1469154, _1469156, _1469158, _1469160, _1469438]), _1469160)))]]]]], (13472 ^ _781404) ^ [_1015775, _1015777, _1015779] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015775), _1015777)), _1015779) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015775), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015777), _1015779)))], (39305 ^ _781404) ^ [_1536293, _1536295] : [-(c_Fun_Oinj__on(tc_fun(_1536293, _1536295), tc_fun(tc_prod(_1536293, _1536295), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1536293, _1536295), tc_HOL_Obool), tc_fun(tc_prod(_1536293, _1536295), tc_HOL_Obool), tc_fun(_1536293, _1536295)), c_Set_OCollect(tc_prod(_1536293, _1536295))), hAPP(hAPP(c_COMBB(tc_fun(_1536293, tc_fun(_1536295, tc_HOL_Obool)), tc_fun(tc_prod(_1536293, _1536295), tc_HOL_Obool), tc_fun(_1536293, _1536295)), c_Product__Type_Oprod_Oprod__case(_1536293, _1536295, tc_HOL_Obool)), hAPP(c_COMBB(_1536295, tc_fun(_1536295, tc_HOL_Obool), _1536293), hAPP(c_COMBC(_1536295, _1536295, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1536293, _1536295), tc_HOL_Obool))))], (13778 ^ _781404) ^ [_1021701, _1021703] : [class_Groups_Olinordered__ab__group__add(_1021701), 13781 ^ _781404 : [(13788 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021701), _1021703), c_Groups_Ozero__class_Ozero(_1021701))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021701), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021701), _1021703), _1021703)), c_Groups_Ozero__class_Ozero(_1021701))))], (13782 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021701), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021701), _1021703), _1021703)), c_Groups_Ozero__class_Ozero(_1021701))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021701), _1021703), c_Groups_Ozero__class_Ozero(_1021701))))]]], (44096 ^ _781404) ^ [_1661253, _1661255, _1661257] : [c_List_Olist_ONil(_1661253) = hAPP(hAPP(c_List_Oappend(_1661253), _1661255), _1661257), 44099 ^ _781404 : [(44102 ^ _781404) ^ [] : [-(_1661257 = c_List_Olist_ONil(_1661253))], (44100 ^ _781404) ^ [] : [-(_1661255 = c_List_Olist_ONil(_1661253))]]], (42027 ^ _781404) ^ [_1608542, _1608544, _1608546, _1608548, _1608550] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608542, _1608542)), hAPP(hAPP(c_Product__Type_OPair(_1608542, _1608542), _1608544), _1608546)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608542, _1608542), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1608548)), _1608550))), 42031 ^ _781404 : [(42034 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608542, _1608542)), hAPP(hAPP(c_Product__Type_OPair(_1608542, _1608542), 42030 ^ [_1608542, _1608544, _1608546, _1608548, _1608550]), _1608546)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608542, _1608542), tc_HOL_Obool), _1608548), _1608550))))], (42032 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608542, _1608542)), hAPP(hAPP(c_Product__Type_OPair(_1608542, _1608542), _1608544), 42030 ^ [_1608542, _1608544, _1608546, _1608548, _1608550])), _1608550)))]]], (44319 ^ _781404) ^ [_1667101, _1667103, _1667105, _1667107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1667101), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667103)), _1667105))), -(hAPP(hAPP(c_List_Olist__update(_1667103, _1667105), _1667101), _1667107) = hAPP(hAPP(c_List_Oappend(_1667103), hAPP(hAPP(c_List_Otake(_1667103), _1667101), _1667105)), hAPP(hAPP(c_List_Olist_OCons(_1667103), _1667107), hAPP(hAPP(c_List_Odrop(_1667103), hAPP(c_Nat_OSuc, _1667101)), _1667105))))], (27329 ^ _781404) ^ [_1269560] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1269560), hAPP(c_Int_Onumber__class_Onumber__of(_1269560), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1269560)), class_Int_Onumber__ring(_1269560), class_Rings_Olinordered__idom(_1269560)], (49102 ^ _781404) ^ [_1771423, _1771425, _1771427, _1771429] : [49104 ^ _781404 : [(49107 ^ _781404) ^ [] : [hBOOL(hAPP(_1771429, 49103 ^ [_1771423, _1771425, _1771427, _1771429]))], (49105 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771423), 49103 ^ [_1771423, _1771425, _1771427, _1771429]), hAPP(c_List_Oset(_1771423), c_List_Oreplicate(_1771423, _1771425, _1771427)))))]], -(hBOOL(hAPP(_1771429, _1771427))), -(_1771425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51898 ^ _781404) ^ [_1831716, _1831718] : [51899 ^ _781404 : [(51902 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831718), _1831716))], (51900 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831716), _1831718)))]], -(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)))), _1831716, _1831718))], (8367 ^ _781404) ^ [_922454, _922456] : [class_Groups_Ogroup__add(_922454), 8370 ^ _781404 : [(8377 ^ _781404) ^ [] : [_922456 = c_Groups_Ozero__class_Ozero(_922454), -(hAPP(c_Groups_Ouminus__class_Ouminus(_922454), _922456) = c_Groups_Ozero__class_Ozero(_922454))], (8371 ^ _781404) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_922454), _922456) = c_Groups_Ozero__class_Ozero(_922454), -(_922456 = c_Groups_Ozero__class_Ozero(_922454))]]], (46499 ^ _781404) ^ [_1715567, _1715569, _1715571] : [hBOOL(hAPP(c_List_Odistinct(_1715567), _1715569)), -(hBOOL(hAPP(c_List_Odistinct(_1715567), hAPP(c_List_Ofilter(_1715567, _1715571), _1715569))))], (44956 ^ _781404) ^ [_1681096, _1681098, _1681100, _1681102, _1681104] : [class_Orderings_Olinorder(_1681096), -(hBOOL(hAPP(hAPP(c_member(_1681096), hAPP(_1681098, _1681100)), hAPP(c_Set_Oimage(_1681102, _1681096, _1681098), hAPP(c_List_Oset(_1681102), _1681104))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1681102, _1681096, _1681098, _1681100, _1681104) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681102, _1681096, _1681098), _1681100), _1681104))], (10721 ^ _781404) ^ [_963489, _963491, _963493, _963495, _963497] : [class_Orderings_Olinorder(_963489), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963489, _963491), _963493) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963489, _963495), _963497), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963489), _963491), _963493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963489), _963495), _963497)), -(_963493 = _963497)], (22521 ^ _781404) ^ [_1183179, _1183181, _1183183] : [class_Rings_Olinordered__ring(_1183179), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183179), c_Groups_Ozero__class_Ozero(_1183179)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183179), _1183181), _1183181)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183179), _1183183), _1183183)))))], (44034 ^ _781404) ^ [_1660147, _1660149, _1660151] : [_1660149 = c_List_Olist_ONil(_1660147), -(hAPP(hAPP(c_List_Oappend(_1660147), _1660149), _1660151) = _1660151)], (46351 ^ _781404) ^ [_1711500, _1711502] : [-(c_List_Oconcat(_1711500, _1711502) = hAPP(c_List_Ofoldl(tc_List_Olist(_1711500), tc_List_Olist(_1711500), c_List_Oappend(_1711500), c_List_Olist_ONil(_1711500)), _1711502))], (15453 ^ _781404) ^ [_1054846, _1054848] : [hAPP(c_Finite__Set_Ocard(_1054846), _1054848) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1054848 = c_Orderings_Obot__class_Obot(tc_fun(_1054846, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054846), _1054848))], (24973 ^ _781404) ^ [_1228768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1228768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1228768))))], (8421 ^ _781404) ^ [_923370, _923372, _923374] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923370, tc_HOL_Obool)), _923372), _923374) = c_Orderings_Obot__class_Obot(tc_fun(_923370, tc_HOL_Obool)), 8424 ^ _781404 : [(8425 ^ _781404) ^ [_923494] : [hBOOL(hAPP(hAPP(c_member(_923370), _923494), _923372)), 8428 ^ _781404 : [(8429 ^ _781404) ^ [_923584] : [hBOOL(hAPP(hAPP(c_member(_923370), _923584), _923374)), _923494 = _923584]]]]], (46782 ^ _781404) ^ [_1722561, _1722563] : [46783 ^ _781404 : [(46786 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1722563), _1722561))], (46784 ^ _781404) ^ [] : [_1722563 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1722561, _1722563) = c_List_Olist_ONil(tc_Nat_Onat))], (47163 ^ _781404) ^ [_1729452, _1729454, _1729456] : [class_Orderings_Olinorder(_1729452), -(c_List_Olinorder__class_Osorted(_1729452, hAPP(c_List_Ofilter(_1729452, hAPP(hAPP(c_COMBC(_1729452, _1729452, tc_HOL_Obool), c_fequal), hAPP(_1729454, _1729456))), _1729456)))], (47867 ^ _781404) ^ [_1744100, _1744102] : [-(c_List_OdropWhile(_1744100, _1744102, c_List_Olist_ONil(_1744100)) = c_List_Olist_ONil(_1744100))], (52318 ^ _781404) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (44455 ^ _781404) ^ [_1670215, _1670217, _1670219, _1670221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1670215), _1670217)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670219)), _1670221))), -(hAPP(hAPP(c_List_Onth(_1670219), hAPP(hAPP(c_List_Odrop(_1670219), _1670215), _1670221)), _1670217) = hAPP(hAPP(c_List_Onth(_1670219), _1670221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1670215), _1670217)))], (27697 ^ _781404) ^ [_1276276, _1276278, _1276280, _1276282] : [_1276280 = _1276282, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1276276, _1276278, hAPP(hAPP(c_Set_Oinsert(_1276276), _1276280), c_Orderings_Obot__class_Obot(tc_fun(_1276276, tc_HOL_Obool)))), _1276282)))], (21859 ^ _781404) ^ [_1170197, _1170199, _1170201, _1170203] : [class_Rings_Olinordered__ring__strict(_1170197), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170197), _1170199), _1170201)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170197), _1170203), c_Groups_Ozero__class_Ozero(_1170197))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170197), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170197), _1170201), _1170203)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170197), _1170199), _1170203))))], (23683 ^ _781404) ^ [_1206808, _1206810] : [-(_1206808 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23686 ^ _781404 : [(23693 ^ _781404) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206810, _1206808) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206810), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1206808)) = 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), _1206810), _1206808))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23687 ^ _781404) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206810, _1206808) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206810), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1206808)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206810), _1206808)))]]], (7239 ^ _781404) ^ [_899056, _899058, _899060] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899056, tc_HOL_Obool)), _899058), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899056, tc_HOL_Obool)), _899060), _899058))))], (48929 ^ _781404) ^ [_1767037, _1767039, _1767041, _1767043, _1767045, _1767047, _1767049] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1767037, _1767039, _1767041, _1767043), _1767045), _1767047), _1767049) = c_New__DSequence_Oneg__bind(_1767037, _1767039, hAPP(hAPP(hAPP(_1767041, _1767045), _1767047), _1767049), hAPP(hAPP(c_COMBC(_1767037, 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(_1767039)))), hAPP(hAPP(c_COMBC(_1767037, 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(_1767039))))), hAPP(hAPP(c_COMBC(_1767037, 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(_1767039)))))), _1767043), _1767045)), _1767047)), _1767049)))], (35541 ^ _781404) ^ [_1444712, _1444714, _1444716] : [-(c_Fun_Oinj__on(tc_prod(_1444712, _1444714), tc_prod(_1444714, _1444712), hAPP(c_Product__Type_Oprod_Oprod__case(_1444712, _1444714, tc_prod(_1444714, _1444712)), hAPP(c_COMBC(_1444714, _1444712, tc_prod(_1444714, _1444712)), c_Product__Type_OPair(_1444714, _1444712))), _1444716))], (39742 ^ _781404) ^ [_1552930, _1552932, _1552934, _1552936, _1552938, _1552940, _1552942] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1552930, _1552932, _1552934, hAPP(hAPP(c_COMBC(_1552930, tc_fun(tc_prod(_1552930, _1552932), tc_HOL_Obool), tc_fun(_1552932, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552932, tc_fun(tc_fun(tc_prod(_1552930, _1552932), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1552930, _1552932), tc_HOL_Obool), tc_fun(_1552932, tc_HOL_Obool)), _1552930), c_COMBC(_1552932, tc_fun(tc_prod(_1552930, _1552932), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552932, tc_prod(_1552930, _1552932)), tc_fun(_1552932, tc_fun(tc_fun(tc_prod(_1552930, _1552932), tc_HOL_Obool), tc_HOL_Obool)), _1552930), hAPP(c_COMBB(tc_prod(_1552930, _1552932), tc_fun(tc_fun(tc_prod(_1552930, _1552932), tc_HOL_Obool), tc_HOL_Obool), _1552932), c_member(tc_prod(_1552930, _1552932)))), c_Product__Type_OPair(_1552930, _1552932)))), _1552936), hAPP(hAPP(c_COMBC(_1552932, tc_fun(tc_prod(_1552932, _1552934), tc_HOL_Obool), tc_fun(_1552934, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552934, tc_fun(tc_fun(tc_prod(_1552932, _1552934), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1552932, _1552934), tc_HOL_Obool), tc_fun(_1552934, tc_HOL_Obool)), _1552932), c_COMBC(_1552934, tc_fun(tc_prod(_1552932, _1552934), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552934, tc_prod(_1552932, _1552934)), tc_fun(_1552934, tc_fun(tc_fun(tc_prod(_1552932, _1552934), tc_HOL_Obool), tc_HOL_Obool)), _1552932), hAPP(c_COMBB(tc_prod(_1552932, _1552934), tc_fun(tc_fun(tc_prod(_1552932, _1552934), tc_HOL_Obool), tc_HOL_Obool), _1552934), c_member(tc_prod(_1552932, _1552934)))), c_Product__Type_OPair(_1552932, _1552934)))), _1552938)), _1552940), _1552942)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1552930, _1552934)), hAPP(hAPP(c_Product__Type_OPair(_1552930, _1552934), _1552940), _1552942)), hAPP(hAPP(c_Relation_Orel__comp(_1552930, _1552932, _1552934), _1552936), _1552938))))], (36604 ^ _781404) ^ [_1465712, _1465714, _1465716] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1465712, _1465714), _1465716)), 36607 ^ _781404 : [(36616 ^ _781404) ^ [] : [-(_1465714 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36619 ^ _781404 : [(36628 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1465714))), 36631 ^ _781404 : [(36634 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1465716)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36632 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1465714), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1465716))))]]], (36620 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1465714)), 36623 ^ _781404 : [(36626 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1465716)), _1465714)))], (36624 ^ _781404) ^ [] : [-(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), _1465716))))]]]]], (36610 ^ _781404) ^ [] : [_1465714 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1465716) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36608 ^ _781404) ^ [] : [-(_1465712 = 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), _1465716)), _1465714)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1465716)))]]], (42715 ^ _781404) ^ [_1628839, _1628841, _1628843, _1628845] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628839) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1628841), hAPP(hAPP(c_List_Olist_OCons(_1628841), _1628843), _1628845)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628839)) = hAPP(hAPP(c_List_Onth(_1628841), _1628845), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628839)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (27051 ^ _781404) ^ [_1264195, _1264197] : [class_Groups_Oordered__ab__group__add__abs(_1264195), 27054 ^ _781404 : [(27061 ^ _781404) ^ [] : [-(_1264197 = c_Groups_Ozero__class_Ozero(_1264195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264195), c_Groups_Ozero__class_Ozero(_1264195)), hAPP(c_Groups_Oabs__class_Oabs(_1264195), _1264197))))], (27055 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264195), c_Groups_Ozero__class_Ozero(_1264195)), hAPP(c_Groups_Oabs__class_Oabs(_1264195), _1264197))), _1264197 = c_Groups_Ozero__class_Ozero(_1264195)]]], (38284 ^ _781404) ^ [_1507640, _1507642, _1507644] : [hBOOL(hAPP(hAPP(c_member(_1507640), _1507642), c_Wellfounded_Oacc(_1507640, _1507644))), 38287 ^ _781404 : [(38288 ^ _781404) ^ [_1507754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1507640, _1507640)), hAPP(hAPP(c_Product__Type_OPair(_1507640, _1507640), _1507754), _1507642)), _1507644)), -(hBOOL(hAPP(hAPP(c_member(_1507640), _1507754), c_Wellfounded_Oacc(_1507640, _1507644))))]]], (39221 ^ _781404) ^ [_1533102, _1533104, _1533106, _1533108, _1533110, _1533112] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1533102), _1533104)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533106), _1533108)), 39231 ^ _781404 : [(39234 ^ _781404) ^ [] : [hAPP(c_Finite__Set_Ocard(_1533102), hAPP(c_Set_OCollect(_1533102), hAPP(hAPP(c_COMBS(_1533102, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533102), c_fconj), hAPP(hAPP(c_COMBC(_1533102, tc_fun(_1533102, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533102)), _1533104))), hAPP(hAPP(c_COMBC(_1533102, _1533106, tc_HOL_Obool), _1533110), 39230 ^ [_1533102, _1533104, _1533106, _1533108, _1533110, _1533112])))) = _1533112], (39232 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1533106), 39230 ^ [_1533102, _1533104, _1533106, _1533108, _1533110, _1533112]), _1533108)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1533102, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1533106, tc_HOL_Obool), tc_Nat_Onat, _1533102), c_Finite__Set_Ocard(_1533106)), hAPP(hAPP(c_COMBB(tc_fun(_1533106, tc_HOL_Obool), tc_fun(_1533106, tc_HOL_Obool), _1533102), c_Set_OCollect(_1533106)), hAPP(hAPP(c_COMBB(tc_fun(_1533106, tc_HOL_Obool), tc_fun(_1533106, tc_HOL_Obool), _1533102), hAPP(c_COMBS(_1533106, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533106), c_fconj), hAPP(hAPP(c_COMBC(_1533106, tc_fun(_1533106, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533106)), _1533108)))), _1533110)))), _1533104) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1533112), hAPP(c_Finite__Set_Ocard(_1533106), _1533108)))], (25245 ^ _781404) ^ [_1233018, _1233020] : [class_Int_Onumber__ring(_1233018), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1233018), _1233020), hAPP(c_Int_Onumber__class_Onumber__of(_1233018), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1233018), _1233020))], (41047 ^ _781404) ^ [_1583321, _1583323] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583321, _1583321), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1583321, _1583323)), hAPP(hAPP(c_Product__Type_OSigma(_1583321, _1583321), hAPP(c_Relation_OField(_1583321), _1583323)), hAPP(c_COMBK(tc_fun(_1583321, tc_HOL_Obool), _1583321), hAPP(c_Relation_OField(_1583321), _1583323))))))], (28819 ^ _781404) ^ [_1297327, _1297329, _1297331] : [class_Fields_Olinordered__field__inverse__zero(_1297327), -(hAPP(c_Groups_Oabs__class_Oabs(_1297327), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297327), _1297329), _1297331)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297327), hAPP(c_Groups_Oabs__class_Oabs(_1297327), _1297329)), hAPP(c_Groups_Oabs__class_Oabs(_1297327), _1297331)))], (49425 ^ _781404) ^ [_1777969, _1777971, _1777973] : [-(c_List_Olist__ex1(_1777969, _1777971, _1777973)), 49426 ^ _781404 : [(49427 ^ _781404) ^ [_1778063] : [hBOOL(hAPP(hAPP(c_member(_1777969), _1778063), hAPP(c_List_Oset(_1777969), _1777973))), hBOOL(hAPP(_1777971, _1778063)), 49435 ^ _781404 : [(49440 ^ _781404) ^ [] : [49434 ^ [_1777969, _1777971, _1777973, _1778063] = _1778063], (49438 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1777971, 49434 ^ [_1777969, _1777971, _1777973, _1778063])))], (49436 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777969), 49434 ^ [_1777969, _1777971, _1777973, _1778063]), hAPP(c_List_Oset(_1777969), _1777973))))]]]]], (41123 ^ _781404) ^ [_1585155, _1585157] : [-(c_Transitive__Closure_Otrancl(_1585155, _1585157) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585155, _1585155), tc_HOL_Obool)), _1585157), hAPP(hAPP(c_Relation_Orel__comp(_1585155, _1585155, _1585155), c_Transitive__Closure_Otrancl(_1585155, _1585157)), _1585157)))], (21699 ^ _781404) ^ [_1167224, _1167226, _1167228] : [class_Rings_Olinordered__semiring__strict(_1167224), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167224), c_Groups_Ozero__class_Ozero(_1167224)), _1167226)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167224), c_Groups_Ozero__class_Ozero(_1167224)), _1167228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167224), c_Groups_Ozero__class_Ozero(_1167224)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167224), _1167226), _1167228))))], (35223 ^ _781404) ^ [_1437331, _1437333, _1437335, _1437337, _1437339, _1437341] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437331, tc_fun(_1437333, tc_HOL_Obool))), _1437335), _1437337), _1437339), _1437341)), -(hBOOL(hAPP(hAPP(_1437335, _1437339), _1437341))), -(hBOOL(hAPP(hAPP(_1437337, _1437339), _1437341)))], (40122 ^ _781404) ^ [_1562009, _1562011, _1562013, _1562015] : [c_Wellfounded_Owf(_1562009, _1562011), c_Fun_Oinj__on(_1562009, _1562013, _1562015, c_Orderings_Otop__class_Otop(tc_fun(_1562009, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1562013, hAPP(c_Set_Oimage(tc_prod(_1562009, _1562009), tc_prod(_1562013, _1562013), c_Product__Type_Omap__pair(_1562009, _1562013, _1562009, _1562013, _1562015, _1562015)), _1562011)))], (34681 ^ _781404) ^ [_1425183, _1425185] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1425183), _1425185)), -(hAPP(c_Finite__Set_Ocard(_1425183), _1425185) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1425183, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1425183), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1425185))], (34881 ^ _781404) ^ [_1429808, _1429810] : [class_Rings_Ocomm__semiring__1(_1429808), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1429808), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429808), c_Groups_Oone__class_Oone(_1429808)), c_Groups_Oone__class_Oone(_1429808))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429808), c_Nat_Osemiring__1__class_Oof__nat(_1429808)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1429810))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1429808), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1429808), _1429810)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429808), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1429808), _1429810)), c_Groups_Oone__class_Oone(_1429808))))], (41149 ^ _781404) ^ [_1586379, _1586381, _1586383, _1586385] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586379, _1586379)), hAPP(hAPP(c_Product__Type_OPair(_1586379, _1586379), _1586383), _1586385)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586379, _1586379), tc_HOL_Obool)), _1586381), c_Relation_OId(_1586379)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1586379, tc_fun(_1586379, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1586379, tc_fun(tc_prod(_1586379, _1586379), tc_HOL_Obool), tc_fun(_1586379, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586379, tc_fun(tc_fun(tc_prod(_1586379, _1586379), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1586379, _1586379), tc_HOL_Obool), tc_fun(_1586379, tc_HOL_Obool)), _1586379), c_COMBC(_1586379, tc_fun(tc_prod(_1586379, _1586379), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586379, tc_prod(_1586379, _1586379)), tc_fun(_1586379, tc_fun(tc_fun(tc_prod(_1586379, _1586379), tc_HOL_Obool), tc_HOL_Obool)), _1586379), hAPP(c_COMBB(tc_prod(_1586379, _1586379), tc_fun(tc_fun(tc_prod(_1586379, _1586379), tc_HOL_Obool), tc_HOL_Obool), _1586379), c_member(tc_prod(_1586379, _1586379)))), c_Product__Type_OPair(_1586379, _1586379)))), _1586381)), c_fequal), _1586383), _1586385)))], (37041 ^ _781404) ^ [_1475872, _1475874, _1475876, _1475878, _1475880, _1475882] : [class_Groups_Oordered__ab__group__add(_1475872), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475874), _1475876)), 37051 ^ _781404 : [(37054 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1475872), c_Groups_Ozero__class_Ozero(_1475872)), hAPP(_1475878, 37050 ^ [_1475872, _1475874, _1475876, _1475878, _1475880, _1475882])))], (37052 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475874), 37050 ^ [_1475872, _1475874, _1475876, _1475878, _1475880, _1475882]), _1475876)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475874, _1475872), _1475878), _1475876) = _1475880, hBOOL(hAPP(hAPP(c_member(_1475874), _1475882), _1475876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1475872), hAPP(_1475878, _1475882)), _1475880)))], (34439 ^ _781404) ^ [_1419538, _1419540, _1419542, _1419544, _1419546] : [_1419538 = c_Orderings_Obot__class_Obot(tc_fun(_1419540, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1419540, tc_fun(_1419542, tc_HOL_Obool)), _1419538), hAPP(hAPP(c_COMBB(tc_fun(_1419542, tc_HOL_Obool), tc_fun(_1419542, tc_HOL_Obool), _1419540), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1419542, tc_HOL_Obool)), _1419544)), _1419546)) = c_Orderings_Otop__class_Otop(tc_fun(_1419542, tc_HOL_Obool)))], (48115 ^ _781404) ^ [_1749563, _1749565] : [-(c_List_Omeasures(_1749563, _1749565) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1749563), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1749563, tc_List_Olist(tc_fun(_1749563, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1749563, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1749563, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1749563), c_List_Omap(tc_fun(_1749563, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1749563, tc_Nat_Onat), _1749563, tc_Nat_Onat), c_COMBI(tc_fun(_1749563, tc_Nat_Onat))))), _1749565)))], (33661 ^ _781404) ^ [_1395211, _1395213, _1395215, _1395217] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395211, tc_fun(_1395213, tc_HOL_Obool)), _1395215), _1395217) = c_Orderings_Obot__class_Obot(tc_fun(_1395213, tc_HOL_Obool)), 33664 ^ _781404 : [(33665 ^ _781404) ^ [_1395327] : [hBOOL(hAPP(hAPP(c_member(_1395211), _1395327), _1395215)), -(hAPP(_1395217, _1395327) = c_Orderings_Obot__class_Obot(tc_fun(_1395213, tc_HOL_Obool)))]]], (52002 ^ _781404) ^ [_1833587, _1833589, _1833591] : [class_Divides_Osemiring__div(_1833587), 52005 ^ _781404 : [(52012 ^ _781404) ^ [] : [c_Divides_Odiv__class_Omod(_1833587, _1833591, _1833589) = c_Groups_Ozero__class_Ozero(_1833587), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833587), _1833589), _1833591)))], (52006 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833587), _1833589), _1833591)), -(c_Divides_Odiv__class_Omod(_1833587, _1833591, _1833589) = c_Groups_Ozero__class_Ozero(_1833587))]]], (38973 ^ _781404) ^ [_1526016] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1526016, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1526016), hAPP(c_COMBK(tc_HOL_Obool, _1526016), c_fTrue)))], (24144 ^ _781404) ^ [_1214430, _1214432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1214432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214430), _1214432)), _1214430)))], (12007 ^ _781404) ^ [_987221, _987223, _987225, _987227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987221, tc_HOL_Obool)), _987223), _987225)), hBOOL(hAPP(hAPP(c_member(_987221), _987227), _987223)), -(hBOOL(hAPP(hAPP(c_member(_987221), _987227), _987225)))], (1246 ^ _781404) ^ [_800019, _800021] : [-(class_Rings_Oordered__ring__abs(_800019)), _800021 = _800019, class_Rings_Oordered__ring__abs(_800021)], (51060 ^ _781404) ^ [_1813346] : [-(c_Fun_Obij__betw(_1813346, _1813346, c_Fun_Oid(_1813346), c_Orderings_Otop__class_Otop(tc_fun(_1813346, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1813346, tc_HOL_Obool))))], (7569 ^ _781404) ^ [_905402, _905404, _905406] : [-(hAPP(hAPP(c_Set_Oinsert(_905402), _905404), hAPP(hAPP(c_Set_Oinsert(_905402), _905404), _905406)) = hAPP(hAPP(c_Set_Oinsert(_905402), _905404), _905406))], (50517 ^ _781404) ^ [_1801752, _1801754, _1801756, _1801758, _1801760] : [hBOOL(hAPP(hAPP(c_member(_1801752), _1801754), hAPP(c_Set_Oimage(_1801756, _1801752, _1801758), _1801760))), -(hAPP(_1801758, hAPP(c_Hilbert__Choice_Oinv__into(_1801756, _1801752, _1801760, _1801758), _1801754)) = _1801754)], (23273 ^ _781404) ^ [_1198220, _1198222, _1198224, _1198226, _1198228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198220), _1198222)), -(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), _1198220), _1198224)), _1198226)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198222), _1198224)), _1198228)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1198226), 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), _1198222), _1198220)), _1198224)), _1198228)))], (42693 ^ _781404) ^ [_1628400, _1628402, _1628404, _1628406] : [-(hAPP(hAPP(c_List_Onth(_1628400), hAPP(hAPP(c_List_Olist_OCons(_1628400), _1628402), _1628404)), hAPP(c_Nat_OSuc, _1628406)) = hAPP(hAPP(c_List_Onth(_1628400), _1628404), _1628406))], (22893 ^ _781404) ^ [_1190743, _1190745] : [_1190743 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1190745), _1190743) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (33873 ^ _781404) ^ [_1401398, _1401400] : [-(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)), _1401398), _1401400))], (25913 ^ _781404) ^ [_1244560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244560)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1244560) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1244560), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (424 ^ _781404) ^ [_787836, _787838, _787840, _787842] : [-(c_Wellfounded_OwfP(_787840, _787836)), c_Wellfounded_OwfP(_787842, _787838), _787842 = _787840, _787838 = _787836], (43455 ^ _781404) ^ [_1647895, _1647897, _1647899] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647895), tc_List_Olist(_1647895))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647895), tc_List_Olist(_1647895)), _1647897), c_List_Olist_ONil(_1647895))), c_List_Olistrel(_1647895, _1647899))), -(_1647897 = c_List_Olist_ONil(_1647895))], (48939 ^ _781404) ^ [_1767451, _1767453, _1767455] : [-(hAPP(c_New__DSequence_Oneg__single(_1767451, _1767453), _1767455) = c_Lazy__Sequence_Ohb__single(_1767451, _1767453))], (41403 ^ _781404) ^ [_1592666, _1592668, _1592670, _1592672] : [hBOOL(hAPP(hAPP(c_member(_1592666), _1592668), c_Wellfounded_Oacc(_1592666, _1592670))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1592666, _1592666)), hAPP(hAPP(c_Product__Type_OPair(_1592666, _1592666), _1592672), _1592668)), c_Transitive__Closure_Ortrancl(_1592666, _1592670))), -(hBOOL(hAPP(hAPP(c_member(_1592666), _1592672), c_Wellfounded_Oacc(_1592666, _1592670))))], (49017 ^ _781404) ^ [_1769137, _1769139, _1769141, _1769143, _1769145] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1769137, _1769139, _1769141), _1769143), _1769145)), -(hBOOL(hAPP(hAPP(_1769141, _1769145), _1769143)))], (43334 ^ _781404) ^ [_1645092, _1645094, _1645096, _1645098] : [hBOOL(hAPP(c_List_Odistinct(_1645092), _1645094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645096), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645092)), _1645094))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645098), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645092)), _1645094))), 43345 ^ _781404 : [(43352 ^ _781404) ^ [] : [_1645096 = _1645098, -(hAPP(hAPP(c_List_Onth(_1645092), _1645094), _1645096) = hAPP(hAPP(c_List_Onth(_1645092), _1645094), _1645098))], (43346 ^ _781404) ^ [] : [hAPP(hAPP(c_List_Onth(_1645092), _1645094), _1645096) = hAPP(hAPP(c_List_Onth(_1645092), _1645094), _1645098), -(_1645096 = _1645098)]]], (52352 ^ _781404) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (43156 ^ _781404) ^ [_1641066, _1641068, _1641070, _1641072, _1641074, _1641076] : [-(_1641066 = _1641068), -(hAPP(hAPP(c_List_Olist__update(_1641070, hAPP(hAPP(c_List_Olist__update(_1641070, _1641072), _1641066), _1641074)), _1641068), _1641076) = hAPP(hAPP(c_List_Olist__update(_1641070, hAPP(hAPP(c_List_Olist__update(_1641070, _1641072), _1641068), _1641076)), _1641066), _1641074))], (27277 ^ _781404) ^ [_1268704, _1268706] : [class_Groups_Oordered__ab__group__add__abs(_1268704), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268704), _1268706), c_Groups_Ozero__class_Ozero(_1268704))), -(hAPP(c_Groups_Oabs__class_Oabs(_1268704), _1268706) = hAPP(c_Groups_Ouminus__class_Ouminus(_1268704), _1268706))], (48807 ^ _781404) ^ [_1764535, _1764537, _1764539] : [c_List_Olist__all(tc_Nat_Onat, _1764535, c_List_Oupt(_1764537, _1764539)), -(c_List_Oall__interval__nat(_1764535, _1764537, _1764539))], (52680 ^ _781404) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (19829 ^ _781404) ^ [_1133560, _1133562] : [class_Int_Onumber__ring(_1133560), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133560), c_Groups_Oone__class_Oone(_1133560)), hAPP(c_Int_Onumber__class_Onumber__of(_1133560), _1133562)) = hAPP(c_Int_Onumber__class_Onumber__of(_1133560), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1133562)))], (23073 ^ _781404) ^ [_1194534, _1194536, _1194538] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194534), _1194536) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194534), _1194538), -(_1194534 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1194536 = _1194538)], (26145 ^ _781404) ^ [_1248284] : [c_Nat__Transfer_Onat__set(_1248284), 26148 ^ _781404 : [(26149 ^ _781404) ^ [_1248350] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1248350), _1248284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248350)))]]], (48901 ^ _781404) ^ [_1766405, _1766407, _1766409, _1766411, _1766413] : [-(_1766405 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1766407, _1766409, _1766411, _1766413), _1766405) = c_Lazy__Sequence_Ohb__bind(_1766407, _1766409, hAPP(_1766411, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1766405), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1766407, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1766409))), _1766413), _1766405)))], (37916 ^ _781404) ^ [_1498160, _1498162] : [c_Equiv__Relations_Oequivp(_1498160, _1498162), 37919 ^ _781404 : [(37926 ^ _781404) ^ [_1498353, _1498355] : [hAPP(_1498162, _1498355) = hAPP(_1498162, _1498353), -(hBOOL(hAPP(hAPP(_1498162, _1498355), _1498353)))], (37920 ^ _781404) ^ [_1498254, _1498256] : [hBOOL(hAPP(hAPP(_1498162, _1498256), _1498254)), -(hAPP(_1498162, _1498256) = hAPP(_1498162, _1498254))]]], (4538 ^ _781404) ^ [_850333, _850335] : [_850335 = _850333, -(c_List_Olist_OCons(_850335) = c_List_Olist_OCons(_850333))], (38586 ^ _781404) ^ [_1515016, _1515018, _1515020, _1515022, _1515024] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1515016, _1515018), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1515016, tc_HOL_Obool)), _1515020), _1515022)), _1515024) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1515016, _1515018), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1515016, _1515018), _1515020), _1515024)), hAPP(hAPP(c_Product__Type_OSigma(_1515016, _1515018), _1515022), _1515024)))], (38963 ^ _781404) ^ [_1525630] : [-(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)), _1525630)))))], (39199 ^ _781404) ^ [_1532510, _1532512, _1532514, _1532516, _1532518, _1532520] : [class_Groups_Ocomm__monoid__add(_1532510), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532512), _1532514)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1532512, _1532510), hAPP(hAPP(c_COMBS(_1532512, _1532510, _1532510), hAPP(hAPP(c_COMBS(_1532512, _1532510, tc_fun(_1532510, _1532510)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1532510, tc_fun(_1532510, _1532510)), _1532512), c_If(_1532510)), _1532516)), _1532518)), _1532520)), _1532514) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1532510), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1532512, _1532510), _1532518), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1532512, tc_HOL_Obool)), _1532514), hAPP(c_Set_OCollect(_1532512), _1532516)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1532512, _1532510), _1532520), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1532512, tc_HOL_Obool)), _1532514), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1532512, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1532512), _1532516))))))], (23667 ^ _781404) ^ [_1206535, _1206537] : [-(_1206535 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23670 ^ _781404 : [(23677 ^ _781404) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206537, _1206535) = 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), _1206537)), _1206535) = 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), _1206537), _1206535))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23671 ^ _781404) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206537, _1206535) = 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), _1206537)), _1206535) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206537), _1206535)))]]], (19671 ^ _781404) ^ [_1131021] : [class_Rings_Osemiring__1(_1131021), -(hBOOL(hAPP(hAPP(c_member(_1131021), c_Groups_Ozero__class_Ozero(_1131021)), c_Nat_Osemiring__1__class_ONats(_1131021))))], (43406 ^ _781404) ^ [_1646857, _1646859] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1646857), _1646859))), -(c_Nitpick_Ocard_H(_1646857, _1646859) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24166 ^ _781404) ^ [_1214813, _1214815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214813)), 24169 ^ _781404 : [(24172 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1214815, _1214813)), _1214813)))], (24170 ^ _781404) ^ [] : [-(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, _1214815, _1214813))))]]], (35894 ^ _781404) ^ [_1451376, _1451378, _1451380] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451376, _1451376), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1451378), _1451380))), -(_1451376 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1451378 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (27367 ^ _781404) ^ [_1270177] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1270177), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1270177) = _1270177)], (11947 ^ _781404) ^ [_986140, _986142] : [hBOOL(hAPP(hAPP(c_member(_986140), _986142), c_Orderings_Obot__class_Obot(tc_fun(_986140, tc_HOL_Obool))))], (34225 ^ _781404) ^ [_1412306, _1412308, _1412310, _1412312] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1412306, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1412308)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1412306, tc_HOL_Obool), tc_Nat_Onat), _1412310), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1412312))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1412306, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1412312, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1412308), _1412312))), _1412310))], (20327 ^ _781404) ^ [_1142177, _1142179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1142177), _1142179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1142177)), c_Int_OBit1(_1142179))))], (7910 ^ _781404) ^ [_912448, _912450, _912452, _912454, _912456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912448, tc_HOL_Obool)), _912450), _912452)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912448, tc_HOL_Obool)), _912454), _912456)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912448, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912448, tc_HOL_Obool)), _912450), _912454)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912448, tc_HOL_Obool)), _912452), _912456))))], (51490 ^ _781404) ^ [_1824165, _1824167, _1824169, _1824171] : [class_Rings_Ocomm__ring(_1824165), class_Rings_Odvd(_1824165), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824165), _1824167), _1824169)), 51501 ^ _781404 : [(51508 ^ _781404) ^ [_1824591, _1824593] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824165), _1824167), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824165), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1824165), _1824593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824165), _1824591), _1824169))), _1824171))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824165), _1824167), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824165), _1824593), _1824171))))], (51502 ^ _781404) ^ [_1824418, _1824420] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824165), _1824167), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824165), _1824420), _1824171))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824165), _1824167), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824165), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1824165), _1824420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824165), _1824418), _1824169))), _1824171))))]]], (942 ^ _781404) ^ [_795519, _795521, _795523, _795525] : [-(c_Predicate_Osymp(_795523, _795519)), c_Predicate_Osymp(_795525, _795521), _795525 = _795523, _795521 = _795519], (48520 ^ _781404) ^ [_1758913, _1758915, _1758917] : [hBOOL(hAPP(hAPP(c_member(_1758913), _1758915), hAPP(c_List_Oset(_1758913), _1758917))), 48525 ^ _781404 : [(48528 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1758913), _1758915), hAPP(c_List_Oset(_1758913), 48523 ^ [_1758913, _1758915, _1758917])))], (48526 ^ _781404) ^ [] : [-(_1758917 = hAPP(hAPP(c_List_Oappend(_1758913), 48523 ^ [_1758913, _1758915, _1758917]), hAPP(hAPP(c_List_Olist_OCons(_1758913), _1758915), 48524 ^ [_1758913, _1758915, _1758917])))]]], (52668 ^ _781404) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (33929 ^ _781404) ^ [_1403714, _1403716, _1403718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403714, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1403714, tc_fun(_1403714, tc_HOL_Obool), tc_HOL_Obool), c_member(_1403714)), _1403716)), hAPP(hAPP(c_COMBC(_1403714, tc_fun(_1403714, tc_HOL_Obool), tc_HOL_Obool), c_member(_1403714)), _1403718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403714, tc_HOL_Obool)), _1403716), _1403718)))], (32576 ^ _781404) ^ [_1368173, _1368175] : [class_Orderings_Olinorder(_1368173), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368173), _1368175)), -(_1368175 = c_Orderings_Obot__class_Obot(tc_fun(_1368173, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1368173), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1368173), 32589 ^ [_1368173, _1368175]), 32590 ^ [_1368173, _1368175])), hAPP(hAPP(c_Set_Oinsert(_1368173), 32589 ^ [_1368173, _1368175]), hAPP(hAPP(c_Set_Oinsert(_1368173), 32590 ^ [_1368173, _1368175]), c_Orderings_Obot__class_Obot(tc_fun(_1368173, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1368173), c_Big__Operators_Olinorder__class_OMax(_1368173, _1368175)), _1368175)))], (33540 ^ _781404) ^ [_1391843, _1391845, _1391847, _1391849, _1391851, _1391853] : [class_Complete__Lattice_Ocomplete__lattice(_1391843), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391845, _1391843), _1391847), hAPP(hAPP(c_COMBB(tc_fun(_1391849, _1391843), _1391843, _1391845), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391849, _1391843), _1391851)), _1391853)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391849, _1391843), _1391851), hAPP(hAPP(c_COMBB(tc_fun(_1391845, _1391843), _1391843, _1391849), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391845, _1391843), _1391847)), hAPP(c_COMBC(_1391845, _1391849, _1391843), _1391853))))], (42204 ^ _781404) ^ [_1613476, _1613478, _1613480] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613476)), c_List_Osublist(_1613476, _1613478, _1613480)) = 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(_1613476)), _1613478)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1613480)))))], (46603 ^ _781404) ^ [_1717632, _1717634, _1717636] : [-(c_List_Oremdups(_1717632, hAPP(c_List_Ofilter(_1717632, _1717634), _1717636)) = hAPP(c_List_Ofilter(_1717632, _1717634), c_List_Oremdups(_1717632, _1717636)))], (18891 ^ _781404) ^ [_1117921, _1117923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117921), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1117921)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1117923)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1117923))], (47950 ^ _781404) ^ [_1745998, _1746000, _1746002] : [47952 ^ _781404 : [(47955 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1746000, 47951 ^ [_1745998, _1746000, _1746002])))], (47953 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745998), 47951 ^ [_1745998, _1746000, _1746002]), hAPP(c_List_Oset(_1745998), c_List_OdropWhile(_1745998, _1746000, _1746002)))))]], -(c_List_OtakeWhile(_1745998, _1746000, _1746002) = hAPP(c_List_Ofilter(_1745998, _1746000), _1746002))], (12388 ^ _781404) ^ [_994824, _994826, _994828, _994830] : [hBOOL(hAPP(hAPP(c_member(_994824), _994826), _994828)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994824, tc_HOL_Obool)), _994828), hAPP(hAPP(c_Set_Oinsert(_994824), _994826), _994830)) = hAPP(hAPP(c_Set_Oinsert(_994824), _994826), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994824, tc_HOL_Obool)), _994828), _994830)))], (24915 ^ _781404) ^ [_1227861, _1227863] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1227861)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1227863)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227861), _1227863)))], (50648 ^ _781404) ^ [_1804975, _1804977, _1804979] : [hAPP(c_Fun_Ocomp(_1804975, _1804977, _1804977, _1804979), c_Hilbert__Choice_Oinv__into(_1804975, _1804977, c_Orderings_Otop__class_Otop(tc_fun(_1804975, tc_HOL_Obool)), _1804979)) = c_Fun_Oid(_1804977), -(hAPP(c_Set_Oimage(_1804975, _1804977, _1804979), c_Orderings_Otop__class_Otop(tc_fun(_1804975, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1804977, tc_HOL_Obool)))], (36326 ^ _781404) ^ [_1459790, _1459792, _1459794, _1459796, _1459798, _1459800] : [c_Finite__Set_Ofolding(_1459790, _1459792, _1459794, _1459796), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459790), _1459798)), -(hAPP(c_Fun_Ocomp(_1459792, _1459792, _1459792, hAPP(_1459794, _1459800)), hAPP(_1459796, _1459798)) = hAPP(c_Fun_Ocomp(_1459792, _1459792, _1459792, hAPP(_1459796, _1459798)), hAPP(_1459794, _1459800)))], (26822 ^ _781404) ^ [_1260130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260130)), 26826 ^ _781404 : [(26829 ^ _781404) ^ [] : [-(_1260130 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 26825 ^ [_1260130]))], (26827 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 26825 ^ [_1260130])))]]], (20793 ^ _781404) ^ [_1150547, _1150549, _1150551, _1150553] : [class_Rings_Ocomm__semiring__1(_1150547), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150547), _1150549), _1150551)), _1150553) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150547), _1150549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150547), _1150551), _1150553)))], (6315 ^ _781404) ^ [_881827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _881827)), _881827))], (41423 ^ _781404) ^ [_1593129, _1593131, _1593133, _1593135] : [c_Wellfounded_Owf(_1593129, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593129, _1593129)), hAPP(hAPP(c_Product__Type_OPair(_1593129, _1593129), _1593131), _1593133)), _1593135)), 41426 ^ _781404 : [(41429 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593129, _1593129)), hAPP(hAPP(c_Product__Type_OPair(_1593129, _1593129), _1593133), _1593131)), c_Transitive__Closure_Ortrancl(_1593129, _1593135)))], (41427 ^ _781404) ^ [] : [-(c_Wellfounded_Owf(_1593129, _1593135))]]], (23445 ^ _781404) ^ [_1202147, _1202149, _1202151, _1202153] : [class_Divides_Osemiring__div(_1202147), -(c_Divides_Odiv__class_Omod(_1202147, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202147), _1202149), _1202151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202147), _1202149), _1202153)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202147), _1202149), c_Divides_Odiv__class_Omod(_1202147, _1202151, _1202153)))], (45489 ^ _781404) ^ [_1692757, _1692759] : [_1692757 = _1692759, -(hAPP(c_Code__Numeral_Oof__nat, _1692757) = hAPP(c_Code__Numeral_Oof__nat, _1692759))], (30065 ^ _781404) ^ [_1320496, _1320498, _1320500, _1320502] : [class_Groups_Ocomm__monoid__mult(_1320496), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320498), _1320500)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1320498, _1320496), _1320502), _1320500) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1320496, _1320498, c_Groups_Otimes__class_Otimes(_1320496)), _1320502), c_Groups_Oone__class_Oone(_1320496)), _1320500))], (39524 ^ _781404) ^ [_1546106, _1546108, _1546110] : [c_Predicate_Oreflp(_1546106, _1546108), -(hBOOL(hAPP(hAPP(_1546108, _1546110), _1546110)))], (32959 ^ _781404) ^ [_1375535] : [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), _1375535))), 32962 ^ _781404 : [(32969 ^ _781404) ^ [] : [-(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), _1375535))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375535)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375535)), 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), _1375535)))))], (32963 ^ _781404) ^ [] : [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), _1375535)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375535)) = 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), _1375535))))]]], (20011 ^ _781404) ^ [_1136871] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136871)))], (16398 ^ _781404) ^ [_1072792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1072792)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1072792), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1072792)], (3552 ^ _781404) ^ [_834502, _834504] : [_834504 = _834502, -(c_SetInterval_Oord__class_OlessThan(_834504) = c_SetInterval_Oord__class_OlessThan(_834502))], (21369 ^ _781404) ^ [_1161189, _1161191, _1161193, _1161195, _1161197] : [class_Rings_Oordered__semiring(_1161189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161189), _1161191), _1161193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161189), _1161195), _1161197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161189), c_Groups_Ozero__class_Ozero(_1161189)), _1161191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161189), c_Groups_Ozero__class_Ozero(_1161189)), _1161195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161189), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161189), _1161191), _1161195)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161189), _1161193), _1161197))))], (45908 ^ _781404) ^ [_1702047, _1702049, _1702051, _1702053, _1702055, _1702057, _1702059] : [c_List_Olist__all2(_1702047, _1702049, _1702051, hAPP(hAPP(c_List_Omap(_1702053, _1702047), _1702055), _1702057), _1702059), -(c_List_Olist__all2(_1702053, _1702049, hAPP(hAPP(c_COMBB(_1702047, tc_fun(_1702049, tc_HOL_Obool), _1702053), _1702051), _1702055), _1702057, _1702059))], (37573 ^ _781404) ^ [_1489635, _1489637, _1489639, _1489641] : [c_Fun_Oinj__on(_1489635, tc_fun(tc_fun(_1489635, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1489635, tc_fun(tc_prod(_1489635, _1489635), tc_HOL_Obool), tc_fun(tc_fun(_1489635, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1489635, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1489635, _1489635), tc_HOL_Obool), tc_fun(tc_fun(_1489635, tc_HOL_Obool), tc_HOL_Obool)), _1489635), c_Equiv__Relations_Oquotient(_1489635)), hAPP(hAPP(c_COMBC(_1489635, tc_fun(_1489635, tc_HOL_Obool), tc_fun(_1489635, tc_HOL_Obool)), c_Set_Oinsert(_1489635)), c_Orderings_Obot__class_Obot(tc_fun(_1489635, tc_HOL_Obool))))), _1489637), _1489639), hBOOL(hAPP(hAPP(c_member(_1489635), _1489641), _1489639)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1489635), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1489635, tc_HOL_Obool)), _1489639), hAPP(hAPP(c_Set_Oinsert(_1489635), _1489641), c_Orderings_Obot__class_Obot(tc_fun(_1489635, tc_HOL_Obool))))), _1489637) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1489635, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1489635), _1489639), _1489637)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1489635), hAPP(hAPP(c_Set_Oinsert(_1489635), _1489641), c_Orderings_Obot__class_Obot(tc_fun(_1489635, tc_HOL_Obool)))), _1489637)))], (19486 ^ _781404) ^ [_1127919, _1127921] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1127919)), _1127921) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1127919), _1127921)))], (49541 ^ _781404) ^ [_1780809, _1780811, _1780813] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1780809) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1780809, _1780811, _1780813)], (33516 ^ _781404) ^ [_1391224, _1391226, _1391228, _1391230, _1391232, _1391234] : [-(hAPP(hAPP(c_Fun_Ocomp(_1391224, _1391226, _1391228, _1391230), _1391232), _1391234) = hAPP(_1391230, hAPP(_1391232, _1391234)))], (9062 ^ _781404) ^ [_935047, _935049, _935051] : [class_Groups_Oab__group__add(_935047), 9065 ^ _781404 : [(9072 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_935047), _935049), _935051) = c_Groups_Ozero__class_Ozero(_935047), -(_935049 = _935051)], (9066 ^ _781404) ^ [] : [_935049 = _935051, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_935047), _935049), _935051) = c_Groups_Ozero__class_Ozero(_935047))]]], (9511 ^ _781404) ^ [_944351, _944353, _944355, _944357] : [class_Orderings_Opreorder(_944351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944351), _944353), _944355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944351), _944355), _944357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944351), _944353), _944357)))], (27646 ^ _781404) ^ [_1275145, _1275147, _1275149, _1275151, _1275153, _1275155, _1275157] : [c_Finite__Set_Ofun__left__comm(_1275145, _1275147, _1275149), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1275145, _1275147, _1275149, _1275151, _1275153), _1275155)), hBOOL(hAPP(hAPP(c_member(_1275145), _1275157), _1275153)), 27658 ^ _781404 : [(27661 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1275145, _1275147, _1275149, _1275151, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1275145, tc_HOL_Obool)), _1275153), hAPP(hAPP(c_Set_Oinsert(_1275145), _1275157), c_Orderings_Obot__class_Obot(tc_fun(_1275145, tc_HOL_Obool))))), 27657 ^ [_1275145, _1275147, _1275149, _1275151, _1275153, _1275155, _1275157])))], (27659 ^ _781404) ^ [] : [-(_1275155 = hAPP(hAPP(_1275149, _1275157), 27657 ^ [_1275145, _1275147, _1275149, _1275151, _1275153, _1275155, _1275157]))]]], (21517 ^ _781404) ^ [_1163977, _1163979, _1163981] : [class_Rings_Oordered__cancel__semiring(_1163977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163977), c_Groups_Ozero__class_Ozero(_1163977)), _1163979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163977), c_Groups_Ozero__class_Ozero(_1163977)), _1163981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163977), c_Groups_Ozero__class_Ozero(_1163977)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163977), _1163979), _1163981))))], (45722 ^ _781404) ^ [_1697346, _1697348] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1697346), _1697348) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1697346)), hAPP(c_Code__Numeral_Onat__of, _1697348))))], (32128 ^ _781404) ^ [_1359673, _1359675, _1359677, _1359679] : [class_Orderings_Olinorder(_1359673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359673), _1359675), _1359677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359673), _1359679), _1359677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359673), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359673), _1359675), _1359679)), _1359677)))], (8072 ^ _781404) ^ [_916598, _916600, _916602] : [class_Lattices_Oboolean__algebra(_916598), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916598), _916600), _916602) = c_Orderings_Obot__class_Obot(_916598), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916598), _916600), _916602) = c_Orderings_Otop__class_Otop(_916598), -(hAPP(c_Groups_Ouminus__class_Ouminus(_916598), _916600) = _916602)], (52542 ^ _781404) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (13570 ^ _781404) ^ [_1017814, _1017816, _1017818, _1017820, _1017822] : [class_Groups_Ocomm__monoid__add(_1017814), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017816), _1017818)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017816), _1017820)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1017816, tc_HOL_Obool)), _1017818), _1017820) = c_Orderings_Obot__class_Obot(tc_fun(_1017816, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1017816, _1017814), _1017822), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017816, tc_HOL_Obool)), _1017818), _1017820)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017814), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1017816, _1017814), _1017822), _1017818)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1017816, _1017814), _1017822), _1017820)))], (43597 ^ _781404) ^ [_1650301] : [-(hAPP(c_List_Oset(_1650301), c_List_Olist_ONil(_1650301)) = c_Orderings_Obot__class_Obot(tc_fun(_1650301, tc_HOL_Obool)))], (32014 ^ _781404) ^ [_1357748, _1357750] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1357748)), hAPP(c_Nat_OSuc, _1357750)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1357748), _1357750)))], (30766 ^ _781404) ^ [_1334477, _1334479, _1334481] : [class_Orderings_Olinorder(_1334477), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334477), _1334479), _1334481)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334477), _1334479), _1334481) = _1334479)], (25085 ^ _781404) ^ [_1230434] : [-(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), _1230434)) = 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), _1230434))))], (23417 ^ _781404) ^ [_1201505, _1201507, _1201509, _1201511] : [class_Divides_Oring__div(_1201505), -(c_Divides_Odiv__class_Omod(_1201505, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201505), _1201507), _1201509), _1201511) = c_Divides_Odiv__class_Omod(_1201505, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201505), _1201507), c_Divides_Odiv__class_Omod(_1201505, _1201509, _1201511)), _1201511))], (39711 ^ _781404) ^ [_1551264, _1551266, _1551268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1551264, _1551264), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1551264, _1551264, _1551264), _1551266), _1551268)), _1551266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1551264, tc_HOL_Obool), tc_fun(_1551264, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1551264, tc_HOL_Obool), tc_fun(_1551264, tc_HOL_Obool), tc_fun(_1551264, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1551264, _1551266)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1551264, tc_HOL_Obool), tc_fun(_1551264, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1551264, _1551268)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1551264, tc_HOL_Obool), tc_fun(_1551264, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1551264, tc_HOL_Obool), tc_fun(_1551264, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1551264, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1551264, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1551264, tc_HOL_Obool), tc_fun(_1551264, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1551264, _1551266))))], (5172 ^ _781404) ^ [_860306, _860308, _860310, _860312] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_860312, _860308) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_860310, _860306)), _860312 = _860310, _860308 = _860306], (43769 ^ _781404) ^ [_1653781, _1653783, _1653785, _1653787] : [-(hAPP(c_List_Olist_Olist__case(_1653781, _1653783, _1653785, _1653787), c_List_Olist_ONil(_1653783)) = _1653785)], (10661 ^ _781404) ^ [_962606, _962608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962606), _962608)), 10664 ^ _781404 : [(10667 ^ _781404) ^ [] : [_962606 = _962608], (10665 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962606), _962608)))]]], (10629 ^ _781404) ^ [_962092, _962094, _962096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962092), _962094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962094), _962096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962092)), _962096)))], (12420 ^ _781404) ^ [_995595, _995597, _995599, _995601] : [hBOOL(hAPP(hAPP(c_member(_995595), _995597), _995599)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995595, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_995595), _995597), _995601)), _995599) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995595, tc_HOL_Obool)), _995601), _995599))], (22315 ^ _781404) ^ [_1179253, _1179255, _1179257, _1179259] : [class_Rings_Olinordered__semiring__strict(_1179253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179253), _1179255), _1179257)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179253), _1179255), _1179259))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179253), c_Groups_Ozero__class_Ozero(_1179253)), _1179255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179253), _1179257), _1179259)))], (17557 ^ _781404) ^ [_1094467, _1094469, _1094471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094467), _1094469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094469), _1094471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094467), _1094471)))], (40132 ^ _781404) ^ [_1562200, _1562202, _1562204] : [-(hAPP(c_Relation_ODomain(_1562200, _1562202), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1562200, _1562202), tc_HOL_Obool), _1562204)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1562200, _1562202), tc_HOL_Obool), tc_fun(_1562200, tc_HOL_Obool)), _1562204), c_Relation_ODomain(_1562200, _1562202)))], (38692 ^ _781404) ^ [_1517627, _1517629, _1517631, _1517633] : [-(_1517627 = c_Orderings_Obot__class_Obot(tc_fun(_1517629, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1517629, _1517631), _1517631, c_Product__Type_Osnd(_1517629, _1517631)), hAPP(hAPP(c_Product__Type_OSigma(_1517629, _1517631), _1517627), hAPP(c_COMBK(tc_fun(_1517631, tc_HOL_Obool), _1517629), _1517633))) = _1517633)], (37520 ^ _781404) ^ [_1488212, _1488214, _1488216] : [-(hAPP(c_Relation_OField(_1488212), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1488212, _1488212), tc_HOL_Obool)), _1488214), _1488216)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488212, tc_HOL_Obool)), hAPP(c_Relation_OField(_1488212), _1488214)), hAPP(c_Relation_OField(_1488212), _1488216)))], (15090 ^ _781404) ^ [_1047540, _1047542] : [class_Rings_Ocomm__semiring__1(_1047540), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047540), _1047542), c_Groups_Ozero__class_Ozero(_1047540)) = _1047542)], (31808 ^ _781404) ^ [_1353662, _1353664] : [-(_1353662 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1353664, _1353662) = c_Nitpick_Onat__gcd(_1353662, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1353664, _1353662)))], (7401 ^ _781404) ^ [_902198, _902200] : [class_Groups_Oordered__ab__group__add(_902198), -(hAPP(c_Set_Oimage(_902198, _902198, c_Groups_Ouminus__class_Ouminus(_902198)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_902198), _902200)) = hAPP(c_SetInterval_Oord__class_OlessThan(_902198), hAPP(c_Groups_Ouminus__class_Ouminus(_902198), _902200)))], (47800 ^ _781404) ^ [_1742652] : [-(c_List_Oembed__list(_1742652) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1742652))], (5044 ^ _781404) ^ [_858318, _858320, _858322, _858324, _858326, _858328, _858330, _858332] : [-(c_Fun_Othe__inv__into(_858332, _858328, _858324, _858320) = c_Fun_Othe__inv__into(_858330, _858326, _858322, _858318)), _858332 = _858330, _858328 = _858326, _858324 = _858322, _858320 = _858318], (38266 ^ _781404) ^ [_1506797, _1506799, _1506801] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1506797, hAPP(hAPP(c_COMBC(_1506797, tc_fun(tc_prod(_1506797, _1506797), tc_HOL_Obool), tc_fun(_1506797, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506797, tc_fun(tc_fun(tc_prod(_1506797, _1506797), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1506797, _1506797), tc_HOL_Obool), tc_fun(_1506797, tc_HOL_Obool)), _1506797), c_COMBC(_1506797, tc_fun(tc_prod(_1506797, _1506797), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506797, tc_prod(_1506797, _1506797)), tc_fun(_1506797, tc_fun(tc_fun(tc_prod(_1506797, _1506797), tc_HOL_Obool), tc_HOL_Obool)), _1506797), hAPP(c_COMBB(tc_prod(_1506797, _1506797), tc_fun(tc_fun(tc_prod(_1506797, _1506797), tc_HOL_Obool), tc_HOL_Obool), _1506797), c_member(tc_prod(_1506797, _1506797)))), c_Product__Type_OPair(_1506797, _1506797)))), _1506799)), _1506801)), -(hBOOL(hAPP(hAPP(c_member(_1506797), _1506801), c_Wellfounded_Oacc(_1506797, _1506799))))], (4712 ^ _781404) ^ [_853088, _853090] : [_853090 = _853088, -(c_DSequence_Oempty(_853090) = c_DSequence_Oempty(_853088))], (48609 ^ _781404) ^ [_1760635, _1760637, _1760639] : [c_List_Olist__ex(tc_Nat_Onat, _1760635, c_List_Oupt(_1760637, _1760639)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1760635), _1760637, _1760639)], (14083 ^ _781404) ^ [_1027095, _1027097, _1027099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027095), _1027097)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027099), _1027097)), _1027095) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027099), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027097), _1027095)))], (43767 ^ _781404) ^ [_1653726, _1653728, _1653730, _1653732, _1653734, _1653736] : [-(hAPP(c_List_Olist_Olist__case(_1653726, _1653728, _1653730, _1653732), hAPP(hAPP(c_List_Olist_OCons(_1653728), _1653734), _1653736)) = hAPP(hAPP(_1653732, _1653734), _1653736))], (20675 ^ _781404) ^ [_1147878] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147878)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147878)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1147878)))], (8227 ^ _781404) ^ [_919797] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _919797), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (6641 ^ _781404) ^ [_887639, _887641, _887643] : [class_Orderings_Oorder(_887639), class_Orderings_Oorder(_887641), c_Orderings_Oorder__class_Ostrict__mono(_887641, _887639, _887643), -(c_Orderings_Oorder__class_Omono(_887641, _887639, _887643))], (8265 ^ _781404) ^ [_920583, _920585, _920587, _920589, _920591] : [-(hAPP(hAPP(c_Set_Oinsert(_920583), _920585), hAPP(hAPP(c_Set_Oinsert(_920583), _920587), c_Orderings_Obot__class_Obot(tc_fun(_920583, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_920583), _920589), hAPP(hAPP(c_Set_Oinsert(_920583), _920591), c_Orderings_Obot__class_Obot(tc_fun(_920583, tc_HOL_Obool))))), 8266 ^ _781404 : [(8273 ^ _781404) ^ [] : [_920585 = _920591, _920587 = _920589], (8267 ^ _781404) ^ [] : [_920585 = _920589, _920587 = _920591]]], (5829 ^ _781404) ^ [_873845, _873847, _873849] : [_873845 = _873847, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873849, tc_HOL_Obool)), _873845), _873847)))], (34285 ^ _781404) ^ [_1415618, _1415620, _1415622, _1415624, _1415626] : [-(_1415618 = c_Orderings_Obot__class_Obot(tc_fun(_1415620, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415620, tc_fun(_1415622, tc_HOL_Obool)), _1415618), hAPP(hAPP(c_COMBB(tc_fun(_1415622, tc_HOL_Obool), tc_fun(_1415622, tc_HOL_Obool), _1415620), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415622, tc_HOL_Obool)), _1415624)), _1415626)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415622, tc_HOL_Obool)), _1415624), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415620, tc_fun(_1415622, tc_HOL_Obool)), _1415618), _1415626)))], (228 ^ _781404) ^ [_785006, _785008] : [-(class_Rings_Odivision__ring__inverse__zero(_785006)), _785008 = _785006, class_Rings_Odivision__ring__inverse__zero(_785008)], (51714 ^ _781404) ^ [_1828464, _1828466, _1828468, _1828470, _1828472] : [class_Divides_Osemiring__div(_1828464), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828464), _1828466), _1828468)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828464), _1828470), _1828472)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828464), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1828464), _1828468), _1828466)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1828464), _1828472), _1828470)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1828464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828464), _1828468), _1828472)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828464), _1828466), _1828470)))], (44609 ^ _781404) ^ [_1673703, _1673705, _1673707] : [-(hAPP(hAPP(c_List_Odrop(_1673703), _1673705), hAPP(c_List_Otl(_1673703), _1673707)) = hAPP(c_List_Otl(_1673703), hAPP(hAPP(c_List_Odrop(_1673703), _1673705), _1673707)))], (36336 ^ _781404) ^ [_1460003, _1460005, _1460007, _1460009, _1460011, _1460013, _1460015, _1460017] : [c_Finite__Set_Ofolding(_1460003, _1460005, _1460007, _1460009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460003), _1460011)), -(hAPP(c_Fun_Ocomp(_1460005, _1460005, _1460013, hAPP(_1460007, _1460015)), hAPP(c_Fun_Ocomp(_1460005, _1460005, _1460013, hAPP(_1460009, _1460011)), _1460017)) = hAPP(c_Fun_Ocomp(_1460005, _1460005, _1460013, hAPP(_1460009, _1460011)), hAPP(c_Fun_Ocomp(_1460005, _1460005, _1460013, hAPP(_1460007, _1460015)), _1460017)))], (9791 ^ _781404) ^ [_948672, _948674, _948676] : [class_Orderings_Olinorder(_948672), 9794 ^ _781404 : [(9801 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948672), _948674), _948676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_948672, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_948672), _948674)), hAPP(c_SetInterval_Oord__class_OlessThan(_948672), _948676))))], (9795 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_948672, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_948672), _948674)), hAPP(c_SetInterval_Oord__class_OlessThan(_948672), _948676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948672), _948674), _948676)))]]], (33376 ^ _781404) ^ [_1385837, _1385839, _1385841, _1385843, _1385845, _1385847] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385837, tc_fun(_1385839, tc_fun(_1385841, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1385837, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1385839, _1385841), tc_HOL_Obool), tc_fun(_1385839, tc_fun(_1385841, tc_HOL_Obool)), _1385837), hAPP(c_COMBC(_1385839, tc_fun(tc_prod(_1385839, _1385841), tc_HOL_Obool), tc_fun(_1385841, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1385841, tc_fun(tc_fun(tc_prod(_1385839, _1385841), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1385839, _1385841), tc_HOL_Obool), tc_fun(_1385841, tc_HOL_Obool)), _1385839), c_COMBC(_1385841, tc_fun(tc_prod(_1385839, _1385841), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1385841, tc_prod(_1385839, _1385841)), tc_fun(_1385841, tc_fun(tc_fun(tc_prod(_1385839, _1385841), tc_HOL_Obool), tc_HOL_Obool)), _1385839), hAPP(c_COMBB(tc_prod(_1385839, _1385841), tc_fun(tc_fun(tc_prod(_1385839, _1385841), tc_HOL_Obool), tc_HOL_Obool), _1385841), c_member(tc_prod(_1385839, _1385841)))), c_Product__Type_OPair(_1385839, _1385841))))), _1385843)), _1385845), _1385847)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1385839, _1385841)), hAPP(hAPP(c_Product__Type_OPair(_1385839, _1385841), _1385845), _1385847)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385837, tc_fun(tc_prod(_1385839, _1385841), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1385837, tc_HOL_Obool))), _1385843))))], (50973 ^ _781404) ^ [_1811877, _1811879, _1811881, _1811883, _1811885] : [c_Fun_Obij__betw(_1811877, _1811879, _1811881, _1811883, _1811885), -(c_Fun_Oinj__on(_1811877, _1811879, _1811881, _1811883))], (37298 ^ _781404) ^ [_1481945, _1481947, _1481949, _1481951] : [c_FunDef_Oreduction__pair(_1481945, _1481947), -(c_FunDef_Oreduction__pair(_1481949, hAPP(hAPP(c_FunDef_Orp__inv__image(_1481945, _1481949), _1481947), _1481951)))], (52290 ^ _781404) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (3704 ^ _781404) ^ [_836946, _836948, _836950, _836952] : [-(c_List_Otranspose(_836952, _836948) = c_List_Otranspose(_836950, _836946)), _836952 = _836950, _836948 = _836946], (7297 ^ _781404) ^ [_900240, _900242, _900244] : [class_Orderings_Olinorder(_900240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900240), _900242), _900244)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900240, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_900240, _900242), _900244)), hAPP(c_SetInterval_Oord__class_OatLeast(_900240), _900244)) = hAPP(c_SetInterval_Oord__class_OatLeast(_900240), _900242))], (51129 ^ _781404) ^ [_1814930, _1814932, _1814934, _1814936, _1814938, _1814940] : [c_Fun_Oinj__on(_1814930, _1814932, _1814934, _1814936), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814932, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1814930, _1814932, _1814934), _1814936)), _1814938)), c_Fun_Oinj__on(_1814932, _1814930, _1814940, _1814938), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814930, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1814932, _1814930, _1814940), _1814938)), _1814936)), -(c_Fun_Obij__betw(_1814930, _1814932, 51144 ^ [_1814930, _1814932, _1814934, _1814936, _1814938, _1814940], _1814936, _1814938))], (12017 ^ _781404) ^ [_987406, _987408, _987410, _987412] : [hBOOL(hAPP(hAPP(c_member(_987406), _987408), _987410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987406, tc_HOL_Obool)), _987410), _987412)), -(hBOOL(hAPP(hAPP(c_member(_987406), _987408), _987412)))], (7437 ^ _781404) ^ [_902837, _902839] : [class_Lattices_Obounded__lattice__top(_902837), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_902837), _902839), c_Orderings_Otop__class_Otop(_902837)) = _902839)], (18239 ^ _781404) ^ [_1106369, _1106371, _1106373, _1106375] : [class_Rings_Olinordered__semidom(_1106369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1106371), _1106373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106369), c_Groups_Oone__class_Oone(_1106369)), _1106375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106369), hAPP(hAPP(c_Power_Opower__class_Opower(_1106369), _1106375), _1106371)), hAPP(hAPP(c_Power_Opower__class_Opower(_1106369), _1106375), _1106373))))], (33528 ^ _781404) ^ [_1391538, _1391540, _1391542, _1391544, _1391546, _1391548, _1391550, _1391552] : [hAPP(c_Fun_Ocomp(_1391538, _1391540, _1391542, _1391544), _1391546) = hAPP(c_Fun_Ocomp(_1391548, _1391540, _1391542, _1391550), _1391552), 33531 ^ _781404 : [(33532 ^ _781404) ^ [_1391653] : [-(hAPP(_1391544, hAPP(_1391546, _1391653)) = hAPP(_1391550, hAPP(_1391552, _1391653)))]]], (37242 ^ _781404) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (13474 ^ _781404) ^ [_1015826, _1015828, _1015830] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015826), _1015828)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015826), _1015830)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015828), _1015830))], (9138 ^ _781404) ^ [_936651, _936653, _936655, _936657] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936651, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936651, tc_HOL_Obool)), _936653), _936655)), _936657) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936651, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936651, tc_HOL_Obool)), _936653), _936657)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936651, tc_HOL_Obool)), _936655), _936657)))], (38530 ^ _781404) ^ [_1513252, _1513254, _1513256, _1513258] : [hAPP(hAPP(c_Product__Type_OSigma(_1513252, _1513254), _1513256), hAPP(c_COMBK(tc_fun(_1513254, tc_HOL_Obool), _1513252), _1513258)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513252, _1513254), tc_HOL_Obool)), -(_1513256 = c_Orderings_Obot__class_Obot(tc_fun(_1513252, tc_HOL_Obool))), -(_1513258 = c_Orderings_Obot__class_Obot(tc_fun(_1513254, tc_HOL_Obool)))], (43278 ^ _781404) ^ [_1643989, _1643991] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1643989, _1643991))))], (17395 ^ _781404) ^ [_1091708, _1091710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1091710), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091708), _1091710)))], (39612 ^ _781404) ^ [_1548426, _1548428, _1548430, _1548432, _1548434, _1548436, _1548438] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1548426, _1548428, _1548430), _1548432), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1548434, tc_fun(tc_prod(_1548428, _1548430), tc_HOL_Obool)), _1548436), _1548438)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1548434, tc_fun(tc_prod(_1548426, _1548430), tc_HOL_Obool)), _1548436), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1548428, _1548430), tc_HOL_Obool), tc_fun(tc_prod(_1548426, _1548430), tc_HOL_Obool), _1548434), hAPP(c_Relation_Orel__comp(_1548426, _1548428, _1548430), _1548432)), _1548438)))], (50578 ^ _781404) ^ [_1803214, _1803216, _1803218, _1803220, _1803222] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1803214, _1803216, _1803218, _1803220), _1803222) = c_Hilbert__Choice_OEps(_1803214, hAPP(hAPP(c_COMBS(_1803214, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1803214), c_fconj), hAPP(hAPP(c_COMBC(_1803214, tc_fun(_1803214, tc_HOL_Obool), tc_HOL_Obool), c_member(_1803214)), _1803218))), hAPP(hAPP(c_COMBC(_1803214, _1803216, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1803216, tc_fun(_1803216, tc_HOL_Obool), _1803214), c_fequal), _1803220)), _1803222))))], (12446 ^ _781404) ^ [_996080, _996082, _996084] : [class_Orderings_Oord(_996080), 12449 ^ _781404 : [(12456 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996080), _996082), _996084)), -(hBOOL(hAPP(hAPP(c_member(_996080), _996082), hAPP(c_SetInterval_Oord__class_OlessThan(_996080), _996084))))], (12450 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_996080), _996082), hAPP(c_SetInterval_Oord__class_OlessThan(_996080), _996084))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996080), _996082), _996084)))]]], (17489 ^ _781404) ^ [_1093401, _1093403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1093401), _1093403)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093401), _1093403)))], (39999 ^ _781404) ^ [_1558992, _1558994, _1558996] : [_1558996 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1558992, _1558994), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1558992, _1558994), _1558996) = c_Orderings_Obot__class_Obot(tc_fun(_1558992, tc_HOL_Obool)))], (43154 ^ _781404) ^ [_1640977, _1640979, _1640981, _1640983, _1640985, _1640987] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1640977, _1640979), hAPP(hAPP(c_List_Ozip(_1640977, _1640979), _1640981), _1640983)), _1640985), _1640987) = hAPP(hAPP(c_List_Ozip(_1640977, _1640979), hAPP(hAPP(c_List_Olist__update(_1640977, _1640981), _1640985), hAPP(c_Product__Type_Ofst(_1640977, _1640979), _1640987))), hAPP(hAPP(c_List_Olist__update(_1640979, _1640983), _1640985), hAPP(c_Product__Type_Osnd(_1640977, _1640979), _1640987))))], (25642 ^ _781404) ^ [_1239566, _1239568, _1239570] : [-(hBOOL(hAPP(_1239566, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1239568, _1239570)))), 25645 ^ _781404 : [(25648 ^ _781404) ^ [] : [hBOOL(hAPP(_1239566, _1239568))], (25646 ^ _781404) ^ [] : [-(_1239570 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25649 ^ _781404 : [(25654 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25652 ^ [_1239566, _1239568, _1239570]), _1239570)))], (25656 ^ _781404) ^ [] : [-(_1239568 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239570), 25651 ^ [_1239566, _1239568, _1239570])), 25652 ^ [_1239566, _1239568, _1239570]))], (25658 ^ _781404) ^ [] : [hBOOL(hAPP(_1239566, 25652 ^ [_1239566, _1239568, _1239570]))], (25650 ^ _781404) ^ [] : [_1239570 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (46945 ^ _781404) ^ [_1725902, _1725904, _1725906] : [class_Orderings_Olinorder(_1725902), c_List_Olinorder__class_Osorted(_1725902, _1725904), -(c_List_Olinorder__class_Osorted(_1725902, c_List_Olinorder__class_Oinsort__insert__key(_1725902, _1725902, c_COMBI(_1725902), _1725906, _1725904)))], (20125 ^ _781404) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (48951 ^ _781404) ^ [_1767758, _1767760] : [-(c_List_Osplice(_1767758, c_List_Olist_ONil(_1767758), _1767760) = _1767760)], (46505 ^ _781404) ^ [_1715674, _1715676, _1715678] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1715674, tc_HOL_Obool)), hAPP(c_List_Oset(_1715674), hAPP(c_List_Ofilter(_1715674, _1715676), _1715678))), hAPP(c_List_Oset(_1715674), _1715678))))], (22281 ^ _781404) ^ [_1178568, _1178570, _1178572] : [class_Rings_Ocomm__semiring__1(_1178568), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1178568), _1178570), 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)))), _1178572)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178568), hAPP(hAPP(c_Power_Opower__class_Opower(_1178568), _1178570), _1178572)), hAPP(hAPP(c_Power_Opower__class_Opower(_1178568), _1178570), _1178572)))], (48907 ^ _781404) ^ [_1766503, _1766505, _1766507, _1766509, _1766511] : [_1766503 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1766505, _1766507, _1766509, _1766511), _1766503) = c_Lazy__Sequence_Oempty(_1766507))], (38119 ^ _781404) ^ [_1503220, _1503222, _1503224, _1503226, _1503228, _1503230, _1503232] : [c_Equiv__Relations_Oequiv(_1503220, _1503222, _1503224), c_Equiv__Relations_Ocongruent(_1503220, tc_fun(_1503226, tc_HOL_Obool), _1503224, _1503228), hBOOL(hAPP(hAPP(c_member(tc_fun(_1503220, tc_HOL_Obool)), _1503230), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1503220), _1503222), _1503224))), 38133 ^ _781404 : [(38136 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1503226, tc_HOL_Obool)), hAPP(_1503228, 38132 ^ [_1503220, _1503222, _1503224, _1503226, _1503228, _1503230, _1503232])), _1503232))], (38134 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503220), 38132 ^ [_1503220, _1503222, _1503224, _1503226, _1503228, _1503230, _1503232]), _1503222)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1503226, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1503220, tc_fun(_1503226, tc_HOL_Obool)), _1503230), _1503228)), _1503232)))], (33069 ^ _781404) ^ [_1377873, _1377875, _1377877, _1377879, _1377881, _1377883] : [hBOOL(hAPP(hAPP(c_member(_1377873), _1377875), _1377877)), hBOOL(hAPP(hAPP(_1377879, _1377875), _1377881)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377873, tc_fun(_1377883, tc_HOL_Obool)), _1377877), _1377879), _1377881)))], (8927 ^ _781404) ^ [_932480, _932482] : [8929 ^ _781404 : [(8932 ^ _781404) ^ [] : [hBOOL(hAPP(_932482, 8928 ^ [_932480, _932482]))], (8930 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 8928 ^ [_932480, _932482]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _932480))))]], 8933 ^ _781404 : [(8934 ^ _781404) ^ [_932635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932635), _932480)), -(hBOOL(hAPP(_932482, _932635)))]]], (45788 ^ _781404) ^ [_1699272, _1699274, _1699276] : [45790 ^ _781404 : [(45793 ^ _781404) ^ [] : [hBOOL(hAPP(_1699274, 45789 ^ [_1699272, _1699274, _1699276]))], (45791 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699272), 45789 ^ [_1699272, _1699274, _1699276]), hAPP(c_List_Oset(_1699272), _1699276))))]], -(hBOOL(hAPP(c_List_Olistsp(_1699272, _1699274), _1699276)))], (51277 ^ _781404) ^ [_1817915, _1817917, _1817919, _1817921] : [c_Equiv__Relations_Oequivp(_1817915, _1817917), -(c_Quotient_OBabs(_1817915, _1817919, c_Quotient_ORespects(_1817915, _1817917), _1817921) = _1817921)], (21327 ^ _781404) ^ [_1160390, _1160392, _1160394] : [class_Rings_Oordered__ring(_1160390), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160390), c_Groups_Ozero__class_Ozero(_1160390)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160390), _1160392), _1160394)))), 21332 ^ _781404 : [(21339 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160390), _1160392), c_Groups_Ozero__class_Ozero(_1160390))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160390), _1160394), c_Groups_Ozero__class_Ozero(_1160390)))], (21333 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160390), c_Groups_Ozero__class_Ozero(_1160390)), _1160392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160390), c_Groups_Ozero__class_Ozero(_1160390)), _1160394))]]], (11857 ^ _781404) ^ [_984314, _984316, _984318, _984320, _984322] : [hBOOL(hAPP(hAPP(c_member(_984314), _984316), hAPP(c_Set_Ovimage(_984314, _984318, _984320), _984322))), -(hBOOL(hAPP(hAPP(c_member(_984318), hAPP(_984320, _984316)), _984322)))], (40493 ^ _781404) ^ [_1570300, _1570302, _1570304, _1570306] : [-(c_Hilbert__Choice_OEps(tc_prod(_1570300, _1570302), hAPP(c_Product__Type_Oprod_Oprod__case(_1570300, _1570302, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1570300, tc_fun(_1570302, tc_HOL_Obool), tc_fun(_1570302, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1570302, tc_HOL_Obool), tc_fun(_1570302, tc_HOL_Obool)), _1570300), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1570302)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570300), c_fconj), hAPP(c_fequal, _1570304)))), hAPP(c_fequal, _1570306)))) = hAPP(hAPP(c_Product__Type_OPair(_1570300, _1570302), _1570304), _1570306))], (52546 ^ _781404) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (17361 ^ _781404) ^ [_1091112] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091112)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1091112)))], (17935 ^ _781404) ^ [_1101294, _1101296] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1101294, _1101296))))], (45827 ^ _781404) ^ [_1700135, _1700137, _1700139, _1700141] : [hBOOL(hAPP(c_List_Olistsp(_1700135, _1700137), hAPP(hAPP(c_List_Olist_OCons(_1700135), _1700139), _1700141))), 45830 ^ _781404 : [(45833 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1700135, _1700137), _1700141)))], (45831 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1700137, _1700139)))]]], (33009 ^ _781404) ^ [_1376534, _1376536, _1376538, _1376540, _1376542, _1376544, _1376546, _1376548] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1376534, tc_fun(_1376536, tc_fun(_1376538, tc_HOL_Obool))), _1376540), _1376542), _1376544), _1376546)), hBOOL(hAPP(hAPP(c_member(_1376534), _1376548), _1376540)), -(hBOOL(hAPP(hAPP(hAPP(_1376542, _1376548), _1376544), _1376546)))], (44745 ^ _781404) ^ [_1676573, _1676575] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1676573), _1676575) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44748 ^ _781404 : [(44751 ^ _781404) ^ [_1676687] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1676687), hAPP(c_List_Oset(tc_Nat_Onat), _1676575))), -(_1676687 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44749 ^ _781404) ^ [] : [-(_1676573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3406 ^ _781404) ^ [_832253, _832255, _832257, _832259] : [-(c_HOL_OLet(_832259, _832255) = c_HOL_OLet(_832257, _832253)), _832259 = _832257, _832255 = _832253], (19299 ^ _781404) ^ [_1124653, _1124655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124653)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124653), _1124655)))], (7233 ^ _781404) ^ [_898933, _898935, _898937] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898933, tc_HOL_Obool)), _898935), _898937) = _898937, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898933, tc_HOL_Obool)), _898935), _898937)))], (9941 ^ _781404) ^ [_951239, _951241] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _951239), _951241) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _951241), _951239) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_951239 = _951241)], (3192 ^ _781404) ^ [_828918, _828920, _828922, _828924] : [-(c_Big__Operators_Olattice__class_OSup__fin(_828924, _828920) = c_Big__Operators_Olattice__class_OSup__fin(_828922, _828918)), _828924 = _828922, _828920 = _828918], (25738 ^ _781404) ^ [_1241345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241345)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1241345) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (44008 ^ _781404) ^ [_1659503, _1659505, _1659507] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659503)), hAPP(hAPP(c_List_Oappend(_1659503), _1659505), _1659507)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659503)), _1659505)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659503)), _1659507)))], (43817 ^ _781404) ^ [_1655027, _1655029, _1655031, _1655033, _1655035] : [-(_1655027 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1655029, _1655031, _1655033), _1655027), _1655035) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1655031), _1655029), tc_prod(_1655031, _1655029), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655031), _1655029), c_List_Olist_ONil(_1655031)), _1655035), hAPP(c_Product__Type_Oprod_Oprod__case(_1655031, _1655029, tc_prod(tc_List_Olist(_1655031), _1655029)), hAPP(hAPP(c_COMBC(_1655031, tc_fun(_1655029, tc_prod(tc_List_Olist(_1655031), _1655029)), tc_fun(_1655029, tc_prod(tc_List_Olist(_1655031), _1655029))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1655031), _1655029), tc_prod(tc_List_Olist(_1655031), _1655029)), tc_fun(tc_fun(_1655029, tc_prod(tc_List_Olist(_1655031), _1655029)), tc_fun(_1655029, tc_prod(tc_List_Olist(_1655031), _1655029))), _1655031), c_COMBB(tc_prod(tc_List_Olist(_1655031), _1655029), tc_prod(tc_List_Olist(_1655031), _1655029), _1655029)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1655031), tc_fun(_1655029, tc_prod(tc_List_Olist(_1655031), _1655029))), tc_fun(tc_prod(tc_List_Olist(_1655031), _1655029), tc_prod(tc_List_Olist(_1655031), _1655029)), _1655031), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1655031), _1655029, tc_prod(tc_List_Olist(_1655031), _1655029))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1655031), tc_List_Olist(_1655031)), tc_fun(tc_List_Olist(_1655031), tc_fun(_1655029, tc_prod(tc_List_Olist(_1655031), _1655029))), _1655031), hAPP(c_COMBB(tc_List_Olist(_1655031), tc_fun(_1655029, tc_prod(tc_List_Olist(_1655031), _1655029)), tc_List_Olist(_1655031)), c_Product__Type_OPair(tc_List_Olist(_1655031), _1655029))), c_List_Olist_OCons(_1655031))))), hAPP(c_Lazy__Sequence_Oanamorph(_1655029, _1655031, _1655033), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1655027), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1655033, _1655035)))], (24504 ^ _781404) ^ [_1220973, _1220975, _1220977, _1220979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1220975), _1220977)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1220977), 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), _1220975), _1220973)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1220975), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1220979, _1220973))), _1220977))))], (22077 ^ _781404) ^ [_1174596, _1174598] : [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), _1174596), _1174598))), 22080 ^ _781404 : [(22083 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174598)))], (22081 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174596)))]]], (38183 ^ _781404) ^ [_1505226, _1505228] : [-(c_Relation_Orefl__on(_1505226, _1505228, c_Relation_OId__on(_1505226, _1505228)))], (49319 ^ _781404) ^ [_1775440] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1775440) = c_Lazy__Sequence_Osmall__lazy_H(_1775440, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1775440)))], (32442 ^ _781404) ^ [_1365806, _1365808, _1365810] : [class_Orderings_Olinorder(_1365806), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365806), _1365808)), -(_1365808 = c_Orderings_Obot__class_Obot(tc_fun(_1365806, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365806), _1365810)), -(_1365810 = c_Orderings_Obot__class_Obot(tc_fun(_1365806, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1365806, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1365806, tc_HOL_Obool)), _1365808), _1365810)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365806), c_Big__Operators_Olinorder__class_OMax(_1365806, _1365808)), c_Big__Operators_Olinorder__class_OMax(_1365806, _1365810)))], (40142 ^ _781404) ^ [_1562666, _1562668, _1562670, _1562672] : [hBOOL(hAPP(hAPP(c_member(_1562666), _1562672), hAPP(c_Relation_ODomain(_1562666, _1562668), _1562670))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1562666, _1562668, hAPP(hAPP(c_COMBC(_1562666, tc_fun(tc_prod(_1562666, _1562668), tc_HOL_Obool), tc_fun(_1562668, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562668, tc_fun(tc_fun(tc_prod(_1562666, _1562668), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1562666, _1562668), tc_HOL_Obool), tc_fun(_1562668, tc_HOL_Obool)), _1562666), c_COMBC(_1562668, tc_fun(tc_prod(_1562666, _1562668), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562668, tc_prod(_1562666, _1562668)), tc_fun(_1562668, tc_fun(tc_fun(tc_prod(_1562666, _1562668), tc_HOL_Obool), tc_HOL_Obool)), _1562666), hAPP(c_COMBB(tc_prod(_1562666, _1562668), tc_fun(tc_fun(tc_prod(_1562666, _1562668), tc_HOL_Obool), tc_HOL_Obool), _1562668), c_member(tc_prod(_1562666, _1562668)))), c_Product__Type_OPair(_1562666, _1562668)))), _1562670)), _1562672)))], (3656 ^ _781404) ^ [_836174, _836176, _836178, _836180] : [-(c_List_Orotate(_836180, _836176) = c_List_Orotate(_836178, _836174)), _836180 = _836178, _836176 = _836174], (48530 ^ _781404) ^ [_1759168, _1759170, _1759172] : [-(hBOOL(hAPP(hAPP(c_member(_1759168), _1759170), hAPP(c_List_Oset(_1759168), _1759172)))), 48531 ^ _781404 : [(48532 ^ _781404) ^ [_1759257] : [48533 ^ _781404 : [(48534 ^ _781404) ^ [_1759330] : [_1759172 = hAPP(hAPP(c_List_Oappend(_1759168), _1759257), hAPP(hAPP(c_List_Olist_OCons(_1759168), _1759170), _1759330))]], -(hBOOL(hAPP(hAPP(c_member(_1759168), _1759170), hAPP(c_List_Oset(_1759168), _1759257))))]]], (48778 ^ _781404) ^ [_1763931, _1763933, _1763935] : [c_List_Olist__all(_1763931, _1763935, _1763933), 48781 ^ _781404 : [(48782 ^ _781404) ^ [_1764012] : [hBOOL(hAPP(hAPP(c_member(_1763931), _1764012), hAPP(c_List_Oset(_1763931), _1763933))), -(hBOOL(hAPP(_1763935, _1764012)))]]], (24190 ^ _781404) ^ [_1215206, _1215208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215206), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24193 ^ _781404 : [(24196 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215206), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215208, _1215206))))], (24194 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215208, _1215206)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (34073 ^ _781404) ^ [_1406943, _1406945, _1406947, _1406949, _1406951] : [hBOOL(hAPP(hAPP(c_member(_1406943), _1406945), _1406947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1406949, tc_HOL_Obool)), hAPP(_1406951, _1406945)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406943, tc_fun(_1406949, tc_HOL_Obool)), _1406947), _1406951))))], (20307 ^ _781404) ^ [_1141781] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141781))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1141781)))))], (27083 ^ _781404) ^ [_1264718, _1264720, _1264722, _1264724, _1264726] : [class_Rings_Olinordered__idom(_1264718), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264718), hAPP(c_Groups_Oabs__class_Oabs(_1264718), _1264720)), _1264722)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264718), hAPP(c_Groups_Oabs__class_Oabs(_1264718), _1264724)), _1264726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264718), hAPP(c_Groups_Oabs__class_Oabs(_1264718), _1264720)), hAPP(c_Groups_Oabs__class_Oabs(_1264718), _1264724))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264718), _1264722), _1264726))))], (14101 ^ _781404) ^ [_1027506, _1027508, _1027510, _1027512] : [class_Groups_Ocomm__monoid__add(_1027506), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1027508), _1027510))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027508, _1027506), _1027512), _1027510) = c_Groups_Ozero__class_Ozero(_1027506))], (39520 ^ _781404) ^ [_1546039, _1546041] : [-(hAPP(c_Fun_Oid(_1546039), _1546041) = _1546041)], (4196 ^ _781404) ^ [_844984, _844986, _844988, _844990, _844992, _844994] : [-(c_List_Osplice(_844994, _844990, _844986) = c_List_Osplice(_844992, _844988, _844984)), _844994 = _844992, _844990 = _844988, _844986 = _844984], (52632 ^ _781404) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (49347 ^ _781404) ^ [_1776275] : [-(c_Lazy__Sequence_Oyieldn(_1776275) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1776275), _1776275, c_Lazy__Sequence_Oyield(_1776275)))], (38612 ^ _781404) ^ [_1515767, _1515769, _1515771, _1515773, _1515775, _1515777] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515767, _1515769)), hAPP(hAPP(c_Product__Type_OPair(_1515767, _1515769), _1515771), _1515773)), hAPP(hAPP(c_Product__Type_OSigma(_1515767, _1515769), _1515775), _1515777))), 38615 ^ _781404 : [(38618 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515769), _1515773), hAPP(_1515777, _1515771))))], (38616 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515767), _1515771), _1515775)))]]], (51854 ^ _781404) ^ [_1831068, _1831070] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831070, _1831068) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831068), _1831070)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831070), _1831068)))], (31580 ^ _781404) ^ [_1349516, _1349518, _1349520] : [class_Orderings_Olinorder(_1349516), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349516), _1349518)), -(_1349518 = c_Orderings_Obot__class_Obot(tc_fun(_1349516, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349516), _1349520)), -(_1349520 = c_Orderings_Obot__class_Obot(tc_fun(_1349516, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349516, tc_HOL_Obool)), _1349518), _1349520) = c_Orderings_Obot__class_Obot(tc_fun(_1349516, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1349516, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1349516, tc_HOL_Obool)), _1349518), _1349520)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349516), c_Big__Operators_Olinorder__class_OMin(_1349516, _1349518)), c_Big__Operators_Olinorder__class_OMin(_1349516, _1349520)))], (8624 ^ _781404) ^ [_926795, _926797] : [class_Groups_Olinordered__ab__group__add(_926795), 8627 ^ _781404 : [(8634 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926795), _926797), c_Groups_Ozero__class_Ozero(_926795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926795), _926797), hAPP(c_Groups_Ouminus__class_Ouminus(_926795), _926797))))], (8628 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926795), _926797), hAPP(c_Groups_Ouminus__class_Ouminus(_926795), _926797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926795), _926797), c_Groups_Ozero__class_Ozero(_926795))))]]], (41471 ^ _781404) ^ [_1594329, _1594331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1594329), _1594331)), -(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), _1594329), _1594331)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (38319 ^ _781404) ^ [_1508461, _1508463, _1508465, _1508467, _1508469] : [c_Typedef_Otype__definition(_1508461, _1508463, _1508465, _1508467, _1508469), -(hAPP(c_Set_Oimage(_1508463, _1508461, _1508467), _1508469) = c_Orderings_Otop__class_Otop(tc_fun(_1508461, tc_HOL_Obool)))], (21475 ^ _781404) ^ [_1163212, _1163214, _1163216] : [class_Rings_Oordered__cancel__semiring(_1163212), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163212), _1163214), c_Groups_Ozero__class_Ozero(_1163212))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163212), c_Groups_Ozero__class_Ozero(_1163212)), _1163216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163212), _1163214), _1163216)), c_Groups_Ozero__class_Ozero(_1163212))))], (29866 ^ _781404) ^ [_1316817, _1316819, _1316821, _1316823] : [class_Rings_Ocomm__semiring__1(_1316817), class_Rings_Ono__zero__divisors(_1316817), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316819), _1316821)), 29877 ^ _781404 : [(29887 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1316819, _1316817), _1316823), _1316821) = c_Groups_Ozero__class_Ozero(_1316817)), 29888 ^ _781404 : [(29889 ^ _781404) ^ [_1317195] : [hBOOL(hAPP(hAPP(c_member(_1316819), _1317195), _1316821)), hAPP(_1316823, _1317195) = c_Groups_Ozero__class_Ozero(_1316817)]]], (29878 ^ _781404) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1316819, _1316817), _1316823), _1316821) = c_Groups_Ozero__class_Ozero(_1316817), 29882 ^ _781404 : [(29885 ^ _781404) ^ [] : [-(hAPP(_1316823, 29881 ^ [_1316817, _1316819, _1316821, _1316823]) = c_Groups_Ozero__class_Ozero(_1316817))], (29883 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1316819), 29881 ^ [_1316817, _1316819, _1316821, _1316823]), _1316821)))]]]]], (24262 ^ _781404) ^ [_1216354, _1216356, _1216358] : [class_Divides_Osemiring__div(_1216354), -(_1216356 = c_Groups_Ozero__class_Ozero(_1216354)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216354), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216354), _1216358), _1216356)), _1216356) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216354), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216354), _1216358), _1216356)), c_Groups_Oone__class_Oone(_1216354)))], (17351 ^ _781404) ^ [_1090906, _1090908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1090906), _1090908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090906)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090908))))], (39518 ^ _781404) ^ [_1546002, _1546004] : [-(c_Product__Type_Oapfst(_1546002, _1546002, _1546004, c_Fun_Oid(_1546002)) = c_Fun_Oid(tc_prod(_1546002, _1546004)))], (35756 ^ _781404) ^ [_1448774, _1448776, _1448778, _1448780] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1448774, _1448776), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1448778), _1448780))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1448774, _1448776) = _1448780)], (28131 ^ _781404) ^ [_1284168, _1284170] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284168), _1284170), hAPP(c_Int_Onumber__class_Onumber__of(_1284168), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1284168)), class_Fields_Ofield__inverse__zero(_1284168), class_Int_Onumber__ring(_1284168)], (33819 ^ _781404) ^ [_1399813, _1399815, _1399817, _1399819, _1399821, _1399823] : [c_Fun_Oinj__on(_1399813, _1399815, hAPP(c_Fun_Ocomp(_1399817, _1399815, _1399813, _1399819), _1399821), _1399823), -(c_Fun_Oinj__on(_1399813, _1399817, _1399821, _1399823))], (42922 ^ _781404) ^ [_1634002, _1634004] : [-(c_List_Olists(_1634002, _1634004) = hAPP(c_Set_OCollect(tc_List_Olist(_1634002)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1634002), tc_fun(_1634002, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1634002, tc_HOL_Obool), tc_fun(tc_fun(_1634002, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1634002)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1634002, tc_HOL_Obool))), c_List_Oset(_1634002))), _1634004)))], (47523 ^ _781404) ^ [_1736899, _1736901, _1736903] : [_1736901 = _1736903, -(hAPP(c_List_Orev(_1736899), _1736901) = hAPP(c_List_Orev(_1736899), _1736903))], (47111 ^ _781404) ^ [_1728425, _1728427, _1728429, _1728431, _1728433] : [class_Orderings_Olinorder(_1728425), c_List_Olinorder__class_Osorted(_1728425, hAPP(hAPP(c_List_Omap(_1728427, _1728425), _1728429), _1728431)), -(c_List_Olinorder__class_Osorted(_1728425, hAPP(hAPP(c_List_Omap(_1728427, _1728425), _1728429), c_List_Olinorder__class_Oinsort__insert__key(_1728427, _1728425, _1728429, _1728433, _1728431))))], (10689 ^ _781404) ^ [_963008, _963010] : [10690 ^ _781404 : [(10693 ^ _781404) ^ [] : [_963008 = _963010], (10691 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963008), _963010))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963008), _963010)))], (29373 ^ _781404) ^ [_1307229, _1307231, _1307233, _1307235] : [class_Fields_Olinordered__field(_1307229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307229), _1307231), c_Groups_Ozero__class_Ozero(_1307229))), 29380 ^ _781404 : [(29387 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307229), _1307235), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307229), _1307233), _1307231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307229), _1307233), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307229), _1307235), _1307231))))], (29381 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307229), _1307233), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307229), _1307235), _1307231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307229), _1307235), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307229), _1307233), _1307231))))]]], (46708 ^ _781404) ^ [_1721053, _1721055] : [class_Groups_Omonoid__add(_1721053), -(hAPP(c_List_Ofoldl(_1721053, _1721053, c_Groups_Oplus__class_Oplus(_1721053), c_Groups_Ozero__class_Ozero(_1721053)), _1721055) = c_List_Ofoldr(_1721053, _1721053, c_Groups_Oplus__class_Oplus(_1721053), _1721055, c_Groups_Ozero__class_Ozero(_1721053)))], (36006 ^ _781404) ^ [_1453334, _1453336] : [-(c_Divides_Odivmod__int__rel(_1453334, _1453336) = 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, _1453334))), 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), _1453336)))))), 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)), _1453336))), 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)), _1453336))))), 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)), _1453336)))), 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), _1453336))), 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))))))))], (7509 ^ _781404) ^ [_904245, _904247, _904249] : [class_Lattices_Obounded__lattice__top(_904245), 7512 ^ _781404 : [(7521 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904245), _904247), _904249) = c_Orderings_Otop__class_Otop(_904245)), _904247 = c_Orderings_Otop__class_Otop(_904245), _904249 = c_Orderings_Otop__class_Otop(_904245)], (7513 ^ _781404) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904245), _904247), _904249) = c_Orderings_Otop__class_Otop(_904245), 7516 ^ _781404 : [(7519 ^ _781404) ^ [] : [-(_904249 = c_Orderings_Otop__class_Otop(_904245))], (7517 ^ _781404) ^ [] : [-(_904247 = c_Orderings_Otop__class_Otop(_904245))]]]]], (46483 ^ _781404) ^ [_1714811, _1714813, _1714815, _1714817] : [-(c_List_Oconcat(_1714811, hAPP(hAPP(c_List_Omap(_1714813, tc_List_Olist(_1714811)), hAPP(hAPP(c_COMBC(_1714813, tc_List_Olist(_1714811), tc_List_Olist(_1714811)), hAPP(hAPP(c_COMBB(_1714811, tc_fun(tc_List_Olist(_1714811), tc_List_Olist(_1714811)), _1714813), c_List_Olist_OCons(_1714811)), _1714815)), c_List_Olist_ONil(_1714811))), _1714817)) = hAPP(hAPP(c_List_Omap(_1714813, _1714811), _1714815), _1714817))], (10575 ^ _781404) ^ [_961269, _961271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961269)), hAPP(c_Nat_OSuc, _961271))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961269), _961271)))], (45307 ^ _781404) ^ [_1688571, _1688573, _1688575, _1688577, _1688579] : [-(hAPP(hAPP(c_List_Otake(_1688571), _1688573), hAPP(hAPP(c_List_Omap(_1688575, _1688571), _1688577), _1688579)) = hAPP(hAPP(c_List_Omap(_1688575, _1688571), _1688577), hAPP(hAPP(c_List_Otake(_1688575), _1688573), _1688579)))], (47732 ^ _781404) ^ [_1741334, _1741336, _1741338, _1741340] : [-(hBOOL(hAPP(_1741334, _1741336))), -(c_List_OtakeWhile(_1741338, _1741334, hAPP(hAPP(c_List_Olist_OCons(_1741338), _1741336), _1741340)) = c_List_Olist_ONil(_1741338))], (28093 ^ _781404) ^ [_1283558, _1283560, _1283562, _1283564] : [class_Fields_Ofield__inverse__zero(_1283558), class_Int_Onumber(_1283558), 28100 ^ _781404 : [(28101 ^ _781404) ^ [] : [_1283560 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1283558), _1283562), hAPP(c_Int_Onumber__class_Onumber__of(_1283558), _1283564)), 28104 ^ _781404 : [(28111 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1283558), _1283564) = c_Groups_Ozero__class_Ozero(_1283558), -(_1283560 = c_Groups_Ozero__class_Ozero(_1283558))], (28105 ^ _781404) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1283558), _1283564) = c_Groups_Ozero__class_Ozero(_1283558)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283558), _1283560), hAPP(c_Int_Onumber__class_Onumber__of(_1283558), _1283564)) = _1283562)]]], (28117 ^ _781404) ^ [] : [-(_1283560 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1283558), _1283562), hAPP(c_Int_Onumber__class_Onumber__of(_1283558), _1283564))), 28120 ^ _781404 : [(28123 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283558), _1283560), hAPP(c_Int_Onumber__class_Onumber__of(_1283558), _1283564)) = _1283562], (28121 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1283558), _1283564) = c_Groups_Ozero__class_Ozero(_1283558)]], 28124 ^ _781404 : [(28127 ^ _781404) ^ [] : [_1283560 = c_Groups_Ozero__class_Ozero(_1283558)], (28125 ^ _781404) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1283558), _1283564) = c_Groups_Ozero__class_Ozero(_1283558))]]]]], (44128 ^ _781404) ^ [_1661761, _1661763, _1661765, _1661767] : [-(hAPP(hAPP(c_List_Onth(_1661761), hAPP(hAPP(c_List_Oappend(_1661761), _1661763), hAPP(hAPP(c_List_Olist_OCons(_1661761), _1661765), _1661767))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661761)), _1661763)) = _1661765)], (9170 ^ _781404) ^ [_937326, _937328, _937330, _937332] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937326, tc_HOL_Obool)), _937328), hAPP(hAPP(c_Set_Oinsert(_937326), _937330), _937332)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937326, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937326, tc_HOL_Obool)), _937328), _937332)), hAPP(hAPP(c_Set_Oinsert(_937326), _937330), c_Orderings_Obot__class_Obot(tc_fun(_937326, tc_HOL_Obool)))))], (52730 ^ _781404) ^ [_1842164, _1842166, _1842168, _1842170, _1842172, _1842174] : [-(hAPP(hAPP(hAPP(c_COMBB(_1842164, _1842166, _1842168), _1842170), _1842172), _1842174) = hAPP(_1842170, hAPP(_1842172, _1842174)))], (28141 ^ _781404) ^ [_1284323, _1284325] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284323), _1284325), hAPP(c_Int_Onumber__class_Onumber__of(_1284323), c_Int_OBit1(c_Int_OPls))) = _1284325), class_Fields_Ofield(_1284323), class_Int_Onumber__ring(_1284323)], (42721 ^ _781404) ^ [_1628941, _1628943, _1628945, _1628947] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628941), tc_List_Olist(_1628941))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628941), tc_List_Olist(_1628941)), _1628943), _1628945)), c_List_Olexord(_1628941, _1628947))), 42726 ^ _781404 : [(42729 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1628941), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628941)), _1628943)), _1628945) = _1628943)], (42727 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628941)), _1628943)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628941)), _1628945))))]], 42731 ^ _781404 : [(42736 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628941, _1628941)), hAPP(hAPP(c_Product__Type_OPair(_1628941, _1628941), hAPP(hAPP(c_List_Onth(_1628941), _1628943), 42730 ^ [_1628941, _1628943, _1628945, _1628947])), hAPP(hAPP(c_List_Onth(_1628941), _1628945), 42730 ^ [_1628941, _1628943, _1628945, _1628947]))), _1628947)))], (42734 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1628941), 42730 ^ [_1628941, _1628943, _1628945, _1628947]), _1628943) = hAPP(hAPP(c_List_Otake(_1628941), 42730 ^ [_1628941, _1628943, _1628945, _1628947]), _1628945))], (42732 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42730 ^ [_1628941, _1628943, _1628945, _1628947]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628941)), _1628943)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628941)), _1628945)))))]]], (39616 ^ _781404) ^ [_1548564, _1548566, _1548568, _1548570, _1548572, _1548574, _1548576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1548564, _1548566), tc_HOL_Obool)), _1548568), _1548570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1548566, _1548572), tc_HOL_Obool)), _1548574), _1548576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1548564, _1548572), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1548564, _1548566, _1548572), _1548568), _1548574)), hAPP(hAPP(c_Relation_Orel__comp(_1548564, _1548566, _1548572), _1548570), _1548576))))], (46429 ^ _781404) ^ [_1713105, _1713107, _1713109, _1713111, _1713113] : [class_Orderings_Olinorder(_1713105), -(c_List_Olinorder__class_Osort__key(_1713107, _1713105, _1713109, hAPP(hAPP(c_List_Olist_OCons(_1713107), _1713111), _1713113)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1713107, _1713105, _1713109), _1713111), c_List_Olinorder__class_Osort__key(_1713107, _1713105, _1713109, _1713113)))], (52726 ^ _781404) ^ [_1842096, _1842098] : [-(hAPP(c_COMBI(_1842096), _1842098) = _1842098)], (33351 ^ _781404) ^ [_1385297, _1385299, _1385301, _1385303] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1385297, tc_HOL_Obool), hAPP(c_Set_Oimage(_1385299, tc_fun(_1385297, tc_HOL_Obool), _1385301), _1385303)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385299, tc_fun(_1385297, tc_HOL_Obool)), _1385303), _1385301))], (41588 ^ _781404) ^ [_1597248, _1597250] : [c_Wellfounded_Owf(_1597248, hAPP(c_Relation_Oconverse(_1597248, _1597248), _1597250)), -(c_Wellfounded_Owf(_1597248, hAPP(c_Relation_Oconverse(_1597248, _1597248), c_Transitive__Closure_Otrancl(_1597248, _1597250))))], (37567 ^ _781404) ^ [_1489454, _1489456] : [-(c_Relation_OId__on(_1489454, _1489456) = hAPP(c_Product__Type_Oprod_Oprod__case(_1489454, _1489454, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1489454, tc_HOL_Obool, tc_fun(_1489454, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1489454, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1489454, tc_HOL_Obool)), _1489454), c_COMBC(_1489454, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1489454, tc_HOL_Obool), tc_fun(_1489454, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1489454), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1489454), c_fconj)), c_fequal))), _1489456)))], (50383 ^ _781404) ^ [_1798985, _1798987] : [-(c_Equiv__Relations_Opart__equivp(_1798985, _1798987)), 50386 ^ _781404 : [(50387 ^ _781404) ^ [_1799105] : [hBOOL(hAPP(hAPP(_1798987, _1799105), _1799105))]], 50404 ^ _781404 : [(50407 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1798987, 50389 ^ [_1798985, _1798987]), 50389 ^ [_1798985, _1798987])))], (50409 ^ _781404) ^ [] : [-(hAPP(_1798987, 50388 ^ [_1798985, _1798987]) = hAPP(_1798987, 50389 ^ [_1798985, _1798987]))], (50411 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1798987, 50388 ^ [_1798985, _1798987]), 50389 ^ [_1798985, _1798987]))], (50405 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1798987, 50388 ^ [_1798985, _1798987]), 50388 ^ [_1798985, _1798987])))]], 50392 ^ _781404 : [(50395 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1798987, 50388 ^ [_1798985, _1798987]), 50388 ^ [_1798985, _1798987])), hBOOL(hAPP(hAPP(_1798987, 50389 ^ [_1798985, _1798987]), 50389 ^ [_1798985, _1798987])), hAPP(_1798987, 50388 ^ [_1798985, _1798987]) = hAPP(_1798987, 50389 ^ [_1798985, _1798987])], (50393 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1798987, 50388 ^ [_1798985, _1798987]), 50389 ^ [_1798985, _1798987])))]]], (38680 ^ _781404) ^ [_1517377, _1517379, _1517381, _1517383] : [-(_1517377 = c_Orderings_Obot__class_Obot(tc_fun(_1517379, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1517381, _1517379), _1517381, c_Product__Type_Ofst(_1517381, _1517379)), hAPP(hAPP(c_Product__Type_OSigma(_1517381, _1517379), _1517383), hAPP(c_COMBK(tc_fun(_1517379, tc_HOL_Obool), _1517381), _1517377))) = _1517383)], (35486 ^ _781404) ^ [_1443512, _1443514, _1443516, _1443518, _1443520, _1443522] : [hAPP(hAPP(c_Product__Type_OPair(_1443512, _1443514), _1443516), _1443518) = hAPP(hAPP(c_Product__Type_OPair(_1443512, _1443514), _1443520), _1443522), 35489 ^ _781404 : [(35492 ^ _781404) ^ [] : [-(_1443518 = _1443522)], (35490 ^ _781404) ^ [] : [-(_1443516 = _1443520)]]], (26155 ^ _781404) ^ [_1248441] : [26157 ^ _781404 : [(26160 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26156 ^ [_1248441]))], (26158 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26156 ^ [_1248441]), _1248441)))]], -(c_Nat__Transfer_Onat__set(_1248441))], (43044 ^ _781404) ^ [_1638730, _1638732] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1638730, _1638732) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1638730), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1638732), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (22085 ^ _781404) ^ [_1174719, _1174721] : [-(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), _1174719), _1174721)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174719)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174721))], (16002 ^ _781404) ^ [_1065075, _1065077, _1065079] : [class_Lattices_Olattice(_1065075), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065075), _1065077)), -(hBOOL(hAPP(hAPP(c_member(_1065075), _1065079), _1065077))), -(_1065077 = c_Orderings_Obot__class_Obot(tc_fun(_1065075, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1065075, hAPP(hAPP(c_Set_Oinsert(_1065075), _1065079), _1065077)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065075), _1065079), c_Big__Operators_Olattice__class_OInf__fin(_1065075, _1065077)))], (49005 ^ _781404) ^ [_1768913, _1768915, _1768917, _1768919, _1768921] : [hBOOL(hAPP(hAPP(_1768917, _1768921), _1768919)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1768913, _1768915, _1768917), _1768919), _1768921)))], (4144 ^ _781404) ^ [_844148, _844150, _844152, _844154] : [-(c_Lazy__Sequence_Ohb__single(_844154, _844150) = c_Lazy__Sequence_Ohb__single(_844152, _844148)), _844154 = _844152, _844150 = _844148], (52364 ^ _781404) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (19197 ^ _781404) ^ [_1122849] : [_1122849 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1122849) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5166 ^ _781404) ^ [_860221, _860223] : [_860223 = _860221, -(c_Finite__Set_Ocard(_860223) = c_Finite__Set_Ocard(_860221))], (18693 ^ _781404) ^ [_1114820] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1114820), c_Int_OPls) = _1114820)], (36572 ^ _781404) ^ [_1464989, _1464991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1464989), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1464991), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1464989), _1464991) = 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), _1464989), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1464991)))))], (7307 ^ _781404) ^ [_900439, _900441] : [class_Groups_Ogroup__add(_900439), -(hAPP(c_Groups_Ouminus__class_Ouminus(_900439), hAPP(c_Groups_Ouminus__class_Ouminus(_900439), _900441)) = _900441)], (10271 ^ _781404) ^ [_956005, _956007] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _956005)), hAPP(c_Nat_OSuc, _956007)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956005), _956007))], (30007 ^ _781404) ^ [_1319252, _1319254, _1319256, _1319258, _1319260] : [class_Groups_Ocomm__monoid__mult(_1319252), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319254), _1319256)), -(hBOOL(hAPP(hAPP(c_member(_1319254), _1319258), _1319256))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319254, _1319252), _1319260), hAPP(hAPP(c_Set_Oinsert(_1319254), _1319258), _1319256)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319252), hAPP(_1319260, _1319258)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319254, _1319252), _1319260), _1319256)))], (46161 ^ _781404) ^ [_1707698, _1707700, _1707702] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1707698))), c_Enum_On__lists(_1707698, _1707700, _1707702)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707698)), _1707702)), _1707700))], (1256 ^ _781404) ^ [_800144, _800146] : [-(class_Rings_Olinordered__ring(_800144)), _800146 = _800144, class_Rings_Olinordered__ring(_800146)], (52292 ^ _781404) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (30800 ^ _781404) ^ [_1335048, _1335050, _1335052, _1335054] : [class_Orderings_Olinorder(_1335048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335048), _1335050), _1335052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335048), _1335050), _1335054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335048), _1335050), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1335048), _1335052), _1335054))))], (25257 ^ _781404) ^ [_1233255, _1233257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1233255), hAPP(c_Int_Onat, _1233257))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233255)), _1233257)))], (28825 ^ _781404) ^ [_1297466, _1297468, _1297470] : [class_Fields_Olinordered__field__inverse__zero(_1297466), 28828 ^ _781404 : [(28843 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297466), c_Groups_Ozero__class_Ozero(_1297466)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297466), _1297468), _1297470)))), 28844 ^ _781404 : [(28851 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297466), _1297468), c_Groups_Ozero__class_Ozero(_1297466))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297466), _1297470), c_Groups_Ozero__class_Ozero(_1297466)))], (28845 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297466), c_Groups_Ozero__class_Ozero(_1297466)), _1297468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297466), c_Groups_Ozero__class_Ozero(_1297466)), _1297470))]]], (28829 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297466), c_Groups_Ozero__class_Ozero(_1297466)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297466), _1297468), _1297470))), 28834 ^ _781404 : [(28837 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297466), c_Groups_Ozero__class_Ozero(_1297466)), _1297470)))], (28835 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297466), c_Groups_Ozero__class_Ozero(_1297466)), _1297468)))]], 28838 ^ _781404 : [(28841 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297466), _1297470), c_Groups_Ozero__class_Ozero(_1297466))))], (28839 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297466), _1297468), c_Groups_Ozero__class_Ozero(_1297466))))]]]]], (39610 ^ _781404) ^ [_1548294, _1548296, _1548298, _1548300, _1548302, _1548304, _1548306] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1548294, _1548296, _1548298), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1548300, tc_fun(tc_prod(_1548294, _1548296), tc_HOL_Obool)), _1548302), _1548304)), _1548306) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1548300, tc_fun(tc_prod(_1548294, _1548298), tc_HOL_Obool)), _1548302), hAPP(hAPP(c_COMBC(_1548300, tc_fun(tc_prod(_1548296, _1548298), tc_HOL_Obool), tc_fun(tc_prod(_1548294, _1548298), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1548294, _1548296), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1548296, _1548298), tc_HOL_Obool), tc_fun(tc_prod(_1548294, _1548298), tc_HOL_Obool)), _1548300), c_Relation_Orel__comp(_1548294, _1548296, _1548298)), _1548304)), _1548306)))], (40646 ^ _781404) ^ [_1573807, _1573809] : [class_Complete__Lattice_Ocomplete__lattice(_1573807), c_Orderings_Oorder__class_Omono(_1573807, _1573807, _1573809), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1573807), c_Inductive_Ocomplete__lattice__class_Ogfp(_1573807, _1573809)), hAPP(_1573809, c_Inductive_Ocomplete__lattice__class_Ogfp(_1573807, _1573809)))))], (26965 ^ _781404) ^ [_1262733, _1262735, _1262737] : [class_Groups_Oordered__ab__group__add__abs(_1262733), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262733), hAPP(c_Groups_Oabs__class_Oabs(_1262733), _1262735)), _1262737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262733), _1262735), _1262737)))], (7491 ^ _781404) ^ [_903816, _903818, _903820, _903822] : [class_Lattices_Osemilattice__inf(_903816), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903816), _903818), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903816), _903820), _903822)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903816), _903820), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903816), _903818), _903822)))], (27735 ^ _781404) ^ [_1277237, _1277239, _1277241, _1277243, _1277245] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1277237, _1277239, hAPP(hAPP(c_Set_Oinsert(_1277237), _1277241), _1277243)), _1277245)), 27740 ^ _781404 : [(27745 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1277237), 27738 ^ [_1277237, _1277239, _1277241, _1277243, _1277245]), 27739 ^ [_1277237, _1277239, _1277241, _1277243, _1277245]))], (27743 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1277237, _1277237, _1277239, 27738 ^ [_1277237, _1277239, _1277241, _1277243, _1277245], 27739 ^ [_1277237, _1277239, _1277241, _1277243, _1277245]), _1277245)))], (27741 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1277237), _1277241), _1277243) = hAPP(hAPP(c_Set_Oinsert(_1277237), 27738 ^ [_1277237, _1277239, _1277241, _1277243, _1277245]), 27739 ^ [_1277237, _1277239, _1277241, _1277243, _1277245]))]]], (38918 ^ _781404) ^ [_1524480, _1524482, _1524484, _1524486, _1524488, _1524490, _1524492, _1524494] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524480, _1524482)), _1524484), hAPP(c_Set_Oimage(tc_prod(_1524486, _1524488), tc_prod(_1524480, _1524482), c_Product__Type_Omap__pair(_1524486, _1524480, _1524488, _1524482, _1524490, _1524492)), _1524494))), 38923 ^ _781404 : [(38926 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524486, _1524488)), hAPP(hAPP(c_Product__Type_OPair(_1524486, _1524488), 38921 ^ [_1524480, _1524482, _1524484, _1524486, _1524488, _1524490, _1524492, _1524494]), 38922 ^ [_1524480, _1524482, _1524484, _1524486, _1524488, _1524490, _1524492, _1524494])), _1524494)))], (38924 ^ _781404) ^ [] : [-(_1524484 = hAPP(hAPP(c_Product__Type_OPair(_1524480, _1524482), hAPP(_1524490, 38921 ^ [_1524480, _1524482, _1524484, _1524486, _1524488, _1524490, _1524492, _1524494])), hAPP(_1524492, 38922 ^ [_1524480, _1524482, _1524484, _1524486, _1524488, _1524490, _1524492, _1524494])))]]], (39041 ^ _781404) ^ [_1527389, _1527391, _1527393] : [hBOOL(hAPP(hAPP(c_member(_1527389), _1527391), hAPP(c_Set_OCollect(_1527389), _1527393))), -(hBOOL(hAPP(_1527393, _1527391)))], (39934 ^ _781404) ^ [] : [-(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)))))], (19293 ^ _781404) ^ [_1124527, _1124529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124527), _1124529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124527)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124529))))], (40570 ^ _781404) ^ [_1572421, _1572423, _1572425, _1572427] : [c_Orderings_Oorder__class_Omono(tc_fun(_1572421, tc_HOL_Obool), tc_fun(_1572421, tc_HOL_Obool), _1572423), hBOOL(hAPP(hAPP(c_member(_1572421), _1572425), _1572427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1572421, tc_HOL_Obool)), _1572427), hAPP(_1572423, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572421, tc_HOL_Obool)), _1572427), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1572421, tc_HOL_Obool), _1572423))))), -(hBOOL(hAPP(hAPP(c_member(_1572421), _1572425), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1572421, tc_HOL_Obool), _1572423))))], (29407 ^ _781404) ^ [_1307879, _1307881, _1307883, _1307885] : [class_Fields_Olinordered__field(_1307879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307879), c_Groups_Ozero__class_Ozero(_1307879)), _1307881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307879), _1307883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307879), _1307885), _1307881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307879), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307879), _1307883), _1307881)), _1307885)))], (30294 ^ _781404) ^ [_1325502] : [class_Lattices_Osemilattice__sup(_1325502), -(c_Finite__Set_Ofun__left__comm__idem(_1325502, _1325502, c_Lattices_Osemilattice__sup__class_Osup(_1325502)))], (26359 ^ _781404) ^ [_1251552, _1251554] : [c_Nat__Transfer_Ois__nat(_1251552), c_Nat__Transfer_Ois__nat(_1251554), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1251552), _1251554)))], (46149 ^ _781404) ^ [_1707535, _1707537] : [_1707535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1707537, _1707535, c_List_Olist_ONil(_1707537)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1707537)), c_List_Olist_ONil(_1707537)), c_List_Olist_ONil(tc_List_Olist(_1707537))))], (8814 ^ _781404) ^ [] : [-(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))))], (42891 ^ _781404) ^ [_1633296, _1633298, _1633300] : [hBOOL(hAPP(hAPP(c_member(_1633296), _1633298), hAPP(c_List_Oset(_1633296), _1633300))), -(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(_1633296)), _1633300))))], (23591 ^ _781404) ^ [_1205038] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1205038, _1205038) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44441 ^ _781404) ^ [_1669929, _1669931, _1669933, _1669935] : [-(hAPP(hAPP(c_List_Odrop(_1669929), _1669931), hAPP(hAPP(c_List_Olist_OCons(_1669929), _1669933), _1669935)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1669929), hAPP(hAPP(c_List_Olist_OCons(_1669929), _1669933), _1669935), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1669929), tc_List_Olist(_1669929)), c_List_Odrop(_1669929)), _1669935), _1669931))], (39979 ^ _781404) ^ [_1558413, _1558415, _1558417] : [c_Wellfounded_Owf(_1558413, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1558413, _1558413), tc_HOL_Obool)), _1558415), _1558417)), -(c_Wellfounded_Owf(_1558413, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1558413, _1558413), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1558413, _1558413), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1558413, _1558413, _1558413), _1558415), _1558415)), hAPP(hAPP(c_Relation_Orel__comp(_1558413, _1558413, _1558413), _1558417), _1558415))), _1558417)))], (19275 ^ _781404) ^ [_1124211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1124211)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124211), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25251 ^ _781404) ^ [_1233129, _1233131] : [class_Int_Onumber__ring(_1233129), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1233129), hAPP(c_Int_Onumber__class_Onumber__of(_1233129), c_Int_OMin)), _1233131) = hAPP(c_Groups_Ouminus__class_Ouminus(_1233129), _1233131))], (26593 ^ _781404) ^ [_1255286, _1255288] : [class_Rings_Olinordered__idom(_1255286), 26596 ^ _781404 : [(26603 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255288), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255286), hAPP(c_Int_Oring__1__class_Oof__int(_1255286), _1255288)), c_Groups_Ozero__class_Ozero(_1255286))))], (26597 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255286), hAPP(c_Int_Oring__1__class_Oof__int(_1255286), _1255288)), c_Groups_Ozero__class_Ozero(_1255286))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255288), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (8237 ^ _781404) ^ [_919951, _919953, _919955] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919951, tc_HOL_Obool)), _919953), _919955) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_919951, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_919951, tc_HOL_Obool)), _919953), hAPP(hAPP(c_Set_Oinsert(tc_fun(_919951, tc_HOL_Obool)), _919955), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_919951, tc_HOL_Obool), tc_HOL_Obool))))))], (35368 ^ _781404) ^ [_1440646] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1440646) = 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)))], (18755 ^ _781404) ^ [] : [-(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))))], (1686 ^ _781404) ^ [_805519, _805521] : [-(class_Rings_Olinordered__semidom(_805519)), _805521 = _805519, class_Rings_Olinordered__semidom(_805521)], (24660 ^ _781404) ^ [_1223835, _1223837, _1223839] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223835), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223837), _1223839)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223835), _1223837)), _1223839))], (39127 ^ _781404) ^ [_1529417, _1529419, _1529421] : [-(hAPP(hAPP(c_Set_Oinsert(_1529417), _1529419), _1529421) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1529417, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1529417), hAPP(hAPP(c_COMBC(_1529417, _1529417, tc_HOL_Obool), c_fequal), _1529419))), _1529421))], (10713 ^ _781404) ^ [_963354, _963356] : [10714 ^ _781404 : [(10717 ^ _781404) ^ [] : [_963354 = _963356], (10715 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963354), _963356))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963354), _963356)))], (42505 ^ _781404) ^ [_1623214, _1623216, _1623218, _1623220] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623214), tc_List_Olist(_1623214))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623214), tc_List_Olist(_1623214)), _1623218), _1623220)), c_List_Olistrel(_1623214, _1623216))), -(c_List_Olistrelp(_1623214, hAPP(hAPP(c_COMBC(_1623214, tc_fun(tc_prod(_1623214, _1623214), tc_HOL_Obool), tc_fun(_1623214, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1623214, tc_fun(tc_fun(tc_prod(_1623214, _1623214), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1623214, _1623214), tc_HOL_Obool), tc_fun(_1623214, tc_HOL_Obool)), _1623214), c_COMBC(_1623214, tc_fun(tc_prod(_1623214, _1623214), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1623214, tc_prod(_1623214, _1623214)), tc_fun(_1623214, tc_fun(tc_fun(tc_prod(_1623214, _1623214), tc_HOL_Obool), tc_HOL_Obool)), _1623214), hAPP(c_COMBB(tc_prod(_1623214, _1623214), tc_fun(tc_fun(tc_prod(_1623214, _1623214), tc_HOL_Obool), tc_HOL_Obool), _1623214), c_member(tc_prod(_1623214, _1623214)))), c_Product__Type_OPair(_1623214, _1623214)))), _1623216), _1623218, _1623220))], (7741 ^ _781404) ^ [_908742, _908744, _908746, _908748] : [class_Lattices_Osemilattice__inf(_908742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908742), _908744), _908746)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908742), _908744), _908748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908742), _908744), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_908742), _908746), _908748))))], (36778 ^ _781404) ^ [_1469731, _1469733, _1469735, _1469737, _1469739, _1469741, _1469743, _1469745] : [c_Finite__Set_Ofolding__image(_1469731, _1469733, _1469735, _1469737, _1469739), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469733), _1469741)), c_Fun_Oinj__on(_1469733, _1469733, _1469743, _1469741), -(hAPP(hAPP(_1469739, _1469745), hAPP(c_Set_Oimage(_1469733, _1469733, _1469743), _1469741)) = hAPP(hAPP(_1469739, hAPP(c_Fun_Ocomp(_1469733, _1469731, _1469733, _1469745), _1469743)), _1469741))], (42852 ^ _781404) ^ [_1632433, _1632435, _1632437, _1632439, _1632441] : [hBOOL(hAPP(hAPP(c_member(_1632433), _1632435), hAPP(c_List_Oset(_1632433), _1632437))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632439), hAPP(_1632441, _1632435))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632439), c_List_Olist_Olist__size(_1632433, _1632441, _1632437))))], (26439 ^ _781404) ^ [_1252717, _1252719, _1252721] : [class_Rings_Olinordered__idom(_1252717), 26442 ^ _781404 : [(26449 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1252719), _1252721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252717), hAPP(c_Int_Oring__1__class_Oof__int(_1252717), _1252719)), hAPP(c_Int_Oring__1__class_Oof__int(_1252717), _1252721))))], (26443 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252717), hAPP(c_Int_Oring__1__class_Oof__int(_1252717), _1252719)), hAPP(c_Int_Oring__1__class_Oof__int(_1252717), _1252721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1252719), _1252721)))]]], (38908 ^ _781404) ^ [_1524253, _1524255, _1524257, _1524259, _1524261, _1524263, _1524265, _1524267] : [c_Fun_Oinj__on(_1524253, _1524255, _1524257, _1524259), c_Fun_Oinj__on(_1524261, _1524263, _1524265, _1524267), -(c_Fun_Oinj__on(tc_prod(_1524253, _1524261), tc_prod(_1524255, _1524263), c_Product__Type_Omap__pair(_1524253, _1524255, _1524261, _1524263, _1524257, _1524265), hAPP(hAPP(c_Product__Type_OSigma(_1524253, _1524261), _1524259), hAPP(c_COMBK(tc_fun(_1524261, tc_HOL_Obool), _1524253), _1524267))))], (16168 ^ _781404) ^ [_1068346, _1068348] : [class_Lattices_Olattice(_1068346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068346), _1068348)), -(_1068348 = c_Orderings_Obot__class_Obot(tc_fun(_1068346, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1068346), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068346), 16181 ^ [_1068346, _1068348]), 16182 ^ [_1068346, _1068348])), hAPP(hAPP(c_Set_Oinsert(_1068346), 16181 ^ [_1068346, _1068348]), hAPP(hAPP(c_Set_Oinsert(_1068346), 16182 ^ [_1068346, _1068348]), c_Orderings_Obot__class_Obot(tc_fun(_1068346, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1068346), c_Big__Operators_Olattice__class_OSup__fin(_1068346, _1068348)), _1068348)))], (13964 ^ _781404) ^ [_1024851, _1024853] : [13965 ^ _781404 : [(13968 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024853))], (13966 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024851))]], -(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), _1024851), _1024853))))], (51864 ^ _781404) ^ [_1831245, _1831247] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831245, _1831247) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831245), _1831247))], (35462 ^ _781404) ^ [_1442932, _1442934, _1442936, _1442938, _1442940] : [hBOOL(hAPP(hAPP(_1442932, _1442934), _1442936)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1442938, _1442940, tc_HOL_Obool), _1442932), hAPP(hAPP(c_Product__Type_OPair(_1442938, _1442940), _1442934), _1442936))))], (31680 ^ _781404) ^ [_1351495, _1351497, _1351499] : [class_Orderings_Olinorder(_1351495), hAPP(_1351497, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1351495), 31685 ^ [_1351495, _1351497, _1351499]), 31686 ^ [_1351495, _1351497, _1351499])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1351495), hAPP(_1351497, 31685 ^ [_1351495, _1351497, _1351499])), hAPP(_1351497, 31686 ^ [_1351495, _1351497, _1351499])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351495), _1351499)), -(_1351499 = c_Orderings_Obot__class_Obot(tc_fun(_1351495, tc_HOL_Obool))), -(hAPP(_1351497, c_Big__Operators_Olattice_OInf__fin(_1351495, c_Orderings_Oord__class_Omin(_1351495), _1351499)) = c_Big__Operators_Olattice_OInf__fin(_1351495, c_Orderings_Oord__class_Omin(_1351495), hAPP(c_Set_Oimage(_1351495, _1351495, _1351497), _1351499)))], (36197 ^ _781404) ^ [_1456948, _1456950, _1456952, _1456954, _1456956] : [-(hAPP(c_Product__Type_Osnd(_1456948, _1456950), hAPP(c_Product__Type_Oapsnd(_1456952, _1456950, _1456948, _1456954), _1456956)) = hAPP(_1456954, hAPP(c_Product__Type_Osnd(_1456948, _1456952), _1456956)))], (39634 ^ _781404) ^ [_1549143, _1549145, _1549147, _1549149] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1549143, _1549145, _1549147), _1549149), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549145, _1549147), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549143, _1549147), tc_HOL_Obool)))], (44553 ^ _781404) ^ [_1672941, _1672943, _1672945] : [-(_1672941 = c_List_Olist_ONil(_1672943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672945), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672943)), _1672941))), -(hAPP(c_List_Ohd(_1672943), hAPP(hAPP(c_List_Odrop(_1672943), _1672945), _1672941)) = hAPP(hAPP(c_List_Onth(_1672943), _1672941), _1672945))], (10387 ^ _781404) ^ [_958140, _958142, _958144, _958146] : [class_Lattices_Osemilattice__inf(_958140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958140), _958142), _958144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958140), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_958140), _958146), _958142)), _958144)))], (44776 ^ _781404) ^ [_1677155, _1677157] : [class_Complete__Lattice_Ocomplete__lattice(_1677155), -(c_Complete__Lattice_OSup__class_OSup(_1677155, hAPP(c_List_Oset(_1677155), _1677157)) = hAPP(c_List_Ofoldl(_1677155, _1677155, c_Lattices_Osemilattice__sup__class_Osup(_1677155), c_Orderings_Obot__class_Obot(_1677155)), _1677157))], (2758 ^ _781404) ^ [_822209, _822211] : [_822211 = _822209, -(c_Int_Oint__ge__less__than2(_822211) = c_Int_Oint__ge__less__than2(_822209))], (44595 ^ _781404) ^ [_1673513, _1673515] : [-(_1673513 = c_List_Olist_ONil(_1673515)), -(hAPP(c_List_Orotate1(_1673515), _1673513) = hAPP(hAPP(c_List_Oappend(_1673515), hAPP(c_List_Otl(_1673515), _1673513)), hAPP(hAPP(c_List_Olist_OCons(_1673515), hAPP(c_List_Ohd(_1673515), _1673513)), c_List_Olist_ONil(_1673515))))], (41041 ^ _781404) ^ [_1583158, _1583160, _1583162, _1583164] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583158, _1583158)), hAPP(hAPP(c_Product__Type_OPair(_1583158, _1583158), _1583160), _1583162)), _1583164)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583158, _1583158)), hAPP(hAPP(c_Product__Type_OPair(_1583158, _1583158), _1583160), _1583162)), c_Transitive__Closure_Otrancl(_1583158, _1583164))))], (44292 ^ _781404) ^ [_1666283, _1666285, _1666287, _1666289] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1666283), tc_List_Olist(_1666283))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1666283), tc_List_Olist(_1666283)), _1666285), _1666287)), c_List_Olistrel1(_1666283, _1666289))), 44297 ^ _781404 : [(44304 ^ _781404) ^ [] : [-(_1666287 = hAPP(hAPP(c_List_Oappend(_1666283), 44299 ^ [_1666283, _1666285, _1666287, _1666289]), hAPP(hAPP(c_List_Olist_OCons(_1666283), 44296 ^ [_1666283, _1666285, _1666287, _1666289]), 44300 ^ [_1666283, _1666285, _1666287, _1666289])))], (44302 ^ _781404) ^ [] : [-(_1666285 = hAPP(hAPP(c_List_Oappend(_1666283), 44299 ^ [_1666283, _1666285, _1666287, _1666289]), hAPP(hAPP(c_List_Olist_OCons(_1666283), 44295 ^ [_1666283, _1666285, _1666287, _1666289]), 44300 ^ [_1666283, _1666285, _1666287, _1666289])))], (44298 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1666283, _1666283)), hAPP(hAPP(c_Product__Type_OPair(_1666283, _1666283), 44295 ^ [_1666283, _1666285, _1666287, _1666289]), 44296 ^ [_1666283, _1666285, _1666287, _1666289])), _1666289)))]]], (35876 ^ _781404) ^ [_1451180] : [-(_1451180 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1451180), 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)))))], (48501 ^ _781404) ^ [_1758505, _1758507, _1758509] : [c_List_Olist__ex(_1758505, _1758507, _1758509), 48505 ^ _781404 : [(48508 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1758507, hAPP(hAPP(c_List_Onth(_1758505), _1758509), 48504 ^ [_1758505, _1758507, _1758509]))))], (48506 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48504 ^ [_1758505, _1758507, _1758509]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758505)), _1758509))))]]], (50281 ^ _781404) ^ [_1797315, _1797317, _1797319] : [-(c_Equiv__Relations_Oequiv(_1797315, _1797317, _1797319)), c_Relation_Orefl__on(_1797315, _1797317, _1797319), c_Relation_Osym(_1797315, _1797319), c_Relation_Otrans(_1797315, _1797319)], (52298 ^ _781404) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (44637 ^ _781404) ^ [_1674268, _1674270, _1674272] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674268)), hAPP(c_List_Orotate(_1674268, _1674270), _1674272)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674268)), _1674272))], (52098 ^ _781404) ^ [_1835226, _1835228, _1835230, _1835232] : [class_Divides_Osemiring__div(_1835226), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835226), _1835228), _1835230)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835226), _1835228), _1835232)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835226), _1835228), c_Divides_Odiv__class_Omod(_1835226, _1835230, _1835232))))], (8311 ^ _781404) ^ [_921570, _921572, _921574, _921576] : [c_Orderings_Obot__class_Obot(tc_fun(_921570, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_921572, _921570, _921574), _921576), -(_921576 = c_Orderings_Obot__class_Obot(tc_fun(_921572, tc_HOL_Obool)))], (23495 ^ _781404) ^ [_1203116, _1203118] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1203116, _1203118)), _1203118) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35444 ^ _781404) ^ [_1442527, _1442529, _1442531, _1442533, _1442535] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1442527, _1442529, _1442531), _1442533), _1442535)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1442527, _1442529)), hAPP(hAPP(c_Product__Type_OPair(_1442527, _1442529), _1442533), _1442535)), _1442531)))], (39814 ^ _781404) ^ [_1555489, _1555491] : [-(c_HOL_OThe(_1555489, hAPP(hAPP(c_COMBC(_1555489, _1555489, tc_HOL_Obool), c_fequal), _1555491)) = _1555491)], (17805 ^ _781404) ^ [_1098866, _1098868, _1098870, _1098872, _1098874, _1098876, _1098878, _1098880] : [c_Finite__Set_Ofolding__image__simple__idem(_1098866, _1098868, _1098870, _1098872, _1098874, _1098876), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098868), _1098878)), -(hAPP(_1098876, hAPP(hAPP(c_Set_Oinsert(_1098868), _1098880), _1098878)) = hAPP(hAPP(_1098870, hAPP(_1098874, _1098880)), hAPP(_1098876, _1098878)))], (15643 ^ _781404) ^ [_1058088, _1058090, _1058092] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1058088), _1058090)), 15646 ^ _781404 : [(15653 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1058088), _1058092), _1058090))), -(hAPP(c_Finite__Set_Ocard(_1058088), hAPP(hAPP(c_Set_Oinsert(_1058088), _1058092), _1058090)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1058088), _1058090)))], (15647 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1058088), _1058092), _1058090)), -(hAPP(c_Finite__Set_Ocard(_1058088), hAPP(hAPP(c_Set_Oinsert(_1058088), _1058092), _1058090)) = hAPP(c_Finite__Set_Ocard(_1058088), _1058090))]]], (1566 ^ _781404) ^ [_804019, _804021] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_804019)), _804021 = _804019, class_Groups_Oordered__cancel__ab__semigroup__add(_804021)], (13856 ^ _781404) ^ [_1023065, _1023067, _1023069] : [class_Groups_Ogroup__add(_1023065), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023065), _1023067), _1023069) = c_Groups_Ozero__class_Ozero(_1023065), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1023065), _1023067) = _1023069)], (33203 ^ _781404) ^ [_1381285, _1381287, _1381289, _1381291] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1381285), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381287, tc_Int_Oint), _1381289), _1381291)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381287, _1381285), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1381285, _1381287), c_Int_Oring__1__class_Oof__int(_1381285)), _1381289)), _1381291)), class_Groups_Ocomm__monoid__mult(_1381285), class_Rings_Oring__1(_1381285)], (44910 ^ _781404) ^ [_1680207, _1680209, _1680211, _1680213, _1680215] : [class_Orderings_Olinorder(_1680207), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680209)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680209, _1680207, _1680211), _1680213), _1680215)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680209)), _1680215)))], (11869 ^ _781404) ^ [_984576, _984578, _984580, _984582, _984584] : [c_Fun_Oinj__on(_984576, _984578, _984580, _984582), hBOOL(hAPP(hAPP(c_member(_984576), _984584), _984582)), -(hAPP(c_Fun_Othe__inv__into(_984576, _984578, _984582, _984580), hAPP(_984580, _984584)) = _984584)], (19488 ^ _781404) ^ [_1127962, _1127964] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1127962)), _1127964) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1127962), _1127964)))], (13884 ^ _781404) ^ [_1023598, _1023600] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1023598), _1023600), 13889 ^ _781404 : [(13892 ^ _781404) ^ [] : [-(_1023600 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13890 ^ _781404) ^ [] : [-(_1023598 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 13893 ^ _781404 : [(13896 ^ _781404) ^ [] : [-(_1023600 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13894 ^ _781404) ^ [] : [-(_1023598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25283 ^ _781404) ^ [_1233709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1233709))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1233709)))], (48727 ^ _781404) ^ [_1762990, _1762992, _1762994] : [c_FunDef_Ois__measure(_1762990, _1762992), -(c_FunDef_Ois__measure(tc_prod(_1762990, _1762994), hAPP(hAPP(c_COMBB(_1762990, tc_Nat_Onat, tc_prod(_1762990, _1762994)), _1762992), c_Product__Type_Ofst(_1762990, _1762994))))], (38564 ^ _781404) ^ [_1514344, _1514346, _1514348, _1514350] : [-(hAPP(c_Set_Oimage(tc_prod(_1514344, _1514346), tc_prod(_1514346, _1514344), hAPP(c_Product__Type_Oprod_Oprod__case(_1514344, _1514346, tc_prod(_1514346, _1514344)), hAPP(c_COMBC(_1514346, _1514344, tc_prod(_1514346, _1514344)), c_Product__Type_OPair(_1514346, _1514344)))), hAPP(hAPP(c_Product__Type_OSigma(_1514344, _1514346), _1514348), hAPP(c_COMBK(tc_fun(_1514346, tc_HOL_Obool), _1514344), _1514350))) = hAPP(hAPP(c_Product__Type_OSigma(_1514346, _1514344), _1514350), hAPP(c_COMBK(tc_fun(_1514344, tc_HOL_Obool), _1514346), _1514348)))], (28587 ^ _781404) ^ [_1292869, _1292871, _1292873, _1292875] : [class_Fields_Olinordered__field__inverse__zero(_1292869), class_Int_Onumber(_1292869), 28594 ^ _781404 : [(28595 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292869), _1292871), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292869), _1292873), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875)))), 28598 ^ _781404 : [(28605 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292869), c_Groups_Ozero__class_Ozero(_1292869)), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875)))), 28608 ^ _781404 : [(28615 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292869), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875)), c_Groups_Ozero__class_Ozero(_1292869)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292869), _1292871), c_Groups_Ozero__class_Ozero(_1292869))))], (28609 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292869), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875)), c_Groups_Ozero__class_Ozero(_1292869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292869), _1292873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292869), _1292871), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875)))))]]], (28599 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292869), c_Groups_Ozero__class_Ozero(_1292869)), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292869), _1292871), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875))), _1292873)))]]], (28621 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292869), _1292871), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292869), _1292873), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875))))), 28624 ^ _781404 : [(28627 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292869), _1292871), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875))), _1292873))], (28625 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292869), c_Groups_Ozero__class_Ozero(_1292869)), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875))))]], 28628 ^ _781404 : [(28631 ^ _781404) ^ [] : [28632 ^ _781404 : [(28635 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292869), _1292873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292869), _1292871), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875))))], (28633 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292869), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875)), c_Groups_Ozero__class_Ozero(_1292869))))]], 28636 ^ _781404 : [(28639 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292869), _1292871), c_Groups_Ozero__class_Ozero(_1292869)))], (28637 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292869), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875)), c_Groups_Ozero__class_Ozero(_1292869)))]]], (28629 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292869), c_Groups_Ozero__class_Ozero(_1292869)), hAPP(c_Int_Onumber__class_Onumber__of(_1292869), _1292875)))]]]]], (50469 ^ _781404) ^ [_1800842, _1800844, _1800846] : [c_Fun_Oinj__on(_1800842, _1800844, _1800846, c_Orderings_Otop__class_Otop(tc_fun(_1800842, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1800844, _1800842, _1800842, c_Hilbert__Choice_Oinv__into(_1800842, _1800844, c_Orderings_Otop__class_Otop(tc_fun(_1800842, tc_HOL_Obool)), _1800846)), _1800846) = c_Fun_Oid(_1800842))], (20101 ^ _781404) ^ [_1138398] : [c_Int_OBit0(_1138398) = c_Int_OPls, -(_1138398 = c_Int_OPls)], (20857 ^ _781404) ^ [_1151821, _1151823, _1151825] : [class_Rings_Oring__no__zero__divisors(_1151821), 20860 ^ _781404 : [(20861 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151821), _1151823), _1151825) = c_Groups_Ozero__class_Ozero(_1151821), -(_1151823 = c_Groups_Ozero__class_Ozero(_1151821)), -(_1151825 = c_Groups_Ozero__class_Ozero(_1151821))], (20871 ^ _781404) ^ [] : [20872 ^ _781404 : [(20875 ^ _781404) ^ [] : [_1151825 = c_Groups_Ozero__class_Ozero(_1151821)], (20873 ^ _781404) ^ [] : [_1151823 = c_Groups_Ozero__class_Ozero(_1151821)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151821), _1151823), _1151825) = c_Groups_Ozero__class_Ozero(_1151821))]]], (45591 ^ _781404) ^ [_1694772, _1694774, _1694776] : [-(c_List_Olist_Olist__size(_1694772, _1694774, _1694776) = 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(_1694772, tc_Nat_Onat), _1694774), _1694776))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694772)), _1694776)))], (40446 ^ _781404) ^ [_1569472, _1569474, _1569476] : [40447 ^ _781404 : [(40448 ^ _781404) ^ [_1569526] : [hBOOL(hAPP(_1569472, _1569526))]], _1569474 = c_Hilbert__Choice_OEps(_1569476, _1569472), -(hBOOL(hAPP(_1569472, _1569474)))], (17511 ^ _781404) ^ [_1093648, _1093650] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1093648), _1093650) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093648), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1093650)))], (14538 ^ _781404) ^ [_1036165, _1036167, _1036169] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036165), _1036167) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036169), _1036167), -(_1036165 = _1036169)], (48397 ^ _781404) ^ [_1756550, _1756552, _1756554, _1756556] : [class_Orderings_Oorder(_1756550), class_Enum_Oenum(_1756552), 48404 ^ _781404 : [(48411 ^ _781404) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1756552), hAPP(hAPP(c_COMBS(_1756552, _1756550, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1756550, tc_fun(_1756550, tc_HOL_Obool), _1756552), c_Orderings_Oord__class_Oless__eq(_1756550)), _1756554)), _1756556))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1756552, _1756550)), _1756554), _1756556)))], (48405 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1756552, _1756550)), _1756554), _1756556)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1756552), hAPP(hAPP(c_COMBS(_1756552, _1756550, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1756550, tc_fun(_1756550, tc_HOL_Obool), _1756552), c_Orderings_Oord__class_Oless__eq(_1756550)), _1756554)), _1756556))))]]], (45425 ^ _781404) ^ [_1691292, _1691294, _1691296] : [c_Fun_Oinj__on(_1691292, _1691294, _1691296, c_Orderings_Otop__class_Otop(tc_fun(_1691292, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1691292), tc_List_Olist(_1691294), hAPP(c_List_Omap(_1691292, _1691294), _1691296), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1691292), tc_HOL_Obool))))], (32957 ^ _781404) ^ [_1375448, _1375450, _1375452] : [-(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), _1375448)), 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))), _1375450))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1375452))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1375452)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1375448), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1375448), 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), _1375452), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1375450)))))], (8808 ^ _781404) ^ [_930034, _930036, _930038] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_930034, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_930034, tc_HOL_Obool), tc_HOL_Obool)), _930036), _930038)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_930034, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_930034, tc_HOL_Obool), _930036)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_930034, tc_HOL_Obool), _930038)))], (50450 ^ _781404) ^ [_1800199, _1800201] : [c_Equiv__Relations_Opart__equivp(_1800199, _1800201), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1800199, tc_HOL_Obool)), 50453 ^ [_1800199, _1800201]), hAPP(hAPP(c_COMBB(tc_fun(_1800199, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1800199, tc_HOL_Obool)), c_HOL_OEx(_1800199)), hAPP(hAPP(c_COMBB(tc_fun(_1800199, tc_HOL_Obool), tc_fun(_1800199, tc_HOL_Obool), tc_fun(_1800199, tc_HOL_Obool)), hAPP(c_COMBS(_1800199, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1800199), c_fconj), hAPP(hAPP(c_COMBS(_1800199, _1800199, tc_HOL_Obool), _1800201), c_COMBI(_1800199))))), hAPP(hAPP(c_COMBC(tc_fun(_1800199, tc_HOL_Obool), tc_fun(_1800199, tc_fun(_1800199, tc_HOL_Obool)), tc_fun(_1800199, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1800199, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1800199, tc_fun(_1800199, tc_HOL_Obool)), tc_fun(_1800199, tc_HOL_Obool)), tc_fun(_1800199, tc_HOL_Obool)), c_COMBB(tc_fun(_1800199, tc_HOL_Obool), tc_HOL_Obool, _1800199)), c_fequal)), _1800201))))))], (10951 ^ _781404) ^ [_967366, _967368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967366), _967368)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967366), _967368) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14045 ^ _781404) ^ [_1026436, _1026438, _1026440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026436), _1026438)), 14048 ^ _781404 : [(14055 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026440), _1026436)), _1026438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026440), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026438), _1026436))))], (14049 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026440), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026438), _1026436))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026440), _1026436)), _1026438)))]]], (34147 ^ _781404) ^ [_1408593, _1408595, _1408597, _1408599, _1408601] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408593, tc_fun(_1408595, tc_HOL_Obool)), _1408597), hAPP(hAPP(c_COMBS(_1408593, tc_fun(_1408595, tc_HOL_Obool), tc_fun(_1408595, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408595, tc_HOL_Obool), tc_fun(tc_fun(_1408595, tc_HOL_Obool), tc_fun(_1408595, tc_HOL_Obool)), _1408593), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408595, tc_HOL_Obool))), _1408599)), _1408601)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408595, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408593, tc_fun(_1408595, tc_HOL_Obool)), _1408597), _1408599)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408593, tc_fun(_1408595, tc_HOL_Obool)), _1408597), _1408601)))], (34921 ^ _781404) ^ [_1430900, _1430902] : [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(_1430900))), 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)), _1430902)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430900)), hAPP(c_Nat_OSuc, _1430902))))], (2630 ^ _781404) ^ [_820213, _820215] : [_820215 = _820213, -(c_Nitpick_Ozero__frac(_820215) = c_Nitpick_Ozero__frac(_820213))], (24907 ^ _781404) ^ [_1227700, _1227702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1227700), _1227702)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1227702, _1227700) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1227702), _1227700), _1227700))], (8463 ^ _781404) ^ [_924147] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _924147)))], (7932 ^ _781404) ^ [_913090, _913092, _913094, _913096] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913090, tc_HOL_Obool)), _913092), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913090, tc_HOL_Obool)), _913094), _913096)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913090, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913090, tc_HOL_Obool)), _913092), _913094)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913090, tc_HOL_Obool)), _913092), _913096)))], (8146 ^ _781404) ^ [_918116] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _918116)))], (18577 ^ _781404) ^ [_1112795, _1112797, _1112799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1112795)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1112797), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1112799)), 18587 ^ _781404 : [(18593 ^ _781404) ^ [] : [-(_1112797 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 18589 ^ [_1112795, _1112797, _1112799]), 18586 ^ [_1112795, _1112797, _1112799]))], (18591 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18589 ^ [_1112795, _1112797, _1112799]), _1112799)))], (18588 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18586 ^ [_1112795, _1112797, _1112799]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1112795))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1112797), _1112795) = _1112797)], (48655 ^ _781404) ^ [_1761673, _1761675, _1761677] : [c_List_Olist__all(_1761673, _1761675, _1761677), 48658 ^ _781404 : [(48659 ^ _781404) ^ [_1761762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761762), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761673)), _1761677))), -(hBOOL(hAPP(_1761675, hAPP(hAPP(c_List_Onth(_1761673), _1761677), _1761762))))]]], (38174 ^ _781404) ^ [_1505027, _1505029, _1505031] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1505027, _1505027)), _1505029), c_Relation_OId__on(_1505027, _1505031))), 38178 ^ _781404 : [(38181 ^ _781404) ^ [] : [-(_1505029 = hAPP(hAPP(c_Product__Type_OPair(_1505027, _1505027), 38177 ^ [_1505027, _1505029, _1505031]), 38177 ^ [_1505027, _1505029, _1505031]))], (38179 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1505027), 38177 ^ [_1505027, _1505029, _1505031]), _1505031)))]]], (19524 ^ _781404) ^ [_1128579] : [_1128579 = 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), _1128579)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51670 ^ _781404) ^ [_1827748, _1827750, _1827752, _1827754] : [class_Rings_Oidom(_1827748), 51673 ^ _781404 : [(51674 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827748), _1827750), _1827752)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827748), _1827750), _1827754))), -(_1827750 = c_Groups_Ozero__class_Ozero(_1827748)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827748), _1827752), _1827754)))], (51684 ^ _781404) ^ [] : [51685 ^ _781404 : [(51688 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827748), _1827752), _1827754))], (51686 ^ _781404) ^ [] : [_1827750 = c_Groups_Ozero__class_Ozero(_1827748)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827748), _1827750), _1827752)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827748), _1827750), _1827754))))]]], (48739 ^ _781404) ^ [_1763242, _1763244, _1763246] : [c_List_Olist__all(_1763242, _1763244, hAPP(c_List_Orev(_1763242), _1763246)), -(c_List_Olist__all(_1763242, _1763244, _1763246))], (28055 ^ _781404) ^ [_1282963, _1282965, _1282967, _1282969] : [class_Fields_Ofield__inverse__zero(_1282963), class_Int_Onumber(_1282963), 28062 ^ _781404 : [(28063 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1282963), _1282965) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1282963), _1282967), _1282969), 28066 ^ _781404 : [(28073 ^ _781404) ^ [] : [_1282969 = c_Groups_Ozero__class_Ozero(_1282963), -(hAPP(c_Int_Onumber__class_Onumber__of(_1282963), _1282965) = c_Groups_Ozero__class_Ozero(_1282963))], (28067 ^ _781404) ^ [] : [-(_1282969 = c_Groups_Ozero__class_Ozero(_1282963)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282963), hAPP(c_Int_Onumber__class_Onumber__of(_1282963), _1282965)), _1282969) = _1282967)]]], (28079 ^ _781404) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1282963), _1282965) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1282963), _1282967), _1282969)), 28082 ^ _781404 : [(28085 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282963), hAPP(c_Int_Onumber__class_Onumber__of(_1282963), _1282965)), _1282969) = _1282967], (28083 ^ _781404) ^ [] : [_1282969 = c_Groups_Ozero__class_Ozero(_1282963)]], 28086 ^ _781404 : [(28089 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1282963), _1282965) = c_Groups_Ozero__class_Ozero(_1282963)], (28087 ^ _781404) ^ [] : [-(_1282969 = c_Groups_Ozero__class_Ozero(_1282963))]]]]], (7846 ^ _781404) ^ [_911068, _911070, _911072] : [class_Lattices_Olattice(_911068), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911068), _911070), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_911068), _911070), _911072)) = _911070)], (12901 ^ _781404) ^ [_1005332, _1005334] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1005332, _1005334))))], (40059 ^ _781404) ^ [_1560271, _1560273, _1560275, _1560277] : [hBOOL(hAPP(hAPP(c_member(_1560271), _1560273), hAPP(c_Relation_ODomain(_1560271, _1560275), _1560277))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560271, _1560275)), hAPP(hAPP(c_Product__Type_OPair(_1560271, _1560275), _1560273), 40062 ^ [_1560271, _1560273, _1560275, _1560277])), _1560277)))], (24592 ^ _781404) ^ [_1222560, _1222562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222560)), -(c_SMT_Oz3div(_1222562, _1222560) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222562), _1222560))], (16334 ^ _781404) ^ [_1071577, _1071579] : [class_Rings_Olinordered__semidom(_1071577), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071577), _1071579), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071577), _1071579), c_Groups_Oone__class_Oone(_1071577)))))], (16492 ^ _781404) ^ [_1074543, _1074545, _1074547, _1074549] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1074543), _1074545)), hBOOL(hAPP(hAPP(c_member(_1074543), _1074547), _1074545)), -(hBOOL(hAPP(hAPP(c_member(_1074543), _1074547), _1074549))), -(hAPP(c_Finite__Set_Ocard(_1074543), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074543, tc_HOL_Obool)), _1074545), hAPP(hAPP(c_Set_Oinsert(_1074543), _1074547), _1074549))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1074543), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074543, tc_HOL_Obool)), _1074545), _1074549))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45561 ^ _781404) ^ [_1694087, _1694089] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1694087)), hAPP(c_Code__Numeral_Oof__nat, _1694089)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1694087), _1694089)))], (24993 ^ _781404) ^ [_1229095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1229095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1229095)))], (37398 ^ _781404) ^ [_1484914, _1484916, _1484918, _1484920, _1484922, _1484924] : [hBOOL(hAPP(hAPP(c_member(_1484914), _1484916), _1484918)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1484914, _1484920)), hAPP(hAPP(c_Product__Type_OPair(_1484914, _1484920), _1484916), _1484922)), _1484924)), -(hBOOL(hAPP(hAPP(c_member(_1484920), _1484922), hAPP(c_Relation_OImage(_1484914, _1484920, _1484924), _1484918))))], (30828 ^ _781404) ^ [_1335568, _1335570, _1335572, _1335574] : [class_Orderings_Olinorder(_1335568), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335568), _1335570), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1335568), _1335572), _1335574))), 30835 ^ _781404 : [(30838 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335568), _1335570), _1335574)))], (30836 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335568), _1335570), _1335572)))]]], (43234 ^ _781404) ^ [_1642773, _1642775, _1642777, _1642779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642773), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642775)), _1642777))), -(hBOOL(hAPP(hAPP(c_member(_1642775), _1642779), hAPP(c_List_Oset(_1642775), hAPP(hAPP(c_List_Olist__update(_1642775, _1642777), _1642773), _1642779)))))], (35456 ^ _781404) ^ [_1442803, _1442805, _1442807, _1442809, _1442811] : [hBOOL(hAPP(hAPP(_1442803, _1442805), _1442807)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1442809, _1442811, tc_HOL_Obool), _1442803), hAPP(hAPP(c_Product__Type_OPair(_1442809, _1442811), _1442805), _1442807))))], (23629 ^ _781404) ^ [_1205775, _1205777, _1205779] : [-(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, _1205775, _1205777)), _1205779), _1205777) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1205775), _1205779), _1205777))], (50543 ^ _781404) ^ [_1802337, _1802339, _1802341] : [hAPP(c_Set_Oimage(_1802337, _1802339, _1802341), c_Orderings_Otop__class_Otop(tc_fun(_1802337, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1802339, tc_HOL_Obool)), 50546 ^ _781404 : [(50547 ^ _781404) ^ [_1802448] : [-(hAPP(_1802341, hAPP(c_Hilbert__Choice_Oinv__into(_1802337, _1802339, c_Orderings_Otop__class_Otop(tc_fun(_1802337, tc_HOL_Obool)), _1802341), _1802448)) = _1802448)]]], (36374 ^ _781404) ^ [_1460862, _1460864, _1460866, _1460868, _1460870, _1460872] : [c_Finite__Set_Ofolding(_1460862, _1460864, _1460866, _1460868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460862), _1460870)), -(hAPP(hAPP(_1460868, _1460870), _1460872) = hAPP(hAPP(c_Finite__Set_Ofold(_1460862, _1460864, _1460866), _1460872), _1460870))], (37842 ^ _781404) ^ [_1496021, _1496023, _1496025, _1496027, _1496029] : [c_Equiv__Relations_Oequiv(_1496021, _1496023, _1496025), hBOOL(hAPP(hAPP(c_member(_1496021), _1496027), _1496023)), hBOOL(hAPP(hAPP(c_member(_1496021), _1496029), _1496023)), 37853 ^ _781404 : [(37860 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1496021, _1496021)), hAPP(hAPP(c_Product__Type_OPair(_1496021, _1496021), _1496027), _1496029)), _1496025)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1496021), hAPP(hAPP(c_Set_Oinsert(_1496021), _1496027), c_Orderings_Obot__class_Obot(tc_fun(_1496021, tc_HOL_Obool)))), _1496025) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1496021), hAPP(hAPP(c_Set_Oinsert(_1496021), _1496029), c_Orderings_Obot__class_Obot(tc_fun(_1496021, tc_HOL_Obool)))), _1496025))], (37854 ^ _781404) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1496021), hAPP(hAPP(c_Set_Oinsert(_1496021), _1496027), c_Orderings_Obot__class_Obot(tc_fun(_1496021, tc_HOL_Obool)))), _1496025) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1496021), hAPP(hAPP(c_Set_Oinsert(_1496021), _1496029), c_Orderings_Obot__class_Obot(tc_fun(_1496021, tc_HOL_Obool)))), _1496025), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1496021, _1496021)), hAPP(hAPP(c_Product__Type_OPair(_1496021, _1496021), _1496027), _1496029)), _1496025)))]]], (52496 ^ _781404) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (27143 ^ _781404) ^ [_1265985, _1265987, _1265989] : [class_Groups_Oordered__ab__group__add__abs(_1265985), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265985), _1265987), _1265989)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265985), hAPP(c_Groups_Ouminus__class_Ouminus(_1265985), _1265987)), _1265989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265985), hAPP(c_Groups_Oabs__class_Oabs(_1265985), _1265987)), _1265989)))], (45994 ^ _781404) ^ [_1704056, _1704058, _1704060] : [_1704056 = _1704058, -(c_List_Olist__all2(_1704060, _1704060, c_fequal, _1704056, _1704058))], (52548 ^ _781404) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (30484 ^ _781404) ^ [_1329071, _1329073, _1329075] : [class_Divides_Osemiring__div(_1329071), -(_1329073 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1329071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329071), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1329071), _1329073), _1329075)), _1329075)), c_Divides_Odiv__class_Omod(_1329071, _1329073, _1329075)))], (7335 ^ _781404) ^ [_900870, _900872, _900874] : [class_Orderings_Olinorder(_900870), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900870), _900872), _900874)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900870, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_900870, _900872, _900874)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_900870), _900874)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_900870), _900872))], (52322 ^ _781404) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (24626 ^ _781404) ^ [_1223057] : [class_Power_Opower(_1223057), -(c_Power_Opower__class_Opower(_1223057) = c_Power_Opower_Opower(_1223057, c_Groups_Oone__class_Oone(_1223057), c_Groups_Otimes__class_Otimes(_1223057)))], (37100 ^ _781404) ^ [_1477201, _1477203, _1477205, _1477207, _1477209, _1477211, _1477213] : [-(hAPP(c_Product__Type_Oapfst(_1477201, _1477203, _1477205, _1477207), hAPP(c_Product__Type_Oapsnd(_1477209, _1477205, _1477201, _1477211), _1477213)) = hAPP(hAPP(c_Product__Type_OPair(_1477203, _1477205), hAPP(_1477207, hAPP(c_Product__Type_Ofst(_1477201, _1477209), _1477213))), hAPP(_1477211, hAPP(c_Product__Type_Osnd(_1477201, _1477209), _1477213))))], (27829 ^ _781404) ^ [_1279381, _1279383, _1279385, _1279387] : [class_Rings_Odivision__ring(_1279381), -(_1279383 = c_Groups_Ozero__class_Ozero(_1279381)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279381), _1279385), _1279383) = _1279387, -(_1279385 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279381), _1279387), _1279383))], (33611 ^ _781404) ^ [_1394052, _1394054, _1394056, _1394058, _1394060, _1394062] : [class_Complete__Lattice_Ocomplete__lattice(_1394052), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394054, _1394052), _1394056), hAPP(hAPP(c_COMBB(tc_fun(_1394058, _1394052), _1394052, _1394054), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394058, _1394052), _1394060)), _1394062)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394058, _1394052), _1394060), hAPP(hAPP(c_COMBB(tc_fun(_1394054, _1394052), _1394052, _1394058), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394054, _1394052), _1394056)), hAPP(c_COMBC(_1394054, _1394058, _1394052), _1394062))))], (3042 ^ _781404) ^ [_826549, _826551] : [_826551 = _826549, -(c_HOL_Obool_Obool__size(_826551) = c_HOL_Obool_Obool__size(_826549))], (4402 ^ _781404) ^ [_848145, _848147, _848149, _848151, _848153, _848155, _848157, _848159, _848161, _848163, _848165, _848167] : [-(c_New__Random__Sequence_Opos__union(_848167, _848163, _848159, _848155, _848151, _848147) = c_New__Random__Sequence_Opos__union(_848165, _848161, _848157, _848153, _848149, _848145)), _848167 = _848165, _848163 = _848161, _848159 = _848157, _848155 = _848153, _848151 = _848149, _848147 = _848145], (50085 ^ _781404) ^ [_1793581, _1793583] : [50088 ^ _781404 : [(50093 ^ _781404) ^ [] : [50086 ^ [_1793581, _1793583] = 50087 ^ [_1793581, _1793583]], (50091 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1793581, _1793581)), hAPP(hAPP(c_Product__Type_OPair(_1793581, _1793581), 50087 ^ [_1793581, _1793583]), 50086 ^ [_1793581, _1793583])), _1793583)))], (50089 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1793581, _1793581)), hAPP(hAPP(c_Product__Type_OPair(_1793581, _1793581), 50086 ^ [_1793581, _1793583]), 50087 ^ [_1793581, _1793583])), _1793583)))]], -(c_Relation_Oantisym(_1793581, _1793583))], (17549 ^ _781404) ^ [_1094397] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094397), _1094397)))], (13828 ^ _781404) ^ [_1022599, _1022601, _1022603] : [class_Groups_Ogroup__add(_1022599), 13831 ^ _781404 : [(13838 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022599), _1022601), _1022603) = c_Groups_Ozero__class_Ozero(_1022599), -(_1022601 = hAPP(c_Groups_Ouminus__class_Ouminus(_1022599), _1022603))], (13832 ^ _781404) ^ [] : [_1022601 = hAPP(c_Groups_Ouminus__class_Ouminus(_1022599), _1022603), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022599), _1022601), _1022603) = c_Groups_Ozero__class_Ozero(_1022599))]]], (52480 ^ _781404) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (6903 ^ _781404) ^ [_892225, _892227, _892229, _892231] : [class_Lattices_Osemilattice__sup(_892225), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892225), _892227), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892225), _892229), _892231)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892225), _892229), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892225), _892227), _892231)))], (1186 ^ _781404) ^ [_799269, _799271] : [-(class_Groups_Olinordered__ab__group__add(_799269)), _799271 = _799269, class_Groups_Olinordered__ab__group__add(_799271)], (15299 ^ _781404) ^ [_1051623, _1051625, _1051627] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1051623, tc_HOL_Obool)), _1051625), _1051627))), 15305 ^ _781404 : [(15309 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1051623, tc_HOL_Obool)), 15307 ^ [_1051623, _1051625, _1051627]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1051623, tc_HOL_Obool)), _1051625), _1051627))))], (15311 ^ _781404) ^ [] : [15304 ^ [_1051623, _1051625, _1051627] = 15307 ^ [_1051623, _1051625, _1051627]], (15313 ^ _781404) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1051623, tc_HOL_Obool)), 15304 ^ [_1051623, _1051625, _1051627]), 15307 ^ [_1051623, _1051625, _1051627]) = c_Orderings_Obot__class_Obot(tc_fun(_1051623, tc_HOL_Obool))], (15306 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1051623, tc_HOL_Obool)), 15304 ^ [_1051623, _1051625, _1051627]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1051623, tc_HOL_Obool)), _1051625), _1051627))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1051623, tc_HOL_Obool)), _1051625), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1051623, tc_HOL_Obool), _1051627)) = c_Orderings_Obot__class_Obot(tc_fun(_1051623, tc_HOL_Obool)))], (48337 ^ _781404) ^ [_1754956, _1754958, _1754960, _1754962, _1754964] : [-(hAPP(c_List_Ofilter(_1754956, _1754958), _1754960) = hAPP(hAPP(c_List_Olist_OCons(_1754956), _1754962), _1754964)), 48338 ^ _781404 : [(48339 ^ _781404) ^ [_1755084, _1755086] : [_1754960 = hAPP(hAPP(c_List_Oappend(_1754956), _1755086), hAPP(hAPP(c_List_Olist_OCons(_1754956), _1754962), _1755084)), 48345 ^ _781404 : [(48348 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1754958, 48344 ^ [_1754956, _1754958, _1754960, _1754962, _1754964, _1755084, _1755086])))], (48346 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754956), 48344 ^ [_1754956, _1754958, _1754960, _1754962, _1754964, _1755084, _1755086]), hAPP(c_List_Oset(_1754956), _1755086))))]], hBOOL(hAPP(_1754958, _1754962)), _1754964 = hAPP(c_List_Ofilter(_1754956, _1754958), _1755084)]]], (23387 ^ _781404) ^ [_1200824, _1200826, _1200828] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200824), _1200826)), _1200828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200824), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1200826), _1200828))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200824), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1200826, _1200828))), _1200828)))], (2518 ^ _781404) ^ [_818397, _818399, _818401, _818403, _818405, _818407, _818409, _818411, _818413, _818415] : [-(c_Finite__Set_Ofold__graph(_818415, _818411, _818407, _818403, _818399) = c_Finite__Set_Ofold__graph(_818413, _818409, _818405, _818401, _818397)), _818415 = _818413, _818411 = _818409, _818407 = _818405, _818403 = _818401, _818399 = _818397], (1636 ^ _781404) ^ [_804894, _804896] : [-(class_Groups_Ocancel__ab__semigroup__add(_804894)), _804896 = _804894, class_Groups_Ocancel__ab__semigroup__add(_804896)], (25233 ^ _781404) ^ [_1232889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232889)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1232889)) = _1232889)], (25117 ^ _781404) ^ [_1231012, _1231014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1231012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1231014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1231014), _1231012)), _1231014)))], (14849 ^ _781404) ^ [_1042014, _1042016, _1042018, _1042020, _1042022] : [c_Finite__Set_Ofolding__one(_1042014, _1042016, _1042018), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042014), _1042020)), hBOOL(hAPP(hAPP(c_member(_1042014), _1042022), _1042020)), 14860 ^ _781404 : [(14867 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042014, tc_HOL_Obool)), _1042020), hAPP(hAPP(c_Set_Oinsert(_1042014), _1042022), c_Orderings_Obot__class_Obot(tc_fun(_1042014, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1042014, tc_HOL_Obool))), -(hAPP(_1042018, _1042020) = hAPP(hAPP(_1042016, _1042022), hAPP(_1042018, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042014, tc_HOL_Obool)), _1042020), hAPP(hAPP(c_Set_Oinsert(_1042014), _1042022), c_Orderings_Obot__class_Obot(tc_fun(_1042014, tc_HOL_Obool)))))))], (14861 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042014, tc_HOL_Obool)), _1042020), hAPP(hAPP(c_Set_Oinsert(_1042014), _1042022), c_Orderings_Obot__class_Obot(tc_fun(_1042014, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1042014, tc_HOL_Obool)), -(hAPP(_1042018, _1042020) = _1042022)]]], (17463 ^ _781404) ^ [_1092917, _1092919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092917), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1092919), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092917), _1092919)))], (25859 ^ _781404) ^ [_1243582, _1243584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243582)), 25862 ^ _781404 : [(25869 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243582), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1243582)), _1243584)))], (25863 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1243582)), _1243584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243582), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243584))))]]], (10275 ^ _781404) ^ [_956105, _956107] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956105), _956107)), _956105)))], (44966 ^ _781404) ^ [_1681268, _1681270, _1681272] : [class_Orderings_Olinorder(_1681268), -(hBOOL(hAPP(hAPP(c_member(_1681268), _1681270), hAPP(c_List_Oset(_1681268), _1681272)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1681268, _1681268, c_COMBI(_1681268), _1681270, _1681272) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681268, _1681268, c_COMBI(_1681268)), _1681270), _1681272))], (46325 ^ _781404) ^ [_1710901, _1710903] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710901)), c_List_Oremdups(_1710901, _1710903)) = hAPP(c_Finite__Set_Ocard(_1710901), hAPP(c_List_Oset(_1710901), _1710903)))], (36191 ^ _781404) ^ [_1456813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1456813)), 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), _1456813)) = 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), _1456813))))))], (9877 ^ _781404) ^ [_950135, _950137, _950139, _950141, _950143] : [c_Fun_Oinj__on(_950135, _950137, _950139, c_Orderings_Otop__class_Otop(tc_fun(_950135, tc_HOL_Obool))), hAPP(_950139, _950141) = hAPP(_950139, _950143), -(_950141 = _950143)], (35336 ^ _781404) ^ [_1440010, _1440012, _1440014, _1440016, _1440018, _1440020] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440010, tc_fun(_1440012, tc_HOL_Obool))), _1440014), _1440016), _1440018), _1440020)), -(hBOOL(hAPP(hAPP(_1440014, _1440018), _1440020)))], (9525 ^ _781404) ^ [_944584, _944586, _944588, _944590] : [class_Orderings_Oorder(_944584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944584), _944586), _944588)), _944586 = _944590, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944584), _944590), _944588)))], (29993 ^ _781404) ^ [_1319002, _1319004, _1319006, _1319008, _1319010] : [class_Groups_Ocomm__monoid__mult(_1319002), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319004), _1319006)), -(hBOOL(hAPP(hAPP(c_member(_1319004), _1319008), _1319006))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319004, _1319002), _1319010), hAPP(hAPP(c_Set_Oinsert(_1319004), _1319008), _1319006)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319002), hAPP(_1319010, _1319008)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319004, _1319002), _1319010), _1319006)))], (33231 ^ _781404) ^ [_1381999, _1382001, _1382003, _1382005] : [_1381999 = c_Orderings_Obot__class_Obot(tc_fun(_1382001, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1382001, _1382003, hAPP(c_COMBK(_1382003, _1382001), _1382005)), _1381999) = c_Orderings_Obot__class_Obot(tc_fun(_1382003, tc_HOL_Obool)))], (35539 ^ _781404) ^ [_1444644, _1444646, _1444648, _1444650] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1444644, _1444646, _1444648), hAPP(hAPP(c_COMBB(tc_fun(_1444646, tc_prod(_1444644, _1444646)), tc_fun(_1444646, _1444648), _1444644), hAPP(c_COMBB(tc_prod(_1444644, _1444646), _1444648, _1444646), _1444650)), c_Product__Type_OPair(_1444644, _1444646))) = _1444650)], (8578 ^ _781404) ^ [_926055] : [class_Complete__Lattice_Ocomplete__lattice(_926055), -(c_Complete__Lattice_OInf__class_OInf(_926055, c_Orderings_Otop__class_Otop(tc_fun(_926055, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_926055))], (52398 ^ _781404) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (26937 ^ _781404) ^ [_1262251, _1262253, _1262255] : [class_Groups_Oordered__ab__group__add__abs(_1262251), -(hAPP(c_Groups_Oabs__class_Oabs(_1262251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1262251), hAPP(c_Groups_Oabs__class_Oabs(_1262251), _1262253)), hAPP(c_Groups_Oabs__class_Oabs(_1262251), _1262255))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1262251), hAPP(c_Groups_Oabs__class_Oabs(_1262251), _1262253)), hAPP(c_Groups_Oabs__class_Oabs(_1262251), _1262255)))], (33123 ^ _781404) ^ [_1379247, _1379249, _1379251, _1379253, _1379255] : [class_Groups_Ocomm__monoid__add(_1379247), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379247), _1379249), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1379251), _1379253)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1379255), _1379253))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379247), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1379247, tc_Nat_Onat), _1379249), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1379253))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1379251), _1379255)))], (45192 ^ _781404) ^ [_1685630, _1685632, _1685634, _1685636, _1685638, _1685640] : [-(hAPP(hAPP(c_List_Ozip(_1685630, _1685632), _1685634), hAPP(hAPP(c_List_Omap(_1685636, _1685632), _1685638), _1685640)) = hAPP(hAPP(c_List_Omap(tc_prod(_1685630, _1685636), tc_prod(_1685630, _1685632)), hAPP(c_Product__Type_Oprod_Oprod__case(_1685630, _1685636, tc_prod(_1685630, _1685632)), hAPP(hAPP(c_COMBC(_1685630, tc_fun(_1685636, _1685632), tc_fun(_1685636, tc_prod(_1685630, _1685632))), hAPP(hAPP(c_COMBB(tc_fun(_1685632, tc_prod(_1685630, _1685632)), tc_fun(tc_fun(_1685636, _1685632), tc_fun(_1685636, tc_prod(_1685630, _1685632))), _1685630), c_COMBB(_1685632, tc_prod(_1685630, _1685632), _1685636)), c_Product__Type_OPair(_1685630, _1685632))), _1685638))), hAPP(hAPP(c_List_Ozip(_1685630, _1685636), _1685634), _1685640)))], (41574 ^ _781404) ^ [_1596798, _1596800, _1596802, _1596804, _1596806] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596798, _1596800)), hAPP(hAPP(c_Product__Type_OPair(_1596798, _1596800), _1596802), _1596804)), hAPP(c_Relation_Oconverse(_1596800, _1596798), _1596806))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596800, _1596798)), hAPP(hAPP(c_Product__Type_OPair(_1596800, _1596798), _1596804), _1596802)), _1596806)))], (25363 ^ _781404) ^ [_1234891, _1234893] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1234891, _1234893) = 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), _1234891), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234893))))], (42326 ^ _781404) ^ [_1617461, _1617463, _1617465, _1617467, _1617469, _1617471] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617461, _1617461)), hAPP(hAPP(c_Product__Type_OPair(_1617461, _1617461), _1617463), _1617465)), c_Transitive__Closure_Ortrancl(_1617461, _1617467))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617461), tc_List_Olist(_1617461))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617461), tc_List_Olist(_1617461)), _1617469), _1617471)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1617461), c_List_Olistrel1(_1617461, _1617467)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617461), tc_List_Olist(_1617461))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617461), tc_List_Olist(_1617461)), hAPP(hAPP(c_List_Olist_OCons(_1617461), _1617463), _1617469)), hAPP(hAPP(c_List_Olist_OCons(_1617461), _1617465), _1617471))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1617461), c_List_Olistrel1(_1617461, _1617467)))))], (20459 ^ _781404) ^ [_1144425, _1144427, _1144429] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1144425)))), 20462 ^ _781404 : [(20469 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1144427)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144425)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144427)), _1144429)) = 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), _1144425), _1144427))), _1144429))], (20463 ^ _781404) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1144427))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144425)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144427)), _1144429)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144425)), _1144429))]]], (46700 ^ _781404) ^ [_1720853, _1720855, _1720857, _1720859, _1720861, _1720863, _1720865] : [-(c_List_Ofoldr(_1720853, _1720855, _1720857, hAPP(hAPP(c_List_Omap(_1720859, _1720853), _1720861), _1720863), _1720865) = c_List_Ofoldr(_1720859, _1720855, hAPP(c_Fun_Ocomp(_1720853, tc_fun(_1720855, _1720855), _1720859, _1720857), _1720861), _1720863, _1720865))], (18979 ^ _781404) ^ [_1119358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119358), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1119358)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31954 ^ _781404) ^ [_1356458, _1356460, _1356462] : [class_Orderings_Olinorder(_1356458), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356458), _1356460), _1356462) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356458), _1356462), _1356460))], (49739 ^ _781404) ^ [_1785361, _1785363] : [c_Relation_Otrans(_1785361, _1785363), -(c_Relation_Otrans(_1785361, hAPP(c_Relation_Oconverse(_1785361, _1785361), _1785363)))], (49341 ^ _781404) ^ [_1775924, _1775926] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1775924)), _1775926) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1775924, tc_Lazy__Sequence_Olazy__sequence(_1775924)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1775924, tc_Lazy__Sequence_Olazy__sequence(_1775924), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1775924), tc_Nat_Onat), _1775924), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1775924), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1775924)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1775924)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1775924), _1775926)))], (25017 ^ _781404) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29185 ^ _781404) ^ [_1303683, _1303685, _1303687] : [class_Fields_Olinordered__field(_1303683), -(_1303685 = c_Groups_Ozero__class_Ozero(_1303683)), -(hAPP(c_Groups_Oabs__class_Oabs(_1303683), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303683), _1303687), _1303685)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303683), hAPP(c_Groups_Oabs__class_Oabs(_1303683), _1303687)), hAPP(c_Groups_Oabs__class_Oabs(_1303683), _1303685)))], (41680 ^ _781404) ^ [_1599656, _1599658, _1599660] : [c_Relation_Ototal__on(_1599656, _1599658, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1599656, _1599656), tc_HOL_Obool)), _1599660), c_Relation_OId(_1599656))), -(c_Relation_Ototal__on(_1599656, _1599658, _1599660))], (49624 ^ _781404) ^ [_1782786, _1782788, _1782790, _1782792] : [-(hAPP(c_Relation_OImage(_1782786, _1782788, hAPP(c_Set_OCollect(tc_prod(_1782786, _1782788)), hAPP(c_Product__Type_Oprod_Oprod__case(_1782786, _1782788, tc_HOL_Obool), _1782790))), _1782792) = hAPP(c_Set_OCollect(_1782788), hAPP(hAPP(c_COMBB(tc_fun(_1782786, tc_HOL_Obool), tc_HOL_Obool, _1782788), c_HOL_OEx(_1782786)), hAPP(hAPP(c_COMBB(tc_fun(_1782786, tc_HOL_Obool), tc_fun(_1782786, tc_HOL_Obool), _1782788), hAPP(c_COMBS(_1782786, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1782786), c_fconj), hAPP(hAPP(c_COMBC(_1782786, tc_fun(_1782786, tc_HOL_Obool), tc_HOL_Obool), c_member(_1782786)), _1782792)))), hAPP(c_COMBC(_1782786, _1782788, tc_HOL_Obool), _1782790)))))], (30724 ^ _781404) ^ [_1333739, _1333741, _1333743, _1333745] : [class_Orderings_Olinorder(_1333739), 30727 ^ _781404 : [(30736 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333739), _1333741), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333739), _1333743), _1333745)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333739), _1333741), _1333743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333739), _1333741), _1333745))], (30728 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333739), _1333741), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333739), _1333743), _1333745))), 30731 ^ _781404 : [(30734 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333739), _1333741), _1333745)))], (30732 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333739), _1333741), _1333743)))]]]]], (4560 ^ _781404) ^ [_850652, _850654, _850656, _850658] : [-(c_HOL_OThe(_850658, _850654) = c_HOL_OThe(_850656, _850652)), _850658 = _850656, _850654 = _850652], (12102 ^ _781404) ^ [_989169, _989171, _989173, _989175] : [hBOOL(hAPP(hAPP(c_member(_989169), _989171), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989169, tc_HOL_Obool)), _989173), _989175))), 12105 ^ _781404 : [(12108 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_989169), _989171), _989175)))], (12106 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_989169), _989171), _989173)))]]], (23822 ^ _781404) ^ [_1209030, _1209032, _1209034, _1209036] : [class_Divides_Osemiring__div(_1209030), -(_1209032 = c_Groups_Ozero__class_Ozero(_1209030)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209030), _1209034), _1209032)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209030), _1209036), _1209032)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209030), _1209034), _1209036))], (40943 ^ _781404) ^ [_1580774, _1580776, _1580778] : [c_Wellfounded_Owf(_1580774, _1580776), hBOOL(hAPP(hAPP(c_member(tc_prod(_1580774, _1580774)), hAPP(hAPP(c_Product__Type_OPair(_1580774, _1580774), hAPP(_1580778, hAPP(c_Nat_OSuc, 40946 ^ [_1580774, _1580776, _1580778]))), hAPP(_1580778, 40946 ^ [_1580774, _1580776, _1580778]))), _1580776))], (22555 ^ _781404) ^ [_1183841, _1183843, _1183845] : [class_Rings_Olinordered__idom(_1183841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183841), c_Groups_Ozero__class_Ozero(_1183841)), _1183843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183841), c_Groups_Ozero__class_Ozero(_1183841)), _1183845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183841), _1183845), c_Groups_Oone__class_Oone(_1183841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183841), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183841), _1183845), _1183843)), _1183843)))], (45714 ^ _781404) ^ [_1697203, _1697205] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1697203), _1697205) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1697203)), hAPP(c_Code__Numeral_Onat__of, _1697205))))], (46977 ^ _781404) ^ [_1726371, _1726373, _1726375] : [class_Orderings_Olinorder(_1726371), c_List_Olinorder__class_Osorted(_1726371, _1726373), -(c_List_Olinorder__class_Osorted(_1726371, c_List_Oremove1(_1726371, _1726375, _1726373)))], (13898 ^ _781404) ^ [_1023782, _1023784] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1023782), _1023784)), 13899 ^ _781404 : [(13906 ^ _781404) ^ [] : [_1023782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1023784 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13900 ^ _781404) ^ [] : [_1023782 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1023784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (17525 ^ _781404) ^ [_1093898, _1093900] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093898), _1093900) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093900), _1093898))], (48297 ^ _781404) ^ [_1753861, _1753863, _1753865, _1753867] : [48299 ^ _781404 : [(48302 ^ _781404) ^ [] : [hBOOL(hAPP(_1753865, 48298 ^ [_1753861, _1753863, _1753865, _1753867]))], (48300 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753861), 48298 ^ [_1753861, _1753863, _1753865, _1753867]), hAPP(c_List_Oset(_1753861), _1753863))))]], -(c_List_OtakeWhile(_1753861, _1753865, hAPP(hAPP(c_List_Oappend(_1753861), _1753863), _1753867)) = hAPP(hAPP(c_List_Oappend(_1753861), _1753863), c_List_OtakeWhile(_1753861, _1753865, _1753867)))], (7978 ^ _781404) ^ [_914344, _914346, _914348, _914350] : [class_Lattices_Olattice(_914344), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914344), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914344), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_914344), _914346), _914348)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_914344), _914346), _914350))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_914344), _914346), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914344), _914348), _914350)))))], (49539 ^ _781404) ^ [_1780761, _1780763, _1780765] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1780761, _1780763, _1780765) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1780761)], (49053 ^ _781404) ^ [_1770491, _1770493, _1770495, _1770497] : [-(hAPP(hAPP(c_List_Oappend(_1770491), c_List_Oreplicate(_1770491, _1770493, _1770495)), hAPP(hAPP(c_List_Olist_OCons(_1770491), _1770495), _1770497)) = hAPP(hAPP(c_List_Olist_OCons(_1770491), _1770495), hAPP(hAPP(c_List_Oappend(_1770491), c_List_Oreplicate(_1770491, _1770493, _1770495)), _1770497)))], (6498 ^ _781404) ^ [_884881, _884883, _884885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_884881, tc_HOL_Obool), tc_HOL_Obool)), _884883), _884885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884881, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_884881, tc_HOL_Obool), _884885)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_884881, tc_HOL_Obool), _884883))))], (29195 ^ _781404) ^ [_1303841, _1303843, _1303845] : [class_Fields_Olinordered__field(_1303841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303841), _1303843), c_Groups_Ozero__class_Ozero(_1303841))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303841), _1303845), c_Groups_Ozero__class_Ozero(_1303841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303841), c_Groups_Ozero__class_Ozero(_1303841)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303841), _1303843), _1303845))))], (48913 ^ _781404) ^ [_1766600, _1766602, _1766604, _1766606, _1766608] : [-(_1766600 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1766602, _1766604, _1766606, _1766608), _1766600) = hAPP(c_Lazy__Sequence_Obind(_1766602, _1766604, hAPP(_1766606, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1766600), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1766602, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1766604)), _1766608), _1766600)))], (16472 ^ _781404) ^ [_1074094, _1074096, _1074098] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1074094), _1074096)), -(hBOOL(hAPP(hAPP(c_member(_1074094), _1074098), _1074096))), -(hAPP(c_Finite__Set_Ocard(_1074094), hAPP(hAPP(c_Set_Oinsert(_1074094), _1074098), _1074096)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1074094), _1074096)))], (42778 ^ _781404) ^ [_1630712, _1630714, _1630716] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630712, tc_HOL_Obool)), hAPP(c_List_Oset(_1630712), c_List_Osublist(_1630712, _1630714, _1630716))), hAPP(c_List_Oset(_1630712), _1630714))))], (49955 ^ _781404) ^ [_1791243, _1791245] : [c_Predicate_Oreflp(_1791243, _1791245), c_Predicate_Osymp(_1791243, _1791245), c_Predicate_Otransp(_1791243, _1791245), -(c_Equiv__Relations_Oequivp(_1791243, _1791245))], (19410 ^ _781404) ^ [_1126599, _1126601, _1126603] : [class_Rings_Olinordered__semidom(_1126599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126601), _1126603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126599), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1126599), _1126601)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1126599), _1126603))))], (35221 ^ _781404) ^ [_1437270] : [-(c_Divides_Oadjust(_1437270) = 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)), _1437270))))), 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)), _1437270))))), 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))))))))], (34159 ^ _781404) ^ [_1409202, _1409204, _1409206, _1409208, _1409210, _1409212, _1409214] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409202, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409204, tc_fun(_1409202, tc_HOL_Obool)), _1409206), _1409208)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409210, tc_fun(_1409202, tc_HOL_Obool)), _1409212), _1409214)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409204, tc_fun(_1409202, tc_HOL_Obool)), _1409206), hAPP(hAPP(c_COMBB(tc_fun(_1409210, tc_fun(_1409202, tc_HOL_Obool)), tc_fun(_1409202, tc_HOL_Obool), _1409204), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409210, tc_fun(_1409202, tc_HOL_Obool)), _1409212)), hAPP(hAPP(c_COMBC(_1409204, tc_fun(_1409210, tc_fun(_1409202, tc_HOL_Obool)), tc_fun(_1409210, tc_fun(_1409202, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1409202, tc_HOL_Obool), tc_fun(_1409202, tc_HOL_Obool)), tc_fun(tc_fun(_1409210, tc_fun(_1409202, tc_HOL_Obool)), tc_fun(_1409210, tc_fun(_1409202, tc_HOL_Obool))), _1409204), c_COMBB(tc_fun(_1409202, tc_HOL_Obool), tc_fun(_1409202, tc_HOL_Obool), _1409210)), hAPP(hAPP(c_COMBB(tc_fun(_1409202, tc_HOL_Obool), tc_fun(tc_fun(_1409202, tc_HOL_Obool), tc_fun(_1409202, tc_HOL_Obool)), _1409204), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409202, tc_HOL_Obool))), _1409208))), _1409214))))], (49727 ^ _781404) ^ [_1785155, _1785157, _1785159] : [hBOOL(hAPP(hAPP(c_member(_1785157), _1785155), c_Orderings_Obot__class_Obot(tc_fun(_1785157, tc_HOL_Obool)))), hBOOL(hAPP(_1785159, _1785155))], (25608 ^ _781404) ^ [_1238910, _1238912, _1238914, _1238916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1238910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1238912), _1238914)), -(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), _1238914), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1238916, _1238910))), _1238912)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1238914), _1238910))))], (1216 ^ _781404) ^ [_799644, _799646] : [-(class_Rings_Oring__no__zero__divisors(_799644)), _799646 = _799644, class_Rings_Oring__no__zero__divisors(_799646)], (32951 ^ _781404) ^ [_1375331, _1375333] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1375331), _1375333) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1375331), _1375333))], (45249 ^ _781404) ^ [_1687078, _1687080, _1687082, _1687084, _1687086] : [class_Groups_Oab__group__add(_1687078), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687078), hAPP(hAPP(c_List_Omap(_1687080, _1687078), hAPP(hAPP(c_COMBS(_1687080, _1687078, _1687078), hAPP(hAPP(c_COMBB(_1687078, tc_fun(_1687078, _1687078), _1687080), c_Groups_Ominus__class_Ominus(_1687078)), _1687082)), _1687084)), _1687086)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1687078), hAPP(c_List_Omonoid__add__class_Olistsum(_1687078), hAPP(hAPP(c_List_Omap(_1687080, _1687078), _1687082), _1687086))), hAPP(c_List_Omonoid__add__class_Olistsum(_1687078), hAPP(hAPP(c_List_Omap(_1687080, _1687078), _1687084), _1687086))))], (44325 ^ _781404) ^ [_1667294, _1667296, _1667298] : [-(hAPP(hAPP(c_List_Oappend(_1667294), hAPP(hAPP(c_List_Otake(_1667294), _1667296), _1667298)), hAPP(hAPP(c_List_Odrop(_1667294), _1667296), _1667298)) = _1667298)], (19490 ^ _781404) ^ [_1128005, _1128007] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1128005), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1128007)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128005), _1128007)))], (38207 ^ _781404) ^ [_1505686] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1505686)), c_Int_OInteg)))], (3752 ^ _781404) ^ [_837648, _837650, _837652, _837654, _837656, _837658] : [-(c_List_Oinsert(_837658, _837654, _837650) = c_List_Oinsert(_837656, _837652, _837648)), _837658 = _837656, _837654 = _837652, _837650 = _837648], (25768 ^ _781404) ^ [_1241873, _1241875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1241873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1241873), _1241875)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1241875), _1241873) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1241875), _1241873)), _1241873)))], (14003 ^ _781404) ^ [_1025613, _1025615] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025613), _1025615))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025615), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025613), _1025615)) = _1025613)], (13363 ^ _781404) ^ [_1013694, _1013696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013694), _1013696)), _1013696))], (9108 ^ _781404) ^ [_935824, _935826, _935828, _935830, _935832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935824, tc_HOL_Obool)), _935826), _935828)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935824, tc_HOL_Obool)), _935830), _935832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935824, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935824, tc_HOL_Obool)), _935826), _935832)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935824, tc_HOL_Obool)), _935828), _935830))))], (23515 ^ _781404) ^ [_1203436, _1203438, _1203440, _1203442] : [class_Divides_Oring__div(_1203436), c_Divides_Odiv__class_Omod(_1203436, _1203438, _1203440) = c_Divides_Odiv__class_Omod(_1203436, _1203442, _1203440), -(c_Divides_Odiv__class_Omod(_1203436, hAPP(c_Groups_Ouminus__class_Ouminus(_1203436), _1203438), _1203440) = c_Divides_Odiv__class_Omod(_1203436, hAPP(c_Groups_Ouminus__class_Ouminus(_1203436), _1203442), _1203440))], (45184 ^ _781404) ^ [_1685031, _1685033, _1685035, _1685037, _1685039, _1685041, _1685043, _1685045] : [-(hAPP(hAPP(c_List_Ozip(_1685031, _1685033), hAPP(hAPP(c_List_Omap(_1685035, _1685031), _1685037), _1685039)), hAPP(hAPP(c_List_Omap(_1685041, _1685033), _1685043), _1685045)) = hAPP(hAPP(c_List_Omap(tc_prod(_1685035, _1685041), tc_prod(_1685031, _1685033)), hAPP(c_Product__Type_Oprod_Oprod__case(_1685035, _1685041, tc_prod(_1685031, _1685033)), hAPP(hAPP(c_COMBC(_1685035, tc_fun(_1685041, _1685033), tc_fun(_1685041, tc_prod(_1685031, _1685033))), hAPP(hAPP(c_COMBB(tc_fun(_1685033, tc_prod(_1685031, _1685033)), tc_fun(tc_fun(_1685041, _1685033), tc_fun(_1685041, tc_prod(_1685031, _1685033))), _1685035), c_COMBB(_1685033, tc_prod(_1685031, _1685033), _1685041)), hAPP(hAPP(c_COMBB(_1685031, tc_fun(_1685033, tc_prod(_1685031, _1685033)), _1685035), c_Product__Type_OPair(_1685031, _1685033)), _1685037))), _1685043))), hAPP(hAPP(c_List_Ozip(_1685035, _1685041), _1685039), _1685045)))], (19893 ^ _781404) ^ [_1134805, _1134807] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134805))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1134805)), _1134807)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1134807))], (18353 ^ _781404) ^ [_1108442, _1108444, _1108446, _1108448, _1108450, _1108452] : [c_Finite__Set_Ofun__left__comm(_1108442, _1108444, _1108446), -(hAPP(hAPP(_1108446, _1108448), hAPP(hAPP(_1108446, _1108450), _1108452)) = hAPP(hAPP(_1108446, _1108450), hAPP(hAPP(_1108446, _1108448), _1108452)))], (34939 ^ _781404) ^ [_1431359, _1431361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431359)), hAPP(c_Nat_OSuc, _1431361))), -(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(_1431359))), 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)), _1431361)))))], (49063 ^ _781404) ^ [_1770744, _1770746, _1770748] : [-(_1770744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1770746), c_List_Oreplicate(_1770746, _1770744, _1770748)) = _1770748)], (30548 ^ _781404) ^ [_1330522, _1330524, _1330526] : [class_Orderings_Olinorder(_1330522), -(_1330524 = c_Orderings_Obot__class_Obot(tc_fun(_1330522, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1330522, tc_HOL_Obool)), _1330524), _1330526)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330522), _1330526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1330522), hAPP(c_Finite__Set_Ofold1(_1330522, c_Orderings_Oord__class_Omin(_1330522)), _1330526)), hAPP(c_Finite__Set_Ofold1(_1330522, c_Orderings_Oord__class_Omin(_1330522)), _1330524))))], (33496 ^ _781404) ^ [_1390500, _1390502, _1390504, _1390506] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1390500, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390502, tc_fun(_1390500, tc_HOL_Obool)), _1390504), _1390506)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390502, tc_fun(_1390500, tc_HOL_Obool)), _1390504), hAPP(hAPP(c_COMBB(tc_fun(_1390500, tc_HOL_Obool), tc_fun(_1390500, tc_HOL_Obool), _1390502), c_Groups_Ouminus__class_Ouminus(tc_fun(_1390500, tc_HOL_Obool))), _1390506)))], (34205 ^ _781404) ^ [_1411789, _1411791, _1411793, _1411795, _1411797] : [-(_1411789 = c_Orderings_Obot__class_Obot(tc_fun(_1411791, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411791, tc_fun(_1411793, tc_HOL_Obool)), _1411789), hAPP(hAPP(c_COMBC(_1411791, tc_fun(_1411793, tc_HOL_Obool), tc_fun(_1411793, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411793, tc_HOL_Obool), tc_fun(tc_fun(_1411793, tc_HOL_Obool), tc_fun(_1411793, tc_HOL_Obool)), _1411791), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411793, tc_HOL_Obool))), _1411795)), _1411797)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411793, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411791, tc_fun(_1411793, tc_HOL_Obool)), _1411789), _1411795)), _1411797))], (42467 ^ _781404) ^ [_1621846, _1621848, _1621850, _1621852] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621846), tc_List_Olist(_1621846))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621846), tc_List_Olist(_1621846)), _1621848), _1621850)), c_List_Olistrel1(_1621846, _1621852))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621846), tc_List_Olist(_1621846))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621846), tc_List_Olist(_1621846)), _1621848), _1621850)), c_List_Olistrel(_1621846, c_Transitive__Closure_Ortrancl(_1621846, _1621852)))))], (34865 ^ _781404) ^ [_1429551] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429551)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1429551)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429551)), 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)))))], (36894 ^ _781404) ^ [_1472095, _1472097, _1472099, _1472101] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472095, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36895 ^ [_1472095, _1472097, _1472099, _1472101])), _1472097) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472095, 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), 36895 ^ [_1472095, _1472097, _1472099, _1472101]), _1472099))), _1472101), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472095, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1472097) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472095, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1472101))], (33849 ^ _781404) ^ [_1400788, _1400790, _1400792, _1400794, _1400796, _1400798, _1400800] : [-(hAPP(c_Fun_Ocomp(_1400788, _1400790, _1400792, _1400794), c_Fun_Ofun__upd(_1400792, _1400788, _1400796, _1400798, _1400800)) = c_Fun_Ofun__upd(_1400792, _1400790, hAPP(c_Fun_Ocomp(_1400788, _1400790, _1400792, _1400794), _1400796), _1400798, hAPP(_1400794, _1400800)))], (40764 ^ _781404) ^ [_1576490, _1576492, _1576494, _1576496, _1576498] : [_1576490 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1576492, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1576492, tc_HOL_Obool), tc_fun(_1576492, tc_HOL_Obool), tc_fun(_1576492, tc_HOL_Obool)), c_Set_OCollect(_1576492)), _1576494)), c_Orderings_Oorder__class_Omono(tc_fun(_1576492, tc_HOL_Obool), tc_fun(_1576492, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1576492, tc_HOL_Obool), tc_fun(_1576492, tc_HOL_Obool), tc_fun(_1576492, tc_HOL_Obool)), c_Set_OCollect(_1576492)), _1576494)), hBOOL(hAPP(hAPP(c_member(_1576492), _1576496), _1576498)), 40778 ^ _781404 : [(40781 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1576494, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1576492, tc_HOL_Obool)), _1576498), _1576490)), 40777 ^ [_1576490, _1576492, _1576494, _1576496, _1576498]))], (40779 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576492), 40777 ^ [_1576490, _1576492, _1576494, _1576496, _1576498]), _1576498)))]], -(hBOOL(hAPP(hAPP(c_member(_1576492), _1576496), _1576490)))], (17937 ^ _781404) ^ [_1101325, _1101327] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1101325, _1101327))))], (21229 ^ _781404) ^ [_1158792, _1158794] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158792), _1158794) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21232 ^ _781404 : [(21235 ^ _781404) ^ [] : [-(_1158794 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (21233 ^ _781404) ^ [] : [-(_1158792 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (24134 ^ _781404) ^ [_1214243, _1214245, _1214247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214243), _1214245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214247), 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), _1214245), _1214247)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214243), _1214247))))], (27685 ^ _781404) ^ [_1276036, _1276038, _1276040, _1276042] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1276036, _1276038, _1276040), _1276042)), _1276040 = c_Orderings_Obot__class_Obot(tc_fun(_1276036, tc_HOL_Obool))], (25361 ^ _781404) ^ [_1234859] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234859), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234859))], (20971 ^ _781404) ^ [_1153956, _1153958, _1153960, _1153962, _1153964] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1153956), 20974 ^ _781404 : [(20975 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153956), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153956), _1153958), _1153960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153956), _1153962), _1153964)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153956), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153956), _1153958), _1153964)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153956), _1153962), _1153960)), -(_1153958 = _1153962), -(_1153960 = _1153964)], (20985 ^ _781404) ^ [] : [20986 ^ _781404 : [(20989 ^ _781404) ^ [] : [_1153960 = _1153964], (20987 ^ _781404) ^ [] : [_1153958 = _1153962]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153956), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153956), _1153958), _1153960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153956), _1153962), _1153964)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153956), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153956), _1153958), _1153964)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153956), _1153962), _1153960)))]]], (22067 ^ _781404) ^ [_1174438, _1174440] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174438), _1174440) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1174438 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174440 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49061 ^ _781404) ^ [_1770697, _1770699, _1770701, _1770703] : [-(hAPP(hAPP(c_List_Odrop(_1770697), _1770699), c_List_Oreplicate(_1770697, _1770701, _1770703)) = c_List_Oreplicate(_1770697, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1770701), _1770699), _1770703))], (40460 ^ _781404) ^ [_1569716, _1569718] : [hBOOL(hAPP(_1569716, c_Hilbert__Choice_OEps(_1569718, _1569716))), -(hBOOL(hAPP(_1569716, 40463 ^ [_1569716, _1569718])))], (2288 ^ _781404) ^ [_814726, _814728, _814730, _814732] : [-(c_Predicate_OPowp(_814732, _814728) = c_Predicate_OPowp(_814730, _814726)), _814732 = _814730, _814728 = _814726], (19981 ^ _781404) ^ [_1136349, _1136351] : [_1136349 = _1136351, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136349) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136351))], (48376 ^ _781404) ^ [_1756024, _1756026, _1756028, _1756030, _1756032] : [-(hAPP(hAPP(c_List_Olist_OCons(_1756024), _1756026), _1756028) = hAPP(c_List_Ofilter(_1756024, _1756030), _1756032)), 48377 ^ _781404 : [(48378 ^ _781404) ^ [_1756152, _1756154] : [_1756032 = hAPP(hAPP(c_List_Oappend(_1756024), _1756154), hAPP(hAPP(c_List_Olist_OCons(_1756024), _1756026), _1756152)), 48384 ^ _781404 : [(48387 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1756030, 48383 ^ [_1756024, _1756026, _1756028, _1756030, _1756032, _1756152, _1756154])))], (48385 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756024), 48383 ^ [_1756024, _1756026, _1756028, _1756030, _1756032, _1756152, _1756154]), hAPP(c_List_Oset(_1756024), _1756154))))]], hBOOL(hAPP(_1756030, _1756026)), _1756028 = hAPP(c_List_Ofilter(_1756024, _1756030), _1756152)]]], (39826 ^ _781404) ^ [_1555675, _1555677, _1555679, _1555681] : [c_Wellfounded_Owf(_1555675, _1555677), c_Wellfounded_Owf(_1555679, _1555681), -(c_Wellfounded_Owf(tc_prod(_1555675, _1555679), c_Wellfounded_Olex__prod(_1555675, _1555679, _1555677, _1555681)))], (17833 ^ _781404) ^ [_1099410, _1099412, _1099414] : [class_Rings_Olinordered__semidom(_1099410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099410), c_Groups_Oone__class_Oone(_1099410)), _1099412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099410), c_Groups_Oone__class_Oone(_1099410)), hAPP(hAPP(c_Power_Opower__class_Opower(_1099410), _1099412), _1099414))))], (7769 ^ _781404) ^ [_909240, _909242, _909244, _909246, _909248] : [class_Lattices_Osemilattice__inf(_909240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909240), _909242), _909244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909240), _909246), _909248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909240), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_909240), _909242), _909246)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_909240), _909244), _909248))))], (19390 ^ _781404) ^ [_1126252] : [-(c_Int_OBit1(_1126252) = 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)), _1126252)), _1126252))], (49874 ^ _781404) ^ [_1789512, _1789514, _1789516, _1789518] : [class_Complete__Lattice_Ocomplete__lattice(_1789512), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1789514, _1789512), _1789516), _1789518) = c_Complete__Lattice_OInf__class_OInf(_1789512, hAPP(c_Set_OCollect(_1789512), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1789514, _1789512), tc_HOL_Obool), tc_HOL_Obool, _1789512), c_HOL_OEx(tc_fun(_1789514, _1789512))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1789514, _1789512), tc_HOL_Obool), tc_fun(tc_fun(_1789514, _1789512), tc_HOL_Obool), _1789512), hAPP(c_COMBS(tc_fun(_1789514, _1789512), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1789514, _1789512)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1789514, _1789512), tc_fun(tc_fun(_1789514, _1789512), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1789514, _1789512))), _1789516)))), hAPP(hAPP(c_COMBC(_1789512, tc_fun(tc_fun(_1789514, _1789512), _1789512), tc_fun(tc_fun(_1789514, _1789512), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1789512, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1789514, _1789512), _1789512), tc_fun(tc_fun(_1789514, _1789512), tc_HOL_Obool)), _1789512), c_COMBB(_1789512, tc_HOL_Obool, tc_fun(_1789514, _1789512))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1789514, _1789512), _1789514, _1789512), c_COMBI(tc_fun(_1789514, _1789512))), _1789518)))))))], (9813 ^ _781404) ^ [_949061, _949063] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _949061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949061), hAPP(c_Nat_OSuc, _949063))), _949061)))], (14206 ^ _781404) ^ [_1029495, _1029497, _1029499, _1029501] : [class_Groups_Oordered__comm__monoid__add(_1029495), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029495), c_Groups_Ozero__class_Ozero(_1029495)), _1029497)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029495), _1029499), _1029501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029495), _1029499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029495), _1029497), _1029501))))], (28935 ^ _781404) ^ [_1299453, _1299455, _1299457, _1299459] : [class_Fields_Olinordered__field(_1299453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299453), _1299455), _1299457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299453), c_Groups_Ozero__class_Ozero(_1299453)), _1299459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299453), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299453), _1299455), _1299459)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299453), _1299457), _1299459))))], (49652 ^ _781404) ^ [_1783462, _1783464, _1783466, _1783468, _1783470] : [c_Relation_Otrans(_1783462, _1783464), hBOOL(hAPP(hAPP(c_member(tc_prod(_1783462, _1783462)), hAPP(hAPP(c_Product__Type_OPair(_1783462, _1783462), _1783466), _1783468)), _1783464)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1783462, _1783462)), hAPP(hAPP(c_Product__Type_OPair(_1783462, _1783462), _1783468), _1783470)), _1783464)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783462, _1783462)), hAPP(hAPP(c_Product__Type_OPair(_1783462, _1783462), _1783466), _1783470)), _1783464)))], (9665 ^ _781404) ^ [_946673, _946675, _946677] : [class_Orderings_Olinorder(_946673), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946673), _946675), _946677))), 9672 ^ _781404 : [(9679 ^ _781404) ^ [] : [_946677 = _946675, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946673), _946677), _946675))], (9673 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946673), _946677), _946675))), -(_946677 = _946675)]]], (22845 ^ _781404) ^ [_1189842, _1189844, _1189846] : [class_Rings_Olinordered__semidom(_1189842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189842), c_Groups_Ozero__class_Ozero(_1189842)), _1189844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189842), _1189844), c_Groups_Oone__class_Oone(_1189842))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189842), _1189844), hAPP(hAPP(c_Power_Opower__class_Opower(_1189842), _1189844), _1189846))), hAPP(hAPP(c_Power_Opower__class_Opower(_1189842), _1189844), _1189846))))], (52336 ^ _781404) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (40194 ^ _781404) ^ [_1563834, _1563836] : [-(c_List_Olex(_1563834, _1563836) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1563834), tc_List_Olist(_1563834)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1563834, _1563836)))], (47846 ^ _781404) ^ [_1743718, _1743720, _1743722] : [47848 ^ _781404 : [(47851 ^ _781404) ^ [] : [hBOOL(hAPP(_1743720, 47847 ^ [_1743718, _1743720, _1743722]))], (47849 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743718), 47847 ^ [_1743718, _1743720, _1743722]), hAPP(c_List_Oset(_1743718), _1743722))))]], -(c_List_OdropWhile(_1743718, _1743720, _1743722) = c_List_Olist_ONil(_1743718))], (12382 ^ _781404) ^ [_994747, _994749, _994751, _994753] : [-(hBOOL(hAPP(hAPP(c_member(_994747), _994749), _994751))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994747, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_994747), _994749), _994753)), _994751) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994747, tc_HOL_Obool)), _994753), _994751))], (29141 ^ _781404) ^ [_1302910, _1302912, _1302914, _1302916] : [class_Fields_Ofield__inverse__zero(_1302910), -(_1302912 = c_Groups_Ozero__class_Ozero(_1302910)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302910), _1302914), _1302912)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302910), _1302916), _1302912)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302910), _1302914), _1302916))], (46609 ^ _781404) ^ [_1717764, _1717766, _1717768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1717764), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1717766))), c_List_Otranspose(_1717766, _1717768)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1717766)), c_List_Otranspose(_1717766, _1717768)), _1717764) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1717766), _1717766), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717766), tc_Nat_Onat, _1717766), c_List_Onth(_1717766)), _1717764)), hAPP(c_List_Ofilter(tc_List_Olist(_1717766), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1717766)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1717764)), c_Nat_Osize__class_Osize(tc_List_Olist(_1717766)))), _1717768)))], (46437 ^ _781404) ^ [_1713296, _1713298] : [class_Orderings_Olinorder(_1713296), -(c_List_Olinorder__class_Osort__key(_1713296, _1713296, c_COMBI(_1713296), _1713298) = hAPP(c_List_Ofoldl(tc_List_Olist(_1713296), _1713296, hAPP(c_COMBC(_1713296, tc_List_Olist(_1713296), tc_List_Olist(_1713296)), c_List_Olinorder__class_Oinsort__key(_1713296, _1713296, c_COMBI(_1713296))), c_List_Olist_ONil(_1713296)), _1713298))], (51778 ^ _781404) ^ [_1829715, _1829717, _1829719] : [51779 ^ _781404 : [(51782 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829717), _1829719))], (51780 ^ _781404) ^ [] : [_1829715 = 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), _1829715), _1829717)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829715), _1829719))))], (8281 ^ _781404) ^ [_920914, _920916, _920918] : [hAPP(hAPP(c_Set_Oinsert(_920914), _920916), _920918) = c_Orderings_Obot__class_Obot(tc_fun(_920914, tc_HOL_Obool))], (32762 ^ _781404) ^ [_1371474, _1371476, _1371478] : [class_Orderings_Olinorder(_1371474), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371474), _1371476)), 32769 ^ _781404 : [(32776 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371474, tc_HOL_Obool)), _1371476), hAPP(hAPP(c_Set_Oinsert(_1371474), _1371478), c_Orderings_Obot__class_Obot(tc_fun(_1371474, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1371474, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1371474, c_Orderings_Oord__class_Omax(_1371474), hAPP(hAPP(c_Set_Oinsert(_1371474), _1371478), _1371476)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371474), _1371478), c_Big__Operators_Olattice_OSup__fin(_1371474, c_Orderings_Oord__class_Omax(_1371474), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371474, tc_HOL_Obool)), _1371476), hAPP(hAPP(c_Set_Oinsert(_1371474), _1371478), c_Orderings_Obot__class_Obot(tc_fun(_1371474, tc_HOL_Obool)))))))], (32770 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371474, tc_HOL_Obool)), _1371476), hAPP(hAPP(c_Set_Oinsert(_1371474), _1371478), c_Orderings_Obot__class_Obot(tc_fun(_1371474, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1371474, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1371474, c_Orderings_Oord__class_Omax(_1371474), hAPP(hAPP(c_Set_Oinsert(_1371474), _1371478), _1371476)) = _1371478)]]], (2840 ^ _781404) ^ [_823492, _823494, _823496, _823498] : [-(c_Inductive_Ocomplete__lattice__class_Ogfp(_823498, _823494) = c_Inductive_Ocomplete__lattice__class_Ogfp(_823496, _823492)), _823498 = _823496, _823494 = _823492], (18661 ^ _781404) ^ [_1114431, _1114433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114431), _1114433)), -(c_Nat__Transfer_Otsub(_1114433, _1114431) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1114433), _1114431))], (40013 ^ _781404) ^ [_1559334, _1559336, _1559338] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1559334, _1559336)), _1559338)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1559334), hAPP(c_Relation_ODomain(_1559334, _1559336), _1559338))))], (41231 ^ _781404) ^ [_1588619, _1588621, _1588623] : [-(c_Transitive__Closure_Ortrancl(_1588619, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588619, _1588619), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588619, _1588621)), c_Transitive__Closure_Ortrancl(_1588619, _1588623))) = c_Transitive__Closure_Ortrancl(_1588619, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588619, _1588619), tc_HOL_Obool)), _1588621), _1588623)))], (7928 ^ _781404) ^ [_912939, _912941, _912943, _912945] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912939, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912939), _912941), _912943)), _912945) = hAPP(hAPP(c_Set_Oinsert(_912939), _912941), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912939, tc_HOL_Obool)), _912943), _912945)))], (2460 ^ _781404) ^ [_817476, _817478] : [_817478 = _817476, -(c_Nat_Onat_Onat__size(_817478) = c_Nat_Onat_Onat__size(_817476))], (17505 ^ _781404) ^ [] : [-(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))], (8060 ^ _781404) ^ [_916298, _916300] : [class_Lattices_Oboolean__algebra(_916298), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916298), _916300), hAPP(c_Groups_Ouminus__class_Ouminus(_916298), _916300)) = c_Orderings_Otop__class_Otop(_916298))], (5038 ^ _781404) ^ [_858233, _858235] : [_858235 = _858233, -(c_Groups_Ouminus__class_Ouminus(_858235) = c_Groups_Ouminus__class_Ouminus(_858233))], (12376 ^ _781404) ^ [_994674, _994676, _994678, _994680] : [-(hBOOL(hAPP(hAPP(c_member(_994674), _994676), _994678))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994674, tc_HOL_Obool)), _994678), hAPP(hAPP(c_Set_Oinsert(_994674), _994676), _994680)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994674, tc_HOL_Obool)), _994678), _994680))], (9078 ^ _781404) ^ [_935288, _935290, _935292] : [class_Groups_Ogroup__add(_935288), 9081 ^ _781404 : [(9088 ^ _781404) ^ [] : [_935290 = _935292, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_935288), _935290), _935292) = c_Groups_Ozero__class_Ozero(_935288))], (9082 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_935288), _935290), _935292) = c_Groups_Ozero__class_Ozero(_935288), -(_935290 = _935292)]]], (43992 ^ _781404) ^ [_1659155, _1659157, _1659159, _1659161, _1659163, _1659165] : [hAPP(hAPP(c_List_Oappend(_1659155), _1659157), _1659159) = _1659161, _1659163 = hAPP(hAPP(c_List_Oappend(_1659155), _1659159), _1659165), -(hAPP(hAPP(c_List_Oappend(_1659155), _1659157), _1659163) = hAPP(hAPP(c_List_Oappend(_1659155), _1659161), _1659165))], (20913 ^ _781404) ^ [_1152610, _1152612] : [class_Rings_Ocomm__semiring__1(_1152610), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152610), c_Groups_Ozero__class_Ozero(_1152610)), _1152612) = c_Groups_Ozero__class_Ozero(_1152610))], (33825 ^ _781404) ^ [_1399922, _1399924, _1399926, _1399928] : [-(hAPP(c_Set_Ovimage(_1399922, _1399924, _1399926), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1399924, tc_HOL_Obool), _1399928)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1399924, tc_HOL_Obool), tc_fun(_1399922, tc_HOL_Obool)), _1399928), c_Set_Ovimage(_1399922, _1399924, _1399926)))], (35259 ^ _781404) ^ [_1438066, _1438068, _1438070, _1438072] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1438066, tc_fun(_1438068, tc_HOL_Obool))), _1438070), _1438072))], (52716 ^ _781404) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (33847 ^ _781404) ^ [_1400726, _1400728, _1400730, _1400732, _1400734, _1400736] : [-(hAPP(c_Set_Ovimage(_1400726, _1400728, hAPP(c_Fun_Ocomp(_1400730, _1400728, _1400726, _1400732), _1400734)), _1400736) = hAPP(c_Set_Ovimage(_1400726, _1400730, _1400734), hAPP(c_Set_Ovimage(_1400730, _1400728, _1400732), _1400736)))], (45295 ^ _781404) ^ [_1688344, _1688346, _1688348, _1688350, _1688352] : [hAPP(hAPP(c_List_Omap(_1688344, _1688346), _1688348), _1688350) = hAPP(hAPP(c_List_Omap(_1688344, _1688346), _1688348), _1688352), c_Fun_Oinj__on(_1688344, _1688346, _1688348, c_Orderings_Otop__class_Otop(tc_fun(_1688344, tc_HOL_Obool))), -(_1688350 = _1688352)], (20781 ^ _781404) ^ [_1150227, _1150229, _1150231, _1150233, _1150235] : [class_Rings_Ocomm__semiring__1(_1150227), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150227), _1150229), _1150231)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150227), _1150233), _1150235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150227), _1150229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150227), _1150231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150227), _1150233), _1150235))))], (35940 ^ _781404) ^ [_1451960, _1451962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451962)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451960, _1451962), c_Divides_OposDivAlg(_1451960, _1451962))))], (15096 ^ _781404) ^ [_1047635, _1047637, _1047639] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1047635), 15099 ^ _781404 : [(15106 ^ _781404) ^ [] : [_1047639 = c_Groups_Ozero__class_Ozero(_1047635), -(_1047637 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047635), _1047637), _1047639))], (15100 ^ _781404) ^ [] : [_1047637 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047635), _1047637), _1047639), -(_1047639 = c_Groups_Ozero__class_Ozero(_1047635))]]], (46507 ^ _781404) ^ [_1715745, _1715747, _1715749] : [hAPP(c_List_Ofilter(_1715745, _1715747), _1715749) = _1715749, 46510 ^ _781404 : [(46511 ^ _781404) ^ [_1715836] : [hBOOL(hAPP(hAPP(c_member(_1715745), _1715836), hAPP(c_List_Oset(_1715745), _1715749))), -(hBOOL(hAPP(_1715747, _1715836)))]]], (33947 ^ _781404) ^ [_1404217, _1404219, _1404221, _1404223, _1404225] : [class_Complete__Lattice_Ocomplete__lattice(_1404217), 33950 ^ _781404 : [(33951 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404217), _1404219), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404221, _1404217), _1404223), _1404225))), 33954 ^ _781404 : [(33955 ^ _781404) ^ [_1404398] : [hBOOL(hAPP(hAPP(c_member(_1404221), _1404398), _1404223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404217), _1404219), hAPP(_1404225, _1404398))))]]], (33961 ^ _781404) ^ [] : [33963 ^ _781404 : [(33966 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404217), _1404219), hAPP(_1404225, 33962 ^ [_1404217, _1404219, _1404221, _1404223, _1404225])))], (33964 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404221), 33962 ^ [_1404217, _1404219, _1404221, _1404223, _1404225]), _1404223)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404217), _1404219), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404221, _1404217), _1404223), _1404225))))]]], (9431 ^ _781404) ^ [_943085, _943087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _943085)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _943087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _943087), _943085)), _943087)))], (32342 ^ _781404) ^ [_1363850, _1363852, _1363854, _1363856, _1363858] : [class_Orderings_Olinorder(_1363850), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1363850, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1363850, _1363852), _1363854)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1363850, _1363856), _1363858)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1363850, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363850), _1363852), _1363856)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1363850), _1363854), _1363858)))], (19551 ^ _781404) ^ [_1128998, _1129000] : [19552 ^ _781404 : [(19553 ^ _781404) ^ [_1129054] : [_1129000 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1128998), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1129054)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128998), _1129000)))], (49075 ^ _781404) ^ [_1770832, _1770834, _1770836, _1770838, _1770840, _1770842] : [-(hAPP(hAPP(c_List_Ozip(_1770832, _1770834), c_List_Oreplicate(_1770832, _1770836, _1770838)), c_List_Oreplicate(_1770834, _1770840, _1770842)) = c_List_Oreplicate(tc_prod(_1770832, _1770834), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1770836), _1770840), hAPP(hAPP(c_Product__Type_OPair(_1770832, _1770834), _1770838), _1770842)))], (48058 ^ _781404) ^ [_1748083, _1748085, _1748087] : [hBOOL(hAPP(hAPP(c_member(_1748083), _1748085), hAPP(c_List_Oset(_1748083), _1748087))), -(c_List_Oinsert(_1748083, _1748085, _1748087) = _1748087)], (868 ^ _781404) ^ [_794478, _794480, _794482, _794484] : [-(c_Wellfounded_Oacyclic(_794482, _794478)), c_Wellfounded_Oacyclic(_794484, _794480), _794484 = _794482, _794480 = _794478], (3464 ^ _781404) ^ [_833142, _833144, _833146, _833148, _833150, _833152] : [-(c_List_Opartition(_833152, _833148, _833144) = c_List_Opartition(_833150, _833146, _833142)), _833152 = _833150, _833148 = _833146, _833144 = _833142], (45034 ^ _781404) ^ [_1682433, _1682435, _1682437] : [_1682433 = c_List_Olist_ONil(_1682435), -(c_List_Olast(_1682435, hAPP(hAPP(c_List_Olist_OCons(_1682435), _1682437), _1682433)) = _1682437)], (10397 ^ _781404) ^ [_958319, _958321, _958323, _958325] : [class_Lattices_Osemilattice__inf(_958319), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958319), _958321), _958323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958319), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_958319), _958321), _958325)), _958323)))], (10814 ^ _781404) ^ [_965044, _965046, _965048] : [class_Complete__Lattice_Ocomplete__lattice(_965044), class_Orderings_Olinorder(_965044), 10821 ^ _781404 : [(10831 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965044), c_Complete__Lattice_OInf__class_OInf(_965044, _965046)), _965048))), 10832 ^ _781404 : [(10833 ^ _781404) ^ [_965350] : [hBOOL(hAPP(hAPP(c_member(_965044), _965350), _965046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965044), _965350), _965048))]]], (10822 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965044), c_Complete__Lattice_OInf__class_OInf(_965044, _965046)), _965048)), 10826 ^ _781404 : [(10829 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965044), 10825 ^ [_965044, _965046, _965048]), _965048)))], (10827 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_965044), 10825 ^ [_965044, _965046, _965048]), _965046)))]]]]], (31984 ^ _781404) ^ [_1357069, _1357071, _1357073, _1357075] : [class_Orderings_Olinorder(_1357069), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357069), _1357071), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357069), _1357073), _1357075)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357069), _1357073), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357069), _1357071), _1357075)))], (26234 ^ _781404) ^ [_1249579, _1249581] : [c_Nat__Transfer_Ois__nat(_1249579), c_Nat__Transfer_Onat__set(_1249581), 26241 ^ _781404 : [(26248 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1249579)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1249581))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1249579), _1249581)))], (26242 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1249579), _1249581)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1249579)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1249581))))]]], (40167 ^ _781404) ^ [_1563401, _1563403, _1563405, _1563407] : [hBOOL(hAPP(c_Predicate_ODomainP(_1563401, _1563403, _1563405), _1563407)), -(hBOOL(hAPP(hAPP(_1563405, _1563407), 40170 ^ [_1563401, _1563403, _1563405, _1563407])))], (22113 ^ _781404) ^ [_1175242, _1175244, _1175246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175242), _1175244)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175246), _1175244))), 22116 ^ _781404 : [(22119 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1175242), _1175246)))], (22117 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175244)))]]], (41866 ^ _781404) ^ [_1603961, _1603963] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603961, _1603961), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1603963) = _1603963)], (12770 ^ _781404) ^ [_1002511, _1002513, _1002515, _1002517, _1002519, _1002521] : [-(hBOOL(hAPP(hAPP(c_member(_1002511), _1002513), c_SetInterval_Oord_OgreaterThanAtMost(_1002511, _1002515, _1002517, _1002519, _1002521)))), hBOOL(hAPP(hAPP(_1002517, _1002519), _1002513)), hBOOL(hAPP(hAPP(_1002515, _1002513), _1002521))], (7395 ^ _781404) ^ [_902075, _902077] : [class_Groups_Oordered__ab__group__add(_902075), -(hAPP(c_Set_Oimage(_902075, _902075, c_Groups_Ouminus__class_Ouminus(_902075)), hAPP(c_SetInterval_Oord__class_OlessThan(_902075), _902077)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_902075), hAPP(c_Groups_Ouminus__class_Ouminus(_902075), _902077)))], (44114 ^ _781404) ^ [_1661545, _1661547] : [-(hAPP(hAPP(c_List_Oappend(_1661545), c_List_Olist_ONil(_1661545)), _1661547) = _1661547)], (17294 ^ _781404) ^ [_1089883, _1089885, _1089887] : [hBOOL(hAPP(hAPP(c_member(_1089883), _1089885), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1089883, tc_HOL_Obool), _1089887))), 17298 ^ _781404 : [(17301 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1089883, tc_HOL_Obool)), 17297 ^ [_1089883, _1089885, _1089887]), _1089887)))], (17299 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1089883), _1089885), 17297 ^ [_1089883, _1089885, _1089887])))]]], (47587 ^ _781404) ^ [_1738161, _1738163, _1738165] : [-(hAPP(c_List_Orev(_1738161), hAPP(hAPP(c_List_Otake(_1738161), _1738163), _1738165)) = hAPP(hAPP(c_List_Odrop(_1738161), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738161)), _1738165)), _1738163)), hAPP(c_List_Orev(_1738161), _1738165)))], (42577 ^ _781404) ^ [_1625369, _1625371, _1625373] : [c_Equiv__Relations_Oequiv(_1625369, _1625371, _1625373), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1625369), c_List_Olists(_1625369, _1625371), c_List_Olistrel(_1625369, _1625373)))], (52702 ^ _781404) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (7027 ^ _781404) ^ [_895032, _895034, _895036] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895032, tc_HOL_Obool)), _895034), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895032, tc_HOL_Obool)), _895034), _895036)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895032, tc_HOL_Obool)), _895034), _895036))], (34565 ^ _781404) ^ [_1422467, _1422469, _1422471, _1422473, _1422475, _1422477] : [c_Fun_Oinj__on(_1422467, _1422469, _1422471, _1422473), c_Fun_Oinj__on(_1422469, _1422475, _1422477, hAPP(c_Set_Oimage(_1422467, _1422469, _1422471), _1422473)), -(c_Fun_Oinj__on(_1422467, _1422475, hAPP(c_Fun_Ocomp(_1422469, _1422475, _1422467, _1422477), _1422471), _1422473))], (34345 ^ _781404) ^ [_1417049, _1417051, _1417053] : [-(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)), _1417049)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1417051), _1417053)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1417051), _1417049)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1417053), _1417049)))], (36422 ^ _781404) ^ [_1461867, _1461869, _1461871, _1461873, _1461875, _1461877] : [c_Finite__Set_Ofolding(_1461867, _1461869, _1461871, _1461873), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461867), _1461875)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461867), _1461877)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461867, tc_HOL_Obool)), _1461875), _1461877) = c_Orderings_Obot__class_Obot(tc_fun(_1461867, tc_HOL_Obool)), -(hAPP(_1461873, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461867, tc_HOL_Obool)), _1461875), _1461877)) = hAPP(c_Fun_Ocomp(_1461869, _1461869, _1461869, hAPP(_1461873, _1461875)), hAPP(_1461873, _1461877)))], (46615 ^ _781404) ^ [_1718007, _1718009, _1718011, _1718013] : [-(c_List_Otranspose(_1718007, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1718009), tc_List_Olist(_1718007)), hAPP(c_List_Omap(_1718009, _1718007), _1718011)), _1718013)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1718009), tc_List_Olist(_1718007)), hAPP(c_List_Omap(_1718009, _1718007), _1718011)), c_List_Otranspose(_1718009, _1718013)))], (52448 ^ _781404) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (34915 ^ _781404) ^ [_1430773, _1430775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430773)), hAPP(c_Nat_OSuc, _1430775))), -(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(_1430773))), 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)), _1430775)))))], (46824 ^ _781404) ^ [_1723346, _1723348, _1723350, _1723352] : [c_List_Oupt(_1723346, _1723348) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1723350), _1723352), 46827 ^ _781404 : [(46832 ^ _781404) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1723346), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1723348) = _1723352)], (46830 ^ _781404) ^ [] : [-(_1723346 = _1723350)], (46828 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723346), _1723348)))]]], (38241 ^ _781404) ^ [_1506316, _1506318, _1506320, _1506322, _1506324] : [class_Groups_Ocomm__monoid__add(_1506316), class_Groups_Ocomm__monoid__mult(_1506316), _1506318 = _1506320, c_Nat__Transfer_Onat__set(_1506320), 38259 ^ _781404 : [(38262 ^ _781404) ^ [] : [hAPP(_1506322, 38258 ^ [_1506316, _1506318, _1506320, _1506322, _1506324]) = hAPP(_1506324, 38258 ^ [_1506316, _1506318, _1506320, _1506322, _1506324])], (38260 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 38258 ^ [_1506316, _1506318, _1506320, _1506322, _1506324])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1506316), _1506322), _1506318) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1506316), _1506324), _1506320))], (3666 ^ _781404) ^ [_836323, _836325, _836327, _836329] : [-(c_List_Olist__update(_836329, _836325) = c_List_Olist__update(_836327, _836323)), _836329 = _836327, _836325 = _836323], (32953 ^ _781404) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (11017 ^ _781404) ^ [_968520, _968522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968520), hAPP(c_Nat_OSuc, _968522))), -(_968520 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11025 ^ _781404 : [(11028 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 11024 ^ [_968520, _968522]), _968522)))], (11026 ^ _781404) ^ [] : [-(_968520 = hAPP(c_Nat_OSuc, 11024 ^ [_968520, _968522]))]]], (18985 ^ _781404) ^ [_1119455] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119455), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1119455)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1119455)))], (52372 ^ _781404) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (22651 ^ _781404) ^ [_1186126, _1186128, _1186130, _1186132, _1186134, _1186136] : [class_Rings_Oordered__ring(_1186126), 22654 ^ _781404 : [(22661 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186126), _1186132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186126), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1186126), _1186134), _1186128)), _1186130)), _1186136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186126), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186126), _1186128), _1186130)), _1186132)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186126), _1186134), _1186130)), _1186136))))], (22655 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186126), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186126), _1186128), _1186130)), _1186132)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186126), _1186134), _1186130)), _1186136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186126), _1186132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186126), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1186126), _1186134), _1186128)), _1186130)), _1186136))))]]], (6927 ^ _781404) ^ [_892797, _892799, _892801, _892803, _892805] : [class_Lattices_Olattice(_892797), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892799, _892797)), _892801), _892803), _892805) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892797), hAPP(_892801, _892805)), hAPP(_892803, _892805)))], (6921 ^ _781404) ^ [_892654, _892656, _892658, _892660] : [class_Lattices_Osemilattice__sup(_892654), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892654), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892654), _892656), _892658)), _892660) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892654), _892656), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892654), _892658), _892660)))], (24226 ^ _781404) ^ [_1215775, _1215777] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215775, _1215777) = 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), _1215775), _1215777) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1215777), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215775, _1215777)))], (45623 ^ _781404) ^ [_1695431, _1695433] : [-(c_Random_Oselect__weight(_1695431, _1695433) = 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(_1695431, 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, _1695431), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1695431)), _1695433)))), hAPP(hAPP(c_COMBB(_1695431, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1695431, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1695431, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1695431, _1695433))))], (20531 ^ _781404) ^ [_1145633] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1145633) = 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(_1145633)))))], (6053 ^ _781404) ^ [_877332, _877334, _877336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877332, tc_HOL_Obool)), _877334), _877336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_877332, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_877332, _877334)), c_Predicate_OPowp(_877332, _877336))))], (20313 ^ _781404) ^ [_1141882] : [-(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, _1141882))))))], (52526 ^ _781404) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (20599 ^ _781404) ^ [_1146761, _1146763, _1146765] : [class_Rings_Olinordered__idom(_1146761), 20602 ^ _781404 : [(20611 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146761), hAPP(hAPP(c_Power_Opower__class_Opower(_1146761), _1146763), 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(_1146761), _1146765), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1146761)), _1146763 = c_Groups_Ozero__class_Ozero(_1146761), _1146765 = c_Groups_Ozero__class_Ozero(_1146761)], (20603 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146761), hAPP(hAPP(c_Power_Opower__class_Opower(_1146761), _1146763), 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(_1146761), _1146765), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1146761), 20606 ^ _781404 : [(20609 ^ _781404) ^ [] : [-(_1146765 = c_Groups_Ozero__class_Ozero(_1146761))], (20607 ^ _781404) ^ [] : [-(_1146763 = c_Groups_Ozero__class_Ozero(_1146761))]]]]], (10229 ^ _781404) ^ [_955469, _955471, _955473] : [class_Orderings_Olinorder(_955469), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955469), _955471), _955473))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955469), _955473), _955471)))], (35308 ^ _781404) ^ [_1439358, _1439360, _1439362, _1439364, _1439366, _1439368, _1439370] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1439358, tc_fun(_1439360, tc_fun(_1439362, tc_HOL_Obool))), _1439364), _1439366), _1439368), _1439370))), 35309 ^ _781404 : [(35310 ^ _781404) ^ [_1439443] : [hBOOL(hAPP(hAPP(c_member(_1439358), _1439443), _1439364)), hBOOL(hAPP(hAPP(hAPP(_1439366, _1439443), _1439368), _1439370))]]], (2166 ^ _781404) ^ [_812815, _812817] : [_812817 = _812815, -(c_Int_Oring__1__class_OInts(_812817) = c_Int_Oring__1__class_OInts(_812815))], (41809 ^ _781404) ^ [_1602644, _1602646, _1602648, _1602650, _1602652] : [c_Relation_Osingle__valued(_1602644, _1602644, _1602646), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602644, _1602644)), hAPP(hAPP(c_Product__Type_OPair(_1602644, _1602644), _1602648), _1602650)), c_Transitive__Closure_Ortrancl(_1602644, _1602646))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602644, _1602644)), hAPP(hAPP(c_Product__Type_OPair(_1602644, _1602644), _1602648), _1602652)), c_Transitive__Closure_Ortrancl(_1602644, _1602646))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602644, _1602644)), hAPP(hAPP(c_Product__Type_OPair(_1602644, _1602644), _1602650), _1602652)), c_Transitive__Closure_Ortrancl(_1602644, _1602646)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602644, _1602644)), hAPP(hAPP(c_Product__Type_OPair(_1602644, _1602644), _1602652), _1602650)), c_Transitive__Closure_Ortrancl(_1602644, _1602646))))], (51616 ^ _781404) ^ [_1826775, _1826777, _1826779, _1826781] : [class_Rings_Ocomm__semiring__1(_1826775), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826775), _1826777), _1826779)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826775), _1826777), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826775), _1826781), _1826779))))], (49025 ^ _781404) ^ [_1769303, _1769305, _1769307, _1769309] : [-(c_Predicate_Oconversep(_1769303, _1769305, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1769303, tc_fun(_1769305, tc_HOL_Obool))), _1769307), _1769309)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1769305, tc_fun(_1769303, tc_HOL_Obool))), c_Predicate_Oconversep(_1769303, _1769305, _1769307)), c_Predicate_Oconversep(_1769303, _1769305, _1769309)))], (37698 ^ _781404) ^ [_1492817, _1492819, _1492821, _1492823, _1492825] : [c_Equiv__Relations_Oequiv(_1492817, _1492819, _1492821), hBOOL(hAPP(hAPP(c_member(tc_prod(_1492817, _1492817)), hAPP(hAPP(c_Product__Type_OPair(_1492817, _1492817), _1492823), _1492825)), _1492821)), -(hAPP(c_Relation_OImage(_1492817, _1492817, _1492821), hAPP(hAPP(c_Set_Oinsert(_1492817), _1492823), c_Orderings_Obot__class_Obot(tc_fun(_1492817, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1492817, _1492817, _1492821), hAPP(hAPP(c_Set_Oinsert(_1492817), _1492825), c_Orderings_Obot__class_Obot(tc_fun(_1492817, tc_HOL_Obool)))))], (5801 ^ _781404) ^ [_873364, _873366, _873368] : [_873364 = _873366, 5804 ^ _781404 : [(5807 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873368, tc_HOL_Obool)), _873366), _873364)))], (5805 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873368, tc_HOL_Obool)), _873364), _873366)))]]], (6897 ^ _781404) ^ [_892082, _892084, _892086, _892088] : [class_Lattices_Olattice(_892082), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892082), _892084), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892082), _892086), _892088)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892082), _892086), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892082), _892084), _892088)))], (23779 ^ _781404) ^ [_1208304, _1208306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1208304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208306, _1208304)), _1208304)))], (18055 ^ _781404) ^ [_1103248, _1103250, _1103252, _1103254] : [class_Rings_Olinordered__semidom(_1103248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103248), c_Groups_Oone__class_Oone(_1103248)), _1103250)), 18062 ^ _781404 : [(18069 ^ _781404) ^ [] : [_1103252 = _1103254, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1103248), _1103250), _1103252) = hAPP(hAPP(c_Power_Opower__class_Opower(_1103248), _1103250), _1103254))], (18063 ^ _781404) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1103248), _1103250), _1103252) = hAPP(hAPP(c_Power_Opower__class_Opower(_1103248), _1103250), _1103254), -(_1103252 = _1103254)]]], (38971 ^ _781404) ^ [_1525963, _1525965] : [-(hAPP(c_Set_OCollect(_1525963), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1525963), c_fNot), _1525965)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1525963, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1525963), _1525965)))], (19713 ^ _781404) ^ [_1131699] : [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, _1131699)))))], (45194 ^ _781404) ^ [_1685793, _1685795, _1685797, _1685799] : [c_List_Olist_ONil(_1685793) = hAPP(hAPP(c_List_Omap(_1685795, _1685793), _1685797), _1685799), -(_1685799 = c_List_Olist_ONil(_1685795))], (44563 ^ _781404) ^ [_1673140, _1673142, _1673144] : [-(hAPP(c_List_Ohd(_1673140), hAPP(hAPP(c_List_Olist_OCons(_1673140), _1673142), _1673144)) = _1673142)], (25897 ^ _781404) ^ [_1244281, _1244283] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1244281, _1244283)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1244283), _1244281)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (46937 ^ _781404) ^ [_1725785, _1725787] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1725785, _1725787)))], (52456 ^ _781404) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (15507 ^ _781404) ^ [_1055813, _1055815, _1055817, _1055819] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055813), _1055815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055817), hAPP(c_Set_Oimage(_1055813, _1055817, _1055819), _1055815))), hAPP(c_Finite__Set_Ocard(_1055813), _1055815))))], (1926 ^ _781404) ^ [_808519, _808521] : [-(class_Power_Opower(_808519)), _808521 = _808519, class_Power_Opower(_808521)], (28283 ^ _781404) ^ [_1286969, _1286971, _1286973, _1286975] : [class_Fields_Olinordered__field__inverse__zero(_1286969), class_Int_Onumber(_1286969), 28290 ^ _781404 : [(28291 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286969), _1286971), _1286973)), hAPP(c_Int_Onumber__class_Onumber__of(_1286969), _1286975))), 28294 ^ _781404 : [(28301 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), c_Groups_Ozero__class_Ozero(_1286969)), _1286973))), 28304 ^ _781404 : [(28311 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), _1286973), c_Groups_Ozero__class_Ozero(_1286969)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), c_Groups_Ozero__class_Ozero(_1286969)), hAPP(c_Int_Onumber__class_Onumber__of(_1286969), _1286975))))], (28305 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), _1286973), c_Groups_Ozero__class_Ozero(_1286969))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286969), hAPP(c_Int_Onumber__class_Onumber__of(_1286969), _1286975)), _1286973)), _1286971)))]]], (28295 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), c_Groups_Ozero__class_Ozero(_1286969)), _1286973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), _1286971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286969), hAPP(c_Int_Onumber__class_Onumber__of(_1286969), _1286975)), _1286973))))]]], (28317 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286969), _1286971), _1286973)), hAPP(c_Int_Onumber__class_Onumber__of(_1286969), _1286975)))), 28320 ^ _781404 : [(28323 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), _1286971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286969), hAPP(c_Int_Onumber__class_Onumber__of(_1286969), _1286975)), _1286973)))], (28321 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), c_Groups_Ozero__class_Ozero(_1286969)), _1286973)))]], 28324 ^ _781404 : [(28327 ^ _781404) ^ [] : [28328 ^ _781404 : [(28331 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286969), hAPP(c_Int_Onumber__class_Onumber__of(_1286969), _1286975)), _1286973)), _1286971))], (28329 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), _1286973), c_Groups_Ozero__class_Ozero(_1286969))))]], 28332 ^ _781404 : [(28335 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), c_Groups_Ozero__class_Ozero(_1286969)), hAPP(c_Int_Onumber__class_Onumber__of(_1286969), _1286975)))], (28333 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), _1286973), c_Groups_Ozero__class_Ozero(_1286969)))]]], (28325 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286969), c_Groups_Ozero__class_Ozero(_1286969)), _1286973))]]]]], (36360 ^ _781404) ^ [_1460537, _1460539, _1460541, _1460543, _1460545, _1460547, _1460549, _1460551] : [c_Finite__Set_Ofolding(_1460537, _1460539, _1460541, _1460543), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460537), _1460545)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460537), _1460547)), -(hAPP(c_Fun_Ocomp(_1460539, _1460539, _1460549, hAPP(_1460543, _1460547)), hAPP(c_Fun_Ocomp(_1460539, _1460539, _1460549, hAPP(_1460543, _1460545)), _1460551)) = hAPP(c_Fun_Ocomp(_1460539, _1460539, _1460549, hAPP(_1460543, _1460545)), hAPP(c_Fun_Ocomp(_1460539, _1460539, _1460549, hAPP(_1460543, _1460547)), _1460551)))], (27215 ^ _781404) ^ [_1267289, _1267291, _1267293, _1267295] : [_1267289 = c_Finite__Set_Ofold1(_1267291, _1267293), -(hAPP(_1267289, hAPP(hAPP(c_Set_Oinsert(_1267291), _1267295), c_Orderings_Obot__class_Obot(tc_fun(_1267291, tc_HOL_Obool)))) = _1267295)], (47822 ^ _781404) ^ [_1743268, _1743270, _1743272] : [-(hAPP(hAPP(c_List_Oappend(_1743268), c_List_OtakeWhile(_1743268, _1743270, _1743272)), c_List_OdropWhile(_1743268, _1743270, _1743272)) = _1743272)], (35652 ^ _781404) ^ [_1446823, _1446825] : [-(c_Divides_Odivmod__nat(_1446823, _1446825) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1446823), _1446825)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1446823, _1446825)))], (19317 ^ _781404) ^ [_1125036, _1125038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125036), _1125038)), -(_1125038 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1125036), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 19320 ^ [_1125036, _1125038])))], (37066 ^ _781404) ^ [_1476392, _1476394, _1476396, _1476398, _1476400] : [class_Groups_Oordered__ab__group__add(_1476392), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476394), _1476396)), 37076 ^ _781404 : [(37079 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1476392), c_Groups_Ozero__class_Ozero(_1476392)), hAPP(_1476398, 37075 ^ [_1476392, _1476394, _1476396, _1476398, _1476400])))], (37077 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476394), 37075 ^ [_1476392, _1476394, _1476396, _1476398, _1476400]), _1476396)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476394, _1476392), _1476398), _1476396) = c_Groups_Ozero__class_Ozero(_1476392), hBOOL(hAPP(hAPP(c_member(_1476394), _1476400), _1476396)), -(hAPP(_1476398, _1476400) = c_Groups_Ozero__class_Ozero(_1476392))], (13944 ^ _781404) ^ [_1024433, _1024435, _1024437, _1024439] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1024433), _1024435)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024433), _1024437)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1024433, tc_Nat_Onat), _1024439), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1024433, tc_HOL_Obool)), _1024435), _1024437)) = 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(_1024433, tc_Nat_Onat), _1024439), _1024435)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1024433, tc_Nat_Onat), _1024439), _1024437))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1024433, tc_Nat_Onat), _1024439), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1024433, tc_HOL_Obool)), _1024435), _1024437))))], (52528 ^ _781404) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (7563 ^ _781404) ^ [_905276, _905278] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905276, tc_HOL_Obool)), _905278), c_Orderings_Otop__class_Otop(tc_fun(_905276, tc_HOL_Obool))) = _905278)], (40345 ^ _781404) ^ [_1567232, _1567234] : [c_Nitpick_Owf_H(_1567232, _1567234), 40348 ^ _781404 : [(40351 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1567232, _1567232)), _1567234))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (40349 ^ _781404) ^ [] : [-(c_Wellfounded_Oacyclic(_1567232, _1567234))]]], (6323 ^ _781404) ^ [_881912, _881914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _881914)), _881912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _881912), _881914))], (25033 ^ _781404) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (23451 ^ _781404) ^ [_1202290, _1202292, _1202294, _1202296] : [class_Divides_Osemiring__div(_1202290), -(c_Divides_Odiv__class_Omod(_1202290, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202290), _1202292), _1202294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202290), _1202296), _1202294)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202290), c_Divides_Odiv__class_Omod(_1202290, _1202292, _1202296)), _1202294))], (38552 ^ _781404) ^ [_1513791, _1513793, _1513795, _1513797, _1513799, _1513801] : [class_Groups_Ocomm__monoid__mult(_1513791), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1513793, _1513791), hAPP(hAPP(c_COMBC(_1513793, tc_fun(_1513795, tc_HOL_Obool), _1513791), hAPP(hAPP(c_COMBB(tc_fun(_1513795, _1513791), tc_fun(tc_fun(_1513795, tc_HOL_Obool), _1513791), _1513793), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1513795, _1513791)), _1513797)), _1513799)), _1513801) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1513793, _1513795), _1513791), hAPP(c_Product__Type_Oprod_Oprod__case(_1513793, _1513795, _1513791), _1513797)), hAPP(hAPP(c_Product__Type_OSigma(_1513793, _1513795), _1513801), hAPP(c_COMBK(tc_fun(_1513795, tc_HOL_Obool), _1513793), _1513799))))], (52256 ^ _781404) ^ [_1837493, _1837495] : [class_Groups_Ominus(_1837493), -(class_Groups_Ominus(tc_fun(_1837495, _1837493)))], (14039 ^ _781404) ^ [_1026299, _1026301, _1026303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026299), _1026301)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026303), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026301), _1026299)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026303), _1026301)), _1026299))], (20821 ^ _781404) ^ [_1151173, _1151175, _1151177, _1151179] : [class_Groups_Oab__semigroup__mult(_1151173), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151173), _1151175), _1151177)), _1151179) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151173), _1151175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151173), _1151177), _1151179)))], (9178 ^ _781404) ^ [_937605, _937607, _937609] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937605, tc_HOL_Obool)), _937607), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937605, tc_HOL_Obool)), _937609), _937607)) = c_Orderings_Obot__class_Obot(tc_fun(_937605, tc_HOL_Obool)))], (35786 ^ _781404) ^ [_1449538, _1449540, _1449542, _1449544] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1449538, _1449540)), c_Nitpick_Opair__box_OPairBox(_1449538, _1449540, _1449542, _1449544)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37607 ^ _781404) ^ [_1490650, _1490652, _1490654, _1490656] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1490650, _1490650)), hAPP(hAPP(c_Product__Type_OPair(_1490650, _1490650), _1490652), _1490654)), c_Relation_OId__on(_1490650, _1490656)))), _1490652 = _1490654, hBOOL(hAPP(hAPP(c_member(_1490650), _1490652), _1490656))], (22059 ^ _781404) ^ [_1174327, _1174329] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174327), _1174329) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22062 ^ _781404 : [(22065 ^ _781404) ^ [] : [-(_1174329 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22063 ^ _781404) ^ [] : [-(_1174327 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (52392 ^ _781404) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (25343 ^ _781404) ^ [_1234592, _1234594] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234592), _1234594) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1234592 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1234592 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (46485 ^ _781404) ^ [_1714898, _1714900, _1714902] : [-(c_Enum_On__lists(_1714898, hAPP(c_Nat_OSuc, _1714900), _1714902) = c_List_Oconcat(tc_List_Olist(_1714898), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714898), tc_List_Olist(tc_List_Olist(_1714898))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714898), tc_List_Olist(_1714898), tc_List_Olist(tc_List_Olist(_1714898))), hAPP(hAPP(c_COMBB(tc_fun(_1714898, tc_List_Olist(_1714898)), tc_fun(tc_List_Olist(_1714898), tc_List_Olist(tc_List_Olist(_1714898))), tc_List_Olist(_1714898)), c_List_Omap(_1714898, tc_List_Olist(_1714898))), hAPP(c_COMBC(_1714898, tc_List_Olist(_1714898), tc_List_Olist(_1714898)), c_List_Olist_OCons(_1714898)))), _1714902)), c_Enum_On__lists(_1714898, _1714900, _1714902))))], (42531 ^ _781404) ^ [_1624170, _1624172, _1624174, _1624176, _1624178, _1624180] : [-(c_List_Olistrelp(_1624170, _1624172, hAPP(hAPP(c_List_Olist_OCons(_1624170), _1624174), _1624176), hAPP(hAPP(c_List_Olist_OCons(_1624170), _1624178), _1624180))), hBOOL(hAPP(hAPP(_1624172, _1624174), _1624178)), c_List_Olistrelp(_1624170, _1624172, _1624176, _1624180)], (13203 ^ _781404) ^ [_1010655, _1010657, _1010659, _1010661, _1010663] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1010655), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010655), _1010657), _1010659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010655), _1010661), _1010663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010655), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010655), _1010657), _1010661)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010655), _1010659), _1010663))))], (40700 ^ _781404) ^ [_1574854, _1574856, _1574858] : [class_Complete__Lattice_Ocomplete__lattice(_1574854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1574854), _1574856), hAPP(_1574858, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1574854), _1574856), c_Inductive_Ocomplete__lattice__class_Ogfp(_1574854, _1574858))))), c_Orderings_Oorder__class_Omono(_1574854, _1574854, _1574858), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1574854), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1574854), _1574856), c_Inductive_Ocomplete__lattice__class_Ogfp(_1574854, _1574858))), hAPP(_1574858, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1574854), _1574856), c_Inductive_Ocomplete__lattice__class_Ogfp(_1574854, _1574858))))))], (21223 ^ _781404) ^ [_1158620, _1158622, _1158624] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158620), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1158622), _1158624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158620), _1158622)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158620), _1158624)))], (47013 ^ _781404) ^ [_1726894, _1726896] : [class_Orderings_Olinorder(_1726894), -(_1726896 = c_List_Olist_ONil(_1726894)), c_List_Olinorder__class_Osorted(_1726894, _1726896), -(c_List_Olinorder__class_Osorted(_1726894, c_List_Obutlast(_1726894, _1726896)))], (33255 ^ _781404) ^ [_1382638, _1382640, _1382642, _1382644] : [hBOOL(hAPP(hAPP(c_member(_1382640), _1382644), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382638, tc_fun(_1382640, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1382638, tc_HOL_Obool))), _1382642))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382638, tc_fun(_1382640, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1382638, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1382640, tc_HOL_Obool), tc_fun(_1382640, tc_HOL_Obool), _1382638), hAPP(c_COMBC(_1382640, tc_fun(_1382640, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382640))), _1382642)), _1382644)))], (7930 ^ _781404) ^ [_913006, _913008, _913010, _913012] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913006, tc_HOL_Obool)), _913008), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913006, tc_HOL_Obool)), _913010), _913012)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913006, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913006, tc_HOL_Obool)), _913008), _913010)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913006, tc_HOL_Obool)), _913008), _913012)))], (13275 ^ _781404) ^ [_1012076] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012076), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1012076)], (20919 ^ _781404) ^ [_1152709, _1152711, _1152713, _1152715, _1152717] : [class_Rings_Osemiring(_1152709), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152709), _1152711), _1152713)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152709), _1152715), _1152713)), _1152717)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152709), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152709), _1152711), _1152715)), _1152713)), _1152717))], (26473 ^ _781404) ^ [_1253365] : [class_Rings_Oring__1(_1253365), -(hAPP(c_Int_Oring__1__class_Oof__int(_1253365), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1253365))], (47802 ^ _781404) ^ [_1742680, _1742682, _1742684] : [hBOOL(hAPP(c_List_Odistinct(_1742680), _1742682)), hBOOL(hAPP(hAPP(c_member(_1742680), _1742684), hAPP(c_List_Oset(_1742680), _1742682))), -(c_List_OtakeWhile(_1742680, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1742680), c_fNot), hAPP(hAPP(c_COMBC(_1742680, _1742680, tc_HOL_Obool), c_fequal), _1742684)), hAPP(c_List_Orev(_1742680), _1742682)) = hAPP(c_List_Orev(_1742680), hAPP(c_List_Otl(_1742680), c_List_OdropWhile(_1742680, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1742680), c_fNot), hAPP(hAPP(c_COMBC(_1742680, _1742680, tc_HOL_Obool), c_fequal), _1742684)), _1742682))))], (52282 ^ _781404) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (8383 ^ _781404) ^ [_922686, _922688] : [class_Groups_Olinordered__ab__group__add(_922686), 8386 ^ _781404 : [(8393 ^ _781404) ^ [] : [_922688 = c_Groups_Ozero__class_Ozero(_922686), -(hAPP(c_Groups_Ouminus__class_Ouminus(_922686), _922688) = _922688)], (8387 ^ _781404) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_922686), _922688) = _922688, -(_922688 = c_Groups_Ozero__class_Ozero(_922686))]]], (20123 ^ _781404) ^ [_1138753] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1138753)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1138753)))], (38025 ^ _781404) ^ [_1500622, _1500624, _1500626, _1500628, _1500630, _1500632] : [c_Equiv__Relations_Ocongruent(_1500622, _1500624, _1500626, _1500628), hBOOL(hAPP(hAPP(c_member(tc_prod(_1500622, _1500622)), hAPP(hAPP(c_Product__Type_OPair(_1500622, _1500622), _1500630), _1500632)), _1500626)), -(hAPP(_1500628, _1500630) = hAPP(_1500628, _1500632))], (42703 ^ _781404) ^ [_1628633, _1628635, _1628637, _1628639] : [-(_1628633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1628635), hAPP(hAPP(c_List_Olist_OCons(_1628635), _1628637), _1628639)), _1628633) = hAPP(hAPP(c_List_Onth(_1628635), _1628639), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1628633), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (42695 ^ _781404) ^ [_1628456, _1628458, _1628460, _1628462] : [-(hAPP(hAPP(c_List_Onth(_1628456), hAPP(hAPP(c_List_Olist_OCons(_1628456), _1628458), _1628460)), _1628462) = c_Nat_Onat_Onat__case(_1628456, _1628458, hAPP(c_List_Onth(_1628456), _1628460), _1628462))], (30662 ^ _781404) ^ [_1332620, _1332622, _1332624, _1332626] : [-(c_Nitpick_Ofold__graph_H(_1332620, _1332622, _1332624, _1332626, c_Orderings_Obot__class_Obot(tc_fun(_1332620, tc_HOL_Obool)), _1332626))], (13762 ^ _781404) ^ [_1021418, _1021420] : [class_Groups_Olinordered__ab__group__add(_1021418), 13765 ^ _781404 : [(13772 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021418), c_Groups_Ozero__class_Ozero(_1021418)), _1021420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021418), c_Groups_Ozero__class_Ozero(_1021418)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021418), _1021420), _1021420))))], (13766 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021418), c_Groups_Ozero__class_Ozero(_1021418)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021418), _1021420), _1021420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021418), c_Groups_Ozero__class_Ozero(_1021418)), _1021420)))]]], (48849 ^ _781404) ^ [] : [-(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)))], (41223 ^ _781404) ^ [_1588439, _1588441, _1588443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1588439, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1588439, _1588439, _1588441), _1588443)), _1588443)), -(hAPP(c_Relation_OImage(_1588439, _1588439, c_Transitive__Closure_Ortrancl(_1588439, _1588441)), _1588443) = _1588443)], (33213 ^ _781404) ^ [_1381488, _1381490, _1381492, _1381494, _1381496] : [class_Fields_Ofield__inverse__zero(_1381488), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381490), _1381492)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381490, _1381488), hAPP(hAPP(c_COMBS(_1381490, _1381488, _1381488), hAPP(hAPP(c_COMBB(_1381488, tc_fun(_1381488, _1381488), _1381490), c_Rings_Oinverse__class_Odivide(_1381488)), _1381494)), _1381496)), _1381492) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381488), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381490, _1381488), _1381494), _1381492)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381490, _1381488), _1381496), _1381492)))], (11955 ^ _781404) ^ [_986281, _986283, _986285] : [-(hBOOL(hAPP(hAPP(c_member(_986281), _986283), hAPP(hAPP(c_Set_Oinsert(_986281), _986283), _986285))))], (42447 ^ _781404) ^ [_1621246, _1621248] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1621246), tc_List_Olist(_1621246)), tc_HOL_Obool)), c_List_Olistrel(_1621246, _1621248)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1621246), c_List_Olistrel1(_1621246, _1621248)))))], (52310 ^ _781404) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (8148 ^ _781404) ^ [_918141, _918143, _918145] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_918141, tc_HOL_Obool)), _918143), _918145) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_918141, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_918141, tc_HOL_Obool)), _918143), hAPP(hAPP(c_Set_Oinsert(tc_fun(_918141, tc_HOL_Obool)), _918145), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_918141, tc_HOL_Obool), tc_HOL_Obool))))))], (52338 ^ _781404) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (37664 ^ _781404) ^ [_1492183, _1492185, _1492187] : [c_Equiv__Relations_Oequiv(_1492183, _1492185, _1492187), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1492183, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1492183), _1492185), _1492187)) = _1492185)], (11735 ^ _781404) ^ [_982365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982365), _982365))], (41540 ^ _781404) ^ [_1595928, _1595930] : [-(hAPP(c_Relation_Oconverse(_1595928, _1595928), c_Relation_OId__on(_1595928, _1595930)) = c_Relation_OId__on(_1595928, _1595930))], (18351 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (39506 ^ _781404) ^ [_1545758, _1545760] : [-(c_Fun_Oinj__on(_1545758, _1545758, c_Fun_Oid(_1545758), _1545760))], (46748 ^ _781404) ^ [_1722077, _1722079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722077), _1722079)), -(c_List_Oupt(_1722077, _1722079) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1722077), c_List_Oupt(hAPP(c_Nat_OSuc, _1722077), _1722079)))], (43605 ^ _781404) ^ [_1650460, _1650462, _1650464, _1650466] : [_1650462 = c_List_Olist_ONil(_1650460), -(hAPP(hAPP(c_List_Olist__update(_1650460, _1650462), _1650464), _1650466) = c_List_Olist_ONil(_1650460))], (13989 ^ _781404) ^ [_1025318, _1025320] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025318), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025318), _1025320)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46207 ^ _781404) ^ [_1708851, _1708853] : [-(hBOOL(hAPP(c_List_Odistinct(_1708851), c_List_Oremdups(_1708851, _1708853))))], (21503 ^ _781404) ^ [_1163722, _1163724, _1163726] : [class_Rings_Oordered__cancel__semiring(_1163722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163722), c_Groups_Ozero__class_Ozero(_1163722)), _1163724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163722), _1163726), c_Groups_Ozero__class_Ozero(_1163722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163722), _1163724), _1163726)), c_Groups_Ozero__class_Ozero(_1163722))))], (38502 ^ _781404) ^ [_1512389, _1512391, _1512393, _1512395, _1512397] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1512389, _1512391), _1512393), hAPP(hAPP(c_COMBS(_1512389, tc_fun(_1512391, tc_HOL_Obool), tc_fun(_1512391, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512391, tc_HOL_Obool), tc_fun(tc_fun(_1512391, tc_HOL_Obool), tc_fun(_1512391, tc_HOL_Obool)), _1512389), c_Groups_Ominus__class_Ominus(tc_fun(_1512391, tc_HOL_Obool))), _1512395)), _1512397)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1512389, _1512391), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1512389, _1512391), _1512393), _1512395)), hAPP(hAPP(c_Product__Type_OSigma(_1512389, _1512391), _1512393), _1512397)))], (21195 ^ _781404) ^ [_1157972, _1157974, _1157976] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1157972), _1157974)), _1157976) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1157972), _1157976)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1157974), _1157976)))], (17483 ^ _781404) ^ [_1093296, _1093298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093296), _1093298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1093296), _1093298)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52406 ^ _781404) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (13307 ^ _781404) ^ [_1012592, _1012594, _1012596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012592), _1012594)), _1012596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012592), _1012596)))], (16462 ^ _781404) ^ [_1073883, _1073885, _1073887, _1073889] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1073883), _1073885)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073887), _1073889)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1073883, _1073887)), c_Sum__Type_OPlus(_1073883, _1073887, _1073885, _1073889)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1073883), _1073885)), hAPP(c_Finite__Set_Ocard(_1073887), _1073889)))], (7783 ^ _781404) ^ [_909511, _909513, _909515, _909517] : [class_Lattices_Osemilattice__inf(_909511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909511), _909513), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_909511), _909515), _909517))), 7790 ^ _781404 : [(7793 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909511), _909513), _909517)))], (7791 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909511), _909513), _909515)))]]], (18697 ^ _781404) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (18273 ^ _781404) ^ [_1106996, _1106998, _1107000, _1107002] : [class_Rings_Olinordered__semidom(_1106996), hAPP(hAPP(c_Power_Opower__class_Opower(_1106996), _1106998), _1107000) = hAPP(hAPP(c_Power_Opower__class_Opower(_1106996), _1107002), _1107000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106996), c_Groups_Ozero__class_Ozero(_1106996)), _1106998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106996), c_Groups_Ozero__class_Ozero(_1106996)), _1107002)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1107000)), -(_1106998 = _1107002)], (48921 ^ _781404) ^ [_1766797, _1766799, _1766801, _1766803, _1766805, _1766807, _1766809] : [-(c_New__Random__Sequence_Opos__decr__bind(_1766797, _1766799, _1766801, _1766803, _1766805, _1766807, _1766809) = c_New__DSequence_Opos__decr__bind(_1766797, _1766799, hAPP(hAPP(hAPP(_1766801, _1766805), _1766807), _1766809), hAPP(hAPP(c_COMBC(_1766797, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1766799))), hAPP(hAPP(c_COMBC(_1766797, 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(_1766799)))), hAPP(hAPP(c_COMBC(_1766797, 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(_1766799))))), _1766803), _1766805)), _1766807)), _1766809)))], (21133 ^ _781404) ^ [_1156634, _1156636, _1156638] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1156634)), _1156636) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1156634)), _1156638), -(_1156636 = _1156638)], (45710 ^ _781404) ^ [_1697132, _1697134] : [-(c_Code__Numeral_Onat__of__aux(_1697132, _1697134) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1697132)), _1697134))], (7097 ^ _781404) ^ [_896330, _896332, _896334] : [class_Lattices_Osemilattice__sup(_896330), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896330), _896332), _896334)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896330), _896332), _896334) = _896334)], (32272 ^ _781404) ^ [_1362303, _1362305, _1362307, _1362309] : [class_Orderings_Olinorder(_1362303), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362303), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362303), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1362303), _1362305), _1362307)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1362303), _1362305), _1362309))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1362303), _1362305), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362303), _1362307), _1362309)))))], (37254 ^ _781404) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (14655 ^ _781404) ^ [_1038341] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1038341), c_Orderings_Otop__class_Otop(tc_fun(_1038341, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1038341)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1038341), tc_HOL_Obool)))))], (6083 ^ _781404) ^ [_877986, _877988, _877990, _877992, _877994] : [class_Orderings_Oorder(_877986), class_Orderings_Olinorder(_877988), c_Orderings_Oorder__class_Ostrict__mono(_877988, _877986, _877990), 6094 ^ _781404 : [(6101 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877988), _877992), _877994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877986), hAPP(_877990, _877992)), hAPP(_877990, _877994))))], (6095 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877986), hAPP(_877990, _877992)), hAPP(_877990, _877994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877988), _877992), _877994)))]]], (1776 ^ _781404) ^ [_806644, _806646] : [-(class_Divides_Osemiring__div(_806644)), _806646 = _806644, class_Divides_Osemiring__div(_806646)], (38458 ^ _781404) ^ [_1511232] : [-(c_Nitpick_Oone__frac(_1511232) = c_Nitpick_OAbs__Frac(_1511232, 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))))], (7663 ^ _781404) ^ [_907426, _907428, _907430] : [class_Lattices_Osemilattice__inf(_907426), 7666 ^ _781404 : [(7673 ^ _781404) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_907426), _907428), _907430) = _907428, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907426), _907428), _907430)))], (7667 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907426), _907428), _907430)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_907426), _907428), _907430) = _907428)]]], (44256 ^ _781404) ^ [_1665185, _1665187, _1665189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665185), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665187)), _1665189))), -(hAPP(hAPP(c_List_Otake(_1665187), hAPP(c_Nat_OSuc, _1665185)), _1665189) = hAPP(hAPP(c_List_Oappend(_1665187), hAPP(hAPP(c_List_Otake(_1665187), _1665185), _1665189)), hAPP(hAPP(c_List_Olist_OCons(_1665187), hAPP(hAPP(c_List_Onth(_1665187), _1665189), _1665185)), c_List_Olist_ONil(_1665187))))], (23489 ^ _781404) ^ [_1203029, _1203031] : [class_Divides_Osemiring__div(_1203029), -(c_Divides_Odiv__class_Omod(_1203029, _1203031, _1203031) = c_Groups_Ozero__class_Ozero(_1203029))], (42270 ^ _781404) ^ [_1615891, _1615893, _1615895, _1615897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1615891), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1615893), _1615895))), -(hAPP(c_Random_Opick(_1615893, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1615893)), _1615895), _1615897)), _1615891) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1615893), _1615895))], (20025 ^ _781404) ^ [] : [-(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))], (26192 ^ _781404) ^ [_1248974, _1248976] : [c_Nat__Transfer_Onat__set(_1248974), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1248976), _1248974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248976)))], (25899 ^ _781404) ^ [] : [-(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))))], (13456 ^ _781404) ^ [_1015479, _1015481, _1015483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015479), _1015481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015479), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015483), _1015481))))], (8419 ^ _781404) ^ [_923311, _923313] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923311, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_923311, tc_HOL_Obool))), _923313) = _923313)], (20251 ^ _781404) ^ [_1140983, _1140985] : [class_Int_Onumber__ring(_1140983), class_Int_Oring__char__0(_1140983), 20258 ^ _781404 : [(20265 ^ _781404) ^ [] : [c_Int_Oiszero(_1140983, hAPP(c_Int_Onumber__class_Onumber__of(_1140983), _1140985)), -(c_Int_Oiszero(_1140983, hAPP(c_Int_Onumber__class_Onumber__of(_1140983), c_Int_OBit0(_1140985))))], (20259 ^ _781404) ^ [] : [c_Int_Oiszero(_1140983, hAPP(c_Int_Onumber__class_Onumber__of(_1140983), c_Int_OBit0(_1140985))), -(c_Int_Oiszero(_1140983, hAPP(c_Int_Onumber__class_Onumber__of(_1140983), _1140985)))]]], (33345 ^ _781404) ^ [_1385087, _1385089, _1385091, _1385093, _1385095, _1385097] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385087, tc_fun(_1385089, tc_HOL_Obool)), _1385091), hAPP(hAPP(c_COMBB(_1385093, tc_fun(_1385089, tc_HOL_Obool), _1385087), _1385095), _1385097)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385093, tc_fun(_1385089, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1385087, _1385093, _1385097), _1385091)), _1385095))], (10639 ^ _781404) ^ [_962261, _962263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962261), hAPP(c_Nat_OSuc, _962263))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962261), _962263))), -(_962261 = _962263)], (25985 ^ _781404) ^ [_1245731] : [-(_1245731 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 25988 ^ _781404 : [(25995 ^ _781404) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1245731, 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, _1245731) = 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), _1245731), 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)))], (25989 ^ _781404) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1245731, 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, _1245731) = 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), _1245731), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (50301 ^ _781404) ^ [_1797626, _1797628] : [c_Relation_Osym(_1797626, hAPP(c_Set_OCollect(tc_prod(_1797626, _1797626)), hAPP(c_Product__Type_Oprod_Oprod__case(_1797626, _1797626, tc_HOL_Obool), _1797628))), -(c_Predicate_Osymp(_1797626, _1797628))], (41355 ^ _781404) ^ [_1591726, _1591728, _1591730, _1591732] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591726, _1591726)), hAPP(hAPP(c_Product__Type_OPair(_1591726, _1591726), _1591728), _1591730)), c_Transitive__Closure_Ortrancl(_1591726, _1591732))), -(_1591728 = _1591730), 41362 ^ _781404 : [(41365 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591726, _1591726)), hAPP(hAPP(c_Product__Type_OPair(_1591726, _1591726), _1591728), _1591730)), c_Transitive__Closure_Otrancl(_1591726, _1591732))))], (41363 ^ _781404) ^ [] : [_1591728 = _1591730]]], (23411 ^ _781404) ^ [_1201370, _1201372, _1201374, _1201376] : [class_Divides_Oring__div(_1201370), -(c_Divides_Odiv__class_Omod(_1201370, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201370), _1201372), _1201374), _1201376) = c_Divides_Odiv__class_Omod(_1201370, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201370), c_Divides_Odiv__class_Omod(_1201370, _1201372, _1201376)), _1201374), _1201376))], (29585 ^ _781404) ^ [_1311172, _1311174, _1311176, _1311178] : [class_Fields_Ofield__inverse__zero(_1311172), -(_1311174 = c_Groups_Ozero__class_Ozero(_1311172)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1311172), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311172), _1311176), _1311174)), _1311178) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311172), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1311172), _1311176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311172), _1311178), _1311174))), _1311174))], (25778 ^ _781404) ^ [_1242076, _1242078, _1242080] : [hBOOL(hAPP(_1242076, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242078), _1242080))), 25783 ^ _781404 : [(25786 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1242076, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25784 ^ _781404) ^ [] : [-(_1242080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25788 ^ _781404 : [(25793 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1242076, 25787 ^ [_1242076, _1242078, _1242080])))], (25791 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1242078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242080), hAPP(c_Nat_OSuc, 25787 ^ [_1242076, _1242078, _1242080])))))], (25789 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242080), 25787 ^ [_1242076, _1242078, _1242080])), _1242078)))]]], (1706 ^ _781404) ^ [_805769, _805771] : [-(class_Groups_Ocomm__monoid__mult(_805769)), _805771 = _805769, class_Groups_Ocomm__monoid__mult(_805771)], (6339 ^ _781404) ^ [_882151, _882153] : [6340 ^ _781404 : [(6343 ^ _781404) ^ [] : [_882151 = hAPP(c_Nat_OSuc, _882153)], (6341 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882151), _882153))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882151), hAPP(c_Nat_OSuc, _882153))))], (25903 ^ _781404) ^ [_1244393, _1244395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244393), _1244395)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1244393), _1244395) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (23767 ^ _781404) ^ [_1208100, _1208102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1208100)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208100, _1208102)), _1208100)))], (7313 ^ _781404) ^ [_900534, _900536] : [class_Lattices_Oboolean__algebra(_900534), -(hAPP(c_Groups_Ouminus__class_Ouminus(_900534), hAPP(c_Groups_Ouminus__class_Ouminus(_900534), _900536)) = _900536)], (35147 ^ _781404) ^ [_1436194, _1436196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436194), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1436196)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1436194)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1436196))], (39888 ^ _781404) ^ [_1556792, _1556794, _1556796, _1556798] : [c_Wellfounded_Owf(_1556792, _1556794), hBOOL(hAPP(hAPP(c_member(tc_prod(_1556792, _1556792)), hAPP(hAPP(c_Product__Type_OPair(_1556792, _1556792), _1556796), _1556798)), _1556794)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1556792, _1556792)), hAPP(hAPP(c_Product__Type_OPair(_1556792, _1556792), _1556798), _1556796)), _1556794))], (49806 ^ _781404) ^ [_1786852, _1786854, _1786856, _1786858] : [c_Relation_Otrans(_1786852, _1786854), -(c_Relation_Otrans(_1786856, hAPP(hAPP(c_Relation_Oinv__image(_1786852, _1786856), _1786854), _1786858)))], (46870 ^ _781404) ^ [_1724191] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1724191) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1724191))))], (16342 ^ _781404) ^ [_1071704] : [-(hAPP(c_Nat_OSuc, _1071704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1071704), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (29897 ^ _781404) ^ [_1317350, _1317352, _1317354, _1317356] : [class_Rings_Ocomm__semiring__1(_1317350), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317352), _1317354)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317352, _1317350), _1317356), _1317354) = c_Groups_Ozero__class_Ozero(_1317350)), 29906 ^ _781404 : [(29907 ^ _781404) ^ [_1317531] : [hBOOL(hAPP(hAPP(c_member(_1317352), _1317531), _1317354)), hAPP(_1317356, _1317531) = c_Groups_Ozero__class_Ozero(_1317350)]]], (3506 ^ _781404) ^ [_833813, _833815, _833817, _833819] : [-(c_Random_Oselect__weight(_833819, _833815) = c_Random_Oselect__weight(_833817, _833813)), _833819 = _833817, _833815 = _833813], (37394 ^ _781404) ^ [_1484736, _1484738, _1484740, _1484742, _1484744, _1484746] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484736, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1484738, _1484736, _1484740), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484742, tc_fun(_1484738, tc_HOL_Obool)), _1484744), _1484746))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484742, tc_fun(_1484736, tc_HOL_Obool)), _1484744), hAPP(hAPP(c_COMBB(tc_fun(_1484738, tc_HOL_Obool), tc_fun(_1484736, tc_HOL_Obool), _1484742), c_Relation_OImage(_1484738, _1484736, _1484740)), _1484746)))))], (52204 ^ _781404) ^ [_1836811, _1836813] : [class_Orderings_Opreorder(_1836811), -(class_Orderings_Opreorder(tc_fun(_1836813, _1836811)))], (17148 ^ _781404) ^ [_1086961, _1086963, _1086965] : [class_Int_Onumber__ring(_1086961), class_Rings_Olinordered__idom(_1086961), 17155 ^ _781404 : [(17162 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086963), _1086965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086961), hAPP(c_Int_Onumber__class_Onumber__of(_1086961), _1086963)), hAPP(c_Int_Onumber__class_Onumber__of(_1086961), _1086965))))], (17156 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086961), hAPP(c_Int_Onumber__class_Onumber__of(_1086961), _1086963)), hAPP(c_Int_Onumber__class_Onumber__of(_1086961), _1086965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086963), _1086965)))]]], (52586 ^ _781404) ^ [_1840662] : [class_Enum_Oenum(_1840662), -(class_Enum_Oenum(tc_Option_Ooption(_1840662)))], (11471 ^ _781404) ^ [_977394, _977396, _977398, _977400, _977402] : [c_Fun_Oinj__on(_977394, _977396, _977398, c_Orderings_Otop__class_Otop(tc_fun(_977394, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977396, tc_HOL_Obool)), _977400), hAPP(c_Set_Oimage(_977394, _977396, _977398), _977402))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977394, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_977394, _977396, _977398), _977400)), _977402)))], (35638 ^ _781404) ^ [_1446548, _1446550, _1446552, _1446554, _1446556, _1446558] : [-(hAPP(c_Product__Type_Oapsnd(_1446548, _1446550, _1446552, _1446554), hAPP(hAPP(c_Product__Type_OPair(_1446552, _1446548), _1446556), _1446558)) = hAPP(hAPP(c_Product__Type_OPair(_1446552, _1446550), _1446556), hAPP(_1446554, _1446558)))], (37325 ^ _781404) ^ [_1482552, _1482554] : [-(c_FunDef_Orp__inv__image(_1482552, _1482554) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool), tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool), tc_fun(tc_fun(_1482554, _1482552), tc_prod(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool), tc_fun(tc_fun(_1482554, _1482552), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool), tc_fun(tc_fun(_1482554, _1482552), tc_prod(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1482554, _1482552), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)), tc_fun(tc_fun(_1482554, _1482552), tc_prod(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool), tc_fun(tc_fun(_1482554, _1482552), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool), tc_fun(tc_fun(_1482554, _1482552), tc_prod(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool))))), tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1482554, _1482552), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)), tc_fun(tc_fun(_1482554, _1482552), tc_prod(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool))), tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1482554, _1482552), tc_fun(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1482554, _1482552), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)), tc_fun(tc_fun(_1482554, _1482552), tc_prod(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)))), tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool)), c_COMBS(tc_fun(_1482554, _1482552), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1482554, _1482552), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)), tc_fun(tc_fun(_1482554, _1482552), tc_fun(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)))), tc_fun(tc_prod(_1482552, _1482552), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool))), tc_fun(_1482554, _1482552)), c_Product__Type_OPair(tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool), tc_fun(tc_prod(_1482554, _1482554), tc_HOL_Obool)))), c_Relation_Oinv__image(_1482552, _1482554))))), c_Relation_Oinv__image(_1482552, _1482554))))], (41562 ^ _781404) ^ [_1596454, _1596456, _1596458, _1596460, _1596462] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596456, _1596454)), hAPP(hAPP(c_Product__Type_OPair(_1596456, _1596454), _1596460), _1596458)), _1596462)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596454, _1596456)), hAPP(hAPP(c_Product__Type_OPair(_1596454, _1596456), _1596458), _1596460)), hAPP(c_Relation_Oconverse(_1596456, _1596454), _1596462))))], (40970 ^ _781404) ^ [_1581475, _1581477, _1581479, _1581481, _1581483, _1581485, _1581487] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1581475, _1581477, _1581479, _1581481), _1581483), _1581485), _1581487) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1581477, _1581479, _1581481), _1581485), hAPP(_1581483, _1581487)))], (45040 ^ _781404) ^ [_1682534, _1682536, _1682538] : [-(_1682534 = c_List_Olist_ONil(_1682536)), -(c_List_Olast(_1682536, hAPP(hAPP(c_List_Olist_OCons(_1682536), _1682538), _1682534)) = c_List_Olast(_1682536, _1682534))], (15112 ^ _781404) ^ [_1047876, _1047878] : [class_Groups_Olinordered__ab__group__add(_1047876), 15115 ^ _781404 : [(15122 ^ _781404) ^ [] : [_1047878 = c_Groups_Ozero__class_Ozero(_1047876), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047876), _1047878), _1047878) = c_Groups_Ozero__class_Ozero(_1047876))], (15116 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047876), _1047878), _1047878) = c_Groups_Ozero__class_Ozero(_1047876), -(_1047878 = c_Groups_Ozero__class_Ozero(_1047876))]]], (25662 ^ _781404) ^ [_1239975, _1239977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239977)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1239975)), hAPP(c_Int_Onat, _1239977)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1239975), _1239977)))], (48963 ^ _781404) ^ [_1768032, _1768034] : [c_Wellfounded_Oacyclic(_1768032, hAPP(c_Set_OCollect(tc_prod(_1768032, _1768032)), hAPP(c_Product__Type_Oprod_Oprod__case(_1768032, _1768032, tc_HOL_Obool), _1768034))), -(c_Wellfounded_Oacyclic(_1768032, hAPP(c_Set_OCollect(tc_prod(_1768032, _1768032)), hAPP(c_Product__Type_Oprod_Oprod__case(_1768032, _1768032, tc_HOL_Obool), c_Predicate_Oconversep(_1768032, _1768032, _1768034)))))], (19569 ^ _781404) ^ [_1129344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1129344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1129344)))], (39522 ^ _781404) ^ [_1546069, _1546071] : [-(c_Product__Type_Oapsnd(_1546069, _1546069, _1546071, c_Fun_Oid(_1546069)) = c_Fun_Oid(tc_prod(_1546071, _1546069)))], (34669 ^ _781404) ^ [_1425009, _1425011] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1425009), _1425011)), -(hAPP(c_Finite__Set_Ocard(_1425009), _1425011) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1425009, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1425009), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1425011))], (50097 ^ _781404) ^ [_1793902, _1793904, _1793906, _1793908] : [c_Relation_Oantisym(_1793902, _1793904), hBOOL(hAPP(hAPP(c_member(tc_prod(_1793902, _1793902)), hAPP(hAPP(c_Product__Type_OPair(_1793902, _1793902), _1793906), _1793908)), _1793904)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1793902, _1793902)), hAPP(hAPP(c_Product__Type_OPair(_1793902, _1793902), _1793908), _1793906)), _1793904)), -(_1793906 = _1793908)], (44996 ^ _781404) ^ [_1681762, _1681764, _1681766] : [class_Orderings_Olinorder(_1681762), -(hAPP(c_List_Oset(_1681762), c_List_Olinorder__class_Oinsort__insert__key(_1681762, _1681762, c_COMBI(_1681762), _1681764, _1681766)) = hAPP(hAPP(c_Set_Oinsert(_1681762), _1681764), hAPP(c_List_Oset(_1681762), _1681766)))], (10377 ^ _781404) ^ [_957961, _957963, _957965, _957967] : [class_Lattices_Osemilattice__sup(_957961), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957961), _957963), _957965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957961), _957963), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_957961), _957967), _957965))))], (44306 ^ _781404) ^ [_1666688, _1666690, _1666692, _1666694, _1666696] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1666688), tc_List_Olist(_1666688))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1666688), tc_List_Olist(_1666688)), hAPP(hAPP(c_List_Oappend(_1666688), _1666690), _1666692)), hAPP(hAPP(c_List_Oappend(_1666688), _1666690), _1666694))), c_List_Olexord(_1666688, _1666696))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1666688, _1666688)), hAPP(hAPP(c_Product__Type_OPair(_1666688, _1666688), 44311 ^ [_1666688, _1666690, _1666692, _1666694, _1666696]), 44311 ^ [_1666688, _1666690, _1666692, _1666694, _1666696])), _1666696))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1666688), tc_List_Olist(_1666688))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1666688), tc_List_Olist(_1666688)), _1666692), _1666694)), c_List_Olexord(_1666688, _1666696))))], (41704 ^ _781404) ^ [_1600077, _1600079, _1600081, _1600083, _1600085] : [c_Relation_Osingle__valued(_1600077, _1600079, _1600081), c_Relation_Osingle__valued(_1600079, _1600083, _1600085), -(c_Relation_Osingle__valued(_1600077, _1600083, hAPP(hAPP(c_Relation_Orel__comp(_1600077, _1600079, _1600083), _1600081), _1600085)))], (24476 ^ _781404) ^ [_1220461, _1220463, _1220465, _1220467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220461)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220463)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1220463), _1220465)), -(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), _1220465), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1220467, _1220461))), _1220463))))], (46365 ^ _781404) ^ [_1711770, _1711772, _1711774, _1711776] : [class_Orderings_Olinorder(_1711770), 46368 ^ _781404 : [(46375 ^ _781404) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1711772), _1711776)), -(hBOOL(hAPP(c_List_Odistinct(_1711772), c_List_Olinorder__class_Osort__key(_1711772, _1711770, _1711774, _1711776))))], (46369 ^ _781404) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1711772), c_List_Olinorder__class_Osort__key(_1711772, _1711770, _1711774, _1711776))), -(hBOOL(hAPP(c_List_Odistinct(_1711772), _1711776)))]]], (46694 ^ _781404) ^ [_1720740, _1720742, _1720744] : [class_Groups_Oab__semigroup__add(_1720740), -(c_List_Ofoldr(_1720740, _1720740, c_Groups_Oplus__class_Oplus(_1720740), _1720742, _1720744) = hAPP(c_List_Ofoldl(_1720740, _1720740, c_Groups_Oplus__class_Oplus(_1720740), _1720744), _1720742))], (45764 ^ _781404) ^ [_1698715, _1698717, _1698719, _1698721] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698715)), _1698717), c_List_Olists(_1698715, _1698719))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698715)), _1698717), c_List_Olists(_1698715, _1698721))), -(hBOOL(hAPP(c_List_Olistsp(_1698715, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1698715, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1698715, tc_fun(_1698715, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698715)), _1698719)), hAPP(hAPP(c_COMBC(_1698715, tc_fun(_1698715, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698715)), _1698721))), _1698717)))], (43673 ^ _781404) ^ [_1651844, _1651846, _1651848, _1651850] : [-(hAPP(hAPP(c_List_Otake(_1651844), _1651846), hAPP(hAPP(c_List_Olist_OCons(_1651844), _1651848), _1651850)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1651844), c_List_Olist_ONil(_1651844), hAPP(hAPP(c_COMBB(tc_List_Olist(_1651844), tc_List_Olist(_1651844), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1651844), _1651848)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1651844), tc_List_Olist(_1651844)), c_List_Otake(_1651844)), _1651850)), _1651846))], (21257 ^ _781404) ^ [_1159201, _1159203] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159201), _1159203)), _1159201 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1159203 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (40120 ^ _781404) ^ [_1561956, _1561958] : [-(hAPP(c_Relation_OField(_1561956), _1561958) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1561956, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1561956, _1561956), _1561958)), hAPP(c_Relation_ORange(_1561956, _1561956), _1561958)))], (20931 ^ _781404) ^ [_1153061, _1153063, _1153065, _1153067] : [class_Rings_Ocomm__semiring__1(_1153061), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153061), _1153063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153061), _1153065), _1153067)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153061), _1153063), _1153065)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153061), _1153063), _1153067)))], (50503 ^ _781404) ^ [_1801507, _1801509, _1801511, _1801513, _1801515, _1801517] : [c_Fun_Oinj__on(_1801507, _1801509, _1801511, _1801513), hBOOL(hAPP(hAPP(c_member(_1801507), _1801515), _1801513)), hAPP(_1801511, _1801515) = _1801517, -(hAPP(c_Hilbert__Choice_Oinv__into(_1801507, _1801509, _1801513, _1801511), _1801517) = _1801515)], (35744 ^ _781404) ^ [_1448560, _1448562, _1448564] : [-(hAPP(c_Nat_Onat_Onat__rec(_1448560, _1448562, _1448564), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1448562)], (17523 ^ _781404) ^ [_1093866] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1093866)), _1093866) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50237 ^ _781404) ^ [_1796651, _1796653] : [-(c_Relation_Osym(_1796651, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1796651, _1796651), tc_HOL_Obool)), _1796653), hAPP(c_Relation_Oconverse(_1796651, _1796651), _1796653))))], (14992 ^ _781404) ^ [_1045341, _1045343, _1045345, _1045347, _1045349] : [14994 ^ _781404 : [(15000 ^ _781404) ^ [] : [hBOOL(hAPP(_1045349, 14996 ^ [_1045341, _1045343, _1045345, _1045347, _1045349]))], (14998 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1045341), 14996 ^ [_1045341, _1045343, _1045345, _1045347, _1045349]), hAPP(_1045347, 14993 ^ [_1045341, _1045343, _1045345, _1045347, _1045349]))))], (14995 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1045343), 14993 ^ [_1045341, _1045343, _1045345, _1045347, _1045349]), _1045345)))]], 15001 ^ _781404 : [(15002 ^ _781404) ^ [_1045651] : [hBOOL(hAPP(hAPP(c_member(_1045341), _1045651), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1045343, tc_fun(_1045341, tc_HOL_Obool)), _1045345), _1045347))), -(hBOOL(hAPP(_1045349, _1045651)))]]], (12899 ^ _781404) ^ [_1005299, _1005301] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1005299), _1005301))))], (39191 ^ _781404) ^ [_1532180, _1532182] : [class_Complete__Lattice_Ocomplete__lattice(_1532180), -(c_Complete__Lattice_OInf__class_OInf(_1532180, _1532182) = c_Complete__Lattice_OSup__class_OSup(_1532180, hAPP(c_Set_OCollect(_1532180), hAPP(hAPP(c_COMBB(tc_fun(_1532180, tc_HOL_Obool), tc_HOL_Obool, _1532180), c_HOL_OAll(_1532180)), hAPP(hAPP(c_COMBB(tc_fun(_1532180, tc_HOL_Obool), tc_fun(_1532180, tc_HOL_Obool), _1532180), hAPP(c_COMBS(_1532180, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532180), c_fimplies), hAPP(hAPP(c_COMBC(_1532180, tc_fun(_1532180, tc_HOL_Obool), tc_HOL_Obool), c_member(_1532180)), _1532182)))), c_Orderings_Oord__class_Oless__eq(_1532180))))))], (31857 ^ _781404) ^ [_1354629, _1354631, _1354633] : [class_Orderings_Olinorder(_1354629), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354629), _1354631)), 31867 ^ _781404 : [(31870 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1354629), 31866 ^ [_1354629, _1354631, _1354633]), _1354633))], (31868 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1354629), 31866 ^ [_1354629, _1354631, _1354633]), _1354631)))]], hBOOL(hAPP(hAPP(c_member(_1354629), _1354633), _1354631)), -(c_Big__Operators_Olinorder__class_OMax(_1354629, _1354631) = _1354633)], (11211 ^ _781404) ^ [_971578, _971580] : [11219 ^ _781404 : [(11222 ^ _781404) ^ [] : [-(hBOOL(hAPP(_971580, 11218 ^ [_971578, _971580])))], (11220 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 11218 ^ [_971578, _971580]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971578))))]], 11212 ^ _781404 : [(11213 ^ _781404) ^ [_971646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _971646), _971578)), hBOOL(hAPP(_971580, _971646))]]], (21023 ^ _781404) ^ [_1154843, _1154845] : [class_Groups_Omonoid__mult(_1154843), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154843), c_Groups_Oone__class_Oone(_1154843)), _1154845) = _1154845)], (22157 ^ _781404) ^ [_1176085, _1176087, _1176089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1176087), _1176089)), -(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, _1176085)), _1176087)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1176085)), _1176089))))], (20545 ^ _781404) ^ [_1145857, _1145859, _1145861] : [class_Rings_Olinordered__semidom(_1145857), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145857), hAPP(hAPP(c_Power_Opower__class_Opower(_1145857), _1145859), 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(_1145857), _1145861), 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(_1145857), c_Groups_Ozero__class_Ozero(_1145857)), _1145861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145857), _1145859), _1145861)))], (25099 ^ _781404) ^ [_1230671, _1230673, _1230675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1230671)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1230671), _1230673)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1230671), _1230675)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1230673), _1230675))], (38965 ^ _781404) ^ [_1525661, _1525663, _1525665, _1525667] : [-(hAPP(c_Set_OCollect(tc_prod(_1525661, _1525663)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525661, _1525663, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1525661, tc_fun(_1525663, tc_HOL_Obool), tc_fun(_1525663, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1525663, tc_HOL_Obool), tc_fun(_1525663, tc_HOL_Obool)), _1525661), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1525663)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525661), c_fconj), _1525665))), _1525667))) = hAPP(hAPP(c_Product__Type_OSigma(_1525661, _1525663), hAPP(c_Set_OCollect(_1525661), _1525665)), hAPP(hAPP(c_COMBB(tc_fun(_1525663, tc_HOL_Obool), tc_fun(_1525663, tc_HOL_Obool), _1525661), c_Set_OCollect(_1525663)), _1525667)))], (52402 ^ _781404) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (4958 ^ _781404) ^ [_856939, _856941, _856943, _856945] : [-(c_Hilbert__Choice_OEps(_856945, _856941) = c_Hilbert__Choice_OEps(_856943, _856939)), _856945 = _856943, _856941 = _856939], (38582 ^ _781404) ^ [_1514791, _1514793, _1514795, _1514797, _1514799] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1514791, _1514793), _1514795), hAPP(hAPP(c_COMBS(_1514791, tc_fun(_1514793, tc_HOL_Obool), tc_fun(_1514793, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514793, tc_HOL_Obool), tc_fun(tc_fun(_1514793, tc_HOL_Obool), tc_fun(_1514793, tc_HOL_Obool)), _1514791), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1514793, tc_HOL_Obool))), _1514797)), _1514799)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1514791, _1514793), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1514791, _1514793), _1514795), _1514797)), hAPP(hAPP(c_Product__Type_OSigma(_1514791, _1514793), _1514795), _1514799)))], (47834 ^ _781404) ^ [_1743450, _1743452, _1743454] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743450)), c_List_OdropWhile(_1743450, _1743452, _1743454))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743450)), _1743454))))], (24698 ^ _781404) ^ [_1224438] : [c_Int_OBit1(_1224438) = c_Int_OMin, -(_1224438 = c_Int_OMin)], (19251 ^ _781404) ^ [_1123752, _1123754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123752)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123754))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123752), _1123754)))], (49590 ^ _781404) ^ [_1781666, _1781668, _1781670, _1781672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1781666), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1781668, _1781670, _1781666, _1781672) = 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(_1781668)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1781668)))], (9260 ^ _781404) ^ [_939649, _939651, _939653, _939655] : [class_Orderings_Olinorder(_939649), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939649), _939651), _939653)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939649), _939653), _939655)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_939649, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_939649, _939651, _939653)), c_SetInterval_Oord__class_OatLeastAtMost(_939649, _939653, _939655)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_939649, _939651, _939655))], (33686 ^ _781404) ^ [_1395822, _1395824, _1395826, _1395828] : [-(_1395822 = c_Orderings_Obot__class_Obot(tc_fun(_1395824, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395824, tc_fun(_1395826, tc_HOL_Obool)), _1395822), hAPP(c_COMBK(tc_fun(_1395826, tc_HOL_Obool), _1395824), _1395828)) = _1395828)], (51960 ^ _781404) ^ [_1832836, _1832838] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832836), _1832838)), -(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)))), _1832838, _1832836) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (8451 ^ _781404) ^ [_923946] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _923946)], (49376 ^ _781404) ^ [_1776969, _1776971, _1776973, _1776975] : [hBOOL(hAPP(hAPP(c_List_Omember(_1776969), hAPP(hAPP(c_List_Olist_OCons(_1776969), _1776971), _1776973)), _1776975)), -(_1776971 = _1776975), -(hBOOL(hAPP(hAPP(c_List_Omember(_1776969), _1776973), _1776975)))], (20959 ^ _781404) ^ [_1153638, _1153640, _1153642, _1153644] : [class_Rings_Ocomm__semiring__1(_1153638), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153638), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153638), _1153640), _1153642)), _1153644) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153638), _1153640), _1153644)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153638), _1153642), _1153644)))], (14492 ^ _781404) ^ [_1035261, _1035263, _1035265] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1035261), _1035263)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035261), hAPP(hAPP(c_Set_Oinsert(_1035261), _1035265), _1035263))))], (4532 ^ _781404) ^ [_850248, _850250] : [_850250 = _850248, -(c_List_Olist_ONil(_850250) = c_List_Olist_ONil(_850248))], (6504 ^ _781404) ^ [_885030, _885032, _885034, _885036] : [-(c_Nat_Onat_Onat__case(_885030, _885032, _885034, hAPP(c_Nat_OSuc, _885036)) = hAPP(_885034, _885036))], (23341 ^ _781404) ^ [_1199701, _1199703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199701)), -(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)))), _1199703)), 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)))), _1199701)) = 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, _1199703, _1199701))))], (17345 ^ _781404) ^ [_1090801, _1090803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090801)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090803))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1090801), _1090803)))], (42112 ^ _781404) ^ [_1610798, _1610800, _1610802, _1610804, _1610806, _1610808] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1610798, _1610800)), _1610802), hAPP(hAPP(c_Relation_Orel__comp(_1610798, _1610804, _1610800), _1610806), _1610808))), 42118 ^ _781404 : [(42123 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610804, _1610800)), hAPP(hAPP(c_Product__Type_OPair(_1610804, _1610800), 42116 ^ [_1610798, _1610800, _1610802, _1610804, _1610806, _1610808]), 42117 ^ [_1610798, _1610800, _1610802, _1610804, _1610806, _1610808])), _1610808)))], (42121 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610798, _1610804)), hAPP(hAPP(c_Product__Type_OPair(_1610798, _1610804), 42115 ^ [_1610798, _1610800, _1610802, _1610804, _1610806, _1610808]), 42116 ^ [_1610798, _1610800, _1610802, _1610804, _1610806, _1610808])), _1610806)))], (42119 ^ _781404) ^ [] : [-(_1610802 = hAPP(hAPP(c_Product__Type_OPair(_1610798, _1610800), 42115 ^ [_1610798, _1610800, _1610802, _1610804, _1610806, _1610808]), 42117 ^ [_1610798, _1610800, _1610802, _1610804, _1610806, _1610808]))]]], (40180 ^ _781404) ^ [] : [-(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))))], (2352 ^ _781404) ^ [_815708, _815710, _815712, _815714, _815716, _815718] : [-(c_Nat_Onat_Onat__rec(_815718, _815714, _815710) = c_Nat_Onat_Onat__rec(_815716, _815712, _815708)), _815718 = _815716, _815714 = _815712, _815710 = _815708], (38576 ^ _781404) ^ [_1514648, _1514650, _1514652] : [c_Equiv__Relations_Oequiv(_1514648, _1514650, _1514652), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1514648, _1514648), tc_HOL_Obool)), _1514652), hAPP(hAPP(c_Product__Type_OSigma(_1514648, _1514648), _1514650), hAPP(c_COMBK(tc_fun(_1514648, tc_HOL_Obool), _1514648), _1514650)))))], (25161 ^ _781404) ^ [_1231728, _1231730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1231728)), hAPP(c_Int_Onat, _1231730))), 25164 ^ _781404 : [(25167 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231728), _1231730)))], (25165 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231730)))]]], (7711 ^ _781404) ^ [_908241, _908243, _908245, _908247] : [class_Lattices_Osemilattice__inf(_908241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908241), _908243), _908245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908241), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_908241), _908247), _908243)), _908245)))], (16310 ^ _781404) ^ [_1071195] : [class_Rings_Olinordered__semidom(_1071195), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071195), c_Groups_Oone__class_Oone(_1071195)), c_Groups_Ozero__class_Ozero(_1071195)))], (32808 ^ _781404) ^ [_1372457, _1372459, _1372461] : [class_Orderings_Olinorder(_1372457), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372457), _1372459)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372457), _1372461)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372457, tc_HOL_Obool)), _1372459), _1372461) = c_Orderings_Obot__class_Obot(tc_fun(_1372457, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372457), c_Big__Operators_Olattice_OSup__fin(_1372457, c_Orderings_Oord__class_Omax(_1372457), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372457, tc_HOL_Obool)), _1372459), _1372461))), c_Big__Operators_Olattice_OSup__fin(_1372457, c_Orderings_Oord__class_Omax(_1372457), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372457, tc_HOL_Obool)), _1372459), _1372461))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372457), c_Big__Operators_Olattice_OSup__fin(_1372457, c_Orderings_Oord__class_Omax(_1372457), _1372459)), c_Big__Operators_Olattice_OSup__fin(_1372457, c_Orderings_Oord__class_Omax(_1372457), _1372461)))], (17112 ^ _781404) ^ [_1086425, _1086427, _1086429] : [class_Int_Onumber__ring(_1086425), class_Int_Oring__char__0(_1086425), 17119 ^ _781404 : [(17126 ^ _781404) ^ [] : [_1086427 = _1086429, -(hAPP(c_Int_Onumber__class_Onumber__of(_1086425), _1086427) = hAPP(c_Int_Onumber__class_Onumber__of(_1086425), _1086429))], (17120 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1086425), _1086427) = hAPP(c_Int_Onumber__class_Onumber__of(_1086425), _1086429), -(_1086427 = _1086429)]]], (33049 ^ _781404) ^ [_1377422, _1377424, _1377426, _1377428, _1377430, _1377432, _1377434, _1377436] : [hBOOL(hAPP(hAPP(c_member(_1377422), _1377424), _1377426)), hBOOL(hAPP(hAPP(hAPP(_1377428, _1377424), _1377430), _1377432)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377422, tc_fun(_1377434, tc_fun(_1377436, tc_HOL_Obool))), _1377426), _1377428), _1377430), _1377432)))], (52348 ^ _781404) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (23361 ^ _781404) ^ [_1200197, _1200199, _1200201] : [-(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), _1200197), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1200199), _1200197))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1200199, _1200197))), _1200201) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1200199), _1200201))], (35672 ^ _781404) ^ [_1447072, _1447074] : [-(c_Divides_Opdivmod(_1447072, _1447074) = 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), _1447072)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1447074))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1447072), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1447074))))], (8229 ^ _781404) ^ [_919826, _919828] : [class_Complete__Lattice_Ocomplete__lattice(_919826), -(c_Complete__Lattice_OSup__class_OSup(_919826, hAPP(hAPP(c_Set_Oinsert(_919826), _919828), c_Orderings_Obot__class_Obot(tc_fun(_919826, tc_HOL_Obool)))) = _919828)], (8744 ^ _781404) ^ [_928745, _928747] : [class_Orderings_Oorder(_928745), -(c_SetInterval_Oord__class_OatLeastAtMost(_928745, _928747, _928747) = hAPP(hAPP(c_Set_Oinsert(_928745), _928747), c_Orderings_Obot__class_Obot(tc_fun(_928745, tc_HOL_Obool))))], (32298 ^ _781404) ^ [_1362970, _1362972, _1362974, _1362976] : [class_Orderings_Olinorder(_1362970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362970), _1362972)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1362970, _1362970, c_Orderings_Oord__class_Omax(_1362970)), _1362974), hAPP(hAPP(c_Set_Oinsert(_1362970), _1362976), _1362972)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362970), _1362976), hAPP(hAPP(c_Finite__Set_Ofold(_1362970, _1362970, c_Orderings_Oord__class_Omax(_1362970)), _1362974), _1362972)))], (48219 ^ _781404) ^ [_1752028, _1752030] : [class_Enum_Oenum(_1752028), 48222 ^ _781404 : [(48230 ^ _781404) ^ [] : [48231 ^ _781404 : [(48232 ^ _781404) ^ [_1752208] : [hBOOL(hAPP(_1752030, _1752208))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1752028), _1752030)))], (48223 ^ _781404) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1752028), _1752030)), -(hBOOL(hAPP(_1752030, 48226 ^ [_1752028, _1752030])))]]], (41668 ^ _781404) ^ [_1599236, _1599238, _1599240] : [-(hAPP(c_Relation_Oconverse(_1599236, _1599238), _1599240) = hAPP(c_Set_OCollect(tc_prod(_1599238, _1599236)), hAPP(c_Product__Type_Oprod_Oprod__case(_1599238, _1599236, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1599238, tc_fun(tc_prod(_1599236, _1599238), tc_HOL_Obool), tc_fun(_1599236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599236, tc_fun(tc_fun(tc_prod(_1599236, _1599238), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1599236, _1599238), tc_HOL_Obool), tc_fun(_1599236, tc_HOL_Obool)), _1599238), c_COMBC(_1599236, tc_fun(tc_prod(_1599236, _1599238), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599236, tc_prod(_1599236, _1599238)), tc_fun(_1599236, tc_fun(tc_fun(tc_prod(_1599236, _1599238), tc_HOL_Obool), tc_HOL_Obool)), _1599238), hAPP(c_COMBB(tc_prod(_1599236, _1599238), tc_fun(tc_fun(tc_prod(_1599236, _1599238), tc_HOL_Obool), tc_HOL_Obool), _1599236), c_member(tc_prod(_1599236, _1599238)))), hAPP(c_COMBC(_1599236, _1599238, tc_prod(_1599236, _1599238)), c_Product__Type_OPair(_1599236, _1599238))))), _1599240))))], (37510 ^ _781404) ^ [_1487963, _1487965] : [-(hAPP(c_Relation_OField(_1487963), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1487963, _1487963), tc_HOL_Obool), _1487965)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1487963, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1487963, _1487963), tc_HOL_Obool), tc_fun(_1487963, tc_HOL_Obool), c_Relation_OField(_1487963)), _1487965)))], (32170 ^ _781404) ^ [_1360442, _1360444, _1360446, _1360448] : [class_Orderings_Olinorder(_1360442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360442), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360442), _1360444), _1360446)), _1360448)), 32177 ^ _781404 : [(32180 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360442), _1360446), _1360448)))], (32178 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360442), _1360444), _1360448)))]]], (7894 ^ _781404) ^ [_912108, _912110, _912112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912108, tc_HOL_Obool)), _912110), _912112)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912108, tc_HOL_Obool)), _912112), _912110) = _912110)], (52690 ^ _781404) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (10963 ^ _781404) ^ [_967566, _967568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967566), _967568)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967568)), _967566) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967568), _967566)))], (19542 ^ _781404) ^ [] : [-(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))], (26455 ^ _781404) ^ [_1252994, _1252996, _1252998] : [class_Rings_Oring__1(_1252994), -(hAPP(c_Int_Oring__1__class_Oof__int(_1252994), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1252996), _1252998)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1252994), hAPP(c_Int_Oring__1__class_Oof__int(_1252994), _1252996)), hAPP(c_Int_Oring__1__class_Oof__int(_1252994), _1252998)))], (7375 ^ _781404) ^ [_901616, _901618, _901620] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901616, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901616, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_901616, tc_HOL_Obool), _901618)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_901616, tc_HOL_Obool), _901620))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_901616, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_901616, tc_HOL_Obool), tc_HOL_Obool)), _901618), _901620)))))], (17401 ^ _781404) ^ [_1091813, _1091815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091813), _1091815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091813), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1091815), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (52482 ^ _781404) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (35187 ^ _781404) ^ [_1436791] : [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), _1436791))), 35190 ^ _781404 : [(35197 ^ _781404) ^ [] : [-(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), _1436791)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436791)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436791)), 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), _1436791)))))], (35191 ^ _781404) ^ [] : [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), _1436791))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436791)) = 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)))]]], (43889 ^ _781404) ^ [_1656805, _1656807, _1656809, _1656811, _1656813] : [-(hAPP(hAPP(c_List_Oappend(_1656805), _1656807), _1656809) = hAPP(hAPP(c_List_Olist_OCons(_1656805), _1656811), _1656813)), 43890 ^ _781404 : [(43897 ^ _781404) ^ [_1656988] : [_1656807 = hAPP(hAPP(c_List_Olist_OCons(_1656805), _1656811), _1656988), hAPP(hAPP(c_List_Oappend(_1656805), _1656988), _1656809) = _1656813], (43891 ^ _781404) ^ [] : [_1656807 = c_List_Olist_ONil(_1656805), _1656809 = hAPP(hAPP(c_List_Olist_OCons(_1656805), _1656811), _1656813)]]], (18101 ^ _781404) ^ [_1103965, _1103967] : [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), _1103965), _1103967))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1103965))), -(_1103967 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35970 ^ _781404) ^ [_1452650, _1452652, _1452654, _1452656] : [_1452650 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1452652), _1452654)), _1452656), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1452650, _1452652), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1452654), _1452656)))), 35977 ^ _781404 : [(35980 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1452656), _1452652))], (35978 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452652)))]], 35985 ^ _781404 : [(35988 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1452652), _1452656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1452656), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35986 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452652))]]], (192 ^ _781404) ^ [_784468, _784470, _784472, _784474, _784476, _784478] : [-(c_Finite__Set_Ofolding__one(_784476, _784472, _784468)), c_Finite__Set_Ofolding__one(_784478, _784474, _784470), _784478 = _784476, _784474 = _784472, _784470 = _784468], (22169 ^ _781404) ^ [_1176353, _1176355, _1176357] : [class_Power_Opower(_1176353), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1176353), _1176355), hAPP(c_Nat_OSuc, _1176357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176353), _1176355), hAPP(hAPP(c_Power_Opower__class_Opower(_1176353), _1176355), _1176357)))], (27265 ^ _781404) ^ [_1268438, _1268440, _1268442] : [class_Groups_Oordered__ab__group__add__abs(_1268438), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268438), hAPP(c_Groups_Oabs__class_Oabs(_1268438), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1268438), _1268440), _1268442))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1268438), hAPP(c_Groups_Oabs__class_Oabs(_1268438), _1268440)), hAPP(c_Groups_Oabs__class_Oabs(_1268438), _1268442)))))], (10163 ^ _781404) ^ [_954478, _954480, _954482] : [class_Orderings_Oorder(_954478), 10166 ^ _781404 : [(10167 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954478), _954480), _954482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954478), _954480), _954482))), -(_954480 = _954482)], (10177 ^ _781404) ^ [] : [10178 ^ _781404 : [(10181 ^ _781404) ^ [] : [_954480 = _954482], (10179 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954478), _954480), _954482))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954478), _954480), _954482)))]]], (52666 ^ _781404) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (7031 ^ _781404) ^ [_895141, _895143] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895141, tc_HOL_Obool)), _895143), _895143) = _895143)], (7872 ^ _781404) ^ [_911601, _911603, _911605, _911607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911601, tc_HOL_Obool)), _911603), _911605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911601, tc_HOL_Obool)), _911603), hAPP(hAPP(c_Set_Oinsert(_911601), _911607), _911605))))], (15429 ^ _781404) ^ [_1054360, _1054362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1054360), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1054362), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054362), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1054360))))), -(_1054360 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1054362), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054362), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1054360))))], (46574 ^ _781404) ^ [_1717099, _1717101, _1717103, _1717105] : [-(hAPP(c_List_Ofilter(_1717099, _1717101), hAPP(hAPP(c_List_Oappend(_1717099), _1717103), _1717105)) = hAPP(hAPP(c_List_Oappend(_1717099), hAPP(c_List_Ofilter(_1717099, _1717101), _1717103)), hAPP(c_List_Ofilter(_1717099, _1717101), _1717105)))], (10551 ^ _781404) ^ [_960878, _960880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960880), hAPP(c_Nat_OSuc, _960878))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960878), _960880))], (29151 ^ _781404) ^ [_1303072, _1303074, _1303076, _1303078] : [class_Fields_Ofield__inverse__zero(_1303072), -(_1303074 = c_Groups_Ozero__class_Ozero(_1303072)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303072), _1303074), _1303076)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303072), _1303074), _1303078)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303072), _1303076), _1303078))], (20925 ^ _781404) ^ [_1152902, _1152904, _1152906, _1152908] : [class_Rings_Ocomm__semiring(_1152902), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152902), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152902), _1152904), _1152906)), _1152908) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152902), _1152904), _1152908)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152902), _1152906), _1152908)))], (5779 ^ _781404) ^ [_872941, _872943, _872945, _872947, _872949] : [class_Orderings_Oord(_872941), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872943, _872941)), _872945), _872947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872941), hAPP(_872945, _872949)), hAPP(_872947, _872949))))], (34303 ^ _781404) ^ [_1416096, _1416098, _1416100, _1416102, _1416104] : [_1416096 = c_Orderings_Obot__class_Obot(tc_fun(_1416098, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1416100, tc_HOL_Obool)), _1416102), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416098, tc_fun(_1416100, tc_HOL_Obool)), _1416096), _1416104)) = _1416102)], (13421 ^ _781404) ^ [_1014798, _1014800, _1014802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014798), _1014800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014798), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014800), _1014802))))], (37378 ^ _781404) ^ [_1484262, _1484264, _1484266, _1484268, _1484270] : [-(hAPP(c_Relation_OImage(_1484262, _1484264, _1484266), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484262, tc_HOL_Obool)), _1484268), _1484270)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484264, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1484262, _1484264, _1484266), _1484268)), hAPP(c_Relation_OImage(_1484262, _1484264, _1484266), _1484270)))], (23483 ^ _781404) ^ [_1202942, _1202944] : [class_Divides_Osemiring__div(_1202942), -(c_Divides_Odiv__class_Omod(_1202942, _1202944, c_Groups_Ozero__class_Ozero(_1202942)) = _1202944)], (46552 ^ _781404) ^ [_1716628, _1716630, _1716632] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1716628), tc_List_Olist(_1716628)), c_List_Opartition(_1716628, _1716630, _1716632)) = hAPP(c_List_Ofilter(_1716628, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1716628, c_fNot), _1716630)), _1716632))], (22635 ^ _781404) ^ [_1185687, _1185689, _1185691, _1185693, _1185695, _1185697] : [class_Rings_Oordered__ring(_1185687), 22638 ^ _781404 : [(22645 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185687), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185687), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185687), _1185689), _1185695)), _1185691)), _1185693)), _1185697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185687), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185687), _1185689), _1185691)), _1185693)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185687), _1185695), _1185691)), _1185697))))], (22639 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185687), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185687), _1185689), _1185691)), _1185693)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185687), _1185695), _1185691)), _1185697))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185687), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185687), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185687), _1185689), _1185695)), _1185691)), _1185693)), _1185697)))]]], (19817 ^ _781404) ^ [_1133314, _1133316] : [class_Int_Onumber__ring(_1133314), -(hAPP(c_Int_Onumber__class_Onumber__of(_1133314), c_Int_Osucc(_1133316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133314), c_Groups_Oone__class_Oone(_1133314)), hAPP(c_Int_Onumber__class_Onumber__of(_1133314), _1133316)))], (17262 ^ _781404) ^ [_1089231, _1089233] : [class_Int_Onumber__ring(_1089231), -(hBOOL(hAPP(hAPP(c_member(_1089231), hAPP(c_Int_Onumber__class_Onumber__of(_1089231), _1089233)), c_Int_Oring__1__class_OInts(_1089231))))], (52296 ^ _781404) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (36584 ^ _781404) ^ [_1465247, _1465249, _1465251, _1465253, _1465255] : [hBOOL(hAPP(hAPP(_1465247, _1465249), _1465251)), -(hBOOL(hAPP(hAPP(_1465247, hAPP(c_Product__Type_Osnd(_1465253, _1465255), hAPP(hAPP(c_Product__Type_OPair(_1465253, _1465255), _1465251), _1465249))), hAPP(c_Product__Type_Ofst(_1465253, _1465255), hAPP(hAPP(c_Product__Type_OPair(_1465253, _1465255), _1465251), _1465249)))))], (49703 ^ _781404) ^ [_1784814, _1784816] : [-(c_Relation_Otrans(_1784814, c_Transitive__Closure_Otrancl(_1784814, _1784816)))], (47069 ^ _781404) ^ [_1727802, _1727804] : [class_Orderings_Olinorder(_1727802), c_List_Olinorder__class_Osorted(_1727802, _1727804), -(c_List_Olinorder__class_Osorted(_1727802, c_List_Oremdups(_1727802, _1727804)))], (39029 ^ _781404) ^ [_1527157, _1527159, _1527161] : [hBOOL(hAPP(hAPP(c_member(_1527157), _1527159), hAPP(c_Set_OCollect(_1527157), _1527161))), -(hBOOL(hAPP(_1527161, _1527159)))], (25837 ^ _781404) ^ [_1243162, _1243164] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1243162)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1243164)) = 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)))), _1243162)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1243164)))], (36199 ^ _781404) ^ [_1457029, _1457031, _1457033, _1457035, _1457037, _1457039] : [hAPP(c_Product__Type_Oapsnd(_1457029, _1457031, _1457033, _1457035), _1457037) = hAPP(c_Product__Type_Oapsnd(_1457029, _1457031, _1457033, _1457039), _1457037), -(hAPP(_1457035, hAPP(c_Product__Type_Osnd(_1457033, _1457029), _1457037)) = hAPP(_1457039, hAPP(c_Product__Type_Osnd(_1457033, _1457029), _1457037)))], (19392 ^ _781404) ^ [_1126298, _1126300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1126298)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1126300))))], (52658 ^ _781404) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (1516 ^ _781404) ^ [_803394, _803396] : [-(class_Orderings_Obot(_803394)), _803396 = _803394, class_Orderings_Obot(_803396)], (49277 ^ _781404) ^ [_1774745, _1774747, _1774749, _1774751, _1774753] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1774745, _1774747, _1774749) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1774745, _1774751, _1774753)), _1774747 = _1774751, _1774749 = _1774753], (9186 ^ _781404) ^ [_937792, _937794, _937796, _937798, _937800] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937792, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937792, tc_HOL_Obool)), hAPP(c_Set_Oimage(_937794, _937792, _937796), _937798)), hAPP(c_Set_Oimage(_937794, _937792, _937796), _937800))), hAPP(c_Set_Oimage(_937794, _937792, _937796), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937794, tc_HOL_Obool)), _937798), _937800)))))], (37240 ^ _781404) ^ [] : [-(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)))], (13255 ^ _781404) ^ [_1011653, _1011655, _1011657] : [class_Groups_Ogroup__add(_1011653), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011653), _1011655), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011653), hAPP(c_Groups_Ouminus__class_Ouminus(_1011653), _1011655)), _1011657)) = _1011657)], (7583 ^ _781404) ^ [_905880, _905882, _905884, _905886] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_905880), _905882), _905884), _905886)), -(_905882 = _905886), -(hBOOL(hAPP(_905884, _905886)))], (43312 ^ _781404) ^ [_1644660, _1644662, _1644664] : [-(hBOOL(hAPP(c_List_Odistinct(_1644660), hAPP(hAPP(c_List_Olist_OCons(_1644660), _1644662), _1644664)))), -(hBOOL(hAPP(hAPP(c_member(_1644660), _1644662), hAPP(c_List_Oset(_1644660), _1644664)))), hBOOL(hAPP(c_List_Odistinct(_1644660), _1644664))], (4622 ^ _781404) ^ [_851645, _851647, _851649, _851651] : [-(c_List_Oupto(_851651, _851647) = c_List_Oupto(_851649, _851645)), _851651 = _851649, _851647 = _851645], (29673 ^ _781404) ^ [_1312808, _1312810, _1312812] : [class_Fields_Olinordered__field__inverse__zero(_1312808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312808), c_Groups_Ozero__class_Ozero(_1312808)), _1312810)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312808), hAPP(c_Groups_Oabs__class_Oabs(_1312808), _1312812)), _1312810) = hAPP(c_Groups_Oabs__class_Oabs(_1312808), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312808), _1312812), _1312810)))], (50123 ^ _781404) ^ [_1794402, _1794404] : [c_Wellfounded_Oacyclic(_1794402, _1794404), -(c_Relation_Oantisym(_1794402, c_Transitive__Closure_Ortrancl(_1794402, _1794404)))], (5420 ^ _781404) ^ [_864184, _864186] : [_864186 = _864184, -(c_Set_Oinsert(_864186) = c_Set_Oinsert(_864184))], (52720 ^ _781404) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (9951 ^ _781404) ^ [_951392] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _951392), _951392) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40011 ^ _781404) ^ [_1559262, _1559264, _1559266, _1559268] : [-(hAPP(c_Relation_ODomain(_1559262, _1559264), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1559262, _1559264), tc_HOL_Obool)), _1559266), _1559268)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1559262, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1559262, _1559264), _1559266)), hAPP(c_Relation_ODomain(_1559262, _1559264), _1559268)))], (20593 ^ _781404) ^ [_1146651, _1146653] : [class_Rings_Olinordered__idom(_1146651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146651), hAPP(hAPP(c_Power_Opower__class_Opower(_1146651), _1146653), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1146651)))], (1916 ^ _781404) ^ [_808394, _808396] : [-(class_Groups_Ominus(_808394)), _808396 = _808394, class_Groups_Ominus(_808396)], (46860 ^ _781404) ^ [_1723981, _1723983, _1723985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1723981), _1723983)), _1723985)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1723981, _1723985)), _1723983) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1723981), _1723983))], (47329 ^ _781404) ^ [_1732544, _1732546] : [class_Orderings_Olinorder(_1732544), 47332 ^ _781404 : [(47333 ^ _781404) ^ [] : [c_List_Olinorder__class_Osorted(_1732544, _1732546), 47336 ^ _781404 : [(47337 ^ _781404) ^ [_1732715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732715), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732544)), _1732546))), 47340 ^ _781404 : [(47341 ^ _781404) ^ [_1732832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1732832), _1732715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732544), hAPP(hAPP(c_List_Onth(_1732544), _1732546), _1732832)), hAPP(hAPP(c_List_Onth(_1732544), _1732546), _1732715))))]]]]], (47347 ^ _781404) ^ [] : [47349 ^ _781404 : [(47355 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732544), hAPP(hAPP(c_List_Onth(_1732544), _1732546), 47351 ^ [_1732544, _1732546])), hAPP(hAPP(c_List_Onth(_1732544), _1732546), 47348 ^ [_1732544, _1732546])))], (47353 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47351 ^ [_1732544, _1732546]), 47348 ^ [_1732544, _1732546])))], (47350 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47348 ^ [_1732544, _1732546]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732544)), _1732546))))]], -(c_List_Olinorder__class_Osorted(_1732544, _1732546))]]], (40196 ^ _781404) ^ [_1563884, _1563886] : [-(hAPP(c_List_Olexn(_1563884, _1563886), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1563884), tc_List_Olist(_1563884)), tc_HOL_Obool)))], (13604 ^ _781404) ^ [_1018492, _1018494] : [class_Groups_Olinordered__ab__group__add(_1018492), 13607 ^ _781404 : [(13614 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018492), _1018494), c_Groups_Ozero__class_Ozero(_1018492))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018492), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018492), _1018494), _1018494)), c_Groups_Ozero__class_Ozero(_1018492))))], (13608 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018492), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018492), _1018494), _1018494)), c_Groups_Ozero__class_Ozero(_1018492))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018492), _1018494), c_Groups_Ozero__class_Ozero(_1018492))))]]], (18359 ^ _781404) ^ [_1108577, _1108579, _1108581, _1108583, _1108585, _1108587] : [c_Finite__Set_Ofun__left__comm(_1108577, _1108579, _1108581), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108577), _1108583)), -(hAPP(hAPP(_1108581, _1108585), hAPP(hAPP(c_Finite__Set_Ofold(_1108577, _1108579, _1108581), _1108587), _1108583)) = hAPP(hAPP(c_Finite__Set_Ofold(_1108577, _1108579, _1108581), hAPP(hAPP(_1108581, _1108585), _1108587)), _1108583))], (23185 ^ _781404) ^ [_1196539, _1196541, _1196543, _1196545, _1196547, _1196549] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1196539), _1196541)), _1196543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1196545), _1196547)), _1196549), 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), _1196545), _1196547)), _1196549))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196549), _1196545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196543)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1196545), _1196539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1196541), _1196547)))], (50903 ^ _781404) ^ [_1810509, _1810511, _1810513] : [-(c_Fun_Obij__betw(_1810509, _1810511, _1810513, c_Orderings_Otop__class_Otop(tc_fun(_1810509, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1810511, tc_HOL_Obool)))), c_Fun_Oinj__on(_1810509, _1810511, _1810513, c_Orderings_Otop__class_Otop(tc_fun(_1810509, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1810509, _1810511, _1810513), c_Orderings_Otop__class_Otop(tc_fun(_1810509, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1810511, tc_HOL_Obool))], (15739 ^ _781404) ^ [_1059990, _1059992, _1059994] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1059990), _1059992)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059990, tc_HOL_Obool)), _1059992), _1059994)), -(hAPP(c_Finite__Set_Ocard(_1059990), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1059990, tc_HOL_Obool)), _1059994), _1059992)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1059990), _1059994)), hAPP(c_Finite__Set_Ocard(_1059990), _1059992)))], (49680 ^ _781404) ^ [_1784232, _1784234] : [49683 ^ _781404 : [(49689 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1784232, _1784232)), hAPP(hAPP(c_Product__Type_OPair(_1784232, _1784232), 49681 ^ [_1784232, _1784234]), 49685 ^ [_1784232, _1784234])), _1784234))], (49687 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1784232, _1784232)), hAPP(hAPP(c_Product__Type_OPair(_1784232, _1784232), 49682 ^ [_1784232, _1784234]), 49685 ^ [_1784232, _1784234])), _1784234)))], (49684 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1784232, _1784232)), hAPP(hAPP(c_Product__Type_OPair(_1784232, _1784232), 49681 ^ [_1784232, _1784234]), 49682 ^ [_1784232, _1784234])), _1784234)))]], -(c_Relation_Otrans(_1784232, _1784234))], (50696 ^ _781404) ^ [_1806416] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1806416), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1806416 = hAPP(c_Code__Numeral_Onat__of, 50699 ^ [_1806416]))], (4968 ^ _781404) ^ [_857088, _857090, _857092, _857094, _857096, _857098] : [-(c_Finite__Set_Ofold__image(_857098, _857094, _857090) = c_Finite__Set_Ofold__image(_857096, _857092, _857088)), _857098 = _857096, _857094 = _857092, _857090 = _857088], (31920 ^ _781404) ^ [_1355934] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1355934) = c_Orderings_Oord__class_Omax(_1355934)), class_Lattices_Osemilattice__sup(_1355934), class_Orderings_Olinorder(_1355934)], (33835 ^ _781404) ^ [_1400380, _1400382, _1400384, _1400386, _1400388] : [class_Rings_Osemiring__0(_1400380), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400380), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400382, _1400380), _1400384), _1400386)), _1400388) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400382, _1400380), hAPP(hAPP(c_COMBC(_1400382, _1400380, _1400380), hAPP(hAPP(c_COMBB(_1400380, tc_fun(_1400380, _1400380), _1400382), c_Groups_Otimes__class_Otimes(_1400380)), _1400384)), _1400388)), _1400386))], (34957 ^ _781404) ^ [_1431875, _1431877, _1431879] : [class_Int_Onumber__ring(_1431875), 34960 ^ _781404 : [(34967 ^ _781404) ^ [] : [-(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), _1431877)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1431875), _1431879), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1431877))) = c_Groups_Oone__class_Oone(_1431875))], (34961 ^ _781404) ^ [] : [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), _1431877))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1431875), _1431879), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1431877))) = hAPP(hAPP(c_HOL_OLet(_1431875, _1431875), hAPP(hAPP(c_Power_Opower__class_Opower(_1431875), _1431879), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431877))), hAPP(hAPP(c_COMBS(_1431875, _1431875, _1431875), hAPP(hAPP(c_COMBB(_1431875, tc_fun(_1431875, _1431875), _1431875), c_Groups_Otimes__class_Otimes(_1431875)), hAPP(c_Groups_Otimes__class_Otimes(_1431875), _1431879))), c_COMBI(_1431875))))]]], (970 ^ _781404) ^ [_795905, _795907, _795909, _795911] : [-(c_Equiv__Relations_Opart__equivp(_795909, _795905)), c_Equiv__Relations_Opart__equivp(_795911, _795907), _795911 = _795909, _795907 = _795905], (34259 ^ _781404) ^ [_1414266, _1414268, _1414270, _1414272, _1414274, _1414276] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1414266, _1414268)), hAPP(hAPP(c_Product__Type_OPair(_1414266, _1414268), _1414274), _1414276)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool)), _1414270), _1414272))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414266, tc_fun(_1414268, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1414266, tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_fun(_1414268, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1414268, tc_fun(tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_fun(_1414268, tc_HOL_Obool)), _1414266), c_COMBC(_1414268, tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1414268, tc_prod(_1414266, _1414268)), tc_fun(_1414268, tc_fun(tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_HOL_Obool)), _1414266), hAPP(c_COMBB(tc_prod(_1414266, _1414268), tc_fun(tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_HOL_Obool), _1414268), c_member(tc_prod(_1414266, _1414268)))), c_Product__Type_OPair(_1414266, _1414268)))), _1414270)), hAPP(hAPP(c_COMBC(_1414266, tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_fun(_1414268, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1414268, tc_fun(tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_fun(_1414268, tc_HOL_Obool)), _1414266), c_COMBC(_1414268, tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1414268, tc_prod(_1414266, _1414268)), tc_fun(_1414268, tc_fun(tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_HOL_Obool)), _1414266), hAPP(c_COMBB(tc_prod(_1414266, _1414268), tc_fun(tc_fun(tc_prod(_1414266, _1414268), tc_HOL_Obool), tc_HOL_Obool), _1414268), c_member(tc_prod(_1414266, _1414268)))), c_Product__Type_OPair(_1414266, _1414268)))), _1414272)), _1414274), _1414276)))], (8822 ^ _781404) ^ [_930302, _930304] : [class_Lattices_Oboolean__algebra(_930302), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930302), hAPP(c_Groups_Ouminus__class_Ouminus(_930302), _930304)), _930304) = c_Orderings_Obot__class_Obot(_930302))], (26497 ^ _781404) ^ [_1253799, _1253801] : [class_Rings_Oring__1(_1253799), -(hBOOL(hAPP(hAPP(c_member(_1253799), hAPP(c_Int_Oring__1__class_Oof__int(_1253799), _1253801)), c_Int_Oring__1__class_OInts(_1253799))))], (5078 ^ _781404) ^ [_858853, _858855] : [_858855 = _858853, -(c_Lattices_Osemilattice__inf__class_Oinf(_858855) = c_Lattices_Osemilattice__inf__class_Oinf(_858853))], (47157 ^ _781404) ^ [_1729289, _1729291, _1729293, _1729295, _1729297] : [class_Orderings_Olinorder(_1729289), -(c_List_Olinorder__class_Osorted(_1729289, hAPP(hAPP(c_List_Omap(_1729291, _1729289), _1729293), hAPP(c_List_Ofilter(_1729291, hAPP(hAPP(c_COMBC(_1729291, _1729289, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1729289, tc_fun(_1729289, tc_HOL_Obool), _1729291), c_fequal), _1729293)), hAPP(_1729295, _1729297))), _1729297))))], (43056 ^ _781404) ^ [_1638992] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1638992) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43059 ^ _781404 : [(43060 ^ _781404) ^ [_1639067] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1639067), hAPP(c_List_Oset(tc_Nat_Onat), _1638992))), -(_1639067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (41283 ^ _781404) ^ [_1589957] : [-(c_Transitive__Closure_Ortrancl(_1589957, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1589957, _1589957), tc_HOL_Obool))) = c_Relation_OId(_1589957))], (31148 ^ _781404) ^ [_1341584, _1341586, _1341588, _1341590, _1341592, _1341594, _1341596] : [c_Nitpick_Ofold__graph_H(_1341584, _1341586, _1341588, _1341590, _1341592, hAPP(hAPP(_1341588, _1341594), _1341596)), 31153 ^ _781404 : [(31156 ^ _781404) ^ [] : [-(hAPP(hAPP(_1341588, _1341594), _1341596) = _1341590)], (31154 ^ _781404) ^ [] : [-(_1341592 = c_Orderings_Obot__class_Obot(tc_fun(_1341584, tc_HOL_Obool)))]], 31159 ^ _781404 : [(31164 ^ _781404) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1341584, _1341586, _1341588, _1341590, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341584, tc_HOL_Obool)), _1341592), hAPP(hAPP(c_Set_Oinsert(_1341584), 31157 ^ [_1341584, _1341586, _1341588, _1341590, _1341592, _1341594, _1341596]), c_Orderings_Obot__class_Obot(tc_fun(_1341584, tc_HOL_Obool)))), 31158 ^ [_1341584, _1341586, _1341588, _1341590, _1341592, _1341594, _1341596]))], (31162 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1341584), 31157 ^ [_1341584, _1341586, _1341588, _1341590, _1341592, _1341594, _1341596]), _1341592)))], (31160 ^ _781404) ^ [] : [-(hAPP(hAPP(_1341588, _1341594), _1341596) = hAPP(hAPP(_1341588, 31157 ^ [_1341584, _1341586, _1341588, _1341590, _1341592, _1341594, _1341596]), 31158 ^ [_1341584, _1341586, _1341588, _1341590, _1341592, _1341594, _1341596]))]]], (33374 ^ _781404) ^ [] : [-(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)))], (27213 ^ _781404) ^ [_1267243, _1267245, _1267247] : [-(hAPP(c_Finite__Set_Ofold1(_1267243, _1267245), hAPP(hAPP(c_Set_Oinsert(_1267243), _1267247), c_Orderings_Obot__class_Obot(tc_fun(_1267243, tc_HOL_Obool)))) = _1267247)], (956 ^ _781404) ^ [_795712, _795714, _795716, _795718] : [-(c_Predicate_Otransp(_795716, _795712)), c_Predicate_Otransp(_795718, _795714), _795718 = _795716, _795714 = _795712], (48255 ^ _781404) ^ [_1752946, _1752948, _1752950, _1752952, _1752954] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752946)), _1752948) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752950)), _1752952), 48261 ^ _781404 : [(48264 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1752954, hAPP(hAPP(c_List_Onth(_1752946), _1752948), 48260 ^ [_1752946, _1752948, _1752950, _1752952, _1752954])), hAPP(hAPP(c_List_Onth(_1752950), _1752952), 48260 ^ [_1752946, _1752948, _1752950, _1752952, _1752954])))], (48262 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48260 ^ [_1752946, _1752948, _1752950, _1752952, _1752954]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752946)), _1752948))))]], -(c_List_Olist__all2(_1752946, _1752950, _1752954, _1752948, _1752952))], (3610 ^ _781404) ^ [_835415, _835417, _835419, _835421, _835423, _835425, _835427, _835429, _835431, _835433] : [-(c_List_Olinorder__class_Oinsort__insert__key(_835433, _835429, _835425, _835421, _835417) = c_List_Olinorder__class_Oinsort__insert__key(_835431, _835427, _835423, _835419, _835415)), _835433 = _835431, _835429 = _835427, _835425 = _835423, _835421 = _835419, _835417 = _835415], (12090 ^ _781404) ^ [_988886, _988888, _988890, _988892] : [hBOOL(hAPP(hAPP(c_member(_988886), _988888), _988890)), -(hBOOL(hAPP(hAPP(c_member(_988886), _988888), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_988886, tc_HOL_Obool)), _988890), _988892))))], (48101 ^ _781404) ^ [_1749193, _1749195, _1749197, _1749199, _1749201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1749193, _1749195)), hAPP(_1749193, _1749197))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1749199, _1749199)), hAPP(hAPP(c_Product__Type_OPair(_1749199, _1749199), _1749195), _1749197)), c_List_Omeasures(_1749199, _1749201))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1749199, _1749199)), hAPP(hAPP(c_Product__Type_OPair(_1749199, _1749199), _1749195), _1749197)), c_List_Omeasures(_1749199, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1749199, tc_Nat_Onat)), _1749193), _1749201)))))], (46617 ^ _781404) ^ [_1718080, _1718082, _1718084] : [-(hAPP(c_List_Oset(_1718080), hAPP(c_List_Ofilter(_1718080, _1718082), _1718084)) = hAPP(c_Set_OCollect(_1718080), hAPP(hAPP(c_COMBS(_1718080, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1718080), c_fconj), hAPP(hAPP(c_COMBC(_1718080, tc_fun(_1718080, tc_HOL_Obool), tc_HOL_Obool), c_member(_1718080)), hAPP(c_List_Oset(_1718080), _1718084)))), _1718082)))], (21155 ^ _781404) ^ [_1157135, _1157137, _1157139] : [class_Groups_Omonoid__mult(_1157135), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157135), hAPP(hAPP(c_Power_Opower__class_Opower(_1157135), _1157137), _1157139)), _1157137) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157135), _1157137), hAPP(hAPP(c_Power_Opower__class_Opower(_1157135), _1157137), _1157139)))], (7593 ^ _781404) ^ [_905994, _905996, _905998, _906000] : [7594 ^ _781404 : [(7597 ^ _781404) ^ [] : [hBOOL(hAPP(_905998, _906000))], (7595 ^ _781404) ^ [] : [_905996 = _906000]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_905994), _905996), _905998), _906000)))], (896 ^ _781404) ^ [_794864, _794866, _794868, _794870, _794872, _794874] : [-(c_Equiv__Relations_Oequiv(_794872, _794868, _794864)), c_Equiv__Relations_Oequiv(_794874, _794870, _794866), _794874 = _794872, _794870 = _794868, _794866 = _794864], (8816 ^ _781404) ^ [_930181, _930183, _930185] : [class_Complete__Lattice_Ocomplete__lattice(_930181), -(c_Complete__Lattice_OSup__class_OSup(_930181, hAPP(hAPP(c_Set_Oinsert(_930181), _930183), _930185)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930181), _930183), c_Complete__Lattice_OSup__class_OSup(_930181, _930185)))], (24604 ^ _781404) ^ [_1222717, _1222719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222717)), -(c_SMT_Oz3mod(_1222719, _1222717) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1222719, _1222717))], (49713 ^ _781404) ^ [_1784953] : [-(c_Relation_Otrans(tc_fun(_1784953, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1784953)))], (15020 ^ _781404) ^ [_1046072, _1046074, _1046076, _1046078] : [class_Rings_Ocomm__semiring__1(_1046072), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046072), _1046074), _1046076)), _1046078) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046072), _1046074), _1046078)), _1046076))], (48074 ^ _781404) ^ [_1748416, _1748418, _1748420, _1748422, _1748424] : [-(c_List_Omaps(_1748416, _1748418, _1748420, hAPP(hAPP(c_List_Olist_OCons(_1748416), _1748422), _1748424)) = hAPP(hAPP(c_List_Oappend(_1748418), hAPP(_1748420, _1748422)), c_List_Omaps(_1748416, _1748418, _1748420, _1748424)))], (42788 ^ _781404) ^ [_1630966, _1630968, _1630970, _1630972] : [hBOOL(hAPP(hAPP(c_member(_1630966), _1630968), hAPP(c_List_Oset(_1630966), hAPP(hAPP(c_List_Olist_OCons(_1630966), _1630970), _1630972)))), -(_1630968 = _1630970), -(hBOOL(hAPP(hAPP(c_member(_1630966), _1630968), hAPP(c_List_Oset(_1630966), _1630972))))], (16482 ^ _781404) ^ [_1074252, _1074254, _1074256, _1074258, _1074260] : [class_Groups_Ocomm__monoid__add(_1074252), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074254), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1074256), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1074252), _1074258), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1074254, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1074256), _1074260))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074252), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1074252), _1074258), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1074254, _1074256))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1074252), _1074258), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1074256), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1074256), _1074260)))))], (40301 ^ _781404) ^ [_1566582] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40297 ^ [_1566582]), c_Int_OInteg)))], (13546 ^ _781404) ^ [_1017184, _1017186, _1017188, _1017190, _1017192] : [class_Groups_Ocomm__monoid__add(_1017184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017186), _1017188)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017186), _1017190)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017184), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1017186, _1017184), _1017192), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017186, tc_HOL_Obool)), _1017188), _1017190))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1017186, _1017184), _1017192), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1017186, tc_HOL_Obool)), _1017188), _1017190))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017184), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1017186, _1017184), _1017192), _1017188)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1017186, _1017184), _1017192), _1017190)))], (33605 ^ _781404) ^ [_1393695, _1393697, _1393699, _1393701, _1393703, _1393705] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393695, tc_fun(_1393697, tc_HOL_Obool)), _1393699), hAPP(hAPP(c_COMBC(_1393695, tc_fun(_1393701, tc_fun(_1393697, tc_HOL_Obool)), tc_fun(_1393697, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393701, tc_HOL_Obool), tc_fun(tc_fun(_1393701, tc_fun(_1393697, tc_HOL_Obool)), tc_fun(_1393697, tc_HOL_Obool)), _1393695), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393701, tc_fun(_1393697, tc_HOL_Obool))), _1393703)), _1393705)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393701, tc_fun(_1393697, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393695, tc_fun(_1393701, tc_HOL_Obool)), _1393699), _1393703)), _1393705))], (41061 ^ _781404) ^ [_1583652, _1583654] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583652, _1583652)), c_Transitive__Closure_Otrancl(_1583652, _1583654))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583652, _1583652)), _1583654)))], (47782 ^ _781404) ^ [_1742281, _1742283, _1742285, _1742287, _1742289] : [class_Orderings_Olinorder(_1742281), c_List_Olinorder__class_Osorted(_1742281, hAPP(c_List_Orev(_1742281), hAPP(hAPP(c_List_Omap(_1742283, _1742281), _1742285), _1742287))), -(hAPP(c_List_Ofilter(_1742283, hAPP(hAPP(c_COMBB(_1742281, tc_HOL_Obool, _1742283), hAPP(c_Orderings_Oord__class_Oless(_1742281), _1742289)), _1742285)), _1742287) = c_List_OtakeWhile(_1742283, hAPP(hAPP(c_COMBB(_1742281, tc_HOL_Obool, _1742283), hAPP(c_Orderings_Oord__class_Oless(_1742281), _1742289)), _1742285), _1742287))], (49203 ^ _781404) ^ [_1773187, _1773189, _1773191, _1773193] : [hBOOL(hAPP(hAPP(c_member(_1773187), _1773189), hAPP(c_List_Oset(_1773187), c_List_Oreplicate(_1773187, _1773191, _1773193)))), 49206 ^ _781404 : [(49209 ^ _781404) ^ [] : [_1773191 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49207 ^ _781404) ^ [] : [-(_1773189 = _1773193)]]], (10873 ^ _781404) ^ [_965998, _966000, _966002, _966004, _966006] : [class_Orderings_Oorder(_965998), class_Orderings_Olinorder(_966000), c_Orderings_Oorder__class_Ostrict__mono(_966000, _965998, _966002), 10884 ^ _781404 : [(10891 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966000), _966004), _966006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965998), hAPP(_966002, _966004)), hAPP(_966002, _966006))))], (10885 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965998), hAPP(_966002, _966004)), hAPP(_966002, _966006))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966000), _966004), _966006)))]]], (50943 ^ _781404) ^ [_1811313, _1811315, _1811317] : [c_Fun_Obij__betw(_1811313, _1811315, _1811317, c_Orderings_Otop__class_Otop(tc_fun(_1811313, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1811315, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1811313, _1811315, _1811317), c_Orderings_Otop__class_Otop(tc_fun(_1811313, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1811315, tc_HOL_Obool)))], (47667 ^ _781404) ^ [_1739946, _1739948] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1739946), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1739946))), _1739948))), -(c_List_Otranspose(_1739946, c_List_Otranspose(_1739946, _1739948)) = c_List_OtakeWhile(tc_List_Olist(_1739946), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1739946)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1739946), tc_List_Olist(_1739946), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1739946))), _1739948))], (3886 ^ _781404) ^ [_839767, _839769, _839771, _839773, _839775, _839777] : [-(c_List_Olinorder__class_Oinsort__key(_839777, _839773, _839769) = c_List_Olinorder__class_Oinsort__key(_839775, _839771, _839767)), _839777 = _839775, _839773 = _839771, _839769 = _839767], (46800 ^ _781404) ^ [_1722894, _1722896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722894), _1722896)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1722894, _1722896)) = _1722894)], (52366 ^ _781404) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (1936 ^ _781404) ^ [_808644, _808646] : [-(class_Groups_Ozero(_808644)), _808646 = _808644, class_Groups_Ozero(_808646)], (5512 ^ _781404) ^ [_865734, _865736] : [_865736 = _865734, -(c_Groups_Oplus__class_Oplus(_865736) = c_Groups_Oplus__class_Oplus(_865734))], (39626 ^ _781404) ^ [_1548831, _1548833, _1548835, _1548837, _1548839, _1548841, _1548843] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1548831, _1548833, _1548835), hAPP(hAPP(c_Relation_Orel__comp(_1548831, _1548837, _1548833), _1548839), _1548841)), _1548843) = hAPP(hAPP(c_Relation_Orel__comp(_1548831, _1548837, _1548835), _1548839), hAPP(hAPP(c_Relation_Orel__comp(_1548837, _1548833, _1548835), _1548841), _1548843)))], (44818 ^ _781404) ^ [_1678036, _1678038, _1678040] : [class_Orderings_Olinorder(_1678036), -(c_Big__Operators_Olattice_OSup__fin(_1678036, c_Orderings_Oord__class_Omax(_1678036), hAPP(c_List_Oset(_1678036), hAPP(hAPP(c_List_Olist_OCons(_1678036), _1678038), _1678040))) = hAPP(c_List_Ofoldl(_1678036, _1678036, c_Orderings_Oord__class_Omax(_1678036), _1678038), _1678040))], (39005 ^ _781404) ^ [_1526527, _1526529] : [-(hAPP(c_Set_OCollect(_1526527), _1526529) = _1526529)], (6329 ^ _781404) ^ [_882033, _882035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882033), hAPP(c_Nat_OSuc, _882035))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882033), _882035))), -(_882033 = hAPP(c_Nat_OSuc, _882035))], (36602 ^ _781404) ^ [_1465657, _1465659] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1465657), _1465659) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1465657, _1465659)))], (9390 ^ _781404) ^ [_942364, _942366, _942368] : [9392 ^ _781404 : [(9395 ^ _781404) ^ [] : [hBOOL(hAPP(_942364, 9391 ^ [_942364, _942366, _942368]))], (9393 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 9391 ^ [_942364, _942366, _942368]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _942366), _942368))))]], -(c_List_Oall__interval__nat(_942364, _942366, _942368))], (38456 ^ _781404) ^ [_1511204] : [-(c_Nitpick_Ozero__frac(_1511204) = c_Nitpick_OAbs__Frac(_1511204, 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))))], (46760 ^ _781404) ^ [_1722234, _1722236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722234), _1722236)), -(c_List_Oupt(_1722234, _1722236) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1722234), c_List_Oupt(hAPP(c_Nat_OSuc, _1722234), _1722236)))], (39276 ^ _781404) ^ [_1535284, _1535286, _1535288, _1535290] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1535284), hAPP(c_Set_OCollect(_1535284), _1535286))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1535288), hAPP(c_Set_OCollect(_1535288), hAPP(hAPP(c_COMBB(tc_fun(_1535284, tc_HOL_Obool), tc_HOL_Obool, _1535288), c_HOL_OEx(_1535284)), hAPP(hAPP(c_COMBC(_1535288, tc_fun(_1535284, tc_HOL_Obool), tc_fun(_1535284, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535284, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1535284, tc_HOL_Obool), tc_fun(_1535284, tc_HOL_Obool)), _1535288), c_COMBS(_1535284, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535284, tc_HOL_Obool), tc_fun(_1535284, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1535288), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535284), c_fconj)), hAPP(hAPP(c_COMBC(_1535288, tc_fun(_1535284, _1535288), tc_fun(_1535284, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535288, tc_HOL_Obool), tc_fun(tc_fun(_1535284, _1535288), tc_fun(_1535284, tc_HOL_Obool)), _1535288), c_COMBB(_1535288, tc_HOL_Obool, _1535284)), c_fequal)), _1535290)))), _1535286))))))], (13005 ^ _781404) ^ [_1007031, _1007033, _1007035, _1007037] : [class_Groups_Ocancel__ab__semigroup__add(_1007031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007031), _1007033), _1007035) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007031), _1007033), _1007037), -(_1007035 = _1007037)], (11481 ^ _781404) ^ [_977617, _977619, _977621] : [class_Groups_Ocomm__monoid__add(_977617), hAPP(_977619, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_977617), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _977617), _977619), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _977621)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _977617), _977619), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _977621)))], (37380 ^ _781404) ^ [_1484336, _1484338, _1484340, _1484342, _1484344] : [-(hAPP(c_Relation_OImage(_1484336, _1484338, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1484336, _1484338), tc_HOL_Obool)), _1484340), _1484342)), _1484344) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484338, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1484336, _1484338, _1484340), _1484344)), hAPP(c_Relation_OImage(_1484336, _1484338, _1484342), _1484344)))], (13041 ^ _781404) ^ [_1007672, _1007674, _1007676, _1007678] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1007672), 13044 ^ _781404 : [(13051 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007672), _1007676), _1007678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007672), _1007674), _1007676)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007672), _1007674), _1007678))))], (13045 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007672), _1007674), _1007676)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007672), _1007674), _1007678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007672), _1007676), _1007678)))]]], (46931 ^ _781404) ^ [_1725690, _1725692] : [class_Orderings_Olinorder(_1725690), -(c_List_Olinorder__class_Osorted(_1725690, hAPP(hAPP(c_List_Olist_OCons(_1725690), _1725692), c_List_Olist_ONil(_1725690))))], (51876 ^ _781404) ^ [_1831400, _1831402] : [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), _1831400, _1831402), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831400), _1831402))], (48113 ^ _781404) ^ [_1749509, _1749511, _1749513] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1749509, _1749509)), hAPP(hAPP(c_Product__Type_OPair(_1749509, _1749509), _1749511), _1749513)), c_List_Omeasures(_1749509, c_List_Olist_ONil(tc_fun(_1749509, tc_Nat_Onat)))))], (16356 ^ _781404) ^ [_1071958, _1071960, _1071962] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1071958), _1071960)), 16359 ^ _781404 : [(16379 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1071958, tc_Nat_Onat), _1071962), _1071960) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 16380 ^ _781404 : [(16381 ^ _781404) ^ [_1072439] : [hBOOL(hAPP(hAPP(c_member(_1071958), _1072439), _1071960)), hAPP(_1071962, _1072439) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 16389 ^ _781404 : [(16394 ^ _781404) ^ [] : [hAPP(_1071962, 16388 ^ [_1071958, _1071960, _1071962, _1072439]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16392 ^ _781404) ^ [] : [_1072439 = 16388 ^ [_1071958, _1071960, _1071962, _1072439]], (16390 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071958), 16388 ^ [_1071958, _1071960, _1071962, _1072439]), _1071960)))]]]]], (16360 ^ _781404) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1071958, tc_Nat_Onat), _1071962), _1071960) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 16364 ^ _781404 : [(16369 ^ _781404) ^ [_1072278] : [hBOOL(hAPP(hAPP(c_member(_1071958), _1072278), _1071960)), -(16363 ^ [_1071958, _1071960, _1071962] = _1072278), -(hAPP(_1071962, _1072278) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16367 ^ _781404) ^ [] : [-(hAPP(_1071962, 16363 ^ [_1071958, _1071960, _1071962]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (16365 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071958), 16363 ^ [_1071958, _1071960, _1071962]), _1071960)))]]]]], (39439 ^ _781404) ^ [_1542183, _1542185, _1542187] : [class_Orderings_Olinorder(_1542183), hBOOL(hAPP(c_Finite__Set_Ofinite(_1542183), _1542185)), -(_1542185 = c_Orderings_Obot__class_Obot(tc_fun(_1542183, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1542183), _1542187)), -(_1542187 = c_Orderings_Obot__class_Obot(tc_fun(_1542183, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1542183), c_Big__Operators_Olattice_OInf__fin(_1542183, c_Orderings_Oord__class_Omin(_1542183), _1542185)), c_Big__Operators_Olattice_OInf__fin(_1542183, c_Orderings_Oord__class_Omin(_1542183), _1542187)) = c_Big__Operators_Olattice_OInf__fin(_1542183, c_Orderings_Oord__class_Omin(_1542183), hAPP(c_Set_OCollect(_1542183), hAPP(hAPP(c_COMBB(tc_fun(_1542183, tc_HOL_Obool), tc_HOL_Obool, _1542183), c_HOL_OEx(_1542183)), hAPP(hAPP(c_COMBB(tc_fun(_1542183, tc_fun(_1542183, tc_HOL_Obool)), tc_fun(_1542183, tc_HOL_Obool), _1542183), hAPP(c_COMBB(tc_fun(_1542183, tc_HOL_Obool), tc_HOL_Obool, _1542183), c_HOL_OEx(_1542183))), hAPP(hAPP(c_COMBC(_1542183, tc_fun(_1542183, tc_fun(_1542183, tc_HOL_Obool)), tc_fun(_1542183, tc_fun(_1542183, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1542183, tc_fun(tc_fun(_1542183, tc_HOL_Obool), tc_fun(_1542183, tc_HOL_Obool))), tc_fun(tc_fun(_1542183, tc_fun(_1542183, tc_HOL_Obool)), tc_fun(_1542183, tc_fun(_1542183, tc_HOL_Obool))), _1542183), c_COMBS(_1542183, tc_fun(_1542183, tc_HOL_Obool), tc_fun(_1542183, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1542183, tc_fun(_1542183, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1542183, tc_fun(tc_fun(_1542183, tc_HOL_Obool), tc_fun(_1542183, tc_HOL_Obool))), _1542183), hAPP(c_COMBB(tc_fun(_1542183, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1542183, tc_HOL_Obool), tc_fun(_1542183, tc_HOL_Obool)), _1542183), c_COMBS(_1542183, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1542183, tc_fun(_1542183, tc_HOL_Obool)), tc_fun(_1542183, tc_fun(_1542183, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1542183), hAPP(c_COMBB(tc_fun(_1542183, tc_HOL_Obool), tc_fun(_1542183, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1542183), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542183), c_fconj))), hAPP(hAPP(c_COMBC(_1542183, tc_fun(_1542183, tc_fun(_1542183, _1542183)), tc_fun(_1542183, tc_fun(_1542183, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542183, _1542183), tc_fun(_1542183, tc_HOL_Obool)), tc_fun(tc_fun(_1542183, tc_fun(_1542183, _1542183)), tc_fun(_1542183, tc_fun(_1542183, tc_HOL_Obool))), _1542183), c_COMBB(tc_fun(_1542183, _1542183), tc_fun(_1542183, tc_HOL_Obool), _1542183)), hAPP(hAPP(c_COMBB(tc_fun(_1542183, tc_HOL_Obool), tc_fun(tc_fun(_1542183, _1542183), tc_fun(_1542183, tc_HOL_Obool)), _1542183), c_COMBB(_1542183, tc_HOL_Obool, _1542183)), c_fequal))), c_Orderings_Oord__class_Omax(_1542183)))))), hAPP(hAPP(c_COMBC(_1542183, tc_fun(_1542183, tc_HOL_Obool), tc_fun(_1542183, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1542183, tc_HOL_Obool), tc_fun(_1542183, tc_HOL_Obool)), _1542183), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1542183)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542183), c_fconj), hAPP(hAPP(c_COMBC(_1542183, tc_fun(_1542183, tc_HOL_Obool), tc_HOL_Obool), c_member(_1542183)), _1542185)))), hAPP(hAPP(c_COMBC(_1542183, tc_fun(_1542183, tc_HOL_Obool), tc_HOL_Obool), c_member(_1542183)), _1542187))))))))], (37134 ^ _781404) ^ [_1478114, _1478116, _1478118, _1478120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1478114), _1478116)), -(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), _1478114), _1478118)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1478116), _1478120))), c_FunDef_Opair__less)))], (27817 ^ _781404) ^ [_1279123, _1279125] : [class_Rings_Odivision__ring(_1279123), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279123), c_Groups_Ozero__class_Ozero(_1279123)), _1279125) = c_Groups_Ozero__class_Ozero(_1279123))], (38872 ^ _781404) ^ [_1522957, _1522959, _1522961, _1522963, _1522965, _1522967, _1522969, _1522971, _1522973] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522957, _1522959)), hAPP(hAPP(c_Product__Type_OPair(_1522957, _1522959), _1522961), _1522963)), _1522965)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1522967, _1522969)), hAPP(hAPP(c_Product__Type_OPair(_1522967, _1522969), hAPP(_1522971, _1522961)), hAPP(_1522973, _1522963))), hAPP(c_Set_Oimage(tc_prod(_1522957, _1522959), tc_prod(_1522967, _1522969), c_Product__Type_Omap__pair(_1522957, _1522967, _1522959, _1522969, _1522971, _1522973)), _1522965))))], (52436 ^ _781404) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (7431 ^ _781404) ^ [_902742, _902744] : [class_Lattices_Obounded__lattice__top(_902742), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_902742), c_Orderings_Otop__class_Otop(_902742)), _902744) = _902744)], (32512 ^ _781404) ^ [_1367047, _1367049, _1367051] : [class_Orderings_Olinorder(_1367047), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367047), _1367049)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367047), _1367051)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367047, tc_HOL_Obool)), _1367049), _1367051) = c_Orderings_Obot__class_Obot(tc_fun(_1367047, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367047), c_Big__Operators_Olinorder__class_OMax(_1367047, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1367047, tc_HOL_Obool)), _1367049), _1367051))), c_Big__Operators_Olinorder__class_OMax(_1367047, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367047, tc_HOL_Obool)), _1367049), _1367051))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367047), c_Big__Operators_Olinorder__class_OMax(_1367047, _1367049)), c_Big__Operators_Olinorder__class_OMax(_1367047, _1367051)))], (3822 ^ _781404) ^ [_838769, _838771] : [_838771 = _838769, -(c_Enum_Oenum__class_Oenum__ex(_838771) = c_Enum_Oenum__class_Oenum__ex(_838769))], (6793 ^ _781404) ^ [_890288, _890290, _890292] : [class_Groups_Ogroup__add(_890288), 6796 ^ _781404 : [(6803 ^ _781404) ^ [] : [_890290 = _890292, -(hAPP(c_Groups_Ouminus__class_Ouminus(_890288), _890290) = hAPP(c_Groups_Ouminus__class_Ouminus(_890288), _890292))], (6797 ^ _781404) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_890288), _890290) = hAPP(c_Groups_Ouminus__class_Ouminus(_890288), _890292), -(_890290 = _890292)]]], (4656 ^ _781404) ^ [_852180, _852182, _852184, _852186, _852188, _852190, _852192, _852194] : [-(c_Random__Sequence_ORandom(_852194, _852190, _852186, _852182) = c_Random__Sequence_ORandom(_852192, _852188, _852184, _852180)), _852194 = _852192, _852190 = _852188, _852186 = _852184, _852182 = _852180], (27451 ^ _781404) ^ [_1271547, _1271549] : [27452 ^ _781404 : [(27455 ^ _781404) ^ [] : [_1271549 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27453 ^ _781404) ^ [] : [-(_1271547 = 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), _1271547)), _1271549))))], (37417 ^ _781404) ^ [_1485379, _1485381, _1485383, _1485385, _1485387] : [-(hBOOL(hAPP(hAPP(c_member(_1485379), _1485381), hAPP(c_Relation_OImage(_1485383, _1485379, _1485385), _1485387)))), 37418 ^ _781404 : [(37419 ^ _781404) ^ [_1485465] : [hBOOL(hAPP(hAPP(c_member(_1485383), _1485465), _1485387)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1485383, _1485379)), hAPP(hAPP(c_Product__Type_OPair(_1485383, _1485379), _1485465), _1485381)), _1485385))]]], (20189 ^ _781404) ^ [_1139892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1139892)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139892), c_Int_OPls)))], (45106 ^ _781404) ^ [_1683527, _1683529, _1683531, _1683533] : [-(hAPP(hAPP(c_List_Oappend(_1683527), _1683529), hAPP(hAPP(c_List_Olist_OCons(_1683527), _1683531), c_List_Olist_ONil(_1683527))) = _1683533), -(_1683533 = c_List_Olist_ONil(_1683527)), c_List_Obutlast(_1683527, _1683533) = _1683529, c_List_Olast(_1683527, _1683533) = _1683531], (32308 ^ _781404) ^ [_1363193, _1363195, _1363197] : [class_Orderings_Olinorder(_1363193), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363193), _1363195)), hBOOL(hAPP(hAPP(c_member(_1363193), _1363197), _1363195)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363193), _1363197), c_Big__Operators_Olinorder__class_OMax(_1363193, _1363195)) = c_Big__Operators_Olinorder__class_OMax(_1363193, _1363195))], (37164 ^ _781404) ^ [_1478735, _1478737, _1478739, _1478741] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1478735), _1478737)), 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)), _1478739), _1478735)), 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)), _1478741), _1478737)), 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)), _1478739), _1478741)), _1478737)), c_FunDef_Omax__strict)))], (24562 ^ _781404) ^ [_1221968, _1221970] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1221968)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1221970))) = 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), _1221968), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1221970))))], (51062 ^ _781404) ^ [_1813384, _1813386, _1813388, _1813390, _1813392, _1813394, _1813396] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1813384, tc_HOL_Obool)), _1813386), _1813388) = c_Orderings_Obot__class_Obot(tc_fun(_1813384, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1813390, tc_HOL_Obool)), _1813392), _1813394) = c_Orderings_Obot__class_Obot(tc_fun(_1813390, tc_HOL_Obool)), c_Fun_Obij__betw(_1813384, _1813390, _1813396, _1813386, _1813392), c_Fun_Obij__betw(_1813384, _1813390, _1813396, _1813388, _1813394), -(c_Fun_Obij__betw(_1813384, _1813390, _1813396, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1813384, tc_HOL_Obool)), _1813386), _1813388), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1813390, tc_HOL_Obool)), _1813392), _1813394)))], (1856 ^ _781404) ^ [_807644, _807646] : [-(class_Rings_Osemiring__1(_807644)), _807646 = _807644, class_Rings_Osemiring__1(_807646)], (16668 ^ _781404) ^ [_1078025, _1078027] : [class_Rings_Oring__1(_1078025), hBOOL(hAPP(hAPP(c_member(_1078025), _1078027), c_Int_Oring__1__class_OInts(_1078025))), -(hBOOL(hAPP(hAPP(c_member(_1078025), hAPP(c_Groups_Ouminus__class_Ouminus(_1078025), _1078027)), c_Int_Oring__1__class_OInts(_1078025))))], (23699 ^ _781404) ^ [_1207082, _1207084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1207082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1207084)), -(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), _1207082), _1207084))))], (48645 ^ _781404) ^ [_1761383, _1761385, _1761387] : [-(hBOOL(hAPP(hAPP(c_member(_1761383), _1761385), hAPP(c_List_Oset(_1761383), _1761387)))), 48646 ^ _781404 : [(48647 ^ _781404) ^ [_1761472, _1761474] : [_1761387 = hAPP(hAPP(c_List_Oappend(_1761383), _1761474), hAPP(hAPP(c_List_Olist_OCons(_1761383), _1761385), _1761472)), -(hBOOL(hAPP(hAPP(c_member(_1761383), _1761385), hAPP(c_List_Oset(_1761383), _1761472))))]]], (12352 ^ _781404) ^ [_994175, _994177, _994179, _994181] : [hBOOL(hAPP(hAPP(c_member(_994175), _994177), _994179)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994175, tc_HOL_Obool)), _994179), hAPP(hAPP(c_Set_Oinsert(_994175), _994177), _994181)) = hAPP(hAPP(c_Set_Oinsert(_994175), _994177), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994175, tc_HOL_Obool)), _994179), _994181)))], (40795 ^ _781404) ^ [_1577201, _1577203] : [class_Complete__Lattice_Ocomplete__lattice(_1577201), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1577201, hAPP(c_COMBK(_1577201, _1577201), _1577203)) = _1577203)], (13692 ^ _781404) ^ [_1020007, _1020009, _1020011] : [class_Groups_Oordered__comm__monoid__add(_1020007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020007), _1020009), c_Groups_Ozero__class_Ozero(_1020007))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020007), _1020011), c_Groups_Ozero__class_Ozero(_1020007))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020007), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020007), _1020009), _1020011)), c_Groups_Ozero__class_Ozero(_1020007))))], (52830 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_ts), v_G)))], (50425 ^ _781404) ^ [_1799810, _1799812, _1799814, _1799816, _1799818] : [c_Equiv__Relations_Opart__equivp(_1799810, _1799812), hBOOL(hAPP(hAPP(_1799812, _1799814), _1799816)), hBOOL(hAPP(hAPP(_1799812, _1799816), _1799818)), -(hBOOL(hAPP(hAPP(_1799812, _1799814), _1799818)))], (33627 ^ _781404) ^ [_1394542, _1394544, _1394546] : [class_Orderings_Obot(_1394542), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1394544, _1394542)), _1394546) = c_Orderings_Obot__class_Obot(_1394542))], (40078 ^ _781404) ^ [_1560695, _1560697, _1560699, _1560701, _1560703] : [-(hAPP(c_Relation_ODomain(_1560695, _1560697), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1560695, _1560697)), hAPP(hAPP(c_Product__Type_OPair(_1560695, _1560697), _1560699), _1560701)), _1560703)) = hAPP(hAPP(c_Set_Oinsert(_1560695), _1560699), hAPP(c_Relation_ODomain(_1560695, _1560697), _1560703)))], (19645 ^ _781404) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (30746 ^ _781404) ^ [_1334119, _1334121, _1334123, _1334125] : [class_Orderings_Olinorder(_1334119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334119), _1334121), _1334123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334119), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334119), _1334121), _1334125)), _1334123)))], (17451 ^ _781404) ^ [_1092686, _1092688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1092686), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1092688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092686), _1092688)))], (36731 ^ _781404) ^ [_1468647, _1468649, _1468651] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468647, tc_HOL_Obool)), _1468649), hAPP(hAPP(c_Set_Oinsert(_1468647), _1468651), c_Orderings_Obot__class_Obot(tc_fun(_1468647, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1468647, _1468651, _1468649) = c_HOL_OThe(_1468647, hAPP(hAPP(c_COMBC(_1468647, tc_fun(_1468647, tc_HOL_Obool), tc_HOL_Obool), c_member(_1468647)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468647, tc_HOL_Obool)), _1468649), hAPP(hAPP(c_Set_Oinsert(_1468647), _1468651), c_Orderings_Obot__class_Obot(tc_fun(_1468647, tc_HOL_Obool)))))))], (22729 ^ _781404) ^ [_1187712, _1187714] : [class_Int_Onumber__ring(_1187712), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187712), hAPP(c_Int_Onumber__class_Onumber__of(_1187712), c_Int_OBit1(c_Int_OPls))), _1187714) = _1187714)], (51080 ^ _781404) ^ [_1813783, _1813785, _1813787, _1813789, _1813791, _1813793, _1813795] : [c_Fun_Obij__betw(_1813783, _1813785, _1813787, _1813789, _1813791), c_Fun_Obij__betw(_1813783, _1813785, _1813787, _1813793, _1813795), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1813785, tc_HOL_Obool)), _1813791), _1813795) = c_Orderings_Obot__class_Obot(tc_fun(_1813785, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1813783, _1813785, _1813787, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1813783, tc_HOL_Obool)), _1813789), _1813793), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1813785, tc_HOL_Obool)), _1813791), _1813795)))], (16422 ^ _781404) ^ [_1073137, _1073139, _1073141, _1073143] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1073137, _1073139)), c_Sum__Type_OPlus(_1073137, _1073139, _1073141, _1073143))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1073139), _1073143)))], (44607 ^ _781404) ^ [_1673650, _1673652, _1673654] : [-(hAPP(c_List_Otl(_1673650), hAPP(hAPP(c_List_Odrop(_1673650), _1673652), _1673654)) = hAPP(hAPP(c_List_Odrop(_1673650), _1673652), hAPP(c_List_Otl(_1673650), _1673654)))], (30198 ^ _781404) ^ [_1323561, _1323563, _1323565, _1323567, _1323569] : [class_Groups_Ocomm__monoid__mult(_1323561), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323563), _1323565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1323563, tc_HOL_Obool)), _1323567), _1323565)), 30212 ^ _781404 : [(30215 ^ _781404) ^ [] : [hAPP(_1323569, 30211 ^ [_1323561, _1323563, _1323565, _1323567, _1323569]) = c_Groups_Oone__class_Oone(_1323561)], (30213 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1323563), 30211 ^ [_1323561, _1323563, _1323565, _1323567, _1323569]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323563, tc_HOL_Obool)), _1323565), _1323567))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1323563, _1323561), _1323569), _1323567) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1323563, _1323561), _1323569), _1323565))], (25618 ^ _781404) ^ [_1239133, _1239135, _1239137] : [hBOOL(hAPP(_1239133, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1239135, _1239137))), 25621 ^ _781404 : [(25628 ^ _781404) ^ [] : [-(_1239137 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25631 ^ _781404 : [(25632 ^ _781404) ^ [_1239381, _1239383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1239381), _1239137)), _1239135 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239137), _1239383)), _1239381), -(hBOOL(hAPP(_1239133, _1239381)))]]], (25622 ^ _781404) ^ [] : [_1239137 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1239133, _1239135)))]]], (6381 ^ _781404) ^ [_882861, _882863] : [hAPP(c_Nat_OSuc, _882861) = hAPP(c_Nat_OSuc, _882863), -(_882861 = _882863)], (44525 ^ _781404) ^ [_1672016, _1672018, _1672020, _1672022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1672016), _1672018)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672020)), _1672022))), -(hAPP(hAPP(c_List_Otake(_1672020), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1672016), _1672018)), _1672022) = hAPP(hAPP(c_List_Oappend(_1672020), hAPP(hAPP(c_List_Otake(_1672020), _1672016), _1672022)), hAPP(hAPP(c_List_Otake(_1672020), _1672018), hAPP(hAPP(c_List_Odrop(_1672020), _1672016), _1672022))))], (16512 ^ _781404) ^ [_1075000, _1075002] : [-(c_Sum__Type_OPlus(_1075000, _1075002, c_Orderings_Otop__class_Otop(tc_fun(_1075000, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1075002, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1075000, _1075002), tc_HOL_Obool)))], (18397 ^ _781404) ^ [_1109300, _1109302, _1109304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109300)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1109302), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1109304)), 18404 ^ _781404 : [(18405 ^ _781404) ^ [_1109508] : [18407 ^ _781404 : [(18413 ^ _781404) ^ [] : [-(_1109508 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 18409 ^ [_1109300, _1109302, _1109304, _1109508]), 18406 ^ [_1109300, _1109302, _1109304, _1109508]))], (18411 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18409 ^ [_1109300, _1109302, _1109304, _1109508]), _1109304)))], (18408 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18406 ^ [_1109300, _1109302, _1109304, _1109508]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1109300))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109508), _1109302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1109508), _1109300)), _1109302)))]]], (3794 ^ _781404) ^ [_838319, _838321, _838323, _838325] : [-(c_List_Omeasures(_838325, _838321) = c_List_Omeasures(_838323, _838319)), _838325 = _838323, _838321 = _838319], (8018 ^ _781404) ^ [_915235, _915237] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _915235, _915237)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _915235), hAPP(c_Nat_OSuc, _915237)))], (15960 ^ _781404) ^ [_1064250, _1064252, _1064254, _1064256] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1064250), _1064252)), hBOOL(hAPP(hAPP(c_member(_1064250), _1064254), _1064252)), hBOOL(hAPP(hAPP(c_member(_1064250), _1064256), _1064252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1064250), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064250, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064250, tc_HOL_Obool)), _1064252), hAPP(hAPP(c_Set_Oinsert(_1064250), _1064254), c_Orderings_Obot__class_Obot(tc_fun(_1064250, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1064250), _1064256), c_Orderings_Obot__class_Obot(tc_fun(_1064250, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1064250), _1064252))))], (21957 ^ _781404) ^ [_1172100, _1172102, _1172104, _1172106, _1172108, _1172110] : [class_Rings_Oring(_1172100), 21960 ^ _781404 : [(21967 ^ _781404) ^ [] : [_1172106 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172100), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1172100), _1172108), _1172102)), _1172104)), _1172110), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172100), _1172102), _1172104)), _1172106) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172100), _1172108), _1172104)), _1172110))], (21961 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172100), _1172102), _1172104)), _1172106) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172100), _1172108), _1172104)), _1172110), -(_1172106 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172100), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1172100), _1172108), _1172102)), _1172104)), _1172110))]]], (38698 ^ _781404) ^ [_1517723, _1517725, _1517727] : [c_Relation_Orefl__on(_1517723, _1517725, _1517727), 38701 ^ _781404 : [(38704 ^ _781404) ^ [_1517905] : [hBOOL(hAPP(hAPP(c_member(_1517723), _1517905), _1517725)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517723, _1517723)), hAPP(hAPP(c_Product__Type_OPair(_1517723, _1517723), _1517905), _1517905)), _1517727)))], (38702 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517723, _1517723), tc_HOL_Obool)), _1517727), hAPP(hAPP(c_Product__Type_OSigma(_1517723, _1517723), _1517725), hAPP(c_COMBK(tc_fun(_1517723, tc_HOL_Obool), _1517723), _1517725)))))]]], (28151 ^ _781404) ^ [_1284474, _1284476] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284474), _1284476), hAPP(c_Int_Onumber__class_Onumber__of(_1284474), c_Int_OBit1(c_Int_OPls))) = _1284476), class_Fields_Ofield(_1284474), class_Int_Onumber__ring(_1284474)], (47413 ^ _781404) ^ [_1734601, _1734603] : [-(c_Fun_Oinj__on(tc_List_Olist(_1734601), tc_List_Olist(_1734601), c_List_Orev(_1734601), _1734603))], (38313 ^ _781404) ^ [_1508348, _1508350, _1508352, _1508354, _1508356] : [c_Typedef_Otype__definition(_1508348, _1508350, _1508352, _1508354, _1508356), -(hAPP(c_Set_Oimage(_1508348, _1508350, _1508352), c_Orderings_Otop__class_Otop(tc_fun(_1508348, tc_HOL_Obool))) = _1508356)], (25139 ^ _781404) ^ [_1231363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231363), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1231363) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19601 ^ _781404) ^ [_1129852] : [-(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), _1129852))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8710 ^ _781404) ^ [_928175, _928177, _928179] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_928175, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_928175, tc_HOL_Obool)), _928177), _928179)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928175, tc_HOL_Obool)), _928177), c_Complete__Lattice_OInf__class_OInf(tc_fun(_928175, tc_HOL_Obool), _928179)))], (48945 ^ _781404) ^ [_1767598, _1767600, _1767602] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767598)), c_List_Osplice(_1767598, _1767600, _1767602)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767598)), _1767600)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767598)), _1767602)))], (23353 ^ _781404) ^ [_1199969, _1199971, _1199973] : [-(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), _1199969), _1199971)), _1199971)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199969, _1199971))), _1199973) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199969), _1199973))], (41893 ^ _781404) ^ [_1604674, _1604676, _1604678, _1604680] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604674, _1604674)), hAPP(hAPP(c_Product__Type_OPair(_1604674, _1604674), _1604676), _1604678)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604674, _1604674), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604680))), -(_1604676 = _1604678)], (15599 ^ _781404) ^ [_1057468, _1057470, _1057472] : [class_Lattices_Olattice(_1057468), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057468), _1057470)), hBOOL(hAPP(hAPP(c_member(_1057468), _1057472), _1057470)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1057468), _1057472), c_Big__Operators_Olattice__class_OInf__fin(_1057468, _1057470)) = c_Big__Operators_Olattice__class_OInf__fin(_1057468, _1057470))], (11409 ^ _781404) ^ [_975883, _975885, _975887, _975889] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_975883, tc_HOL_Obool)), _975885), hAPP(hAPP(c_Set_Oinsert(_975883), _975887), _975889)))), 11412 ^ _781404 : [(11415 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_975883, tc_HOL_Obool)), _975885), _975889))], (11413 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_975883), _975887), _975889)))]], 11416 ^ _781404 : [(11419 ^ _781404) ^ [] : [11420 ^ _781404 : [(11423 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_975883, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975883, tc_HOL_Obool)), _975885), hAPP(hAPP(c_Set_Oinsert(_975883), _975887), c_Orderings_Obot__class_Obot(tc_fun(_975883, tc_HOL_Obool))))), _975889))], (11421 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_975883), _975887), _975885)))]], 11424 ^ _781404 : [(11427 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_975883, tc_HOL_Obool)), _975885), _975889))], (11425 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_975883), _975887), _975885))]]], (11417 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_975883), _975887), _975889))]]], (48552 ^ _781404) ^ [_1759624, _1759626, _1759628, _1759630] : [48553 ^ _781404 : [(48556 ^ _781404) ^ [] : [c_List_Olist__ex(_1759624, _1759626, _1759630)], (48554 ^ _781404) ^ [] : [c_List_Olist__ex(_1759624, _1759626, _1759628)]], -(c_List_Olist__ex(_1759624, _1759626, hAPP(hAPP(c_List_Oappend(_1759624), _1759628), _1759630)))], (44371 ^ _781404) ^ [_1668360, _1668362] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668360)), hAPP(c_List_Orotate1(_1668360), _1668362)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668360)), _1668362))], (46319 ^ _781404) ^ [_1710827, _1710829, _1710831] : [-(hBOOL(hAPP(hAPP(c_member(_1710827), _1710829), hAPP(c_List_Oset(_1710827), _1710831)))), -(c_List_Oremdups(_1710827, hAPP(hAPP(c_List_Olist_OCons(_1710827), _1710829), _1710831)) = hAPP(hAPP(c_List_Olist_OCons(_1710827), _1710829), c_List_Oremdups(_1710827, _1710831)))], (35211 ^ _781404) ^ [_1437201, _1437203] : [-(c_Divides_OposDivAlg(_1437201, _1437203) = hAPP(c_Divides_Oadjust(_1437203), c_Divides_OposDivAlg(_1437201, 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)))), _1437203)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437201), _1437203))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1437203), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (5861 ^ _781404) ^ [_874328, _874330, _874332, _874334] : [class_Orderings_Oorder(_874328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874328), _874330), _874332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874328), _874334), _874330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874328), _874334), _874332)))], (21347 ^ _781404) ^ [_1160766, _1160768, _1160770, _1160772, _1160774] : [class_Rings_Oordered__semiring(_1160766), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160766), _1160768), _1160770)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160766), _1160772), _1160774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160766), c_Groups_Ozero__class_Ozero(_1160766)), _1160770)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160766), c_Groups_Ozero__class_Ozero(_1160766)), _1160772)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160766), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160766), _1160768), _1160772)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160766), _1160770), _1160774))))], (26065 ^ _781404) ^ [_1247092] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1247092)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1247092)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (3282 ^ _781404) ^ [_830345, _830347, _830349, _830351, _830353, _830355, _830357, _830359] : [-(c_Nitpick_Osetsum_H(_830359, _830355, _830351, _830347) = c_Nitpick_Osetsum_H(_830357, _830353, _830349, _830345)), _830359 = _830357, _830355 = _830353, _830351 = _830349, _830347 = _830345], (3912 ^ _781404) ^ [_840158, _840160] : [_840160 = _840158, -(c_Lazy__Sequence_Ohit__bound(_840160) = c_Lazy__Sequence_Ohit__bound(_840158))], (40986 ^ _781404) ^ [_1581845, _1581847] : [c_Wellfounded_Owf(_1581845, _1581847), 40989 ^ _781404 : [(40990 ^ _781404) ^ [_1581977] : [40991 ^ _781404 : [(40992 ^ _781404) ^ [_1582082] : [hBOOL(hAPP(hAPP(c_member(_1581845), _1582082), _1581977))]], 40994 ^ _781404 : [(40997 ^ _781404) ^ [_1582204] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581845, _1581845)), hAPP(hAPP(c_Product__Type_OPair(_1581845, _1581845), _1582204), 40993 ^ [_1581845, _1581847, _1581977])), _1581847)), hBOOL(hAPP(hAPP(c_member(_1581845), _1582204), _1581977))], (40995 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1581845), 40993 ^ [_1581845, _1581847, _1581977]), _1581977)))]]]]], (39926 ^ _781404) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (42963 ^ _781404) ^ [_1636300, _1636302, _1636304, _1636306] : [-(hAPP(c_List_Oset(tc_prod(_1636300, _1636302)), hAPP(hAPP(c_List_Ozip(_1636300, _1636302), _1636304), _1636306)) = hAPP(c_Set_OCollect(tc_prod(_1636300, _1636302)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1636300, _1636302)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1636300, _1636302), 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(_1636300, _1636302)), 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(_1636300, _1636302)), 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(_1636300, _1636302), tc_fun(tc_Nat_Onat, tc_prod(_1636300, _1636302)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1636300, _1636302), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1636300, _1636302)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1636300, _1636302)), c_COMBB(tc_prod(_1636300, _1636302), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1636302, tc_prod(_1636300, _1636302)), hAPP(hAPP(c_COMBB(_1636300, tc_fun(_1636302, tc_prod(_1636300, _1636302)), tc_Nat_Onat), c_Product__Type_OPair(_1636300, _1636302)), hAPP(c_List_Onth(_1636300), _1636304))), hAPP(c_List_Onth(_1636302), _1636306)))))), 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(_1636300)), _1636304)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636302)), _1636306)))))))], (34755 ^ _781404) ^ [_1427035, _1427037, _1427039] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1427035, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1427037)), _1427039) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427035, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1427035, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1427037)), _1427039)), hAPP(_1427039, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12939 ^ _781404) ^ [_1005968, _1005970, _1005972, _1005974, _1005976, _1005978, _1005980] : [-(_1005968 = _1005970), -(c_Fun_Ofun__upd(_1005972, _1005974, c_Fun_Ofun__upd(_1005972, _1005974, _1005976, _1005968, _1005978), _1005970, _1005980) = c_Fun_Ofun__upd(_1005972, _1005974, c_Fun_Ofun__upd(_1005972, _1005974, _1005976, _1005970, _1005980), _1005968, _1005978))], (38466 ^ _781404) ^ [_1511535, _1511537] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1511535), c_Int_OInteg)), hBOOL(hAPP(_1511537, hAPP(c_Int_ORep__Integ, 38471 ^ [_1511535, _1511537]))), -(hBOOL(hAPP(_1511537, _1511535)))], (47493 ^ _781404) ^ [_1736306, _1736308, _1736310, _1736312, _1736314] : [c_List_Olist__all2(_1736306, _1736308, _1736310, hAPP(c_List_Orev(_1736306), _1736312), _1736314), -(c_List_Olist__all2(_1736306, _1736308, _1736310, _1736312, hAPP(c_List_Orev(_1736308), _1736314)))], (14667 ^ _781404) ^ [_1038553, _1038555, _1038557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1038553), _1038555)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038553), _1038557)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038553), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1038553, tc_HOL_Obool)), _1038555), _1038557))))], (36590 ^ _781404) ^ [_1465410, _1465412, _1465414, _1465416, _1465418, _1465420] : [hBOOL(hAPP(_1465410, _1465412)), hBOOL(hAPP(_1465414, _1465416)), 36597 ^ _781404 : [(36600 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1465414, hAPP(c_Product__Type_Osnd(_1465418, _1465420), hAPP(hAPP(c_Product__Type_OPair(_1465418, _1465420), _1465412), _1465416)))))], (36598 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1465410, hAPP(c_Product__Type_Ofst(_1465418, _1465420), hAPP(hAPP(c_Product__Type_OPair(_1465418, _1465420), _1465412), _1465416)))))]]], (39093 ^ _781404) ^ [_1528672, _1528674, _1528676] : [hBOOL(hAPP(_1528672, _1528674)), -(hAPP(c_Set_OCollect(_1528676), hAPP(hAPP(c_COMBS(_1528676, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1528676), c_fconj), hAPP(c_fequal, _1528674))), _1528672)) = hAPP(hAPP(c_Set_Oinsert(_1528676), _1528674), c_Orderings_Obot__class_Obot(tc_fun(_1528676, tc_HOL_Obool))))], (10929 ^ _781404) ^ [_966973, _966975, _966977] : [class_Groups_Oordered__ab__group__add(_966973), 10932 ^ _781404 : [(10939 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966973), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966973), _966975), _966977)), c_Groups_Ozero__class_Ozero(_966973))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966973), _966975), _966977)))], (10933 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966973), _966975), _966977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966973), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966973), _966975), _966977)), c_Groups_Ozero__class_Ozero(_966973))))]]], (52634 ^ _781404) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (13409 ^ _781404) ^ [_1014564, _1014566, _1014568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014564), _1014566)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014564), _1014568)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014566), _1014568))))], (44888 ^ _781404) ^ [_1679751, _1679753, _1679755, _1679757] : [class_Orderings_Olinorder(_1679751), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679751, _1679751, c_COMBI(_1679751)), _1679753), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679751, _1679751, c_COMBI(_1679751)), _1679755), _1679757)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679751, _1679751, c_COMBI(_1679751)), _1679755), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679751, _1679751, c_COMBI(_1679751)), _1679753), _1679757)))], (22229 ^ _781404) ^ [_1177631, _1177633, _1177635] : [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, _1177631)), _1177633)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1177631)), _1177635))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1177633), _1177635)))], (11083 ^ _781404) ^ [_969571, _969573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969571), _969573)), 11086 ^ _781404 : [(11093 ^ _781404) ^ [] : [_969573 = _969571, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969573), hAPP(c_Nat_OSuc, _969571))))], (11087 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969573), hAPP(c_Nat_OSuc, _969571))), -(_969573 = _969571)]]], (13295 ^ _781404) ^ [_1012374, _1012376] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012374), _1012376) = _1012374, -(_1012376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15803 ^ _781404) ^ [_1061252, _1061254, _1061256] : [class_Lattices_Olattice(_1061252), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061252), _1061254)), -(_1061256 = c_Orderings_Obot__class_Obot(tc_fun(_1061252, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1061252, tc_HOL_Obool)), _1061256), _1061254)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1061252), c_Big__Operators_Olattice__class_OSup__fin(_1061252, _1061256)), c_Big__Operators_Olattice__class_OSup__fin(_1061252, _1061254)) = c_Big__Operators_Olattice__class_OSup__fin(_1061252, _1061254))], (7215 ^ _781404) ^ [_898556, _898558, _898560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898556, tc_HOL_Obool)), _898558), _898560)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898556, tc_HOL_Obool)), _898560), _898558) = _898560)], (49372 ^ _781404) ^ [_1776887, _1776889] : [hBOOL(hAPP(hAPP(c_List_Omember(_1776887), c_List_Olist_ONil(_1776887)), _1776889))], (48156 ^ _781404) ^ [_1750826, _1750828, _1750830, _1750832] : [class_Orderings_Oorder(_1750826), class_Enum_Oenum(_1750828), 48163 ^ _781404 : [(48172 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1750828, _1750826)), _1750830), _1750832))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1750828, _1750826)), _1750830), _1750832)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1750828), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1750828), c_fNot), hAPP(hAPP(c_COMBS(_1750828, _1750826, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1750826, tc_fun(_1750826, tc_HOL_Obool), _1750828), c_fequal), _1750830)), _1750832))))], (48164 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1750828, _1750826)), _1750830), _1750832)), 48167 ^ _781404 : [(48170 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1750828), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1750828), c_fNot), hAPP(hAPP(c_COMBS(_1750828, _1750826, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1750826, tc_fun(_1750826, tc_HOL_Obool), _1750828), c_fequal), _1750830)), _1750832)))))], (48168 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1750828, _1750826)), _1750830), _1750832)))]]]]], (12995 ^ _781404) ^ [_1006864, _1006866, _1006868, _1006870] : [class_Groups_Ocancel__semigroup__add(_1006864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006864), _1006866), _1006868) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006864), _1006866), _1006870), -(_1006868 = _1006870)], (18699 ^ _781404) ^ [_1114896] : [class_Int_Onumber__ring(_1114896), -(c_Groups_Ozero__class_Ozero(_1114896) = hAPP(c_Int_Onumber__class_Onumber__of(_1114896), c_Int_OPls))], (33161 ^ _781404) ^ [_1380229, _1380231, _1380233, _1380235] : [c_Finite__Set_Ofun__left__comm__idem(_1380229, _1380231, _1380233), -(hAPP(c_Fun_Ocomp(_1380231, _1380231, _1380231, hAPP(_1380233, _1380235)), hAPP(_1380233, _1380235)) = hAPP(_1380233, _1380235))], (47283 ^ _781404) ^ [_1731755, _1731757] : [class_Orderings_Olinorder(_1731755), hBOOL(hAPP(c_Finite__Set_Ofinite(_1731755), _1731757)), 47290 ^ _781404 : [(47295 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1731755), c_List_Olinorder__class_Osorted__list__of__set(_1731755, _1731757))))], (47293 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1731755, c_List_Olinorder__class_Osorted__list__of__set(_1731755, _1731757)))], (47291 ^ _781404) ^ [] : [-(hAPP(c_List_Oset(_1731755), c_List_Olinorder__class_Osorted__list__of__set(_1731755, _1731757)) = _1731757)]]], (21831 ^ _781404) ^ [_1169659, _1169661, _1169663, _1169665] : [class_Rings_Olinordered__semiring__strict(_1169659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169659), _1169661), _1169663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169659), c_Groups_Ozero__class_Ozero(_1169659)), _1169665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169659), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169659), _1169665), _1169661)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169659), _1169665), _1169663))))], (18781 ^ _781404) ^ [_1116195, _1116197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1116195)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1116197))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116195), _1116197))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116195), c_Int_OPls)))], (17629 ^ _781404) ^ [_1095564, _1095566, _1095568, _1095570] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1095564, _1095566, _1095568), _1095570), c_Orderings_Obot__class_Obot(tc_fun(_1095564, tc_HOL_Obool))) = _1095570)], (43052 ^ _781404) ^ [_1638910, _1638912] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1638910, _1638912)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1638910, _1638912))], (12925 ^ _781404) ^ [_1005756, _1005758, _1005760, _1005762, _1005764] : [-(hAPP(c_Fun_Ofun__upd(_1005756, _1005758, _1005760, _1005762, _1005764), _1005762) = _1005764)], (1786 ^ _781404) ^ [_806769, _806771] : [-(class_Rings_Ocomm__semiring(_806769)), _806771 = _806769, class_Rings_Ocomm__semiring(_806771)], (1906 ^ _781404) ^ [_808269, _808271] : [-(class_Orderings_Oord(_808269)), _808271 = _808269, class_Orderings_Oord(_808271)], (28017 ^ _781404) ^ [_1282368, _1282370, _1282372, _1282374] : [class_Fields_Ofield__inverse__zero(_1282368), class_Int_Onumber(_1282368), 28024 ^ _781404 : [(28025 ^ _781404) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1282368), _1282370), _1282372) = hAPP(c_Int_Onumber__class_Onumber__of(_1282368), _1282374), 28028 ^ _781404 : [(28035 ^ _781404) ^ [] : [_1282372 = c_Groups_Ozero__class_Ozero(_1282368), -(hAPP(c_Int_Onumber__class_Onumber__of(_1282368), _1282374) = c_Groups_Ozero__class_Ozero(_1282368))], (28029 ^ _781404) ^ [] : [-(_1282372 = c_Groups_Ozero__class_Ozero(_1282368)), -(_1282370 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282368), hAPP(c_Int_Onumber__class_Onumber__of(_1282368), _1282374)), _1282372))]]], (28041 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1282368), _1282370), _1282372) = hAPP(c_Int_Onumber__class_Onumber__of(_1282368), _1282374)), 28044 ^ _781404 : [(28047 ^ _781404) ^ [] : [_1282370 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282368), hAPP(c_Int_Onumber__class_Onumber__of(_1282368), _1282374)), _1282372)], (28045 ^ _781404) ^ [] : [_1282372 = c_Groups_Ozero__class_Ozero(_1282368)]], 28048 ^ _781404 : [(28051 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1282368), _1282374) = c_Groups_Ozero__class_Ozero(_1282368)], (28049 ^ _781404) ^ [] : [-(_1282372 = c_Groups_Ozero__class_Ozero(_1282368))]]]]], (7565 ^ _781404) ^ [_905317, _905319] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905317, tc_HOL_Obool)), _905319), _905319) = _905319)], (11949 ^ _781404) ^ [_986177, _986179, _986181] : [_986177 = c_Orderings_Obot__class_Obot(tc_fun(_986179, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_986179), _986181), _986177))], (39802 ^ _781404) ^ [_1555200, _1555202, _1555204] : [c_Wellfounded_Owf(_1555200, _1555202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555200, _1555200), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1555200, _1555200, _1555200), _1555202), _1555204)), _1555202)), -(c_FunDef_Oreduction__pair(_1555200, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1555200, _1555200), tc_HOL_Obool), tc_fun(tc_prod(_1555200, _1555200), tc_HOL_Obool)), _1555202), _1555204)))], (34181 ^ _781404) ^ [_1410966, _1410968, _1410970, _1410972, _1410974] : [hBOOL(hAPP(hAPP(c_member(_1410966), _1410968), _1410970)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410972, tc_HOL_Obool)), hAPP(_1410974, _1410968)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410966, tc_fun(_1410972, tc_HOL_Obool)), _1410970), _1410974)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410966, tc_fun(_1410972, tc_HOL_Obool)), _1410970), _1410974))], (41185 ^ _781404) ^ [_1587478, _1587480] : [-(hAPP(c_Relation_ORange(_1587478, _1587478), c_Transitive__Closure_Ortrancl(_1587478, _1587480)) = c_Orderings_Otop__class_Otop(tc_fun(_1587478, tc_HOL_Obool)))], (40437 ^ _781404) ^ [_1569275, _1569277] : [40439 ^ _781404 : [(40442 ^ _781404) ^ [] : [40438 ^ [_1569275, _1569277] = c_Orderings_Obot__class_Obot(tc_fun(_1569275, tc_HOL_Obool))], (40440 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1569275, tc_HOL_Obool)), 40438 ^ [_1569275, _1569277]), hAPP(c_Relation_OImage(_1569275, _1569275, _1569277), 40438 ^ [_1569275, _1569277]))))]], -(c_Wellfounded_Owf(_1569275, _1569277))], (10423 ^ _781404) ^ [_958781, _958783, _958785] : [class_Groups_Oordered__ab__group__add(_958781), 10426 ^ _781404 : [(10433 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958781), hAPP(c_Groups_Ouminus__class_Ouminus(_958781), _958785)), _958783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958781), hAPP(c_Groups_Ouminus__class_Ouminus(_958781), _958783)), _958785)))], (10427 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958781), hAPP(c_Groups_Ouminus__class_Ouminus(_958781), _958783)), _958785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958781), hAPP(c_Groups_Ouminus__class_Ouminus(_958781), _958785)), _958783)))]]], (27121 ^ _781404) ^ [_1265607, _1265609, _1265611] : [class_Groups_Oordered__ab__group__add__abs(_1265607), 27124 ^ _781404 : [(27133 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265607), hAPP(c_Groups_Oabs__class_Oabs(_1265607), _1265609)), _1265611))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265607), _1265609), _1265611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265607), hAPP(c_Groups_Ouminus__class_Ouminus(_1265607), _1265609)), _1265611))], (27125 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265607), hAPP(c_Groups_Oabs__class_Oabs(_1265607), _1265609)), _1265611)), 27128 ^ _781404 : [(27131 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265607), hAPP(c_Groups_Ouminus__class_Ouminus(_1265607), _1265609)), _1265611)))], (27129 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265607), _1265609), _1265611)))]]]]], (21295 ^ _781404) ^ [_1159817, _1159819, _1159821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159817), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159817)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159819)), _1159821)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43599 ^ _781404) ^ [_1650357, _1650359, _1650361, _1650363] : [hAPP(hAPP(c_List_Olist__update(_1650357, _1650359), _1650361), _1650363) = c_List_Olist_ONil(_1650357), -(_1650359 = c_List_Olist_ONil(_1650357))], (22371 ^ _781404) ^ [_1180329, _1180331, _1180333, _1180335, _1180337] : [class_Rings_Olinordered__semiring__strict(_1180329), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180329), _1180331), _1180333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180329), _1180335), _1180337)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180329), c_Groups_Ozero__class_Ozero(_1180329)), _1180331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180329), c_Groups_Ozero__class_Ozero(_1180329)), _1180335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180329), _1180331), _1180335)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180329), _1180333), _1180337))))], (24794 ^ _781404) ^ [_1225960] : [24795 ^ _781404 : [(24796 ^ _781404) ^ [_1226017] : [hBOOL(hAPP(_1225960, _1226017))]], 24798 ^ _781404 : [(24801 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1225960, hAPP(c_Int_Onat, 24797 ^ [_1225960]))))], (24799 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24797 ^ [_1225960])))]]], (49941 ^ _781404) ^ [_1791060, _1791062] : [-(c_Equiv__Relations_Oequivp(_1791060, _1791062)), c_Predicate_Oreflp(_1791060, _1791062), c_Predicate_Osymp(_1791060, _1791062), c_Predicate_Otransp(_1791060, _1791062)], (24913 ^ _781404) ^ [_1227815, _1227817] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227815), _1227817)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1227815)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1227817)))], (34591 ^ _781404) ^ [_1422946, _1422948, _1422950] : [class_Groups_Ocomm__monoid__add(_1422946), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1422946), _1422948), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1422950))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1422946), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1422946), _1422948), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1422950))), hAPP(_1422948, hAPP(c_Nat_OSuc, _1422950))))], (45335 ^ _781404) ^ [_1689288, _1689290, _1689292, _1689294, _1689296] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1689288), tc_List_Olist(_1689290), tc_List_Olist(_1689292), hAPP(c_List_Omap(_1689288, _1689290), _1689294)), hAPP(c_List_Omap(_1689292, _1689288), _1689296)) = hAPP(c_List_Omap(_1689292, _1689290), hAPP(c_Fun_Ocomp(_1689288, _1689290, _1689292, _1689294), _1689296)))], (5156 ^ _781404) ^ [_860072, _860074, _860076, _860078] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_860078, _860074) = c_SetInterval_Oord__class_OatLeastLessThan(_860076, _860072)), _860078 = _860076, _860074 = _860072], (43176 ^ _781404) ^ [_1641556, _1641558, _1641560, _1641562, _1641564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1641556, tc_HOL_Obool)), hAPP(c_List_Oset(_1641556), _1641558)), _1641560)), hBOOL(hAPP(hAPP(c_member(_1641556), _1641562), _1641560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1641556, tc_HOL_Obool)), hAPP(c_List_Oset(_1641556), hAPP(hAPP(c_List_Olist__update(_1641556, _1641558), _1641564), _1641562))), _1641560)))], (1396 ^ _781404) ^ [_801894, _801896] : [-(class_Rings_Oidom(_801894)), _801896 = _801894, class_Rings_Oidom(_801896)], (38892 ^ _781404) ^ [_1523687, _1523689, _1523691, _1523693, _1523695, _1523697] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1523687, _1523689), _1523689, tc_prod(_1523691, _1523693), c_Product__Type_Osnd(_1523687, _1523689)), c_Product__Type_Omap__pair(_1523691, _1523687, _1523693, _1523689, _1523695, _1523697)) = hAPP(c_Fun_Ocomp(_1523693, _1523689, tc_prod(_1523691, _1523693), _1523697), c_Product__Type_Osnd(_1523691, _1523693)))], (48569 ^ _781404) ^ [_1759939, _1759941, _1759943] : [-(c_List_Olist__ex(_1759939, _1759941, _1759943)), 48570 ^ _781404 : [(48571 ^ _781404) ^ [_1759996] : [hBOOL(hAPP(hAPP(c_member(_1759939), _1759996), hAPP(c_List_Oset(_1759939), _1759943))), hBOOL(hAPP(_1759941, _1759996))]]], (51426 ^ _781404) ^ [_1823041, _1823043, _1823045] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1823041), _1823043)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1823041), _1823045))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1823041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1823043), _1823045)))], (40198 ^ _781404) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (25593 ^ _781404) ^ [_1238647, _1238649] : [-(hBOOL(hAPP(_1238647, hAPP(c_Int_Onat, _1238649)))), 25597 ^ _781404 : [(25600 ^ _781404) ^ [] : [hBOOL(hAPP(_1238647, 25596 ^ [_1238647, _1238649]))], (25598 ^ _781404) ^ [] : [-(_1238649 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 25596 ^ [_1238647, _1238649]))]], 25601 ^ _781404 : [(25604 ^ _781404) ^ [] : [hBOOL(hAPP(_1238647, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25602 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238649), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (8538 ^ _781404) ^ [_925435, _925437] : [class_Lattices_Obounded__lattice__bot(_925435), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925435), _925437), c_Orderings_Obot__class_Obot(_925435)) = _925437)], (25839 ^ _781404) ^ [_1243217, _1243219] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1243217)))), _1243219) = 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)))), _1243217)), _1243219))], (52434 ^ _781404) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (10109 ^ _781404) ^ [_953719, _953721, _953723] : [class_Orderings_Oorder(_953719), -(_953721 = _953723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953719), _953721), _953723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953719), _953721), _953723)))], (20177 ^ _781404) ^ [_1139672, _1139674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1139672)), c_Int_OBit1(_1139674))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1139672), _1139674)))], (25089 ^ _781404) ^ [_1230490, _1230492, _1230494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1230490)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1230490), _1230492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1230494), _1230492)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1230494), _1230490))))], (16943 ^ _781404) ^ [_1083008, _1083010] : [class_Rings_Olinordered__idom(_1083008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083008), c_Groups_Ozero__class_Ozero(_1083008)), _1083010)), -(c_Groups_Osgn__class_Osgn(_1083008, _1083010) = c_Groups_Oone__class_Oone(_1083008))], (29565 ^ _781404) ^ [_1310816, _1310818, _1310820, _1310822] : [class_Fields_Ofield__inverse__zero(_1310816), -(_1310818 = c_Groups_Ozero__class_Ozero(_1310816)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1310816), _1310820), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310816), _1310822), _1310818)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1310816), _1310822), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1310816), _1310820), _1310818))), _1310818))], (47883 ^ _781404) ^ [_1744406, _1744408, _1744410, _1744412, _1744414] : [hBOOL(hAPP(hAPP(c_member(_1744406), _1744408), hAPP(c_List_Oset(_1744406), _1744410))), -(hBOOL(hAPP(_1744412, _1744408))), -(c_List_OdropWhile(_1744406, _1744412, hAPP(hAPP(c_List_Oappend(_1744406), _1744410), _1744414)) = hAPP(hAPP(c_List_Oappend(_1744406), c_List_OdropWhile(_1744406, _1744412, _1744410)), _1744414))], (12484 ^ _781404) ^ [_996747, _996749] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_996747, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_996747, tc_HOL_Obool))), hAPP(c_Set_OPow(_996747), _996749))))], (52344 ^ _781404) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (20219 ^ _781404) ^ [_1140388, _1140390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140388), _1140390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1140388)), c_Int_OBit0(_1140390))))], (36530 ^ _781404) ^ [_1464166, _1464168, _1464170, _1464172, _1464174] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1464166, _1464168, _1464170), _1464172), _1464174) = hAPP(hAPP(_1464172, hAPP(c_Product__Type_Ofst(_1464166, _1464168), _1464174)), hAPP(c_Product__Type_Osnd(_1464166, _1464168), _1464174)))], (706 ^ _781404) ^ [_792041, _792043, _792045, _792047] : [-(c_FunDef_Ois__measure(_792045, _792041)), c_FunDef_Ois__measure(_792047, _792043), _792047 = _792045, _792043 = _792041], (18897 ^ _781404) ^ [_1118033, _1118035] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118033), c_Int_OPls))), 18900 ^ _781404 : [(18907 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118035), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118033)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118035)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1118033), _1118035)))], (18901 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118035), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118033)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118035)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1118033))]]], (45002 ^ _781404) ^ [_1681891, _1681893, _1681895, _1681897, _1681899] : [class_Orderings_Olinorder(_1681891), hBOOL(hAPP(hAPP(c_member(_1681891), hAPP(_1681893, _1681895)), hAPP(c_Set_Oimage(_1681897, _1681891, _1681893), hAPP(c_List_Oset(_1681897), _1681899)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1681897, _1681891, _1681893, _1681895, _1681899) = _1681899)], (8283 ^ _781404) ^ [_920969, _920971, _920973] : [c_Orderings_Obot__class_Obot(tc_fun(_920969, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_920969), _920971), _920973)], (7377 ^ _781404) ^ [_901696, _901698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _901696), hAPP(c_Nat_OSuc, _901698))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _901696, hAPP(c_Nat_OSuc, _901698)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _901698)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _901696, _901698)))], (26423 ^ _781404) ^ [_1252440, _1252442, _1252444] : [class_Rings_Olinordered__idom(_1252440), 26426 ^ _781404 : [(26433 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252442), _1252444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252440), hAPP(c_Int_Oring__1__class_Oof__int(_1252440), _1252442)), hAPP(c_Int_Oring__1__class_Oof__int(_1252440), _1252444))))], (26427 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252440), hAPP(c_Int_Oring__1__class_Oof__int(_1252440), _1252442)), hAPP(c_Int_Oring__1__class_Oof__int(_1252440), _1252444))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252442), _1252444)))]]], (40479 ^ _781404) ^ [_1570025, _1570027] : [40480 ^ _781404 : [(40481 ^ _781404) ^ [_1570071] : [hBOOL(hAPP(_1570025, _1570071))]], -(hBOOL(hAPP(_1570025, c_Hilbert__Choice_OEps(_1570027, _1570025))))], (23019 ^ _781404) ^ [_1193378, _1193380, _1193382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193378)), _1193378 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193378), _1193382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193380), _1193378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1193382)))], (7241 ^ _781404) ^ [_899104, _899106, _899108] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899104, tc_HOL_Obool)), _899106), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899104, tc_HOL_Obool)), _899106), _899108))))], (74 ^ _781404) ^ [_782471, _782473, _782475, _782477, _782479, _782481] : [-(c_Finite__Set_Ofolding__one__idem(_782479, _782475, _782471)), c_Finite__Set_Ofolding__one__idem(_782481, _782477, _782473), _782481 = _782479, _782477 = _782475, _782473 = _782471], (43661 ^ _781404) ^ [_1651430, _1651432, _1651434] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651430), tc_List_Olist(_1651430))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651430), tc_List_Olist(_1651430)), c_List_Olist_ONil(_1651430)), _1651432)), c_List_Olistrel1(_1651430, _1651434)))], (22499 ^ _781404) ^ [_1182783, _1182785, _1182787] : [class_Rings_Olinordered__ring__strict(_1182783), 22502 ^ _781404 : [(22511 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182783), _1182785), _1182785)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182783), _1182787), _1182787))), c_Groups_Ozero__class_Ozero(_1182783)))), _1182785 = c_Groups_Ozero__class_Ozero(_1182783), _1182787 = c_Groups_Ozero__class_Ozero(_1182783)], (22503 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182783), _1182785), _1182785)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182783), _1182787), _1182787))), c_Groups_Ozero__class_Ozero(_1182783))), 22506 ^ _781404 : [(22509 ^ _781404) ^ [] : [-(_1182787 = c_Groups_Ozero__class_Ozero(_1182783))], (22507 ^ _781404) ^ [] : [-(_1182785 = c_Groups_Ozero__class_Ozero(_1182783))]]]]], (2662 ^ _781404) ^ [_820681, _820683] : [_820683 = _820681, -(c_Equiv__Relations_Oquotient(_820683) = c_Equiv__Relations_Oquotient(_820681))], (14422 ^ _781404) ^ [_1033762, _1033764, _1033766, _1033768, _1033770] : [class_Groups_Oab__group__add(_1033762), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033764), _1033766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033764, tc_HOL_Obool)), _1033768), _1033766)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1033764, _1033762), _1033770), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1033764, tc_HOL_Obool)), _1033766), _1033768)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033762), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1033764, _1033762), _1033770), _1033766)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1033764, _1033762), _1033770), _1033768)))], (46806 ^ _781404) ^ [_1722993, _1722995, _1722997] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1722993), c_List_Oupt(_1722995, _1722997)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1722995), _1722993), _1722997))], (21267 ^ _781404) ^ [_1159344] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1159344) = _1159344)], (33281 ^ _781404) ^ [_1383391, _1383393, _1383395, _1383397, _1383399] : [_1383391 = c_Orderings_Obot__class_Obot(tc_fun(_1383393, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1383395), _1383397), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383393, tc_fun(_1383395, tc_HOL_Obool)), _1383391), _1383399)) = hAPP(hAPP(c_Set_Oinsert(_1383395), _1383397), c_Orderings_Obot__class_Obot(tc_fun(_1383395, tc_HOL_Obool))))], (22937 ^ _781404) ^ [_1191534, _1191536] : [class_Int_Onumber__ring(_1191534), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191534), hAPP(c_Int_Onumber__class_Onumber__of(_1191534), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1191536) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1191534), _1191536), _1191536))], (39508 ^ _781404) ^ [_1545787, _1545789, _1545791, _1545793, _1545795, _1545797, _1545799] : [hAPP(c_Fun_Ocomp(_1545787, _1545789, _1545791, _1545793), _1545795) = hAPP(c_Fun_Ocomp(_1545789, _1545789, _1545791, c_Fun_Oid(_1545789)), _1545797), -(hAPP(_1545793, hAPP(_1545795, _1545799)) = hAPP(_1545797, _1545799))], (43535 ^ _781404) ^ [_1649218, _1649220] : [-(hAPP(hAPP(c_List_Otake(_1649218), _1649220), c_List_Olist_ONil(_1649218)) = c_List_Olist_ONil(_1649218))], (48066 ^ _781404) ^ [_1748243, _1748245] : [-(c_List_Oinsert(_1748243, _1748245, c_List_Olist_ONil(_1748243)) = hAPP(hAPP(c_List_Olist_OCons(_1748243), _1748245), c_List_Olist_ONil(_1748243)))], (20395 ^ _781404) ^ [_1143317] : [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), _1143317))), 20398 ^ _781404 : [(20401 ^ _781404) ^ [] : [-(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(_1143317)))))], (20399 ^ _781404) ^ [] : [-(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(_1143317)))))]]], (26801 ^ _781404) ^ [_1259587, _1259589, _1259591, _1259593, _1259595] : [class_Groups_Ocomm__monoid__mult(_1259587), hBOOL(hAPP(c_Finite__Set_Ofinite(_1259589), _1259591)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1259589), _1259593)), 26815 ^ _781404 : [(26818 ^ _781404) ^ [] : [hAPP(_1259595, 26814 ^ [_1259587, _1259589, _1259591, _1259593, _1259595]) = c_Groups_Oone__class_Oone(_1259587)], (26816 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1259589), 26814 ^ [_1259587, _1259589, _1259591, _1259593, _1259595]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1259589, tc_HOL_Obool)), _1259591), _1259593))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1259587, _1259589, c_Groups_Otimes__class_Otimes(_1259587)), _1259595), c_Groups_Oone__class_Oone(_1259587)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259589, tc_HOL_Obool)), _1259591), _1259593)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1259587), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1259587, _1259589, c_Groups_Otimes__class_Otimes(_1259587)), _1259595), c_Groups_Oone__class_Oone(_1259587)), _1259591)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1259587, _1259589, c_Groups_Otimes__class_Otimes(_1259587)), _1259595), c_Groups_Oone__class_Oone(_1259587)), _1259593)))], (8810 ^ _781404) ^ [_930104] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _930104) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _930104))], (33504 ^ _781404) ^ [_1390838, _1390840, _1390842, _1390844] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390838, tc_fun(_1390840, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1390838, tc_HOL_Obool), _1390842)), _1390844) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1390838, tc_HOL_Obool), tc_fun(_1390840, tc_HOL_Obool)), _1390842), hAPP(hAPP(c_COMBC(tc_fun(_1390838, tc_HOL_Obool), tc_fun(_1390838, tc_fun(_1390840, tc_HOL_Obool)), tc_fun(_1390840, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390838, tc_fun(_1390840, tc_HOL_Obool))), _1390844)))], (10255 ^ _781404) ^ [_955796, _955798, _955800] : [class_Orderings_Olinorder(_955796), 10258 ^ _781404 : [(10265 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955796), _955800), _955798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955796), _955798), _955800))], (10259 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955796), _955798), _955800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955796), _955800), _955798)))]]], (51311 ^ _781404) ^ [_1818789, _1818791, _1818793, _1818795, _1818797, _1818799, _1818801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1818789, _1818791), tc_prod(_1818789, _1818791))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1818789, _1818791), tc_prod(_1818789, _1818791)), hAPP(hAPP(c_Product__Type_OPair(_1818789, _1818791), _1818793), _1818795)), hAPP(hAPP(c_Product__Type_OPair(_1818789, _1818791), _1818797), _1818799))), c_Transitive__Closure_Ortrancl(tc_prod(_1818789, _1818791), _1818801))), -(hAPP(hAPP(c_Product__Type_OPair(_1818789, _1818791), _1818793), _1818795) = hAPP(hAPP(c_Product__Type_OPair(_1818789, _1818791), _1818797), _1818799)), 51320 ^ _781404 : [(51323 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1818789, _1818791), tc_prod(_1818789, _1818791))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1818789, _1818791), tc_prod(_1818789, _1818791)), hAPP(hAPP(c_Product__Type_OPair(_1818789, _1818791), 51318 ^ [_1818789, _1818791, _1818793, _1818795, _1818797, _1818799, _1818801]), 51319 ^ [_1818789, _1818791, _1818793, _1818795, _1818797, _1818799, _1818801])), hAPP(hAPP(c_Product__Type_OPair(_1818789, _1818791), _1818797), _1818799))), c_Transitive__Closure_Ortrancl(tc_prod(_1818789, _1818791), _1818801))))], (51321 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1818789, _1818791), tc_prod(_1818789, _1818791))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1818789, _1818791), tc_prod(_1818789, _1818791)), hAPP(hAPP(c_Product__Type_OPair(_1818789, _1818791), _1818793), _1818795)), hAPP(hAPP(c_Product__Type_OPair(_1818789, _1818791), 51318 ^ [_1818789, _1818791, _1818793, _1818795, _1818797, _1818799, _1818801]), 51319 ^ [_1818789, _1818791, _1818793, _1818795, _1818797, _1818799, _1818801]))), _1818801)))]]], (36794 ^ _781404) ^ [_1470058, _1470060, _1470062] : [class_Orderings_Owellorder(_1470058), hBOOL(hAPP(_1470060, _1470062)), -(hBOOL(hAPP(_1470060, c_Orderings_Oord__class_OLeast(_1470058, _1470060))))], (20045 ^ _781404) ^ [_1137424, _1137426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137424), _1137426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1137424)), c_Int_OBit0(_1137426))))], (20377 ^ _781404) ^ [_1143079] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143079))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143079) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8990 ^ _781404) ^ [_933734, _933736, _933738, _933740] : [class_Orderings_Oorder(_933734), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933734, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_933734, _933736, _933738)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_933734, _933738), _933740)) = c_Orderings_Obot__class_Obot(tc_fun(_933734, tc_HOL_Obool)))], (8200 ^ _781404) ^ [_919170, _919172, _919174] : [8202 ^ _781404 : [(8205 ^ _781404) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919170, tc_HOL_Obool)), 8201 ^ [_919170, _919172, _919174]), _919174) = c_Orderings_Obot__class_Obot(tc_fun(_919170, tc_HOL_Obool))], (8203 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_919170, tc_HOL_Obool)), 8201 ^ [_919170, _919172, _919174]), _919172)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919170, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_919170, tc_HOL_Obool), _919172)), _919174) = c_Orderings_Obot__class_Obot(tc_fun(_919170, tc_HOL_Obool)))], (14336 ^ _781404) ^ [_1031999, _1032001, _1032003, _1032005, _1032007] : [class_Groups_Ocomm__monoid__add(_1031999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032001), _1032003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032003), _1032005)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031999), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1031999), _1032007), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1032001), _1032003))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1031999), _1032007), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1032003), _1032005))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1031999), _1032007), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1032001), _1032005)))], (16569 ^ _781404) ^ [_1076130, _1076132, _1076134] : [class_Lattices_Olattice(_1076130), hAPP(_1076132, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076130), 16574 ^ [_1076130, _1076132, _1076134]), 16575 ^ [_1076130, _1076132, _1076134])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076130), hAPP(_1076132, 16574 ^ [_1076130, _1076132, _1076134])), hAPP(_1076132, 16575 ^ [_1076130, _1076132, _1076134])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076130), _1076134)), -(_1076134 = c_Orderings_Obot__class_Obot(tc_fun(_1076130, tc_HOL_Obool))), -(hAPP(_1076132, c_Big__Operators_Olattice__class_OInf__fin(_1076130, _1076134)) = c_Big__Operators_Olattice__class_OInf__fin(_1076130, hAPP(c_Set_Oimage(_1076130, _1076130, _1076132), _1076134)))], (18161 ^ _781404) ^ [_1104985, _1104987, _1104989, _1104991] : [class_Rings_Olinordered__semidom(_1104985), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104985), hAPP(hAPP(c_Power_Opower__class_Opower(_1104985), _1104987), hAPP(c_Nat_OSuc, _1104989))), hAPP(hAPP(c_Power_Opower__class_Opower(_1104985), _1104991), hAPP(c_Nat_OSuc, _1104989)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104985), c_Groups_Ozero__class_Ozero(_1104985)), _1104991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104985), _1104987), _1104991)))], (31290 ^ _781404) ^ [_1344356, _1344358] : [class_Orderings_Olinorder(_1344356), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344356), _1344358)), -(c_Big__Operators_Olinorder__class_OMin(_1344356, _1344358) = hAPP(c_Finite__Set_Ofold1(_1344356, c_Orderings_Oord__class_Omin(_1344356)), _1344358))], (3714 ^ _781404) ^ [_837095, _837097, _837099, _837101] : [-(c_List_Obutlast(_837101, _837097) = c_List_Obutlast(_837099, _837095)), _837101 = _837099, _837097 = _837095], (14873 ^ _781404) ^ [_1042536, _1042538, _1042540, _1042542, _1042544, _1042546, _1042548, _1042550] : [c_Finite__Set_Ofolding__image__simple(_1042536, _1042538, _1042540, _1042542, _1042544, _1042546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042538), _1042548)), hBOOL(hAPP(hAPP(c_member(_1042538), _1042550), _1042548)), -(hAPP(_1042546, _1042548) = hAPP(hAPP(_1042540, hAPP(_1042544, _1042550)), hAPP(_1042546, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042538, tc_HOL_Obool)), _1042548), hAPP(hAPP(c_Set_Oinsert(_1042538), _1042550), c_Orderings_Obot__class_Obot(tc_fun(_1042538, tc_HOL_Obool)))))))], (31124 ^ _781404) ^ [_1341048, _1341050, _1341052] : [class_Orderings_Olinorder(_1341048), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341048), _1341050)), hBOOL(hAPP(hAPP(c_member(_1341048), _1341052), _1341050)), 31135 ^ _781404 : [(31142 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341048, tc_HOL_Obool)), _1341050), hAPP(hAPP(c_Set_Oinsert(_1341048), _1341052), c_Orderings_Obot__class_Obot(tc_fun(_1341048, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1341048, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1341048, _1341050) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1341048), _1341052), c_Big__Operators_Olinorder__class_OMin(_1341048, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341048, tc_HOL_Obool)), _1341050), hAPP(hAPP(c_Set_Oinsert(_1341048), _1341052), c_Orderings_Obot__class_Obot(tc_fun(_1341048, tc_HOL_Obool)))))))], (31136 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1341048, tc_HOL_Obool)), _1341050), hAPP(hAPP(c_Set_Oinsert(_1341048), _1341052), c_Orderings_Obot__class_Obot(tc_fun(_1341048, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1341048, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1341048, _1341050) = _1341052)]]], (27761 ^ _781404) ^ [_1277989, _1277991] : [class_Fields_Olinordered__field__inverse__zero(_1277989), class_Int_Onumber__ring(_1277989), 27768 ^ _781404 : [(27775 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277989), c_Groups_Ozero__class_Ozero(_1277989)), _1277991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277989), c_Groups_Ozero__class_Ozero(_1277989)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277989), _1277991), hAPP(c_Int_Onumber__class_Onumber__of(_1277989), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (27769 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277989), c_Groups_Ozero__class_Ozero(_1277989)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277989), _1277991), hAPP(c_Int_Onumber__class_Onumber__of(_1277989), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277989), c_Groups_Ozero__class_Ozero(_1277989)), _1277991)))]]], (24644 ^ _781404) ^ [_1223456, _1223458] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223456), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223458), _1223456)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223458), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223458, _1223456)))], (51828 ^ _781404) ^ [_1830637, _1830639] : [_1830637 = _1830639, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830637, _1830639) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1830637), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (28227 ^ _781404) ^ [_1285900, _1285902, _1285904, _1285906] : [class_Fields_Olinordered__field__inverse__zero(_1285900), class_Int_Onumber(_1285900), 28234 ^ _781404 : [(28235 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), hAPP(c_Int_Onumber__class_Onumber__of(_1285900), _1285902)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285900), _1285904), _1285906))), 28238 ^ _781404 : [(28245 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), c_Groups_Ozero__class_Ozero(_1285900)), _1285906))), 28248 ^ _781404 : [(28255 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), _1285906), c_Groups_Ozero__class_Ozero(_1285900)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), hAPP(c_Int_Onumber__class_Onumber__of(_1285900), _1285902)), c_Groups_Ozero__class_Ozero(_1285900))))], (28249 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), _1285906), c_Groups_Ozero__class_Ozero(_1285900))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), _1285904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285900), hAPP(c_Int_Onumber__class_Onumber__of(_1285900), _1285902)), _1285906))))]]], (28239 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), c_Groups_Ozero__class_Ozero(_1285900)), _1285906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285900), hAPP(c_Int_Onumber__class_Onumber__of(_1285900), _1285902)), _1285906)), _1285904)))]]], (28261 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), hAPP(c_Int_Onumber__class_Onumber__of(_1285900), _1285902)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285900), _1285904), _1285906)))), 28264 ^ _781404 : [(28267 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285900), hAPP(c_Int_Onumber__class_Onumber__of(_1285900), _1285902)), _1285906)), _1285904))], (28265 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), c_Groups_Ozero__class_Ozero(_1285900)), _1285906)))]], 28268 ^ _781404 : [(28271 ^ _781404) ^ [] : [28272 ^ _781404 : [(28275 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), _1285904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285900), hAPP(c_Int_Onumber__class_Onumber__of(_1285900), _1285902)), _1285906)))], (28273 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), _1285906), c_Groups_Ozero__class_Ozero(_1285900))))]], 28276 ^ _781404 : [(28279 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), hAPP(c_Int_Onumber__class_Onumber__of(_1285900), _1285902)), c_Groups_Ozero__class_Ozero(_1285900)))], (28277 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), _1285906), c_Groups_Ozero__class_Ozero(_1285900)))]]], (28269 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285900), c_Groups_Ozero__class_Ozero(_1285900)), _1285906))]]]]], (47893 ^ _781404) ^ [_1744604, _1744606, _1744608, _1744610, _1744612] : [c_List_OdropWhile(_1744604, _1744606, _1744608) = hAPP(hAPP(c_List_Olist_OCons(_1744604), _1744610), _1744612), 47896 ^ _781404 : [(47899 ^ _781404) ^ [] : [hBOOL(hAPP(_1744606, _1744610))], (47897 ^ _781404) ^ [] : [-(_1744608 = hAPP(hAPP(c_List_Oappend(_1744604), c_List_OtakeWhile(_1744604, _1744606, _1744608)), hAPP(hAPP(c_List_Olist_OCons(_1744604), _1744610), _1744612)))]]], (26113 ^ _781404) ^ [_1247829, _1247831] : [_1247829 = _1247831, -(c_Code__Numeral_OSuc__code__numeral(_1247829) = c_Code__Numeral_OSuc__code__numeral(_1247831))], (46223 ^ _781404) ^ [_1709125, _1709127, _1709129] : [hBOOL(hAPP(c_List_Odistinct(_1709125), _1709127)), -(hBOOL(hAPP(c_List_Odistinct(_1709125), hAPP(c_List_OremoveAll(_1709125, _1709129), _1709127))))], (48985 ^ _781404) ^ [_1768503, _1768505, _1768507] : [-(c_Predicate_Oconversep(_1768503, _1768505, c_Predicate_Oconversep(_1768505, _1768503, _1768507)) = _1768507)], (846 ^ _781404) ^ [_794125, _794127, _794129, _794131, _794133, _794135, _794137, _794139] : [-(c_Wellfounded_Omax__extp(_794137, _794133, _794129, _794125)), c_Wellfounded_Omax__extp(_794139, _794135, _794131, _794127), _794139 = _794137, _794135 = _794133, _794131 = _794129, _794127 = _794125], (44359 ^ _781404) ^ [_1668003, _1668005, _1668007, _1668009] : [-(hAPP(hAPP(c_List_Otake(_1668003), _1668005), hAPP(hAPP(c_List_Odrop(_1668003), _1668007), _1668009)) = hAPP(hAPP(c_List_Odrop(_1668003), _1668007), hAPP(hAPP(c_List_Otake(_1668003), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1668005), _1668007)), _1668009)))], (19079 ^ _781404) ^ [_1120918, _1120920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120918), _1120920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1120918)), c_Int_OBit1(_1120920))))], (6655 ^ _781404) ^ [_887828, _887830] : [class_Orderings_Olinorder(_887828), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_887828, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_887828), _887830)) = hAPP(c_SetInterval_Oord__class_OatLeast(_887828), _887830))], (52544 ^ _781404) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (46169 ^ _781404) ^ [_1707886, _1707888, _1707890, _1707892, _1707894] : [46171 ^ _781404 : [(46174 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1707886, _1707888, tc_HOL_Obool), _1707894), 46170 ^ [_1707886, _1707888, _1707890, _1707892, _1707894]))], (46172 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1707886, _1707888)), 46170 ^ [_1707886, _1707888, _1707890, _1707892, _1707894]), hAPP(c_List_Oset(tc_prod(_1707886, _1707888)), hAPP(hAPP(c_List_Ozip(_1707886, _1707888), _1707890), _1707892)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707886)), _1707890) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707888)), _1707892), -(c_List_Olist__all2(_1707886, _1707888, _1707894, _1707890, _1707892))], (47254 ^ _781404) ^ [_1731229, _1731231, _1731233] : [class_Orderings_Olinorder(_1731229), 47257 ^ _781404 : [(47270 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1731229, hAPP(hAPP(c_List_Olist_OCons(_1731229), _1731231), _1731233))), 47274 ^ _781404 : [(47277 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1731229), _1731231), 47273 ^ [_1731229, _1731231, _1731233]))], (47275 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1731229), 47273 ^ [_1731229, _1731231, _1731233]), hAPP(c_List_Oset(_1731229), _1731233))))]], c_List_Olinorder__class_Osorted(_1731229, _1731233)], (47258 ^ _781404) ^ [] : [c_List_Olinorder__class_Osorted(_1731229, hAPP(hAPP(c_List_Olist_OCons(_1731229), _1731231), _1731233)), 47261 ^ _781404 : [(47262 ^ _781404) ^ [_1731397] : [hBOOL(hAPP(hAPP(c_member(_1731229), _1731397), hAPP(c_List_Oset(_1731229), _1731233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1731229), _1731231), _1731397)))], (47268 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1731229, _1731233))]]]]], (40750 ^ _781404) ^ [_1575997, _1575999, _1576001, _1576003] : [c_Orderings_Oorder__class_Omono(tc_fun(_1575997, tc_HOL_Obool), tc_fun(_1575997, tc_HOL_Obool), _1575999), hBOOL(hAPP(hAPP(c_member(_1575997), _1576001), _1576003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575997, tc_HOL_Obool)), _1576003), hAPP(_1575999, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1575997, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1575997, tc_HOL_Obool), tc_fun(_1575997, tc_HOL_Obool), tc_fun(_1575997, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575997, tc_HOL_Obool), tc_fun(tc_fun(_1575997, tc_HOL_Obool), tc_fun(_1575997, tc_HOL_Obool)), tc_fun(_1575997, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1575997, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1575997, tc_HOL_Obool), tc_fun(_1575997, tc_HOL_Obool), tc_fun(_1575997, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575997, tc_HOL_Obool), tc_fun(tc_fun(_1575997, tc_HOL_Obool), tc_fun(_1575997, tc_HOL_Obool)), tc_fun(_1575997, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1575997, tc_HOL_Obool))), _1575999)), _1576003))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1575997, tc_HOL_Obool), _1575999)))))), -(hBOOL(hAPP(hAPP(c_member(_1575997), _1576001), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1575997, tc_HOL_Obool), _1575999))))], (40335 ^ _781404) ^ [_1567074, _1567076] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1567074, _1567074)), _1567076)), c_Wellfounded_Oacyclic(_1567074, _1567076), -(c_Wellfounded_Owf(_1567074, _1567076))], (46854 ^ _781404) ^ [_1723871, _1723873] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1723871, _1723873)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1723871), hAPP(c_Nat_OSuc, _1723873)))], (12690 ^ _781404) ^ [_1000878, _1000880, _1000882, _1000884] : [hBOOL(hAPP(hAPP(_1000882, _1000880), _1000884)), -(hBOOL(hAPP(hAPP(c_member(_1000878), _1000880), c_SetInterval_Oord_OlessThan(_1000878, _1000882, _1000884))))], (31246 ^ _781404) ^ [_1343665, _1343667] : [class_Orderings_Olinorder(_1343665), -(c_Big__Operators_Olattice_OInf__fin(_1343665, c_Orderings_Oord__class_Omin(_1343665), hAPP(hAPP(c_Set_Oinsert(_1343665), _1343667), c_Orderings_Obot__class_Obot(tc_fun(_1343665, tc_HOL_Obool)))) = _1343667)], (36556 ^ _781404) ^ [_1464689] : [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), _1464689))), -(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), _1464689)) = 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), _1464689))))], (2728 ^ _781404) ^ [_821754, _821756] : [_821756 = _821754, -(c_Wellfounded_Omeasure(_821756) = c_Wellfounded_Omeasure(_821754))], (52450 ^ _781404) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (44076 ^ _781404) ^ [_1660885, _1660887, _1660889] : [_1660889 = c_List_Olist_ONil(_1660887), -(_1660885 = hAPP(hAPP(c_List_Oappend(_1660887), _1660889), _1660885))], (2934 ^ _781404) ^ [_824929, _824931, _824933, _824935, _824937, _824939] : [-(c_Nitpick_Oof__frac(_824939, _824935, _824931) = c_Nitpick_Oof__frac(_824937, _824933, _824929)), _824939 = _824937, _824935 = _824933, _824931 = _824929], (17200 ^ _781404) ^ [_1087893, _1087895, _1087897, _1087899] : [class_Int_Onumber__ring(_1087893), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087893), hAPP(c_Int_Onumber__class_Onumber__of(_1087893), _1087895)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087893), hAPP(c_Int_Onumber__class_Onumber__of(_1087893), _1087897)), _1087899)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087893), hAPP(c_Int_Onumber__class_Onumber__of(_1087893), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1087895), _1087897))), _1087899))], (3114 ^ _781404) ^ [_827715, _827717, _827719, _827721, _827723, _827725] : [-(c_List_Oset__Cons(_827725, _827721, _827717) = c_List_Oset__Cons(_827723, _827719, _827715)), _827725 = _827723, _827721 = _827719, _827717 = _827715], (36532 ^ _781404) ^ [_1464225, _1464227, _1464229, _1464231, _1464233] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1464225, _1464227, _1464229), _1464231), _1464233) = hAPP(hAPP(_1464231, hAPP(c_Product__Type_Ofst(_1464225, _1464227), _1464233)), hAPP(c_Product__Type_Osnd(_1464225, _1464227), _1464233)))], (4922 ^ _781404) ^ [_856407, _856409, _856411, _856413] : [-(c_List_Olistrel(_856413, _856409) = c_List_Olistrel(_856411, _856407)), _856413 = _856411, _856409 = _856407], (52808 ^ _781404) ^ [_1843235, _1843237] : [-(hBOOL(_1843235)), -(hBOOL(hAPP(hAPP(c_fimplies, _1843235), _1843237)))], (20201 ^ _781404) ^ [_1140100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1140100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1140100)))], (814 ^ _781404) ^ [_793663, _793665, _793667, _793669, _793671, _793673] : [-(c_List_Olist__ex(_793671, _793667, _793663)), c_List_Olist__ex(_793673, _793669, _793665), _793673 = _793671, _793669 = _793667, _793665 = _793663], (470 ^ _781404) ^ [_788491, _788493, _788495, _788497, _788499, _788501] : [-(c_Relation_Ototal__on(_788499, _788495, _788491)), c_Relation_Ototal__on(_788501, _788497, _788493), _788501 = _788499, _788497 = _788495, _788493 = _788491], (6873 ^ _781404) ^ [_891564, _891566, _891568] : [class_Lattices_Osemilattice__sup(_891564), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891564), _891566), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891564), _891566), _891568)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891564), _891566), _891568))], (41125 ^ _781404) ^ [_1585210, _1585212, _1585214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585210, _1585210), tc_HOL_Obool)), _1585212), hAPP(hAPP(c_Product__Type_OSigma(_1585210, _1585210), _1585214), hAPP(c_COMBK(tc_fun(_1585210, tc_HOL_Obool), _1585210), _1585214)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585210, _1585210), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1585210, _1585212)), hAPP(hAPP(c_Product__Type_OSigma(_1585210, _1585210), _1585214), hAPP(c_COMBK(tc_fun(_1585210, tc_HOL_Obool), _1585210), _1585214)))))], (48876 ^ _781404) ^ [_1765861, _1765863, _1765865] : [-(c_List_Olist__ex1(_1765861, _1765863, _1765865)), 48877 ^ _781404 : [(48878 ^ _781404) ^ [_1765955] : [hBOOL(hAPP(hAPP(c_member(_1765861), _1765955), hAPP(c_List_Oset(_1765861), _1765865))), hBOOL(hAPP(_1765863, _1765955)), 48886 ^ _781404 : [(48891 ^ _781404) ^ [] : [48885 ^ [_1765861, _1765863, _1765865, _1765955] = _1765955], (48889 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1765863, 48885 ^ [_1765861, _1765863, _1765865, _1765955])))], (48887 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765861), 48885 ^ [_1765861, _1765863, _1765865, _1765955]), hAPP(c_List_Oset(_1765861), _1765865))))]]]]], (44541 ^ _781404) ^ [_1672550, _1672552, _1672554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672550), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672552)), _1672554))), -(_1672554 = hAPP(hAPP(c_List_Oappend(_1672552), hAPP(hAPP(c_List_Otake(_1672552), _1672550), _1672554)), hAPP(hAPP(c_List_Olist_OCons(_1672552), hAPP(hAPP(c_List_Onth(_1672552), _1672554), _1672550)), hAPP(hAPP(c_List_Odrop(_1672552), hAPP(c_Nat_OSuc, _1672550)), _1672554))))], (29826 ^ _781404) ^ [_1315917, _1315919, _1315921] : [29828 ^ _781404 : [(29831 ^ _781404) ^ [] : [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(_1315919, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 29827 ^ [_1315917, _1315919, _1315921]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1315919, 29827 ^ [_1315917, _1315919, _1315921])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29829 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29827 ^ [_1315917, _1315919, _1315921]), _1315917)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1315919, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1315921)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1315921), hAPP(_1315919, _1315917))), 29841 ^ _781404 : [(29844 ^ _781404) ^ [] : [-(hAPP(_1315919, 29840 ^ [_1315917, _1315919, _1315921]) = _1315921)], (29842 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29840 ^ [_1315917, _1315919, _1315921]), _1315917)))]]], (46772 ^ _781404) ^ [_1722459, _1722461] : [c_List_Oupt(_1722459, _1722461) = c_List_Olist_ONil(tc_Nat_Onat), -(_1722461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1722461), _1722459)))], (13478 ^ _781404) ^ [_1015940] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1015940)), 13482 ^ _781404 : [(13483 ^ _781404) ^ [_1016020] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1016020), _1015940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1016020), 13481 ^ [_1015940])))]]], (45413 ^ _781404) ^ [_1691016, _1691018, _1691020] : [c_Fun_Oinj__on(tc_List_Olist(_1691016), tc_List_Olist(_1691018), hAPP(c_List_Omap(_1691016, _1691018), _1691020), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1691016), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1691016, _1691018, _1691020, c_Orderings_Otop__class_Otop(tc_fun(_1691016, tc_HOL_Obool))))], (52718 ^ _781404) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (49167 ^ _781404) ^ [_1772594, _1772596, _1772598, _1772600] : [-(hBOOL(hAPP(_1772594, _1772596))), -(hAPP(c_List_Ofilter(_1772598, _1772594), c_List_Oreplicate(_1772598, _1772600, _1772596)) = c_List_Olist_ONil(_1772598))], (258 ^ _781404) ^ [_785381, _785383, _785385, _785387, _785389, _785391, _785393, _785395, _785397, _785399, _785401, _785403] : [-(c_Nitpick_Ofold__graph_H(_785401, _785397, _785393, _785389, _785385, _785381)), c_Nitpick_Ofold__graph_H(_785403, _785399, _785395, _785391, _785387, _785383), _785403 = _785401, _785399 = _785397, _785395 = _785393, _785391 = _785389, _785387 = _785385, _785383 = _785381], (11619 ^ _781404) ^ [_980190, _980192, _980194, _980196, _980198, _980200] : [hAPP(_980190, _980192) = _980194, hBOOL(hAPP(hAPP(c_member(_980196), _980194), _980198)), -(hBOOL(hAPP(hAPP(c_member(_980200), _980192), hAPP(c_Set_Ovimage(_980200, _980196, _980190), _980198))))], (21789 ^ _781404) ^ [_1168880, _1168882, _1168884] : [class_Rings_Olinordered__semiring__strict(_1168880), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168880), _1168882), c_Groups_Ozero__class_Ozero(_1168880))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168880), c_Groups_Ozero__class_Ozero(_1168880)), _1168884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168880), _1168882), _1168884)), c_Groups_Ozero__class_Ozero(_1168880))))], (42872 ^ _781404) ^ [_1632849, _1632851, _1632853] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1632849)), _1632851), c_List_Olists(_1632849, _1632853))), 42875 ^ _781404 : [(42876 ^ _781404) ^ [_1632957] : [hBOOL(hAPP(hAPP(c_member(_1632849), _1632957), hAPP(c_List_Oset(_1632849), _1632851))), -(hBOOL(hAPP(hAPP(c_member(_1632849), _1632957), _1632853)))]]], (23071 ^ _781404) ^ [_1194479, _1194481] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194479), _1194481) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194481), _1194479))], (33273 ^ _781404) ^ [_1383211, _1383213, _1383215, _1383217, _1383219] : [-(_1383211 = c_Orderings_Obot__class_Obot(tc_fun(_1383213, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383213, tc_fun(_1383215, tc_HOL_Obool)), _1383211), hAPP(hAPP(c_COMBB(tc_fun(_1383215, tc_HOL_Obool), tc_fun(_1383215, tc_HOL_Obool), _1383213), hAPP(c_Set_Oinsert(_1383215), _1383217)), _1383219)) = hAPP(hAPP(c_Set_Oinsert(_1383215), _1383217), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383213, tc_fun(_1383215, tc_HOL_Obool)), _1383211), _1383219)))], (18991 ^ _781404) ^ [_1119510, _1119512] : [class_Int_Onumber__ring(_1119510), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1119512)), -(hBOOL(hAPP(hAPP(c_member(_1119510), hAPP(c_Int_Onumber__class_Onumber__of(_1119510), _1119512)), c_Nat_Osemiring__1__class_ONats(_1119510))))], (18099 ^ _781404) ^ [_1103924] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1103924) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31930 ^ _781404) ^ [_1356063, _1356065, _1356067, _1356069, _1356071] : [class_Orderings_Olinorder(_1356063), class_Orderings_Olinorder(_1356065), c_Orderings_Oorder__class_Omono(_1356065, _1356063, _1356067), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356063), hAPP(_1356067, _1356069)), hAPP(_1356067, _1356071)) = hAPP(_1356067, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356065), _1356069), _1356071)))], (34395 ^ _781404) ^ [] : [-(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)))], (7996 ^ _781404) ^ [_914795, _914797, _914799] : [class_Groups_Oordered__ab__group__add(_914795), -(hAPP(c_Set_Oimage(_914795, _914795, c_Groups_Ouminus__class_Ouminus(_914795)), c_SetInterval_Oord__class_OatLeastAtMost(_914795, _914797, _914799)) = c_SetInterval_Oord__class_OatLeastAtMost(_914795, hAPP(c_Groups_Ouminus__class_Ouminus(_914795), _914799), hAPP(c_Groups_Ouminus__class_Ouminus(_914795), _914797)))], (50853 ^ _781404) ^ [_1809470, _1809472, _1809474, _1809476, _1809478, _1809480, _1809482, _1809484] : [c_Fun_Obij__betw(_1809470, _1809472, _1809474, _1809476, _1809478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809470, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1809480, _1809470, _1809482), _1809484)), _1809476)), 50860 ^ _781404 : [(50867 ^ _781404) ^ [] : [c_Fun_Obij__betw(_1809480, _1809472, hAPP(c_Fun_Ocomp(_1809470, _1809472, _1809480, _1809474), _1809482), _1809484, _1809478), -(c_Fun_Obij__betw(_1809480, _1809470, _1809482, _1809484, _1809476))], (50861 ^ _781404) ^ [] : [c_Fun_Obij__betw(_1809480, _1809470, _1809482, _1809484, _1809476), -(c_Fun_Obij__betw(_1809480, _1809472, hAPP(c_Fun_Ocomp(_1809470, _1809472, _1809480, _1809474), _1809482), _1809484, _1809478))]]], (9463 ^ _781404) ^ [_943636, _943638, _943640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943636), _943638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _943640), _943636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _943636), _943640)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _943638), _943640))))], (46123 ^ _781404) ^ [_1706777, _1706779] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1706777), tc_fun(_1706777, tc_HOL_Obool), c_List_Oset(_1706777)), hAPP(c_List_Oset(tc_List_Olist(_1706777)), c_Enum_Osublists(_1706777, _1706779))) = hAPP(c_Set_OPow(_1706777), hAPP(c_List_Oset(_1706777), _1706779)))], (28409 ^ _781404) ^ [_1289436, _1289438] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289436), hAPP(c_Int_Onumber__class_Onumber__of(_1289436), c_Int_OMin)), _1289438) = hAPP(c_Groups_Ouminus__class_Ouminus(_1289436), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289436), c_Groups_Oone__class_Oone(_1289436)), _1289438))), class_Fields_Ofield__inverse__zero(_1289436), class_Int_Onumber__ring(_1289436)], (19161 ^ _781404) ^ [_1122376] : [class_Rings_Osemiring__1(_1122376), -(c_Int_Oiszero(_1122376, c_Groups_Ozero__class_Ozero(_1122376)))], (38790 ^ _781404) ^ [_1520792, _1520794, _1520796, _1520798, _1520800, _1520802] : [class_Groups_Ocomm__monoid__mult(_1520792), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520794), _1520796)), 38800 ^ _781404 : [(38803 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1520798), hAPP(_1520800, 38799 ^ [_1520792, _1520794, _1520796, _1520798, _1520800, _1520802])))], (38801 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1520794), 38799 ^ [_1520792, _1520794, _1520796, _1520798, _1520800, _1520802]), _1520796)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1520794, _1520792), hAPP(hAPP(c_COMBS(_1520794, tc_fun(_1520798, tc_HOL_Obool), _1520792), hAPP(hAPP(c_COMBB(tc_fun(_1520798, _1520792), tc_fun(tc_fun(_1520798, tc_HOL_Obool), _1520792), _1520794), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1520798, _1520792)), _1520802)), _1520800)), _1520796) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1520794, _1520798), _1520792), hAPP(c_Product__Type_Oprod_Oprod__case(_1520794, _1520798, _1520792), _1520802)), hAPP(hAPP(c_Product__Type_OSigma(_1520794, _1520798), _1520796), _1520800)))], (46141 ^ _781404) ^ [_1707374, _1707376, _1707378] : [hBOOL(hAPP(c_List_Odistinct(_1707374), _1707376)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1707374)), c_Enum_On__lists(_1707374, _1707378, _1707376))))], (21461 ^ _781404) ^ [_1162957, _1162959, _1162961] : [class_Rings_Oordered__ring(_1162957), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162957), _1162959), c_Groups_Ozero__class_Ozero(_1162957))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162957), _1162961), c_Groups_Ozero__class_Ozero(_1162957))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162957), c_Groups_Ozero__class_Ozero(_1162957)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162957), _1162959), _1162961))))], (11809 ^ _781404) ^ [_983514, _983516, _983518, _983520, _983522] : [hBOOL(hAPP(_983520, hAPP(_983518, _983522))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_983514, _983516, _983518), _983520), _983522)))], (42045 ^ _781404) ^ [_1609162, _1609164, _1609166, _1609168] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609162, _1609162)), hAPP(hAPP(c_Product__Type_OPair(_1609162, _1609162), _1609164), _1609166)), c_Transitive__Closure_Otrancl(_1609162, _1609168))), 42049 ^ _781404 : [(42052 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609162, _1609162)), hAPP(hAPP(c_Product__Type_OPair(_1609162, _1609162), 42048 ^ [_1609162, _1609164, _1609166, _1609168]), _1609166)), _1609168)))], (42050 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609162, _1609162)), hAPP(hAPP(c_Product__Type_OPair(_1609162, _1609162), _1609164), 42048 ^ [_1609162, _1609164, _1609166, _1609168])), c_Transitive__Closure_Ortrancl(_1609162, _1609168))))]]], (30624 ^ _781404) ^ [_1331794, _1331796, _1331798] : [class_Orderings_Olinorder(_1331794), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331794), _1331796), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331794), _1331796), _1331798)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331794), _1331796), _1331798))], (35838 ^ _781404) ^ [_1450660, _1450662, _1450664, _1450666, _1450668, _1450670] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450660, _1450662), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1450664), _1450666))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450660, _1450662), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1450668), _1450670))), -(_1450662 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1450666 = _1450670)], (47673 ^ _781404) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (25295 ^ _781404) ^ [_1233893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1233893)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233893), c_Int_OMin)))], (50475 ^ _781404) ^ [_1800975] : [-(c_Hilbert__Choice_Oinv__into(_1800975, _1800975, c_Orderings_Otop__class_Otop(tc_fun(_1800975, tc_HOL_Obool)), c_Fun_Oid(_1800975)) = c_Fun_Oid(_1800975))], (1946 ^ _781404) ^ [_808769, _808771] : [-(class_Int_Onumber(_808769)), _808771 = _808769, class_Int_Onumber(_808771)], (42002 ^ _781404) ^ [_1607671, _1607673, _1607675, _1607677, _1607679] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607671, _1607671)), hAPP(hAPP(c_Product__Type_OPair(_1607671, _1607671), _1607673), _1607675)), c_Transitive__Closure_Ortrancl(_1607671, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1607671, _1607671), tc_HOL_Obool)), _1607677), _1607679)))), 42008 ^ _781404 : [(42014 ^ _781404) ^ [] : [42007 ^ [_1607671, _1607673, _1607675, _1607677, _1607679] = 42010 ^ [_1607671, _1607673, _1607675, _1607677, _1607679]], (42012 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607671, _1607671)), hAPP(hAPP(c_Product__Type_OPair(_1607671, _1607671), 42007 ^ [_1607671, _1607673, _1607675, _1607677, _1607679]), 42010 ^ [_1607671, _1607673, _1607675, _1607677, _1607679])), _1607679)))], (42009 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607671, _1607671)), hAPP(hAPP(c_Product__Type_OPair(_1607671, _1607671), _1607673), 42007 ^ [_1607671, _1607673, _1607675, _1607677, _1607679])), c_Transitive__Closure_Ortrancl(_1607671, _1607677))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607671, _1607671)), hAPP(hAPP(c_Product__Type_OPair(_1607671, _1607671), _1607673), _1607675)), c_Transitive__Closure_Ortrancl(_1607671, _1607677))))], (37866 ^ _781404) ^ [_1496575, _1496577, _1496579, _1496581, _1496583, _1496585, _1496587, _1496589, _1496591, _1496593] : [c_Equiv__Relations_Oequiv(_1496575, _1496577, _1496579), c_Equiv__Relations_Oequiv(_1496581, _1496583, _1496585), c_Equiv__Relations_Ocongruent2(_1496575, _1496581, tc_fun(_1496587, tc_HOL_Obool), _1496579, _1496585, _1496589), hBOOL(hAPP(hAPP(c_member(_1496575), _1496591), _1496577)), hBOOL(hAPP(hAPP(c_member(_1496581), _1496593), _1496583)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1496575, tc_fun(_1496587, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1496575, _1496575, _1496579), hAPP(hAPP(c_Set_Oinsert(_1496575), _1496591), c_Orderings_Obot__class_Obot(tc_fun(_1496575, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1496581, tc_fun(_1496587, tc_HOL_Obool)), tc_fun(_1496587, tc_HOL_Obool), _1496575), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1496581, tc_fun(_1496587, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1496581, _1496581, _1496585), hAPP(hAPP(c_Set_Oinsert(_1496581), _1496593), c_Orderings_Obot__class_Obot(tc_fun(_1496581, tc_HOL_Obool)))))), _1496589)) = hAPP(hAPP(_1496589, _1496591), _1496593))], (20511 ^ _781404) ^ [_1145281] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1145281), 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, _1145281)))], (50923 ^ _781404) ^ [_1810925, _1810927, _1810929, _1810931, _1810933, _1810935, _1810937] : [c_Fun_Obij__betw(_1810925, _1810927, _1810929, _1810931, _1810933), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1810925, tc_HOL_Obool)), _1810935), _1810931)), hAPP(c_Set_Oimage(_1810925, _1810927, _1810929), _1810935) = _1810937, -(c_Fun_Obij__betw(_1810925, _1810927, _1810929, _1810935, _1810937))], (832 ^ _781404) ^ [_793932, _793934, _793936, _793938] : [-(c_Predicate_Oreflp(_793936, _793932)), c_Predicate_Oreflp(_793938, _793934), _793938 = _793936, _793934 = _793932], (16344 ^ _781404) ^ [_1071736] : [-(hAPP(c_Nat_OSuc, _1071736) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1071736))], (46125 ^ _781404) ^ [_1706836, _1706838] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1706836))), c_Enum_Osublists(_1706836, _1706838)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706836)), _1706838)))], (32156 ^ _781404) ^ [_1360171, _1360173, _1360175, _1360177, _1360179] : [class_Orderings_Olinorder(_1360171), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360171), _1360173), _1360175)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360171), _1360177), _1360179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360171), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360171), _1360173), _1360177)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360171), _1360175), _1360179))))], (25223 ^ _781404) ^ [_1232736, _1232738] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232736) = _1232738), _1232736 = hAPP(c_Int_Onat, _1232738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232738))], (11905 ^ _781404) ^ [_985310, _985312, _985314] : [-(hAPP(c_Set_Ovimage(_985310, _985312, _985314), c_Orderings_Obot__class_Obot(tc_fun(_985312, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_985310, tc_HOL_Obool)))], (48733 ^ _781404) ^ [_1763107, _1763109, _1763111] : [c_FunDef_Ois__measure(_1763107, _1763109), -(c_FunDef_Ois__measure(tc_prod(_1763111, _1763107), hAPP(hAPP(c_COMBB(_1763107, tc_Nat_Onat, tc_prod(_1763111, _1763107)), _1763109), c_Product__Type_Osnd(_1763111, _1763107))))], (44836 ^ _781404) ^ [_1678513, _1678515] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1678513), hAPP(c_List_Oset(tc_Nat_Onat), _1678515))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1678513), 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)), _1678515))))], (8666 ^ _781404) ^ [_927511, _927513, _927515] : [-(hAPP(hAPP(c_Set_Oinsert(_927511), _927513), _927515) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927511, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_927511), _927513), c_Orderings_Obot__class_Obot(tc_fun(_927511, tc_HOL_Obool)))), _927515))], (1866 ^ _781404) ^ [_807769, _807771] : [-(class_Rings_Osemiring__0(_807769)), _807771 = _807769, class_Rings_Osemiring__0(_807771)], (52640 ^ _781404) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (20063 ^ _781404) ^ [_1137769, _1137771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1137769)), c_Int_OBit0(_1137771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137769), _1137771)))], (13678 ^ _781404) ^ [_1019754, _1019756, _1019758, _1019760] : [class_Groups_Oordered__comm__monoid__add(_1019754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019754), c_Groups_Ozero__class_Ozero(_1019754)), _1019756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019754), _1019758), _1019760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019754), _1019758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019754), _1019760), _1019756))))], (27401 ^ _781404) ^ [_1270709, _1270711] : [class_Lattices_Olattice(_1270709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270709), _1270711)), -(c_Big__Operators_Olattice__class_OInf__fin(_1270709, _1270711) = hAPP(c_Finite__Set_Ofold1(_1270709, c_Lattices_Osemilattice__inf__class_Oinf(_1270709)), _1270711))], (52656 ^ _781404) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (3246 ^ _781404) ^ [_829735, _829737, _829739, _829741, _829743, _829745] : [-(c_Big__Operators_Olattice_OSup__fin(_829745, _829741, _829737) = c_Big__Operators_Olattice_OSup__fin(_829743, _829739, _829735)), _829745 = _829743, _829741 = _829739, _829737 = _829735], (25061 ^ _781404) ^ [_1230028, _1230030] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1230028))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1230028), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1230030)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5362 ^ _781404) ^ [_863309, _863311, _863313, _863315, _863317, _863319, _863321, _863323] : [-(c_Lazy__Sequence_Omap(_863323, _863319, _863315, _863311) = c_Lazy__Sequence_Omap(_863321, _863317, _863313, _863309)), _863323 = _863321, _863319 = _863317, _863315 = _863313, _863311 = _863309], (39906 ^ _781404) ^ [_1557158, _1557160, _1557162] : [c_Wellfounded_Owf(_1557158, _1557160), -(c_Wellfounded_Owf(_1557158, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1557158, _1557158), tc_HOL_Obool)), _1557160), _1557162)))], (42214 ^ _781404) ^ [_1613993, _1613995, _1613997, _1613999, _1614001] : [hAPP(hAPP(c_List_Olist_OCons(_1613993), _1613995), _1613997) = hAPP(hAPP(c_List_Olist_OCons(_1613993), _1613999), _1614001), 42217 ^ _781404 : [(42220 ^ _781404) ^ [] : [-(_1613997 = _1614001)], (42218 ^ _781404) ^ [] : [-(_1613995 = _1613999)]]], (17377 ^ _781404) ^ [_1091419, _1091421] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1091419), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1091421) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1091419, _1091421))], (31624 ^ _781404) ^ [_1350341, _1350343, _1350345] : [class_Orderings_Olinorder(_1350341), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350341), _1350343)), -(hBOOL(hAPP(hAPP(c_member(_1350341), _1350345), _1350343))), -(c_Big__Operators_Olinorder__class_OMin(_1350341, hAPP(hAPP(c_Set_Oinsert(_1350341), _1350345), _1350343)) = hAPP(hAPP(c_Finite__Set_Ofold(_1350341, _1350341, c_Orderings_Oord__class_Omin(_1350341)), _1350345), _1350343))], (39137 ^ _781404) ^ [_1529828, _1529830] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1529828, tc_HOL_Obool), _1529830) = hAPP(c_Set_OCollect(_1529828), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1529828, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1529828), c_HOL_OAll(tc_fun(_1529828, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1529828, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1529828, tc_HOL_Obool), tc_HOL_Obool), _1529828), hAPP(c_COMBS(tc_fun(_1529828, 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(_1529828, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1529828, tc_HOL_Obool), tc_fun(tc_fun(_1529828, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1529828, tc_HOL_Obool))), _1529830)))), c_member(_1529828)))))], (8303 ^ _781404) ^ [_921388, _921390, _921392, _921394] : [_921394 = c_Orderings_Obot__class_Obot(tc_fun(_921388, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_921388, _921390, _921392), _921394) = c_Orderings_Obot__class_Obot(tc_fun(_921390, tc_HOL_Obool)))], (19635 ^ _781404) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (12780 ^ _781404) ^ [_1002704, _1002706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002704), _1002706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002704), _1002706)))], (52340 ^ _781404) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (41491 ^ _781404) ^ [_1594714, _1594716, _1594718] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1594714, _1594714), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1594714, _1594714), _1594716)), c_Transitive__Closure_Ortrancl(_1594714, _1594716)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1594714, _1594714), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1594714, _1594714)), hAPP(hAPP(c_Product__Type_OPair(_1594714, _1594714), _1594718), _1594718)), c_Transitive__Closure_Otrancl(_1594714, _1594716)))], (39660 ^ _781404) ^ [_1549869, _1549871, _1549873] : [hAPP(c_Relation_ORange(_1549869, _1549871), _1549873) = c_Orderings_Obot__class_Obot(tc_fun(_1549871, tc_HOL_Obool)), -(_1549873 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549869, _1549871), tc_HOL_Obool)))], (11054 ^ _781404) ^ [_969114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _969114)), -(_969114 = hAPP(c_Nat_OSuc, 11057 ^ [_969114]))], (20075 ^ _781404) ^ [_1137992, _1137994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1137992)), c_Int_OBit0(_1137994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137992), _1137994)))], (52538 ^ _781404) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (51424 ^ _781404) ^ [_1822996, _1822998, _1823000, _1823002, _1823004] : [-(c_New__DSequence_Opos__map(_1822996, _1822998, _1823000, _1823002, _1823004) = c_Lazy__Sequence_Omap(_1822996, _1822998, _1823000, hAPP(_1823002, _1823004)))], (9721 ^ _781404) ^ [_947317, _947319, _947321] : [class_Orderings_Olinorder(_947317), 9724 ^ _781404 : [(9725 ^ _781404) ^ [] : [-(_947319 = _947321), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947317), _947319), _947321))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947317), _947321), _947319)))], (9735 ^ _781404) ^ [] : [9736 ^ _781404 : [(9739 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947317), _947321), _947319))], (9737 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947317), _947319), _947321))]], _947319 = _947321]]], (34445 ^ _781404) ^ [_1419707, _1419709, _1419711, _1419713, _1419715] : [-(_1419707 = c_Orderings_Obot__class_Obot(tc_fun(_1419709, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1419709, tc_fun(_1419711, tc_HOL_Obool)), _1419707), hAPP(hAPP(c_COMBB(tc_fun(_1419711, tc_HOL_Obool), tc_fun(_1419711, tc_HOL_Obool), _1419709), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1419711, tc_HOL_Obool)), _1419713)), _1419715)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1419711, tc_HOL_Obool)), _1419713), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419709, tc_fun(_1419711, tc_HOL_Obool)), _1419707), _1419715)))], (19025 ^ _781404) ^ [_1120075, _1120077] : [-(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, _1120075)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1120077))))], (17613 ^ _781404) ^ [_1095372] : [-(_1095372 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 17616 ^ _781404 : [(17623 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1095372))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1095372) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (17617 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1095372)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1095372) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (33438 ^ _781404) ^ [_1389177, _1389179, _1389181, _1389183] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389177, tc_fun(_1389179, tc_HOL_Obool)), _1389181), _1389183) = c_Orderings_Otop__class_Otop(tc_fun(_1389179, tc_HOL_Obool)), 33441 ^ _781404 : [(33442 ^ _781404) ^ [_1389293] : [hBOOL(hAPP(hAPP(c_member(_1389177), _1389293), _1389181)), -(hAPP(_1389183, _1389293) = c_Orderings_Otop__class_Otop(tc_fun(_1389179, tc_HOL_Obool)))]]], (51870 ^ _781404) ^ [_1831337, _1831339] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831337), _1831339))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831337, _1831339) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52180 ^ _781404) ^ [_1836495, _1836497] : [class_Lattices_Olattice(_1836495), -(class_Lattices_Osemilattice__sup(tc_fun(_1836497, _1836495)))], (11791 ^ _781404) ^ [_983123, _983125, _983127, _983129, _983131] : [hBOOL(hAPP(hAPP(c_member(_983123), _983125), hAPP(c_Set_Ovimage(_983123, _983127, _983129), _983131))), -(hBOOL(hAPP(hAPP(c_member(_983127), hAPP(_983129, _983125)), _983131)))], (15194 ^ _781404) ^ [_1049463, _1049465, _1049467, _1049469, _1049471] : [c_Finite__Set_Ofolding__one(_1049463, _1049465, _1049467), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049463), _1049469)), -(_1049469 = c_Orderings_Obot__class_Obot(tc_fun(_1049463, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049463), _1049471)), -(_1049471 = c_Orderings_Obot__class_Obot(tc_fun(_1049463, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1049463, tc_HOL_Obool)), _1049469), _1049471) = c_Orderings_Obot__class_Obot(tc_fun(_1049463, tc_HOL_Obool)), -(hAPP(_1049467, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1049463, tc_HOL_Obool)), _1049469), _1049471)) = hAPP(hAPP(_1049465, hAPP(_1049467, _1049469)), hAPP(_1049467, _1049471)))], (39709 ^ _781404) ^ [_1551182, _1551184, _1551186, _1551188] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1551182, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1551182, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1551184, _1551182), _1551186)), hAPP(c_Relation_ORange(_1551184, _1551182), _1551188))), hAPP(c_Relation_ORange(_1551184, _1551182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1551184, _1551182), tc_HOL_Obool)), _1551186), _1551188)))))], (1676 ^ _781404) ^ [_805394, _805396] : [-(class_Rings_Olinordered__semiring(_805394)), _805396 = _805394, class_Rings_Olinordered__semiring(_805396)], (49291 ^ _781404) ^ [_1775035, _1775037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1775035), _1775037)), -(c_Lazy__Sequence_Osmall__lazy_H(_1775035, _1775037) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (14478 ^ _781404) ^ [_1034987, _1034989, _1034991] : [14479 ^ _781404 : [(14482 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1034987), _1034991))], (14480 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1034987), _1034989))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1034987), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1034987, tc_HOL_Obool)), _1034989), _1034991))))], (7243 ^ _781404) ^ [_899152, _899154, _899156] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_899152, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_899152, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_899152), _899154)), hAPP(c_Set_OPow(_899152), _899156))), hAPP(c_Set_OPow(_899152), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899152, tc_HOL_Obool)), _899154), _899156)))))], (11729 ^ _781404) ^ [_982268, _982270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982268), _982270)), _982270 = _982268], (44531 ^ _781404) ^ [_1672225, _1672227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672225)), _1672227)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1672225), _1672227) = _1672227)], (20345 ^ _781404) ^ [_1142522, _1142524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1142522)), c_Int_OBit0(_1142524))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142522), _1142524)))], (15629 ^ _781404) ^ [_1057916, _1057918] : [class_Complete__Lattice_Ocomplete__lattice(_1057916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057916), _1057918)), -(_1057918 = c_Orderings_Obot__class_Obot(tc_fun(_1057916, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1057916, _1057918) = c_Complete__Lattice_OInf__class_OInf(_1057916, _1057918))], (21085 ^ _781404) ^ [_1155755] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155755) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13470 ^ _781404) ^ [_1015738, _1015740] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015738), _1015740)), _1015738) = _1015740)], (15687 ^ _781404) ^ [_1058862] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1058862), c_Orderings_Otop__class_Otop(tc_fun(_1058862, 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(_1058862), c_Orderings_Otop__class_Otop(tc_fun(_1058862, tc_HOL_Obool))))))], (15128 ^ _781404) ^ [_1048117, _1048119, _1048121, _1048123, _1048125] : [c_Finite__Set_Ofolding__one(_1048117, _1048119, _1048121), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048117), _1048123)), -(hBOOL(hAPP(hAPP(c_member(_1048117), _1048125), _1048123))), -(_1048123 = c_Orderings_Obot__class_Obot(tc_fun(_1048117, tc_HOL_Obool))), -(hAPP(_1048121, hAPP(hAPP(c_Set_Oinsert(_1048117), _1048125), _1048123)) = hAPP(hAPP(_1048119, _1048125), hAPP(_1048121, _1048123)))], (34575 ^ _781404) ^ [_1422654, _1422656, _1422658, _1422660, _1422662, _1422664] : [c_Fun_Oinj__on(_1422654, _1422656, _1422658, _1422660), 34578 ^ _781404 : [(34585 ^ _781404) ^ [] : [c_Fun_Oinj__on(_1422654, _1422662, hAPP(c_Fun_Ocomp(_1422656, _1422662, _1422654, _1422664), _1422658), _1422660), -(c_Fun_Oinj__on(_1422656, _1422662, _1422664, hAPP(c_Set_Oimage(_1422654, _1422656, _1422658), _1422660)))], (34579 ^ _781404) ^ [] : [c_Fun_Oinj__on(_1422656, _1422662, _1422664, hAPP(c_Set_Oimage(_1422654, _1422656, _1422658), _1422660)), -(c_Fun_Oinj__on(_1422654, _1422662, hAPP(c_Fun_Ocomp(_1422656, _1422662, _1422654, _1422664), _1422658), _1422660))]]], (12394 ^ _781404) ^ [_994995, _994997, _994999, _995001] : [hBOOL(hAPP(hAPP(c_member(_994995), _994997), _994999)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994995, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_994995), _994997), _995001)), _994999) = hAPP(hAPP(c_Set_Oinsert(_994995), _994997), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994995, tc_HOL_Obool)), _995001), _994999)))], (11077 ^ _781404) ^ [_969468, _969470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _969468)), _969470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969468), _969470)))], (15317 ^ _781404) ^ [_1052217, _1052219, _1052221, _1052223] : [c_Finite__Set_Ofolding__one(_1052217, _1052219, _1052221), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052217), _1052223)), -(_1052223 = c_Orderings_Obot__class_Obot(tc_fun(_1052217, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1052217), hAPP(hAPP(_1052219, 15330 ^ [_1052217, _1052219, _1052221, _1052223]), 15331 ^ [_1052217, _1052219, _1052221, _1052223])), hAPP(hAPP(c_Set_Oinsert(_1052217), 15330 ^ [_1052217, _1052219, _1052221, _1052223]), hAPP(hAPP(c_Set_Oinsert(_1052217), 15331 ^ [_1052217, _1052219, _1052221, _1052223]), c_Orderings_Obot__class_Obot(tc_fun(_1052217, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1052217), hAPP(_1052221, _1052223)), _1052223)))], (8399 ^ _781404) ^ [_922930, _922932, _922934] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922930, tc_HOL_Obool)), _922932), _922934) = c_Orderings_Obot__class_Obot(tc_fun(_922930, tc_HOL_Obool)), 8402 ^ _781404 : [(8405 ^ _781404) ^ [] : [-(_922934 = c_Orderings_Obot__class_Obot(tc_fun(_922930, tc_HOL_Obool)))], (8403 ^ _781404) ^ [] : [-(_922932 = c_Orderings_Obot__class_Obot(tc_fun(_922930, tc_HOL_Obool)))]]], (24394 ^ _781404) ^ [_1218872, _1218874, _1218876] : [hBOOL(hAPP(_1218872, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1218874, _1218876))), 24397 ^ _781404 : [(24422 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218876), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24425 ^ _781404 : [(24426 ^ _781404) ^ [_1219494, _1219496] : [-(hBOOL(hAPP(_1218872, _1219494))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218876), _1219494)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1219494), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1218874 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218876), _1219496)), _1219494)]]], (24404 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218876)), 24407 ^ _781404 : [(24408 ^ _781404) ^ [_1219202, _1219204] : [-(hBOOL(hAPP(_1218872, _1219202))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219202)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1219202), _1218876)), _1218874 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218876), _1219204)), _1219202)]]], (24398 ^ _781404) ^ [] : [_1218876 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1218872, _1218874)))]]], (26485 ^ _781404) ^ [_1253587, _1253589] : [class_Rings_Oring__1(_1253587), -(hAPP(c_Int_Oring__1__class_Oof__int(_1253587), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1253589)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1253587), _1253589))], (40863 ^ _781404) ^ [_1578267, _1578269, _1578271] : [class_Complete__Lattice_Ocomplete__lattice(_1578267), c_Orderings_Oorder__class_Omono(_1578267, _1578267, _1578269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1578267), hAPP(_1578269, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1578267), c_Inductive_Ocomplete__lattice__class_Olfp(_1578267, _1578269)), _1578271))), _1578271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1578267), c_Inductive_Ocomplete__lattice__class_Olfp(_1578267, _1578269)), _1578271)))], (38558 ^ _781404) ^ [_1514036, _1514038, _1514040, _1514042, _1514044] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1514036, _1514038), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1514036, tc_HOL_Obool)), _1514040), _1514042)), _1514044) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1514036, _1514038), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1514036, _1514038), _1514040), _1514044)), hAPP(hAPP(c_Product__Type_OSigma(_1514036, _1514038), _1514042), _1514044)))], (8066 ^ _781404) ^ [_916403, _916405, _916407, _916409] : [hAPP(c_Set_Oimage(_916403, _916405, _916407), c_Orderings_Otop__class_Otop(tc_fun(_916403, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_916405, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916405, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_916405, tc_HOL_Obool)), hAPP(c_Set_Oimage(_916403, _916405, _916407), _916409))), hAPP(c_Set_Oimage(_916403, _916405, _916407), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_916403, tc_HOL_Obool)), _916409)))))], (46083 ^ _781404) ^ [_1705932, _1705934, _1705936, _1705938, _1705940, _1705942, _1705944, _1705946] : [c_List_Olist__all2(_1705932, _1705934, _1705936, _1705938, _1705940), hBOOL(hAPP(hAPP(_1705936, _1705942), _1705944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1705946), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705934)), _1705940))), -(c_List_Olist__all2(_1705932, _1705934, _1705936, hAPP(hAPP(c_List_Olist__update(_1705932, _1705938), _1705946), _1705942), hAPP(hAPP(c_List_Olist__update(_1705934, _1705940), _1705946), _1705944)))], (39820 ^ _781404) ^ [_1555576, _1555578, _1555580, _1555582] : [c_Wellfounded_Owf(_1555576, _1555578), -(c_Wellfounded_Owf(_1555580, hAPP(hAPP(c_Relation_Oinv__image(_1555576, _1555580), _1555578), _1555582)))], (8020 ^ _781404) ^ [_915298, _915300, _915302, _915304] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915298, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915298, tc_HOL_Obool)), _915300), _915302)), _915304) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915298, tc_HOL_Obool)), _915300), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915298, tc_HOL_Obool)), _915302), _915304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915298, tc_HOL_Obool)), _915304), _915300)))], (49289 ^ _781404) ^ [_1774966, _1774968, _1774970, _1774972] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1774966, _1774968), c_Lazy__Sequence_Olazy__sequence_OInsert(_1774966, _1774970, _1774972)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1774968, _1774970)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1774966, _1774968), _1774972))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51179 ^ _781404) ^ [_1815984, _1815986, _1815988, _1815990] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1815984, _1815986, _1815988), c_Product__Type_Ocurry(_1815984, _1815986, _1815988, _1815990)) = _1815990)], (46155 ^ _781404) ^ [_1707650, _1707652] : [-(_1707650 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1707652, _1707650, c_List_Olist_ONil(_1707652)) = c_List_Olist_ONil(tc_List_Olist(_1707652)))], (49610 ^ _781404) ^ [_1782389, _1782391, _1782393, _1782395, _1782397, _1782399, _1782401] : [hBOOL(hAPP(hAPP(_1782389, hAPP(c_Product__Type_Osnd(_1782391, _1782393), _1782395)), hAPP(c_Product__Type_Ofst(_1782391, _1782393), _1782395))), 49617 ^ _781404 : [(49620 ^ _781404) ^ [] : [hBOOL(hAPP(_1782397, hAPP(hAPP(_1782399, 49615 ^ [_1782389, _1782391, _1782393, _1782395, _1782397, _1782399, _1782401]), 49616 ^ [_1782389, _1782391, _1782393, _1782395, _1782397, _1782399, _1782401])))], (49618 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1782389, 49616 ^ [_1782389, _1782391, _1782393, _1782395, _1782397, _1782399, _1782401]), 49615 ^ [_1782389, _1782391, _1782393, _1782395, _1782397, _1782399, _1782401])))]], -(hBOOL(hAPP(_1782397, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1782391, _1782393, _1782401), _1782399), _1782395))))], (43823 ^ _781404) ^ [_1655321, _1655323, _1655325, _1655327] : [-(c_List_Osublist(_1655321, hAPP(hAPP(c_List_Olist_OCons(_1655321), _1655323), _1655325), _1655327) = hAPP(hAPP(c_List_Oappend(_1655321), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1655321)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1655327)), hAPP(hAPP(c_List_Olist_OCons(_1655321), _1655323), c_List_Olist_ONil(_1655321))), c_List_Olist_ONil(_1655321))), c_List_Osublist(_1655321, _1655325, 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)), _1655327)))))], (26254 ^ _781404) ^ [_1249882, _1249884, _1249886, _1249888, _1249890] : [class_Groups_Oordered__ab__semigroup__add(_1249882), class_Rings_Osemiring__1(_1249882), 26264 ^ _781404 : [(26267 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249882), hAPP(_1249888, 26263 ^ [_1249882, _1249884, _1249886, _1249888, _1249890])), _1249890))], (26265 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1249884), 26263 ^ [_1249882, _1249884, _1249886, _1249888, _1249890]), _1249886)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249882), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1249884, _1249882), _1249888), _1249886)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249882), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1249882), hAPP(c_Finite__Set_Ocard(_1249884), _1249886))), _1249890))))], (31232 ^ _781404) ^ [_1343438, _1343440, _1343442] : [class_Orderings_Olinorder(_1343438), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343438), _1343440)), hBOOL(hAPP(hAPP(c_member(_1343438), _1343442), _1343440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343438), c_Big__Operators_Olinorder__class_OMin(_1343438, _1343440)), _1343442)))], (9338 ^ _781404) ^ [_941286, _941288, _941290, _941292, _941294] : [-(c_Fun_Oinj__on(_941286, _941288, _941290, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941286, tc_HOL_Obool)), _941292), _941294))), c_Fun_Oinj__on(_941286, _941288, _941290, _941292), c_Fun_Oinj__on(_941286, _941288, _941290, _941294), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941288, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941286, _941288, _941290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941286, tc_HOL_Obool)), _941292), _941294))), hAPP(c_Set_Oimage(_941286, _941288, _941290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941286, tc_HOL_Obool)), _941294), _941292))) = c_Orderings_Obot__class_Obot(tc_fun(_941288, tc_HOL_Obool))], (22763 ^ _781404) ^ [_1188301, _1188303, _1188305] : [22764 ^ _781404 : [(22767 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1188301), _1188305))], (22765 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188303)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188301), _1188303)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188305), _1188303))))], (10143 ^ _781404) ^ [_954238, _954240, _954242] : [class_Orderings_Olinorder(_954238), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954238), _954240), _954242))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954238), _954242), _954240)))], (18695 ^ _781404) ^ [_1114849] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1114849), c_Int_OPls) = _1114849)], (13850 ^ _781404) ^ [_1022960, _1022962] : [class_Groups_Oab__group__add(_1022960), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022960), hAPP(c_Groups_Ouminus__class_Ouminus(_1022960), _1022962)), _1022962) = c_Groups_Ozero__class_Ozero(_1022960))], (34211 ^ _781404) ^ [_1411934, _1411936, _1411938, _1411940, _1411942] : [_1411934 = c_Orderings_Obot__class_Obot(tc_fun(_1411936, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411936, tc_fun(_1411938, tc_HOL_Obool)), _1411934), hAPP(hAPP(c_COMBB(tc_fun(_1411938, tc_HOL_Obool), tc_fun(_1411938, tc_HOL_Obool), _1411936), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411938, tc_HOL_Obool)), _1411940)), _1411942)) = c_Orderings_Otop__class_Otop(tc_fun(_1411938, tc_HOL_Obool)))], (11723 ^ _781404) ^ [_982180, _982182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982180), _982182)), _982180 = _982182], (12963 ^ _781404) ^ [_1006334, _1006336, _1006338, _1006340] : [class_Groups_Ocancel__semigroup__add(_1006334), 12966 ^ _781404 : [(12973 ^ _781404) ^ [] : [_1006338 = _1006340, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006334), _1006336), _1006338) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006334), _1006336), _1006340))], (12967 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006334), _1006336), _1006338) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006334), _1006336), _1006340), -(_1006338 = _1006340)]]], (52148 ^ _781404) ^ [_1836074] : [_1836074 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836074), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (47585 ^ _781404) ^ [_1738095, _1738097, _1738099] : [-(hAPP(c_List_Orev(_1738095), hAPP(hAPP(c_List_Odrop(_1738095), _1738097), _1738099)) = hAPP(hAPP(c_List_Otake(_1738095), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738095)), _1738099)), _1738097)), hAPP(c_List_Orev(_1738095), _1738099)))], (1496 ^ _781404) ^ [_803144, _803146] : [-(class_Lattices_Olattice(_803144)), _803146 = _803144, class_Lattices_Olattice(_803146)], (52060 ^ _781404) ^ [_1834538, _1834540, _1834542, _1834544] : [class_Divides_Osemiring__div(_1834538), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834538), _1834540), c_Divides_Odiv__class_Omod(_1834538, _1834542, _1834544))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834538), _1834540), _1834544)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834538), _1834540), _1834542)))], (44196 ^ _781404) ^ [_1663654, _1663656, _1663658] : [-(hBOOL(hAPP(c_List_Odistinct(_1663654), hAPP(hAPP(c_List_Oappend(_1663654), _1663656), _1663658)))), hBOOL(hAPP(c_List_Odistinct(_1663654), _1663656)), hBOOL(hAPP(c_List_Odistinct(_1663654), _1663658)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1663654, tc_HOL_Obool)), hAPP(c_List_Oset(_1663654), _1663656)), hAPP(c_List_Oset(_1663654), _1663658)) = c_Orderings_Obot__class_Obot(tc_fun(_1663654, tc_HOL_Obool))], (438 ^ _781404) ^ [_788029, _788031, _788033, _788035, _788037, _788039] : [-(c_Orderings_Oorder__class_Omono(_788037, _788033, _788029)), c_Orderings_Oorder__class_Omono(_788039, _788035, _788031), _788039 = _788037, _788035 = _788033, _788031 = _788029], (19721 ^ _781404) ^ [_1131823, _1131825] : [class_Rings_Olinordered__semidom(_1131823), 19724 ^ _781404 : [(19731 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1131825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131823), c_Groups_Ozero__class_Ozero(_1131823)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131823), _1131825))))], (19725 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131823), c_Groups_Ozero__class_Ozero(_1131823)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131823), _1131825))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1131825)))]]], (38566 ^ _781404) ^ [_1514445, _1514447, _1514449, _1514451] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514445), _1514447)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514449), _1514451)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1514445, _1514449)), hAPP(hAPP(c_Product__Type_OSigma(_1514445, _1514449), _1514447), hAPP(c_COMBK(tc_fun(_1514449, tc_HOL_Obool), _1514445), _1514451)))))], (45694 ^ _781404) ^ [] : [-(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))], (49768 ^ _781404) ^ [_1786171, _1786173] : [-(hBOOL(hAPP(_1786173, 49775 ^ [_1786171, _1786173]))), 49769 ^ _781404 : [(49770 ^ _781404) ^ [_1786232] : [hBOOL(hAPP(hAPP(c_member(_1786171), _1786232), c_Orderings_Otop__class_Otop(tc_fun(_1786171, tc_HOL_Obool)))), hBOOL(hAPP(_1786173, _1786232))]]], (35396 ^ _781404) ^ [_1441087, _1441089] : [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), _1441087))), 35399 ^ _781404 : [(35406 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441089)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441087)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441089), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441087)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441087)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441089), 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), _1441087)))))], (35400 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441089)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441087))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441089), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441087)) = 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), _1441089)))]]], (17607 ^ _781404) ^ [_1095296] : [_1095296 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1095296) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33424 ^ _781404) ^ [_1388611, _1388613, _1388615, _1388617] : [c_Fun_Oinj__on(_1388611, _1388613, _1388615, c_Orderings_Otop__class_Otop(tc_fun(_1388611, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1388611, tc_fun(_1388617, _1388613), hAPP(hAPP(c_COMBB(_1388613, tc_fun(_1388617, _1388613), _1388611), c_COMBK(_1388613, _1388617)), _1388615), c_Orderings_Otop__class_Otop(tc_fun(_1388611, tc_HOL_Obool))))], (30600 ^ _781404) ^ [_1331360, _1331362] : [class_Orderings_Olinorder(_1331360), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331360), _1331362), _1331362) = _1331362)], (50008 ^ _781404) ^ [_1792133, _1792135, _1792137, _1792139] : [-(c_Wellfounded_Omax__extp(_1792133, _1792135, _1792137, _1792139)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792133), _1792137)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792133), _1792139)), -(_1792139 = c_Orderings_Obot__class_Obot(tc_fun(_1792133, tc_HOL_Obool))), 50022 ^ _781404 : [(50025 ^ _781404) ^ [_1792478] : [hBOOL(hAPP(hAPP(c_member(_1792133), _1792478), _1792139)), hBOOL(hAPP(hAPP(_1792135, 50021 ^ [_1792133, _1792135, _1792137, _1792139]), _1792478))], (50023 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1792133), 50021 ^ [_1792133, _1792135, _1792137, _1792139]), _1792137)))]]], (52568 ^ _781404) ^ [_1840431, _1840433] : [-(class_Enum_Oenum(tc_sum(_1840431, _1840433))), class_Enum_Oenum(_1840431), class_Enum_Oenum(_1840433)], (22459 ^ _781404) ^ [_1182021, _1182023, _1182025, _1182027] : [class_Rings_Olinordered__ring__strict(_1182021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182021), _1182023), c_Groups_Ozero__class_Ozero(_1182021))), 22466 ^ _781404 : [(22473 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182021), _1182027), _1182025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182021), _1182023), _1182025)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182021), _1182023), _1182027))))], (22467 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182021), _1182023), _1182025)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182021), _1182023), _1182027))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182021), _1182027), _1182025)))]]], (22203 ^ _781404) ^ [_1177030, _1177032] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177030), hAPP(c_Nat_OSuc, _1177032)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1177030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177030), _1177032)))], (8774 ^ _781404) ^ [_929355, _929357] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929355, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_929355, tc_HOL_Obool)), _929357)), _929357) = c_Orderings_Obot__class_Obot(tc_fun(_929355, tc_HOL_Obool)))], (39594 ^ _781404) ^ [_1547860, _1547862, _1547864, _1547866, _1547868, _1547870, _1547872, _1547874] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547860, _1547862)), hAPP(hAPP(c_Product__Type_OPair(_1547860, _1547862), _1547864), _1547866)), _1547868)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1547862, _1547870)), hAPP(hAPP(c_Product__Type_OPair(_1547862, _1547870), _1547866), _1547872)), _1547874)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547860, _1547870)), hAPP(hAPP(c_Product__Type_OPair(_1547860, _1547870), _1547864), _1547872)), hAPP(hAPP(c_Relation_Orel__comp(_1547860, _1547862, _1547870), _1547868), _1547874))))], (51606 ^ _781404) ^ [_1826596, _1826598, _1826600, _1826602] : [class_Rings_Ocomm__semiring__1(_1826596), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826596), _1826598), _1826600)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826596), _1826598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826596), _1826600), _1826602))))], (15529 ^ _781404) ^ [_1056230, _1056232, _1056234, _1056236] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1056230), _1056232)), hAPP(c_Finite__Set_Ocard(_1056234), hAPP(c_Set_Oimage(_1056230, _1056234, _1056236), _1056232)) = hAPP(c_Finite__Set_Ocard(_1056230), _1056232), -(c_Fun_Oinj__on(_1056230, _1056234, _1056236, _1056232))], (16298 ^ _781404) ^ [_1071031] : [class_Rings_Ozero__neq__one(_1071031), c_Groups_Ozero__class_Ozero(_1071031) = c_Groups_Oone__class_Oone(_1071031)], (23595 ^ _781404) ^ [_1205108, _1205110] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205108), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205110)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205108)), _1205110))], (12576 ^ _781404) ^ [_998701, _998703, _998705, _998707] : [c_Fun_Oinj__on(_998701, _998703, _998705, c_Orderings_Otop__class_Otop(tc_fun(_998701, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_998701, _998703, _998705), hAPP(c_Set_Oimage(_998701, _998703, _998705), _998707)) = _998707)], (33935 ^ _781404) ^ [_1403889, _1403891, _1403893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403889, tc_HOL_Obool)), _1403891), _1403893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403889, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1403889, tc_fun(_1403889, tc_HOL_Obool), tc_HOL_Obool), c_member(_1403889)), _1403891)), hAPP(hAPP(c_COMBC(_1403889, tc_fun(_1403889, tc_HOL_Obool), tc_HOL_Obool), c_member(_1403889)), _1403893))))], (18509 ^ _781404) ^ [_1111534, _1111536, _1111538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1111534)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1111536), _1111538)), 18516 ^ _781404 : [(18517 ^ _781404) ^ [_1111724] : [18519 ^ _781404 : [(18525 ^ _781404) ^ [] : [-(_1111724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 18521 ^ [_1111534, _1111536, _1111538, _1111724]), 18518 ^ [_1111534, _1111536, _1111538, _1111724]))], (18523 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18521 ^ [_1111534, _1111536, _1111538, _1111724]), _1111538)))], (18520 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18518 ^ [_1111534, _1111536, _1111538, _1111724]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1111534))))]], -(_1111724 = _1111536), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1111724), _1111534) = _1111536]]], (25359 ^ _781404) ^ [_1234799, _1234801, _1234803, _1234805, _1234807] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1234799, _1234801, _1234803), _1234805), hAPP(c_Nat_OSuc, _1234807)) = hAPP(hAPP(_1234803, _1234805), hAPP(hAPP(c_Power_Opower_Opower(_1234799, _1234801, _1234803), _1234805), _1234807)))], (45222 ^ _781404) ^ [_1686374, _1686376, _1686378, _1686380, _1686382] : [hAPP(hAPP(c_List_Omap(_1686374, _1686376), _1686378), _1686380) = hAPP(hAPP(c_List_Omap(_1686374, _1686376), _1686382), _1686380), 45225 ^ _781404 : [(45226 ^ _781404) ^ [_1686497] : [hBOOL(hAPP(hAPP(c_member(_1686374), _1686497), hAPP(c_List_Oset(_1686374), _1686380))), -(hAPP(_1686378, _1686497) = hAPP(_1686382, _1686497))]]], (42222 ^ _781404) ^ [_1614130, _1614132, _1614134, _1614136, _1614138] : [-(hAPP(hAPP(c_List_Olist_OCons(_1614130), _1614132), _1614134) = hAPP(hAPP(c_List_Olist_OCons(_1614130), _1614136), _1614138)), _1614132 = _1614136, _1614134 = _1614138], (17815 ^ _781404) ^ [_1099081, _1099083, _1099085, _1099087] : [class_Rings_Olinordered__semidom(_1099081), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099081), _1099083), _1099085)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099081), c_Groups_Ozero__class_Ozero(_1099081)), _1099083)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099081), hAPP(hAPP(c_Power_Opower__class_Opower(_1099081), _1099083), _1099087)), hAPP(hAPP(c_Power_Opower__class_Opower(_1099081), _1099085), _1099087))))], (11767 ^ _781404) ^ [_982693, _982695, _982697] : [hBOOL(hAPP(hAPP(c_member(_982693), _982695), _982697)), -(hBOOL(hAPP(_982697, _982695)))], (42054 ^ _781404) ^ [_1609422, _1609424, _1609426, _1609428] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609422, _1609422)), hAPP(hAPP(c_Product__Type_OPair(_1609422, _1609422), _1609424), _1609426)), c_Transitive__Closure_Otrancl(_1609422, _1609428))), 42058 ^ _781404 : [(42061 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609422, _1609422)), hAPP(hAPP(c_Product__Type_OPair(_1609422, _1609422), 42057 ^ [_1609422, _1609424, _1609426, _1609428]), _1609426)), c_Transitive__Closure_Ortrancl(_1609422, _1609428))))], (42059 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609422, _1609422)), hAPP(hAPP(c_Product__Type_OPair(_1609422, _1609422), _1609424), 42057 ^ [_1609422, _1609424, _1609426, _1609428])), _1609428)))]]], (19149 ^ _781404) ^ [_1122160, _1122162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1122160), _1122162)), -(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)), _1122160)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1122162))))], (17427 ^ _781404) ^ [_1092295, _1092297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092295), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1092297), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092295), _1092297))), -(_1092295 = _1092297)], (4252 ^ _781404) ^ [_845830, _845832] : [_845832 = _845830, -(c_List_Odrop(_845832) = c_List_Odrop(_845830))], (26467 ^ _781404) ^ [_1253230, _1253232, _1253234] : [class_Rings_Oring__1(_1253230), -(hAPP(c_Int_Oring__1__class_Oof__int(_1253230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1253232), _1253234)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253230), hAPP(c_Int_Oring__1__class_Oof__int(_1253230), _1253232)), hAPP(c_Int_Oring__1__class_Oof__int(_1253230), _1253234)))], (3592 ^ _781404) ^ [_835114, _835116, _835118, _835120, _835122, _835124, _835126, _835128] : [-(c_List_Olinorder__class_Osort__key(_835128, _835124, _835120, _835116) = c_List_Olinorder__class_Osort__key(_835126, _835122, _835118, _835114)), _835128 = _835126, _835124 = _835122, _835120 = _835118, _835116 = _835114], (52382 ^ _781404) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (26989 ^ _781404) ^ [_1263142, _1263144, _1263146, _1263148] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1263142, _1263144, _1263146, _1263148, c_Orderings_Obot__class_Obot(tc_fun(_1263142, tc_HOL_Obool))), _1263148)))], (8584 ^ _781404) ^ [] : [-(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)))], (5875 ^ _781404) ^ [_874561, _874563, _874565] : [class_Orderings_Oorder(_874561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874561), _874563), _874565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874561), _874565), _874563)), -(_874565 = _874563)], (46343 ^ _781404) ^ [_1711353, _1711355, _1711357] : [class_Orderings_Olinorder(_1711353), -(c_List_Olinorder__class_Osort__key(_1711355, _1711353, _1711357, c_List_Olist_ONil(_1711355)) = c_List_Olist_ONil(_1711355))], (41899 ^ _781404) ^ [_1604817, _1604819, _1604821] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604817, _1604817)), hAPP(hAPP(c_Product__Type_OPair(_1604817, _1604817), _1604819), _1604819)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604817, _1604817), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604821))))], (43130 ^ _781404) ^ [_1640501, _1640503, _1640505] : [-(hAPP(hAPP(c_List_Olist__update(_1640501, _1640503), _1640505), hAPP(hAPP(c_List_Onth(_1640501), _1640503), _1640505)) = _1640503)], (41233 ^ _781404) ^ [_1588686, _1588688] : [-(c_Transitive__Closure_Ortrancl(_1588686, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588686, _1588686), tc_HOL_Obool)), _1588688), c_Relation_OId(_1588686))) = c_Transitive__Closure_Ortrancl(_1588686, _1588688))], (33457 ^ _781404) ^ [_1389657, _1389659, _1389661, _1389663] : [c_Orderings_Otop__class_Otop(tc_fun(_1389657, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389659, tc_fun(_1389657, tc_HOL_Obool)), _1389661), _1389663), 33460 ^ _781404 : [(33461 ^ _781404) ^ [_1389773] : [hBOOL(hAPP(hAPP(c_member(_1389659), _1389773), _1389661)), -(hAPP(_1389663, _1389773) = c_Orderings_Otop__class_Otop(tc_fun(_1389657, tc_HOL_Obool)))]]], (46568 ^ _781404) ^ [_1717035, _1717037, _1717039, _1717041] : [-(hBOOL(hAPP(_1717035, _1717037))), -(hAPP(c_List_Ofilter(_1717039, _1717035), hAPP(hAPP(c_List_Olist_OCons(_1717039), _1717037), _1717041)) = hAPP(c_List_Ofilter(_1717039, _1717035), _1717041))], (50719 ^ _781404) ^ [_1806764, _1806766] : [50721 ^ _781404 : [(50724 ^ _781404) ^ [] : [hBOOL(hAPP(_1806764, hAPP(c_Code__Numeral_Oof__nat, 50720 ^ [_1806764, _1806766])))], (50722 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50720 ^ [_1806764, _1806766]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1806764, _1806766)))], (33325 ^ _781404) ^ [_1384504, _1384506, _1384508, _1384510, _1384512] : [-(_1384504 = c_Orderings_Obot__class_Obot(tc_fun(_1384506, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384508, tc_HOL_Obool)), _1384510), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384506, tc_fun(_1384508, tc_HOL_Obool)), _1384504), _1384512)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384506, tc_fun(_1384508, tc_HOL_Obool)), _1384504), hAPP(hAPP(c_COMBB(tc_fun(_1384508, tc_HOL_Obool), tc_fun(_1384508, tc_HOL_Obool), _1384506), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384508, tc_HOL_Obool)), _1384510)), _1384512)))], (20183 ^ _781404) ^ [_1139773, _1139775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1139773), _1139775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1139773)), c_Int_OBit1(_1139775))))], (35770 ^ _781404) ^ [_1449046, _1449048, _1449050, _1449052, _1449054, _1449056, _1449058] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1449046, _1449048), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1449050), _1449052))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1449054, _1449048), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1449056), _1449058))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1449048)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1449046), _1449054), _1449048), 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), _1449050), _1449056)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1449052), _1449058)), _1449048))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1449052), _1449058), _1449048)))))], (1766 ^ _781404) ^ [_806519, _806521] : [-(class_Groups_Osemigroup__add(_806519)), _806521 = _806519, class_Groups_Osemigroup__add(_806521)], (9411 ^ _781404) ^ [_942749, _942751, _942753] : [-(c_Fun_Oinj__on(_942749, _942751, _942753, c_Orderings_Obot__class_Obot(tc_fun(_942749, tc_HOL_Obool))))], (52686 ^ _781404) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (12574 ^ _781404) ^ [_998635, _998637, _998639, _998641] : [-(hAPP(c_Set_Oimage(_998635, _998637, _998639), hAPP(c_Set_Ovimage(_998635, _998637, _998639), _998641)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998637, tc_HOL_Obool)), _998641), hAPP(c_Set_Oimage(_998635, _998637, _998639), c_Orderings_Otop__class_Otop(tc_fun(_998635, tc_HOL_Obool)))))], (40467 ^ _781404) ^ [_1569815, _1569817] : [40468 ^ _781404 : [(40469 ^ _781404) ^ [_1569861] : [hBOOL(hAPP(_1569815, _1569861))]], -(hBOOL(hAPP(_1569815, c_Hilbert__Choice_OEps(_1569817, _1569815))))], (27115 ^ _781404) ^ [_1265498, _1265500] : [class_Groups_Oordered__ab__group__add__abs(_1265498), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265498), hAPP(c_Groups_Ouminus__class_Ouminus(_1265498), _1265500)), hAPP(c_Groups_Oabs__class_Oabs(_1265498), _1265500))))], (50352 ^ _781404) ^ [_1798404, _1798406] : [c_Equiv__Relations_Opart__equivp(_1798404, _1798406), 50356 ^ _781404 : [(50369 ^ _781404) ^ [_1798746, _1798748] : [-(hBOOL(hAPP(hAPP(_1798406, _1798748), _1798746))), hBOOL(hAPP(hAPP(_1798406, _1798748), _1798748)), hBOOL(hAPP(hAPP(_1798406, _1798746), _1798746)), hAPP(_1798406, _1798748) = hAPP(_1798406, _1798746)], (50359 ^ _781404) ^ [_1798577, _1798579] : [hBOOL(hAPP(hAPP(_1798406, _1798579), _1798577)), 50362 ^ _781404 : [(50367 ^ _781404) ^ [] : [-(hAPP(_1798406, _1798579) = hAPP(_1798406, _1798577))], (50365 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1798406, _1798577), _1798577)))], (50363 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1798406, _1798579), _1798579)))]]], (50357 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1798406, 50355 ^ [_1798404, _1798406]), 50355 ^ [_1798404, _1798406])))]]], (46848 ^ _781404) ^ [_1723760, _1723762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723760), _1723762)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1723760, _1723762)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1723762), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45835 ^ _781404) ^ [_1700278, _1700280, _1700282, _1700284] : [-(hBOOL(hAPP(c_List_Olistsp(_1700278, _1700280), hAPP(hAPP(c_List_Olist_OCons(_1700278), _1700282), _1700284)))), hBOOL(hAPP(_1700280, _1700282)), hBOOL(hAPP(c_List_Olistsp(_1700278, _1700280), _1700284))], (33467 ^ _781404) ^ [_1389886, _1389888, _1389890, _1389892] : [33469 ^ _781404 : [(33472 ^ _781404) ^ [] : [hAPP(_1389892, 33468 ^ [_1389886, _1389888, _1389890, _1389892]) = c_Orderings_Otop__class_Otop(tc_fun(_1389886, tc_HOL_Obool))], (33470 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389888), 33468 ^ [_1389886, _1389888, _1389890, _1389892]), _1389890)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1389886, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389888, tc_fun(_1389886, tc_HOL_Obool)), _1389890), _1389892))], (22717 ^ _781404) ^ [_1187446, _1187448, _1187450] : [class_Rings_Oring__1(_1187446), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1187446), hAPP(c_Groups_Ouminus__class_Ouminus(_1187446), _1187448)), _1187450) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187446), hAPP(hAPP(c_Power_Opower__class_Opower(_1187446), hAPP(c_Groups_Ouminus__class_Ouminus(_1187446), c_Groups_Oone__class_Oone(_1187446))), _1187450)), hAPP(hAPP(c_Power_Opower__class_Opower(_1187446), _1187448), _1187450)))], (15703 ^ _781404) ^ [_1059236, _1059238, _1059240] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1059236), _1059238)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059236), _1059240)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1059236), _1059238)), hAPP(c_Finite__Set_Ocard(_1059236), _1059240)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1059236), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1059236, tc_HOL_Obool)), _1059238), _1059240))), hAPP(c_Finite__Set_Ocard(_1059236), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1059236, tc_HOL_Obool)), _1059238), _1059240))))], (45208 ^ _781404) ^ [_1686066, _1686068, _1686070, _1686072] : [hAPP(hAPP(c_List_Omap(_1686066, _1686068), _1686070), _1686072) = c_List_Olist_ONil(_1686068), -(_1686072 = c_List_Olist_ONil(_1686066))], (17631 ^ _781404) ^ [_1095608, _1095610] : [class_Rings_Ocomm__semiring__1(_1095608), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095608), _1095610), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1095610)], (4760 ^ _781404) ^ [_853860, _853862] : [_853862 = _853860, -(c_Random__Sequence_Osingle(_853862) = c_Random__Sequence_Osingle(_853860))], (41297 ^ _781404) ^ [_1590240, _1590242, _1590244] : [_1590242 = _1590244, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590240, _1590240)), hAPP(hAPP(c_Product__Type_OPair(_1590240, _1590240), _1590242), _1590244)), c_Relation_OId(_1590240))))], (5386 ^ _781404) ^ [_863695, _863697] : [_863697 = _863695, -(c_Orderings_Oord__class_Oless(_863697) = c_Orderings_Oord__class_Oless(_863695))], (28475 ^ _781404) ^ [_1290731, _1290733, _1290735, _1290737] : [class_Fields_Olinordered__field__inverse__zero(_1290731), class_Int_Onumber(_1290731), 28482 ^ _781404 : [(28483 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290731), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290731), _1290733), _1290735)), hAPP(c_Int_Onumber__class_Onumber__of(_1290731), _1290737))), 28486 ^ _781404 : [(28493 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290731), c_Groups_Ozero__class_Ozero(_1290731)), _1290735))), 28496 ^ _781404 : [(28503 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290731), _1290735), c_Groups_Ozero__class_Ozero(_1290731)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290731), c_Groups_Ozero__class_Ozero(_1290731)), hAPP(c_Int_Onumber__class_Onumber__of(_1290731), _1290737))))], (28497 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290731), _1290735), c_Groups_Ozero__class_Ozero(_1290731))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290731), hAPP(c_Int_Onumber__class_Onumber__of(_1290731), _1290737)), _1290735)), _1290733)))]]], (28487 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290731), c_Groups_Ozero__class_Ozero(_1290731)), _1290735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290731), _1290733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290731), hAPP(c_Int_Onumber__class_Onumber__of(_1290731), _1290737)), _1290735))))]]], (28509 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290731), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290731), _1290733), _1290735)), hAPP(c_Int_Onumber__class_Onumber__of(_1290731), _1290737)))), 28512 ^ _781404 : [(28515 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290731), _1290733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290731), hAPP(c_Int_Onumber__class_Onumber__of(_1290731), _1290737)), _1290735)))], (28513 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290731), c_Groups_Ozero__class_Ozero(_1290731)), _1290735)))]], 28516 ^ _781404 : [(28519 ^ _781404) ^ [] : [28520 ^ _781404 : [(28523 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290731), hAPP(c_Int_Onumber__class_Onumber__of(_1290731), _1290737)), _1290735)), _1290733))], (28521 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290731), _1290735), c_Groups_Ozero__class_Ozero(_1290731))))]], 28524 ^ _781404 : [(28527 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290731), c_Groups_Ozero__class_Ozero(_1290731)), hAPP(c_Int_Onumber__class_Onumber__of(_1290731), _1290737)))], (28525 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290731), _1290735), c_Groups_Ozero__class_Ozero(_1290731)))]]], (28517 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290731), c_Groups_Ozero__class_Ozero(_1290731)), _1290735))]]]]], (19374 ^ _781404) ^ [_1125999, _1126001] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1125999)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1126001)), _1125999 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1126001 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (33723 ^ _781404) ^ [_1396562, _1396564] : [-(c_Fun_Oinj__on(_1396562, _1396562, c_COMBI(_1396562), _1396564))], (12520 ^ _781404) ^ [_997463, _997465, _997467] : [class_Orderings_Oord(_997463), 12523 ^ _781404 : [(12530 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997463), _997467), _997465)), -(hBOOL(hAPP(hAPP(c_member(_997463), _997465), hAPP(c_SetInterval_Oord__class_OgreaterThan(_997463), _997467))))], (12524 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_997463), _997465), hAPP(c_SetInterval_Oord__class_OgreaterThan(_997463), _997467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997463), _997467), _997465)))]]], (9176 ^ _781404) ^ [_937559, _937561] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937559, tc_HOL_Obool)), _937561), c_Orderings_Otop__class_Otop(tc_fun(_937559, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_937559, tc_HOL_Obool)))], (52594 ^ _781404) ^ [_1840761, _1840763] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1840761, _1840763)))], (3516 ^ _781404) ^ [_833962, _833964, _833966, _833968] : [-(c_Random_Opick(_833968, _833964) = c_Random_Opick(_833966, _833962)), _833968 = _833966, _833964 = _833962], (45863 ^ _781404) ^ [_1700812, _1700814, _1700816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1700812, tc_HOL_Obool)), _1700814), _1700816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1700812), tc_HOL_Obool)), c_List_Olistsp(_1700812, _1700814)), c_List_Olistsp(_1700812, _1700816))))], (52534 ^ _781404) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (39592 ^ _781404) ^ [_1547785, _1547787, _1547789] : [-(hAPP(c_Relation_ORange(_1547785, _1547787), hAPP(c_Set_OCollect(tc_prod(_1547785, _1547787)), hAPP(c_Product__Type_Oprod_Oprod__case(_1547785, _1547787, tc_HOL_Obool), _1547789))) = hAPP(c_Set_OCollect(_1547787), hAPP(hAPP(c_COMBB(tc_fun(_1547785, tc_HOL_Obool), tc_HOL_Obool, _1547787), c_HOL_OEx(_1547785)), hAPP(c_COMBC(_1547785, _1547787, tc_HOL_Obool), _1547789))))], (16340 ^ _781404) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25545 ^ _781404) ^ [_1237844, _1237846] : [-(hAPP(c_Int_Onat, _1237844) = _1237846), 25548 ^ _781404 : [(25551 ^ _781404) ^ [] : [_1237844 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1237846)], (25549 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237844)))]], 25552 ^ _781404 : [(25555 ^ _781404) ^ [] : [_1237846 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25553 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237844))]]], (33133 ^ _781404) ^ [_1379579, _1379581, _1379583, _1379585] : [class_Groups_Ocomm__monoid__add(_1379579), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379579), _1379581), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1379583), hAPP(c_Nat_OSuc, _1379585))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379579), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1379579, tc_Nat_Onat), _1379581), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1379583, _1379585)))], (39938 ^ _781404) ^ [_1557637] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1557637)))], (36468 ^ _781404) ^ [_1462905, _1462907, _1462909, _1462911] : [_1462905 = _1462907, 36471 ^ _781404 : [(36474 ^ _781404) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1462909, _1462911), _1462905) = hAPP(c_Product__Type_Osnd(_1462909, _1462911), _1462907))], (36472 ^ _781404) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1462909, _1462911), _1462905) = hAPP(c_Product__Type_Ofst(_1462909, _1462911), _1462907))]]], (50171 ^ _781404) ^ [_1795641, _1795643] : [c_Relation_Osym(_1795641, _1795643), -(c_Relation_Osym(_1795641, c_Transitive__Closure_Ortrancl(_1795641, _1795643)))], (26319 ^ _781404) ^ [_1251029] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251029) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1251029))], (51888 ^ _781404) ^ [_1831555, _1831557] : [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)))), _1831555, _1831557), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831555), _1831557)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831557), _1831555)))], (18717 ^ _781404) ^ [_1115171, _1115173] : [class_Int_Onumber__ring(_1115171), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115171), hAPP(c_Int_Onumber__class_Onumber__of(_1115171), c_Int_OPls)), _1115173) = _1115173)], (552 ^ _781404) ^ [_789692, _789694] : [-(c_Nat__Transfer_Onat__set(_789692)), _789694 = _789692, c_Nat__Transfer_Onat__set(_789694)], (52308 ^ _781404) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (7455 ^ _781404) ^ [_903114, _903116, _903118] : [class_Lattices_Osemilattice__inf(_903114), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903114), _903116), _903118) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903114), _903118), _903116))], (41833 ^ _781404) ^ [_1603217, _1603219, _1603221] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603217, _1603217)), _1603219), c_Transitive__Closure_Ortrancl(_1603217, _1603221))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603217, _1603217)), _1603219), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1603217, _1603217), 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(_1603217, _1603217), tc_HOL_Obool), tc_fun(tc_prod(_1603217, _1603217), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1603217, _1603217), tc_HOL_Obool)), _1603221)))))], (17407 ^ _781404) ^ [_1091924] : [-(c_Int_Opred(_1091924) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1091924), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (50955 ^ _781404) ^ [_1811581, _1811583, _1811585, _1811587, _1811589] : [c_Fun_Obij__betw(_1811581, _1811583, _1811585, _1811587, _1811589), 50958 ^ _781404 : [(50961 ^ _781404) ^ [] : [-(hAPP(c_Set_Oimage(_1811581, _1811583, _1811585), _1811587) = _1811589)], (50959 ^ _781404) ^ [] : [-(c_Fun_Oinj__on(_1811581, _1811583, _1811585, _1811587))]]], (12927 ^ _781404) ^ [_1005817, _1005819, _1005821, _1005823, _1005825, _1005827] : [_1005817 = _1005819, -(hAPP(c_Fun_Ofun__upd(_1005821, _1005823, _1005825, _1005819, _1005827), _1005817) = _1005827)], (49917 ^ _781404) ^ [_1790693, _1790695, _1790697, _1790699, _1790701] : [c_Predicate_Otransp(_1790693, _1790695), hBOOL(hAPP(hAPP(_1790695, _1790697), _1790699)), hBOOL(hAPP(hAPP(_1790695, _1790699), _1790701)), -(hBOOL(hAPP(hAPP(_1790695, _1790697), _1790701)))], (7117 ^ _781404) ^ [_896670, _896672, _896674, _896676] : [class_Lattices_Osemilattice__sup(_896670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896670), _896672), _896674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896670), _896672), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896670), _896674), _896676))))], (37639 ^ _781404) ^ [_1491584, _1491586, _1491588, _1491590, _1491592] : [c_Equiv__Relations_Oequiv(_1491584, _1491586, _1491588), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491584, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1491584, _1491584, _1491588), hAPP(hAPP(c_Set_Oinsert(_1491584), _1491590), c_Orderings_Obot__class_Obot(tc_fun(_1491584, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1491584, _1491584, _1491588), hAPP(hAPP(c_Set_Oinsert(_1491584), _1491592), c_Orderings_Obot__class_Obot(tc_fun(_1491584, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1491584), _1491590), _1491586)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491584, _1491584)), hAPP(hAPP(c_Product__Type_OPair(_1491584, _1491584), _1491592), _1491590)), _1491588)))], (16634 ^ _781404) ^ [_1077420, _1077422, _1077424] : [class_Rings_Oring__1(_1077420), hBOOL(hAPP(hAPP(c_member(_1077420), _1077422), c_Int_Oring__1__class_OInts(_1077420))), hBOOL(hAPP(hAPP(c_member(_1077420), _1077424), c_Int_Oring__1__class_OInts(_1077420))), -(hBOOL(hAPP(hAPP(c_member(_1077420), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077420), _1077422), _1077424)), c_Int_Oring__1__class_OInts(_1077420))))], (43268 ^ _781404) ^ [_1643771, _1643773, _1643775, _1643777] : [hBOOL(hAPP(c_List_Odistinct(_1643771), _1643773)), -(hBOOL(hAPP(hAPP(c_member(_1643771), _1643775), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1643771, tc_HOL_Obool)), hAPP(c_List_Oset(_1643771), _1643773)), hAPP(hAPP(c_Set_Oinsert(_1643771), hAPP(hAPP(c_List_Onth(_1643771), _1643773), _1643777)), c_Orderings_Obot__class_Obot(tc_fun(_1643771, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1643771), hAPP(hAPP(c_List_Olist__update(_1643771, _1643773), _1643777), _1643775))))], (42926 ^ _781404) ^ [_1634206, _1634208, _1634210] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1634206), _1634208)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1634206)), hAPP(c_Set_OCollect(tc_List_Olist(_1634206)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1634206), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1634206)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1634206), tc_fun(_1634206, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1634206, tc_HOL_Obool), tc_fun(tc_fun(_1634206, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1634206)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1634206, tc_HOL_Obool))), c_List_Oset(_1634206))), _1634208))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1634206), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1634206)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1634206)))), _1634210))))))], (43075 ^ _781404) ^ [_1639316, _1639318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639316), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1639318))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1639318), _1639316)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1639318))))], (20299 ^ _781404) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (31464 ^ _781404) ^ [_1347234, _1347236, _1347238] : [class_Orderings_Olinorder(_1347234), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347234), _1347236)), 31471 ^ _781404 : [(31478 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1347234, tc_HOL_Obool)), _1347236), hAPP(hAPP(c_Set_Oinsert(_1347234), _1347238), c_Orderings_Obot__class_Obot(tc_fun(_1347234, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1347234, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1347234, c_Orderings_Oord__class_Omin(_1347234), hAPP(hAPP(c_Set_Oinsert(_1347234), _1347238), _1347236)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1347234), _1347238), c_Big__Operators_Olattice_OInf__fin(_1347234, c_Orderings_Oord__class_Omin(_1347234), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1347234, tc_HOL_Obool)), _1347236), hAPP(hAPP(c_Set_Oinsert(_1347234), _1347238), c_Orderings_Obot__class_Obot(tc_fun(_1347234, tc_HOL_Obool)))))))], (31472 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1347234, tc_HOL_Obool)), _1347236), hAPP(hAPP(c_Set_Oinsert(_1347234), _1347238), c_Orderings_Obot__class_Obot(tc_fun(_1347234, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1347234, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1347234, c_Orderings_Oord__class_Omin(_1347234), hAPP(hAPP(c_Set_Oinsert(_1347234), _1347238), _1347236)) = _1347238)]]], (20681 ^ _781404) ^ [_1147930, _1147932, _1147934] : [class_Rings_Olinordered__semidom(_1147930), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147930), hAPP(hAPP(c_Power_Opower__class_Opower(_1147930), _1147932), 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(_1147930), _1147934), 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(_1147930), c_Groups_Ozero__class_Ozero(_1147930)), _1147934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147930), _1147932), _1147934)))], (18757 ^ _781404) ^ [_1115767, _1115769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115767)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115769))), 18760 ^ _781404 : [(18761 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1115767), _1115769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1115769)))], (18767 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1115767), _1115769)))]]], (21289 ^ _781404) ^ [_1159741, _1159743] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159741), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159741)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159743)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1159741), _1159743)))], (45678 ^ _781404) ^ [_1696575, _1696577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1696575), _1696577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1696575)), hAPP(c_Code__Numeral_Onat__of, _1696577))))], (1796 ^ _781404) ^ [_806894, _806896] : [-(class_Nat_Osemiring__char__0(_806894)), _806896 = _806894, class_Nat_Osemiring__char__0(_806896)], (594 ^ _781404) ^ [_790295, _790297, _790299, _790301, _790303, _790305] : [-(c_Finite__Set_Ofun__left__comm__idem(_790303, _790299, _790295)), c_Finite__Set_Ofun__left__comm__idem(_790305, _790301, _790297), _790305 = _790303, _790301 = _790299, _790297 = _790295], (33552 ^ _781404) ^ [_1392316, _1392318] : [-(hAPP(c_Set_Ovimage(_1392316, _1392316, c_COMBI(_1392316)), _1392318) = _1392318)], (31266 ^ _781404) ^ [_1343958, _1343960, _1343962] : [class_Orderings_Olinorder(_1343958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343958), _1343960)), hBOOL(hAPP(hAPP(c_member(_1343958), _1343962), _1343960)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1343958), _1343962), c_Big__Operators_Olinorder__class_OMin(_1343958, _1343960)) = c_Big__Operators_Olinorder__class_OMin(_1343958, _1343960))], (12907 ^ _781404) ^ [_1005419, _1005421] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1005419, _1005421))))], (9819 ^ _781404) ^ [_949170, _949172, _949174, _949176, _949178] : [class_Orderings_Oorder(_949170), 9822 ^ _781404 : [(9843 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_949170, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949170, _949172, _949174)), c_SetInterval_Oord__class_OatLeastAtMost(_949170, _949176, _949178)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949170), _949176), _949178)), 9846 ^ _781404 : [(9849 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949170), _949176), _949172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949170), _949174), _949178)), 9856 ^ _781404 : [(9859 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949170), _949174), _949178))], (9857 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949170), _949176), _949172))]]], (9847 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949170), _949172), _949174)))]]], (9823 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_949170, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949170, _949172, _949174)), c_SetInterval_Oord__class_OatLeastAtMost(_949170, _949176, _949178))), 9826 ^ _781404 : [(9827 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949170), _949172), _949174)), 9830 ^ _781404 : [(9835 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949170), _949176), _949172))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949170), _949174), _949178)))], (9833 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949170), _949174), _949178)))], (9831 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949170), _949176), _949172)))]]], (9841 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949170), _949176), _949178)))]]]]], (18267 ^ _781404) ^ [_1106899, _1106901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1106899)), -(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), _1106899), _1106901))))], (39175 ^ _781404) ^ [_1531528, _1531530, _1531532, _1531534, _1531536, _1531538] : [class_Groups_Ocomm__monoid__add(_1531528), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531530), _1531532)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1531530, _1531528), _1531534), _1531532) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1531536, _1531528), hAPP(hAPP(c_COMBB(tc_fun(_1531530, tc_HOL_Obool), _1531528, _1531536), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1531530, _1531528), _1531534)), hAPP(hAPP(c_COMBB(tc_fun(_1531530, tc_HOL_Obool), tc_fun(_1531530, tc_HOL_Obool), _1531536), c_Set_OCollect(_1531530)), hAPP(hAPP(c_COMBB(tc_fun(_1531530, tc_HOL_Obool), tc_fun(_1531530, tc_HOL_Obool), _1531536), hAPP(c_COMBS(_1531530, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1531530), c_fconj), hAPP(hAPP(c_COMBC(_1531530, tc_fun(_1531530, tc_HOL_Obool), tc_HOL_Obool), c_member(_1531530)), _1531532)))), hAPP(c_COMBC(_1531530, _1531536, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1531536, tc_fun(_1531536, tc_HOL_Obool), _1531530), c_fequal), _1531538)))))), hAPP(c_Set_Oimage(_1531530, _1531536, _1531538), _1531532)))], (20027 ^ _781404) ^ [_1137140, _1137142] : [c_Int_OBit0(_1137140) = c_Int_OBit0(_1137142), -(_1137140 = _1137142)], (52596 ^ _781404) ^ [_1840788, _1840790] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1840788, _1840790))), class_Lazy__Sequence_Osmall__lazy(_1840788), class_Lazy__Sequence_Osmall__lazy(_1840790)], (20817 ^ _781404) ^ [_1151085, _1151087, _1151089] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151085), _1151087)), _1151089) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151087), _1151089)))], (52426 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (43232 ^ _781404) ^ [_1642725, _1642727] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642725)), c_List_Obutlast(_1642725, _1642727)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642725)), _1642727)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (37427 ^ _781404) ^ [_1485645, _1485647, _1485649, _1485651] : [-(hAPP(c_Relation_OImage(_1485645, _1485647, _1485649), _1485651) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485645, tc_fun(_1485647, tc_HOL_Obool)), _1485651), hAPP(hAPP(c_COMBB(tc_fun(_1485645, tc_HOL_Obool), tc_fun(_1485647, tc_HOL_Obool), _1485645), c_Relation_OImage(_1485645, _1485647, _1485649)), hAPP(hAPP(c_COMBC(_1485645, tc_fun(_1485645, tc_HOL_Obool), tc_fun(_1485645, tc_HOL_Obool)), c_Set_Oinsert(_1485645)), c_Orderings_Obot__class_Obot(tc_fun(_1485645, tc_HOL_Obool))))))], (52616 ^ _781404) ^ [_1841046, _1841048] : [-(class_Enum_Oenum(tc_prod(_1841046, _1841048))), class_Enum_Oenum(_1841046), class_Enum_Oenum(_1841048)], (9971 ^ _781404) ^ [_951709, _951711, _951713, _951715] : [class_Orderings_Opreorder(_951709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951709), _951711), _951713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951709), _951713), _951715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951709), _951711), _951715)))], (35914 ^ _781404) ^ [_1451618, _1451620, _1451622, _1451624] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451618, _1451620), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1451622), _1451624))), -(_1451620 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1451618), _1451620) = _1451622)], (18309 ^ _781404) ^ [_1107550, _1107552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1107550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1107552)), -(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), _1107550), _1107552))))], (8544 ^ _781404) ^ [_925530, _925532, _925534] : [class_Lattices_Obounded__lattice__bot(_925530), 8547 ^ _781404 : [(8556 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925530), _925532), _925534) = c_Orderings_Obot__class_Obot(_925530)), _925532 = c_Orderings_Obot__class_Obot(_925530), _925534 = c_Orderings_Obot__class_Obot(_925530)], (8548 ^ _781404) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925530), _925532), _925534) = c_Orderings_Obot__class_Obot(_925530), 8551 ^ _781404 : [(8554 ^ _781404) ^ [] : [-(_925534 = c_Orderings_Obot__class_Obot(_925530))], (8552 ^ _781404) ^ [] : [-(_925532 = c_Orderings_Obot__class_Obot(_925530))]]]]], (46307 ^ _781404) ^ [_1710583, _1710585, _1710587] : [hBOOL(hAPP(c_List_Odistinct(_1710583), _1710585)), -(c_List_Oremove1(_1710583, _1710587, _1710585) = hAPP(c_List_OremoveAll(_1710583, _1710587), _1710585))], (34119 ^ _781404) ^ [_1407906, _1407908, _1407910] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407906, tc_HOL_Obool)), _1407908), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1407906, tc_HOL_Obool), _1407910)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1407906, tc_HOL_Obool), tc_fun(_1407906, tc_HOL_Obool)), _1407910), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407906, tc_HOL_Obool)), _1407908)))], (46048 ^ _781404) ^ [_1705015, _1705017, _1705019, _1705021, _1705023, _1705025] : [c_List_Olist__all2(_1705015, _1705017, _1705019, _1705021, _1705023), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1705025), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705015)), _1705021))), -(hBOOL(hAPP(hAPP(_1705019, hAPP(hAPP(c_List_Onth(_1705015), _1705021), _1705025)), hAPP(hAPP(c_List_Onth(_1705017), _1705023), _1705025))))], (656 ^ _781404) ^ [_791278, _791280] : [-(c_List_Onat__list(_791278)), _791280 = _791278, c_List_Onat__list(_791280)], (22667 ^ _781404) ^ [_1186565, _1186567, _1186569] : [class_Rings_Olinordered__semidom(_1186565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186565), c_Groups_Oone__class_Oone(_1186565)), _1186567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186565), c_Groups_Oone__class_Oone(_1186565)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186565), _1186567), hAPP(hAPP(c_Power_Opower__class_Opower(_1186565), _1186567), _1186569)))))], (28963 ^ _781404) ^ [_1299977, _1299979, _1299981] : [class_Fields_Olinordered__field(_1299977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299977), _1299979), c_Groups_Ozero__class_Ozero(_1299977))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299977), c_Groups_Ozero__class_Ozero(_1299977)), _1299981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299977), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299977), _1299979), _1299981)), c_Groups_Ozero__class_Ozero(_1299977))))], (52470 ^ _781404) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (16226 ^ _781404) ^ [_1069648, _1069650, _1069652] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1069648), _1069650)), 16229 ^ _781404 : [(16236 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1069648), _1069652), _1069650))), -(hAPP(c_Finite__Set_Ocard(_1069648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1069648, tc_HOL_Obool)), _1069650), hAPP(hAPP(c_Set_Oinsert(_1069648), _1069652), c_Orderings_Obot__class_Obot(tc_fun(_1069648, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1069648), _1069650))], (16230 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1069648), _1069652), _1069650)), -(hAPP(c_Finite__Set_Ocard(_1069648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1069648, tc_HOL_Obool)), _1069650), hAPP(hAPP(c_Set_Oinsert(_1069648), _1069652), c_Orderings_Obot__class_Obot(tc_fun(_1069648, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1069648), _1069650)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (40968 ^ _781404) ^ [_1581348, _1581350, _1581352, _1581354, _1581356, _1581358, _1581360, _1581362, _1581364] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1581348, _1581350, _1581352, _1581354), hAPP(hAPP(c_Product__Type_Oscomp(_1581348, _1581356, _1581358, tc_prod(_1581350, _1581352)), _1581360), _1581362)), _1581364) = hAPP(hAPP(c_Product__Type_Oscomp(_1581348, _1581356, _1581358, _1581354), _1581360), hAPP(hAPP(c_COMBC(_1581356, tc_fun(_1581350, tc_fun(_1581352, _1581354)), tc_fun(_1581358, _1581354)), hAPP(hAPP(c_COMBB(tc_fun(_1581358, tc_prod(_1581350, _1581352)), tc_fun(tc_fun(_1581350, tc_fun(_1581352, _1581354)), tc_fun(_1581358, _1581354)), _1581356), c_Product__Type_Oscomp(_1581358, _1581350, _1581352, _1581354)), _1581362)), _1581364)))], (41538 ^ _781404) ^ [_1595869, _1595871, _1595873, _1595875] : [-(hAPP(c_Relation_Oconverse(_1595869, _1595869), hAPP(hAPP(c_Relation_Oinv__image(_1595871, _1595869), _1595873), _1595875)) = hAPP(hAPP(c_Relation_Oinv__image(_1595871, _1595869), hAPP(c_Relation_Oconverse(_1595871, _1595871), _1595873)), _1595875))], (26385 ^ _781404) ^ [_1251901, _1251903] : [class_Int_Oring__char__0(_1251901), 26388 ^ _781404 : [(26395 ^ _781404) ^ [] : [_1251903 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1251901), _1251903) = c_Groups_Ozero__class_Ozero(_1251901))], (26389 ^ _781404) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1251901), _1251903) = c_Groups_Ozero__class_Ozero(_1251901), -(_1251903 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (9403 ^ _781404) ^ [_942612, _942614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942612), _942614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _942612)), hAPP(c_Nat_OSuc, _942614))))], (34223 ^ _781404) ^ [_1412211, _1412213, _1412215, _1412217] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1412211, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412213, tc_fun(tc_fun(_1412211, tc_HOL_Obool), tc_HOL_Obool)), _1412215), hAPP(hAPP(c_COMBB(tc_fun(_1412211, tc_HOL_Obool), tc_fun(tc_fun(_1412211, tc_HOL_Obool), tc_HOL_Obool), _1412213), c_Set_OPow(_1412211)), _1412217))), hAPP(c_Set_OPow(_1412211), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412213, tc_fun(_1412211, tc_HOL_Obool)), _1412215), _1412217)))))], (34777 ^ _781404) ^ [_1427479, _1427481, _1427483] : [-(hAPP(c_Divides_Oadjust(_1427479), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1427481), _1427483)) = 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), _1427483), _1427479)), 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)))), _1427481)), 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)))), _1427481)), _1427483))))], (21111 ^ _781404) ^ [_1156297, _1156299, _1156301] : [class_Rings_Oidom(_1156297), 21114 ^ _781404 : [(21115 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156297), _1156299), _1156299) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156297), _1156301), _1156301), -(_1156299 = _1156301), -(_1156299 = hAPP(c_Groups_Ouminus__class_Ouminus(_1156297), _1156301))], (21125 ^ _781404) ^ [] : [21126 ^ _781404 : [(21129 ^ _781404) ^ [] : [_1156299 = hAPP(c_Groups_Ouminus__class_Ouminus(_1156297), _1156301)], (21127 ^ _781404) ^ [] : [_1156299 = _1156301]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156297), _1156299), _1156299) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156297), _1156301), _1156301))]]], (47675 ^ _781404) ^ [_1740157, _1740159, _1740161] : [class_Orderings_Olinorder(_1740157), c_List_Olinorder__class_Osorted(_1740157, _1740159), -(c_List_Olinorder__class_Osorted(_1740157, c_List_OtakeWhile(_1740157, _1740161, _1740159)))], (36144 ^ _781404) ^ [_1456020, _1456022, _1456024] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1456020, _1456022), _1456024)), 36147 ^ _781404 : [(36148 ^ _781404) ^ [_1456105] : [hBOOL(hAPP(hAPP(_1456022, _1456105), _1456024)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1456020, _1456022), _1456105)))]]], (8970 ^ _781404) ^ [_933309] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _933309)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _933309)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _933309), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (18689 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (16549 ^ _781404) ^ [_1075747, _1075749] : [class_Rings_Olinordered__idom(_1075747), hBOOL(hAPP(hAPP(c_member(_1075747), _1075749), c_Int_Oring__1__class_OInts(_1075747))), 16556 ^ _781404 : [(16563 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075747), _1075749), c_Groups_Ozero__class_Ozero(_1075747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075747), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075747), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075747), c_Groups_Oone__class_Oone(_1075747)), _1075749)), _1075749)), c_Groups_Ozero__class_Ozero(_1075747))))], (16557 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075747), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075747), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075747), c_Groups_Oone__class_Oone(_1075747)), _1075749)), _1075749)), c_Groups_Ozero__class_Ozero(_1075747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075747), _1075749), c_Groups_Ozero__class_Ozero(_1075747))))]]], (16730 ^ _781404) ^ [_1079220, _1079222, _1079224, _1079226, _1079228] : [c_Finite__Set_Ofolding__one__idem(_1079220, _1079222, _1079224), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079220), _1079226)), -(_1079226 = c_Orderings_Obot__class_Obot(tc_fun(_1079220, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079220), _1079228)), -(_1079228 = c_Orderings_Obot__class_Obot(tc_fun(_1079220, tc_HOL_Obool))), -(hAPP(_1079224, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1079220, tc_HOL_Obool)), _1079226), _1079228)) = hAPP(hAPP(_1079222, hAPP(_1079224, _1079226)), hAPP(_1079224, _1079228)))], (36925 ^ _781404) ^ [_1473123, _1473125, _1473127, _1473129, _1473131, _1473133, _1473135, _1473137] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1473123, _1473125), tc_prod(_1473123, _1473125))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1473123, _1473125), tc_prod(_1473123, _1473125)), hAPP(hAPP(c_Product__Type_OPair(_1473123, _1473125), _1473127), _1473129)), hAPP(hAPP(c_Product__Type_OPair(_1473123, _1473125), _1473131), _1473133))), c_Wellfounded_Olex__prod(_1473123, _1473125, _1473135, _1473137))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1473123, _1473123)), hAPP(hAPP(c_Product__Type_OPair(_1473123, _1473123), _1473127), _1473131)), _1473135))), 36932 ^ _781404 : [(36935 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1473125, _1473125)), hAPP(hAPP(c_Product__Type_OPair(_1473125, _1473125), _1473129), _1473133)), _1473137)))], (36933 ^ _781404) ^ [] : [-(_1473127 = _1473131)]]], (8834 ^ _781404) ^ [_930512] : [class_Lattices_Oboolean__algebra(_930512), -(hAPP(c_Groups_Ouminus__class_Ouminus(_930512), c_Orderings_Obot__class_Obot(_930512)) = c_Orderings_Otop__class_Otop(_930512))], (7581 ^ _781404) ^ [_905784, _905786, _905788, _905790] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905784, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_905784), _905786), _905788)), hAPP(hAPP(c_Set_Oinsert(_905784), _905786), _905790)) = hAPP(hAPP(c_Set_Oinsert(_905784), _905786), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905784, tc_HOL_Obool)), _905788), _905790)))], (44691 ^ _781404) ^ [_1675381, _1675383, _1675385] : [-(_1675381 = c_List_Olist_ONil(_1675383)), -(hAPP(hAPP(c_List_Otake(_1675383), hAPP(c_Nat_OSuc, _1675385)), _1675381) = hAPP(hAPP(c_List_Olist_OCons(_1675383), hAPP(c_List_Ohd(_1675383), _1675381)), hAPP(hAPP(c_List_Otake(_1675383), _1675385), hAPP(c_List_Otl(_1675383), _1675381))))], (8040 ^ _781404) ^ [_915918] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _915918)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _915918), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _915918)))], (18705 ^ _781404) ^ [_1114983] : [class_Int_Onumber__ring(_1114983), -(hAPP(c_Int_Onumber__class_Onumber__of(_1114983), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1114983))], (3138 ^ _781404) ^ [_828085, _828087, _828089, _828091] : [-(c_List_Olistrel1(_828091, _828087) = c_List_Olistrel1(_828089, _828085)), _828091 = _828089, _828087 = _828085], (6661 ^ _781404) ^ [_887939, _887941] : [class_Orderings_Olinorder(_887939), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_887939, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_887939), _887941)) = hAPP(c_SetInterval_Oord__class_OlessThan(_887939), _887941))], (13077 ^ _781404) ^ [_1008369, _1008371, _1008373, _1008375, _1008377] : [class_Groups_Oordered__ab__semigroup__add(_1008369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008369), _1008371), _1008373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008369), _1008375), _1008377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008369), _1008371), _1008375)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008369), _1008373), _1008377))))], (14587 ^ _781404) ^ [_1037034] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1037034), c_Orderings_Obot__class_Obot(tc_fun(_1037034, tc_HOL_Obool)))))], (47297 ^ _781404) ^ [_1731976, _1731978, _1731980] : [class_Orderings_Olinorder(_1731976), hBOOL(hAPP(hAPP(c_member(_1731976), _1731978), hAPP(c_List_Oset(_1731976), _1731980))), c_List_Olinorder__class_Osorted(_1731976, _1731980), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1731976, _1731976, c_COMBI(_1731976)), _1731978), c_List_Oremove1(_1731976, _1731978, _1731980)) = _1731980)], (48987 ^ _781404) ^ [_1768562, _1768564, _1768566, _1768568, _1768570] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1768562, _1768564, _1768566), _1768568), _1768570)), -(hBOOL(hAPP(hAPP(_1768566, _1768570), _1768568)))], (44657 ^ _781404) ^ [_1674653, _1674655] : [-(c_List_Orotate(_1674653, _1674655) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1674653), tc_List_Olist(_1674653)), _1674655), c_List_Orotate1(_1674653)))], (19563 ^ _781404) ^ [_1129231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129231), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1129231)), c_Int_OPls)))], (41253 ^ _781404) ^ [_1589156, _1589158, _1589160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1589156, _1589156), tc_HOL_Obool)), _1589158), c_Transitive__Closure_Ortrancl(_1589156, _1589160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1589156, _1589156), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1589156, _1589158)), c_Transitive__Closure_Ortrancl(_1589156, _1589160))))], (19191 ^ _781404) ^ [_1122772] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1122772) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1122772 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49823 ^ _781404) ^ [_1787251, _1787253, _1787255] : [-(c_List_Olist__ex(_1787251, _1787253, _1787255)), 49824 ^ _781404 : [(49825 ^ _781404) ^ [_1787308] : [hBOOL(hAPP(hAPP(c_member(_1787251), _1787308), hAPP(c_List_Oset(_1787251), _1787255))), hBOOL(hAPP(_1787253, _1787308))]]], (17597 ^ _781404) ^ [_1095136, _1095138] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095136), _1095138))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095136), _1095138)), -(_1095136 = _1095138)], (27550 ^ _781404) ^ [_1273334, _1273336, _1273338] : [class_Lattices_Oab__semigroup__idem__mult(_1273334), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273334), _1273336)), -(hAPP(c_Finite__Set_Ofold1(_1273334, c_Groups_Otimes__class_Otimes(_1273334)), hAPP(hAPP(c_Set_Oinsert(_1273334), _1273338), _1273336)) = hAPP(hAPP(c_Finite__Set_Ofold(_1273334, _1273334, c_Groups_Otimes__class_Otimes(_1273334)), _1273338), _1273336))], (50523 ^ _781404) ^ [_1801885, _1801887, _1801889, _1801891, _1801893] : [hBOOL(hAPP(hAPP(c_member(_1801885), _1801887), hAPP(c_Set_Oimage(_1801889, _1801885, _1801891), _1801893))), -(hBOOL(hAPP(hAPP(c_member(_1801889), hAPP(c_Hilbert__Choice_Oinv__into(_1801889, _1801885, _1801893, _1801891), _1801887)), _1801893)))], (33331 ^ _781404) ^ [_1384612, _1384614, _1384616, _1384618, _1384620, _1384622] : [-(hAPP(c_Set_Oimage(_1384612, _1384614, hAPP(c_Fun_Ocomp(_1384616, _1384614, _1384612, _1384618), _1384620)), _1384622) = hAPP(c_Set_Oimage(_1384616, _1384614, _1384618), hAPP(c_Set_Oimage(_1384612, _1384616, _1384620), _1384622)))], (24887 ^ _781404) ^ [_1227443, _1227445] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227443), _1227445))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1227443, _1227445) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1227443), _1227445), _1227445))], (46672 ^ _781404) ^ [_1719923, _1719925, _1719927, _1719929] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1719923, tc_Nat_Onat), _1719923), c_Product__Type_Ofst(_1719923, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1719923, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1719923, tc_Nat_Onat)), _1719925), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1719923, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1719923, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1719923, tc_Nat_Onat), _1719927), _1719929))) = hAPP(hAPP(c_List_Omap(tc_prod(_1719923, tc_Nat_Onat), _1719923), c_Product__Type_Ofst(_1719923, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1719923, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1719923, tc_Nat_Onat)), _1719925), c_Product__Type_Osnd(_1719923, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1719923, tc_Nat_Onat), _1719927), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1719929)))))], (39542 ^ _781404) ^ [_1546393] : [-(hAPP(c_Set_Oimage(_1546393, _1546393, c_Fun_Oid(_1546393)), c_Orderings_Otop__class_Otop(tc_fun(_1546393, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1546393, tc_HOL_Obool)))], (30442 ^ _781404) ^ [_1328551, _1328553] : [30443 ^ _781404 : [(30446 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1328553), _1328551))], (30444 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1328551), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1328551, _1328553) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (13091 ^ _781404) ^ [_1008640, _1008642, _1008644, _1008646] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1008640), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008640), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008640), _1008642), _1008644)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008640), _1008646), _1008644))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008640), _1008642), _1008646)))], (47481 ^ _781404) ^ [_1735955, _1735957, _1735959, _1735961] : [-(hAPP(c_List_Orev(_1735955), hAPP(hAPP(c_List_Omap(_1735957, _1735955), _1735959), _1735961)) = hAPP(hAPP(c_List_Omap(_1735957, _1735955), _1735959), hAPP(c_List_Orev(_1735957), _1735961)))], (29303 ^ _781404) ^ [_1305875, _1305877, _1305879] : [class_Fields_Olinordered__field(_1305875), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305875), c_Groups_Ozero__class_Ozero(_1305875)), _1305877)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305875), c_Groups_Ozero__class_Ozero(_1305875)), _1305879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305875), c_Groups_Ozero__class_Ozero(_1305875)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305875), _1305877), _1305879))))], (41923 ^ _781404) ^ [_1605557, _1605559, _1605561, _1605563] : [-(hAPP(hAPP(c_Nat_Ocompow(_1605557, _1605557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1605559), _1605561)), _1605563) = hAPP(c_Fun_Ocomp(_1605557, _1605557, _1605557, hAPP(hAPP(c_Nat_Ocompow(_1605557, _1605557), _1605559), _1605563)), hAPP(hAPP(c_Nat_Ocompow(_1605557, _1605557), _1605561), _1605563)))], (50807 ^ _781404) ^ [_1808472, _1808474, _1808476, _1808478, _1808480] : [c_Fun_Obij__betw(_1808472, _1808474, _1808476, c_Orderings_Otop__class_Otop(tc_fun(_1808472, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808474, tc_HOL_Obool))), c_Fun_Obij__betw(_1808478, _1808472, _1808480, c_Orderings_Otop__class_Otop(tc_fun(_1808478, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808472, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1808478, _1808474, c_Orderings_Otop__class_Otop(tc_fun(_1808478, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1808472, _1808474, _1808478, _1808476), _1808480)) = hAPP(c_Fun_Ocomp(_1808472, _1808478, _1808474, c_Hilbert__Choice_Oinv__into(_1808478, _1808472, c_Orderings_Otop__class_Otop(tc_fun(_1808478, tc_HOL_Obool)), _1808480)), c_Hilbert__Choice_Oinv__into(_1808472, _1808474, c_Orderings_Otop__class_Otop(tc_fun(_1808472, tc_HOL_Obool)), _1808476)))], (720 ^ _781404) ^ [_792234, _792236, _792238, _792240, _792242, _792244] : [-(c_List_Oall__interval__nat(_792242, _792238, _792234)), c_List_Oall__interval__nat(_792244, _792240, _792236), _792244 = _792242, _792240 = _792238, _792236 = _792234], (13237 ^ _781404) ^ [_1011316, _1011318, _1011320] : [class_Groups_Ogroup__add(_1011316), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011316), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011316), _1011318), _1011320)), _1011320) = _1011318)], (32840 ^ _781404) ^ [_1373049, _1373051] : [class_Orderings_Olinorder(_1373049), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373049), _1373051)), -(_1373051 = c_Orderings_Obot__class_Obot(tc_fun(_1373049, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1373049), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373049), 32853 ^ [_1373049, _1373051]), 32854 ^ [_1373049, _1373051])), hAPP(hAPP(c_Set_Oinsert(_1373049), 32853 ^ [_1373049, _1373051]), hAPP(hAPP(c_Set_Oinsert(_1373049), 32854 ^ [_1373049, _1373051]), c_Orderings_Obot__class_Obot(tc_fun(_1373049, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1373049), c_Big__Operators_Olattice_OSup__fin(_1373049, c_Orderings_Oord__class_Omax(_1373049), _1373051)), _1373051)))], (26669 ^ _781404) ^ [_1256709, _1256711, _1256713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256709)), 26675 ^ _781404 : [(26678 ^ _781404) ^ [] : [hBOOL(hAPP(_1256711, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26674 ^ [_1256709, _1256711, _1256713]), _1256709)))], (26676 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1256711, 26674 ^ [_1256709, _1256711, _1256713])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256713)), 26683 ^ _781404 : [(26684 ^ _781404) ^ [_1256998] : [hBOOL(hAPP(_1256711, _1256998)), -(hBOOL(hAPP(_1256711, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1256998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1256713), _1256709)))))]]], (39272 ^ _781404) ^ [_1534945, _1534947] : [-(hAPP(c_Set_OPow(_1534945), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1534945, tc_HOL_Obool)), _1534947)) = hAPP(c_Set_OCollect(tc_fun(_1534945, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1534945, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1534945, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1534945, tc_HOL_Obool), tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1534945, tc_HOL_Obool)), c_COMBS(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1534945, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1534945, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1534945, tc_HOL_Obool), tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_fun(_1534945, tc_HOL_Obool)), tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_fun(_1534945, tc_HOL_Obool)), tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1534945, tc_HOL_Obool)), c_COMBB(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1534945, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1534945, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1534945, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1534945, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1534945, tc_HOL_Obool)), _1534947)), c_Set_OPow(_1534945))))))], (5462 ^ _781404) ^ [_864871, _864873, _864875, _864877, _864879, _864881, _864883, _864885, _864887, _864889] : [-(c_SetInterval_Oord_OatLeastLessThan(_864889, _864885, _864881, _864877, _864873) = c_SetInterval_Oord_OatLeastLessThan(_864887, _864883, _864879, _864875, _864871)), _864889 = _864887, _864885 = _864883, _864881 = _864879, _864877 = _864875, _864873 = _864871], (46605 ^ _781404) ^ [_1717677, _1717679] : [-(c_List_OremoveAll(_1717677, _1717679) = c_List_Ofilter(_1717677, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1717677), c_fNot), hAPP(c_fequal, _1717679))))], (42664 ^ _781404) ^ [_1627701] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1627701)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1627701), tc_HOL_Obool))))], (44806 ^ _781404) ^ [_1677772, _1677774, _1677776] : [class_Orderings_Olinorder(_1677772), -(c_Big__Operators_Olinorder__class_OMax(_1677772, hAPP(c_List_Oset(_1677772), hAPP(hAPP(c_List_Olist_OCons(_1677772), _1677774), _1677776))) = hAPP(c_List_Ofoldl(_1677772, _1677772, c_Orderings_Oord__class_Omax(_1677772), _1677774), _1677776))], (22205 ^ _781404) ^ [_1177076, _1177078] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1177076)), _1177078) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1177078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177076), _1177078)))], (10679 ^ _781404) ^ [_962902, _962904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962902), _962904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962902), _962904))), -(_962902 = _962904)], (36008 ^ _781404) ^ [_1453449, _1453451] : [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), _1453449), _1453451))), 36011 ^ _781404 : [(36020 ^ _781404) ^ [] : [-(c_Divides_OposDivAlg(_1453449, _1453451) = hAPP(c_Divides_Oadjust(_1453451), c_Divides_OposDivAlg(_1453449, 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)))), _1453451)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453449), _1453451))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1453451), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36012 ^ _781404) ^ [] : [36013 ^ _781404 : [(36016 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1453451), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36014 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453449), _1453451))]], -(c_Divides_OposDivAlg(_1453449, _1453451) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1453449))]]], (21713 ^ _781404) ^ [_1167479, _1167481, _1167483] : [class_Rings_Olinordered__semiring__strict(_1167479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167479), c_Groups_Ozero__class_Ozero(_1167479)), _1167481)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167479), _1167483), c_Groups_Ozero__class_Ozero(_1167479))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167479), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167479), _1167481), _1167483)), c_Groups_Ozero__class_Ozero(_1167479))))], (19023 ^ _781404) ^ [_1120036, _1120038] : [-(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), _1120036))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1120038))))], (19384 ^ _781404) ^ [_1126148, _1126150] : [class_Rings_Olinordered__semidom(_1126148), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126148), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1126148), _1126150)), c_Groups_Ozero__class_Ozero(_1126148)))], (8972 ^ _781404) ^ [_933353, _933355, _933357] : [class_Orderings_Oorder(_933353), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933353, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_933353, _933355, _933357)), hAPP(c_SetInterval_Oord__class_OatLeast(_933353), _933357)) = c_Orderings_Obot__class_Obot(tc_fun(_933353, tc_HOL_Obool)))], (2450 ^ _781404) ^ [_817327, _817329, _817331, _817333] : [-(c_Nitpick_Onat__gcd(_817333, _817329) = c_Nitpick_Onat__gcd(_817331, _817327)), _817333 = _817331, _817329 = _817327], (52442 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (3016 ^ _781404) ^ [_826158, _826160] : [_826160 = _826158, -(c_Nitpick_Onum(_826160) = c_Nitpick_Onum(_826158))], (44687 ^ _781404) ^ [_1675276, _1675278] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675276)), hAPP(c_List_Otl(_1675276), _1675278)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675276)), _1675278)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (28761 ^ _781404) ^ [_1296130, _1296132, _1296134, _1296136] : [class_Fields_Olinordered__field(_1296130), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296130), c_Groups_Ozero__class_Ozero(_1296130)), _1296132)), 28768 ^ _781404 : [(28775 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296130), _1296134), _1296132)), _1296136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296130), _1296134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296130), _1296136), _1296132))))], (28769 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296130), _1296134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296130), _1296136), _1296132))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296130), _1296134), _1296132)), _1296136)))]]], (18729 ^ _781404) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (44361 ^ _781404) ^ [_1668070, _1668072, _1668074, _1668076] : [-(hAPP(hAPP(c_List_Odrop(_1668070), _1668072), hAPP(hAPP(c_List_Otake(_1668070), _1668074), _1668076)) = hAPP(hAPP(c_List_Otake(_1668070), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1668074), _1668072)), hAPP(hAPP(c_List_Odrop(_1668070), _1668072), _1668076)))], (13351 ^ _781404) ^ [_1013438, _1013440, _1013442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013438), _1013440)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013438), _1013442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013440), _1013442)))], (41542 ^ _781404) ^ [_1595983, _1595985, _1595987] : [c_Relation_Orefl__on(_1595983, _1595985, hAPP(c_Relation_Oconverse(_1595983, _1595983), _1595987)), -(c_Relation_Orefl__on(_1595983, _1595985, _1595987))], (3324 ^ _781404) ^ [_831016, _831018] : [_831018 = _831016, -(c_Random_Orange(_831018) = c_Random_Orange(_831016))], (8459 ^ _781404) ^ [_924086] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _924086)], (43719 ^ _781404) ^ [_1652724, _1652726] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652724)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652726)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652724), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652726)) = c_List_Olist_ONil(tc_Int_Oint))], (10587 ^ _781404) ^ [_961484, _961486] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961484), _961486))), 10590 ^ _781404 : [(10597 ^ _781404) ^ [] : [_961484 = _961486, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961484), hAPP(c_Nat_OSuc, _961486))))], (10591 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961484), hAPP(c_Nat_OSuc, _961486))), -(_961484 = _961486)]]], (32360 ^ _781404) ^ [_1364339, _1364341, _1364343, _1364345] : [class_Orderings_Olinorder(_1364339), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364339, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1364339, _1364341, _1364343)), hAPP(c_SetInterval_Oord__class_OatLeast(_1364339), _1364345)) = c_SetInterval_Oord__class_OatLeastAtMost(_1364339, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364339), _1364341), _1364345), _1364343))], (49374 ^ _781404) ^ [_1776921] : [-(c_List_Omember(_1776921) = c_List_Oset(_1776921))], (21169 ^ _781404) ^ [_1157469] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157469), _1157469)))))], (4110 ^ _781404) ^ [_843613, _843615] : [_843615 = _843613, -(c_New__Random__Sequence_Oneg__single(_843615) = c_New__Random__Sequence_Oneg__single(_843613))], (5320 ^ _781404) ^ [_862614, _862616, _862618, _862620, _862622, _862624] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_862624, _862620, _862616) = c_Lazy__Sequence_Olazy__sequence_OInsert(_862622, _862618, _862614)), _862624 = _862622, _862620 = _862618, _862616 = _862614], (19797 ^ _781404) ^ [_1133009, _1133011] : [class_Int_Onumber__ring(_1133009), class_Rings_Olinordered__idom(_1133009), 19804 ^ _781404 : [(19811 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1133011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133009), c_Groups_Oone__class_Oone(_1133009)), hAPP(c_Int_Onumber__class_Onumber__of(_1133009), _1133011))))], (19805 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133009), c_Groups_Oone__class_Oone(_1133009)), hAPP(c_Int_Onumber__class_Onumber__of(_1133009), _1133011))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1133011)))]]], (36514 ^ _781404) ^ [_1463760, _1463762, _1463764, _1463766, _1463768] : [hAPP(c_Product__Type_Ofst(_1463760, _1463762), hAPP(hAPP(c_Product__Type_OPair(_1463760, _1463762), _1463764), _1463766)) = _1463768, -(_1463764 = _1463768)], (10957 ^ _781404) ^ [_967467, _967469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967467), _967469)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967467), _967469) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51640 ^ _781404) ^ [_1827225, _1827227, _1827229, _1827231] : [class_Rings_Odvd(_1827225), _1827227 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827225), _1827229), _1827231), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827225), _1827229), _1827227)))], (45481 ^ _781404) ^ [_1692611, _1692613] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1692611)), hAPP(c_Code__Numeral_Oof__nat, _1692613)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1692611), _1692613)))], (2466 ^ _781404) ^ [_817561, _817563, _817565, _817567] : [-(c_Divides_Odivmod__int(_817567, _817563) = c_Divides_Odivmod__int(_817565, _817561)), _817567 = _817565, _817563 = _817561], (13794 ^ _781404) ^ [_1021984, _1021986, _1021988] : [class_Groups_Oordered__comm__monoid__add(_1021984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021984), c_Groups_Ozero__class_Ozero(_1021984)), _1021986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021984), c_Groups_Ozero__class_Ozero(_1021984)), _1021988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021984), c_Groups_Ozero__class_Ozero(_1021984)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021984), _1021986), _1021988))))], (12286 ^ _781404) ^ [_992734, _992736, _992738, _992740] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_992734, tc_HOL_Obool)), hAPP(c_Set_Oimage(_992736, _992734, _992738), hAPP(c_Set_Ovimage(_992736, _992734, _992738), _992740))), _992740)))], (51692 ^ _781404) ^ [_1828106, _1828108, _1828110, _1828112] : [class_Rings_Oidom(_1828106), 51695 ^ _781404 : [(51696 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828106), _1828108), _1828110)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828106), _1828112), _1828110))), -(_1828110 = c_Groups_Ozero__class_Ozero(_1828106)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828106), _1828108), _1828112)))], (51706 ^ _781404) ^ [] : [51707 ^ _781404 : [(51710 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828106), _1828108), _1828112))], (51708 ^ _781404) ^ [] : [_1828110 = c_Groups_Ozero__class_Ozero(_1828106)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828106), _1828108), _1828110)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828106), _1828112), _1828110))))]]], (50221 ^ _781404) ^ [_1796399, _1796401] : [hAPP(c_Relation_Oconverse(_1796399, _1796399), _1796401) = _1796401, -(c_Relation_Osym(_1796399, _1796401))], (20383 ^ _781404) ^ [_1143176] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143176))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143176)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16969 ^ _781404) ^ [_1083410, _1083412] : [class_Rings_Olinordered__idom(_1083410), 16972 ^ _781404 : [(16979 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083410), _1083412), c_Groups_Ozero__class_Ozero(_1083410))), -(c_Groups_Osgn__class_Osgn(_1083410, _1083412) = hAPP(c_Groups_Ouminus__class_Ouminus(_1083410), c_Groups_Oone__class_Oone(_1083410)))], (16973 ^ _781404) ^ [] : [c_Groups_Osgn__class_Osgn(_1083410, _1083412) = hAPP(c_Groups_Ouminus__class_Ouminus(_1083410), c_Groups_Oone__class_Oone(_1083410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083410), _1083412), c_Groups_Ozero__class_Ozero(_1083410))))]]], (46443 ^ _781404) ^ [_1713443, _1713445, _1713447] : [46445 ^ _781404 : [(46448 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1713443), tc_List_Olist(_1713443), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1713443), tc_fun(tc_List_Olist(_1713443), tc_Nat_Onat), tc_fun(tc_List_Olist(_1713443), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1713443), tc_Nat_Onat), tc_fun(tc_List_Olist(_1713443), tc_HOL_Obool)), tc_List_Olist(_1713443)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1713443))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1713443)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1713443))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1713443)))), 46444 ^ [_1713443, _1713445, _1713447]))], (46446 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713443), tc_List_Olist(_1713443))), 46444 ^ [_1713443, _1713445, _1713447]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1713443), tc_List_Olist(_1713443))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1713443), tc_List_Olist(_1713443)), _1713445), _1713447)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1713443))), _1713445) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1713443))), _1713447), 46453 ^ _781404 : [(46460 ^ _781404) ^ [] : [_1713445 = _1713447, -(c_List_Oconcat(_1713443, _1713445) = c_List_Oconcat(_1713443, _1713447))], (46454 ^ _781404) ^ [] : [c_List_Oconcat(_1713443, _1713445) = c_List_Oconcat(_1713443, _1713447), -(_1713445 = _1713447)]]], (11673 ^ _781404) ^ [_981265, _981267, _981269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981265), _981267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981265), _981269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981269), _981267)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981269), _981265))))], (39001 ^ _781404) ^ [_1526415] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1526415, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1526415), hAPP(c_COMBK(tc_HOL_Obool, _1526415), c_fFalse)))], (9002 ^ _781404) ^ [_933992, _933994, _933996, _933998, _934000] : [class_Groups_Ominus(_933992), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_933994, _933992)), _933996), _933998), _934000) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933992), hAPP(_933996, _934000)), hAPP(_933998, _934000)))], (20249 ^ _781404) ^ [_1140954] : [-(c_Int_Opred(c_Int_OBit1(_1140954)) = c_Int_OBit0(_1140954))], (47716 ^ _781404) ^ [_1740989, _1740991, _1740993, _1740995, _1740997] : [-(hAPP(hAPP(c_List_Ozip(_1740989, _1740991), c_List_OtakeWhile(_1740989, _1740993, _1740995)), _1740997) = c_List_OtakeWhile(tc_prod(_1740989, _1740991), hAPP(c_Fun_Ocomp(_1740989, tc_HOL_Obool, tc_prod(_1740989, _1740991), _1740993), c_Product__Type_Ofst(_1740989, _1740991)), hAPP(hAPP(c_List_Ozip(_1740989, _1740991), _1740995), _1740997)))], (46273 ^ _781404) ^ [_1710004, _1710006] : [_1710006 = c_List_Olist_ONil(_1710004), -(c_List_Oremdups(_1710004, _1710006) = c_List_Olist_ONil(_1710004))], (45180 ^ _781404) ^ [_1684906, _1684908, _1684910, _1684912, _1684914] : [-(hAPP(c_List_Orotate(_1684906, _1684908), hAPP(hAPP(c_List_Omap(_1684910, _1684906), _1684912), _1684914)) = hAPP(hAPP(c_List_Omap(_1684910, _1684906), _1684912), hAPP(c_List_Orotate(_1684910, _1684908), _1684914)))], (19544 ^ _781404) ^ [_1128879, _1128881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128879), _1128881)), -(_1128881 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1128879), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 19547 ^ [_1128879, _1128881]))))], (8800 ^ _781404) ^ [_929858, _929860, _929862, _929864] : [class_Orderings_Oorder(_929858), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929858, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_929858, _929860, _929862)), c_SetInterval_Oord__class_OgreaterThanAtMost(_929858, _929862, _929864)) = c_Orderings_Obot__class_Obot(tc_fun(_929858, tc_HOL_Obool)))], (32955 ^ _781404) ^ [_1375386, _1375388, _1375390, _1375392, _1375394, _1375396] : [-(c_Nitpick_Opair__box_Opair__box__size(_1375386, _1375388, _1375390, _1375392, c_Nitpick_Opair__box_OPairBox(_1375386, _1375388, _1375394, _1375396)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1375390, _1375394)), hAPP(_1375392, _1375396))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (30940 ^ _781404) ^ [_1337652, _1337654, _1337656, _1337658, _1337660] : [class_Lattices_Osemilattice__inf(_1337652), class_Orderings_Olinorder(_1337654), c_Orderings_Oorder__class_Omono(_1337654, _1337652, _1337656), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337652), hAPP(_1337656, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1337654), _1337658), _1337660))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1337652), hAPP(_1337656, _1337658)), hAPP(_1337656, _1337660)))))], (2020 ^ _781404) ^ [_810558, _810560, _810562, _810564, _810566, _810568] : [-(c_SetInterval_Oord_OatMost(_810568, _810564, _810560) = c_SetInterval_Oord_OatMost(_810566, _810562, _810558)), _810568 = _810566, _810564 = _810562, _810560 = _810558], (48678 ^ _781404) ^ [_1762162, _1762164, _1762166, _1762168] : [c_List_Olist__all(_1762162, _1762164, hAPP(hAPP(c_List_Oappend(_1762162), _1762166), _1762168)), 48681 ^ _781404 : [(48684 ^ _781404) ^ [] : [-(c_List_Olist__all(_1762162, _1762164, _1762168))], (48682 ^ _781404) ^ [] : [-(c_List_Olist__all(_1762162, _1762164, _1762166))]]], (1656 ^ _781404) ^ [_805144, _805146] : [-(class_Rings_Oordered__comm__semiring(_805144)), _805146 = _805144, class_Rings_Oordered__comm__semiring(_805146)], (23643 ^ _781404) ^ [_1206036, _1206038, _1206040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206036)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206038, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1206040), _1206036)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1206040), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1206038), _1206040), _1206036))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206038, _1206040)))], (39139 ^ _781404) ^ [_1529956, _1529958] : [-(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), _1529956)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1529958))))))], (43014 ^ _781404) ^ [_1637854, _1637856, _1637858, _1637860, _1637862, _1637864] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637854, _1637856)), hAPP(hAPP(c_Product__Type_OPair(_1637854, _1637856), _1637858), _1637860)), hAPP(c_List_Oset(tc_prod(_1637854, _1637856)), hAPP(hAPP(c_List_Ozip(_1637854, _1637856), _1637862), _1637864)))), -(hBOOL(hAPP(hAPP(c_member(_1637854), _1637858), hAPP(c_List_Oset(_1637854), _1637862))))], (38884 ^ _781404) ^ [_1523348, _1523350, _1523352, _1523354, _1523356, _1523358, _1523360] : [-(hAPP(c_Product__Type_Osnd(_1523348, _1523350), hAPP(c_Product__Type_Omap__pair(_1523352, _1523348, _1523354, _1523350, _1523356, _1523358), _1523360)) = hAPP(_1523358, hAPP(c_Product__Type_Osnd(_1523352, _1523354), _1523360)))], (26785 ^ _781404) ^ [_1259319, _1259321, _1259323, _1259325, _1259327, _1259329, _1259331] : [c_Big__Operators_Ocomm__monoid__big(_1259319, _1259321, _1259323, _1259325, _1259327), 26788 ^ _781404 : [(26795 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1259321), _1259329))), -(hAPP(hAPP(_1259327, _1259331), _1259329) = _1259325)], (26789 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1259321), _1259329)), -(hAPP(hAPP(_1259327, _1259331), _1259329) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1259319, _1259321, _1259323), _1259331), _1259325), _1259329))]]], (52780 ^ _781404) ^ [_1842880, _1842882] : [hBOOL(hAPP(hAPP(c_fconj, _1842880), _1842882)), -(hBOOL(_1842882))], (26537 ^ _781404) ^ [_1254407] : [class_Int_Onumber__ring(_1254407), -(hAPP(c_Int_Oring__1__class_Oof__int(_1254407), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1254407), c_Int_OMin))], (7485 ^ _781404) ^ [_903691, _903693, _903695] : [class_Lattices_Osemilattice__inf(_903691), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903691), _903693), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903691), _903693), _903695)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903691), _903693), _903695))], (25901 ^ _781404) ^ [_1244346, _1244348] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1244346, _1244348)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1244348), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244346), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (20275 ^ _781404) ^ [_1141342] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1141342))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141342)))], (49911 ^ _781404) ^ [_1790584, _1790586] : [c_Relation_Otrans(_1790584, hAPP(c_Set_OCollect(tc_prod(_1790584, _1790584)), hAPP(c_Product__Type_Oprod_Oprod__case(_1790584, _1790584, tc_HOL_Obool), _1790586))), -(c_Predicate_Otransp(_1790584, _1790586))], (46404 ^ _781404) ^ [_1712536, _1712538] : [c_List_Oconcat(_1712536, _1712538) = c_List_Olist_ONil(_1712536), 46407 ^ _781404 : [(46408 ^ _781404) ^ [_1712627] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712536)), _1712627), hAPP(c_List_Oset(tc_List_Olist(_1712536)), _1712538))), -(_1712627 = c_List_Olist_ONil(_1712536))]]], (33841 ^ _781404) ^ [_1400563, _1400565, _1400567, _1400569, _1400571] : [class_Rings_Osemiring__0(_1400563), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400563), _1400565), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400567, _1400563), _1400569), _1400571)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400567, _1400563), hAPP(hAPP(c_COMBB(_1400563, _1400563, _1400567), hAPP(c_Groups_Otimes__class_Otimes(_1400563), _1400565)), _1400569)), _1400571))], (12859 ^ _781404) ^ [_1004481, _1004483, _1004485] : [12861 ^ _781404 : [(12864 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1004481, tc_HOL_Obool)), 12860 ^ [_1004481, _1004483, _1004485]), _1004485))], (12862 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1004481, tc_HOL_Obool)), 12860 ^ [_1004481, _1004483, _1004485]), _1004483)))]], -(_1004483 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1004481, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1004481, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1004481, tc_HOL_Obool), _1004483)), _1004485)))], (33187 ^ _781404) ^ [_1380817, _1380819, _1380821, _1380823, _1380825] : [class_Groups_Ocomm__monoid__mult(_1380817), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380819, _1380817), hAPP(hAPP(c_COMBS(_1380819, _1380817, _1380817), hAPP(hAPP(c_COMBB(_1380817, tc_fun(_1380817, _1380817), _1380819), c_Groups_Otimes__class_Otimes(_1380817)), _1380821)), _1380823)), _1380825) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1380817), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380819, _1380817), _1380821), _1380825)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380819, _1380817), _1380823), _1380825)))], (33694 ^ _781404) ^ [_1395969, _1395971, _1395973, _1395975] : [c_Orderings_Obot__class_Obot(tc_fun(_1395969, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395971, tc_fun(_1395969, tc_HOL_Obool)), _1395973), _1395975), 33697 ^ _781404 : [(33698 ^ _781404) ^ [_1396085] : [hBOOL(hAPP(hAPP(c_member(_1395971), _1396085), _1395973)), -(hAPP(_1395975, _1396085) = c_Orderings_Obot__class_Obot(tc_fun(_1395969, tc_HOL_Obool)))]]], (27377 ^ _781404) ^ [_1270312, _1270314, _1270316, _1270318, _1270320] : [class_Groups_Oab__semigroup__mult(_1270312), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1270312, _1270312, c_Groups_Otimes__class_Otimes(_1270312), _1270314, _1270316), _1270318)), -(hBOOL(hAPP(hAPP(c_member(_1270312), _1270314), _1270316))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1270312, _1270312, c_Groups_Otimes__class_Otimes(_1270312), _1270320, hAPP(hAPP(c_Set_Oinsert(_1270312), _1270314), _1270316)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270312), _1270320), _1270318))))], (12224 ^ _781404) ^ [_991548, _991550, _991552, _991554, _991556] : [c_Fun_Oinj__on(_991548, _991550, _991552, _991554), hBOOL(hAPP(hAPP(c_member(_991550), _991556), hAPP(c_Set_Oimage(_991548, _991550, _991552), _991554))), -(hAPP(_991552, hAPP(c_Fun_Othe__inv__into(_991548, _991550, _991554, _991552), _991556)) = _991556)], (33095 ^ _781404) ^ [_1378450, _1378452, _1378454, _1378456] : [class_Groups_Oordered__ab__group__add__abs(_1378450), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378450), c_Groups_Ozero__class_Ozero(_1378450)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1378452, _1378450), hAPP(hAPP(c_COMBB(_1378450, _1378450, _1378452), c_Groups_Oabs__class_Oabs(_1378450)), _1378454)), _1378456))))], (45164 ^ _781404) ^ [_1684560, _1684562, _1684564] : [c_Fun_Oinj__on(_1684560, _1684562, _1684564, c_Orderings_Otop__class_Otop(tc_fun(_1684560, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1684560), tc_List_Olist(_1684562), hAPP(c_List_Omap(_1684560, _1684562), _1684564), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1684560), tc_HOL_Obool))))], (33562 ^ _781404) ^ [_1392542, _1392544, _1392546, _1392548, _1392550, _1392552] : [_1392542 = _1392544, -(hAPP(c_Fun_Ofun__upd(_1392546, _1392548, _1392550, _1392544, _1392552), _1392542) = _1392552)], (33107 ^ _781404) ^ [_1378742, _1378744, _1378746, _1378748] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378742, tc_fun(_1378744, tc_HOL_Obool)), _1378746), _1378748) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1378744, tc_HOL_Obool), hAPP(c_Set_Oimage(_1378742, tc_fun(_1378744, tc_HOL_Obool), _1378748), _1378746)))], (42583 ^ _781404) ^ [_1625468, _1625470, _1625472] : [c_Relation_Orefl__on(_1625468, _1625470, _1625472), -(c_Relation_Orefl__on(tc_List_Olist(_1625468), c_List_Olists(_1625468, _1625470), c_List_Olistrel(_1625468, _1625472)))], (32296 ^ _781404) ^ [_1362927, _1362929] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1362927), _1362929)), _1362929) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1362927), _1362929))], (43091 ^ _781404) ^ [_1639662] : [c_List_Onat__list(_1639662), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1639662)))], (38592 ^ _781404) ^ [_1515219, _1515221, _1515223, _1515225, _1515227, _1515229] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515219, _1515221)), hAPP(hAPP(c_Product__Type_OPair(_1515219, _1515221), _1515223), _1515225)), hAPP(hAPP(c_Product__Type_OSigma(_1515219, _1515221), _1515227), _1515229))), 38595 ^ _781404 : [(38598 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515221), _1515225), hAPP(_1515229, _1515223))))], (38596 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515219), _1515223), _1515227)))]]], (2620 ^ _781404) ^ [_820064, _820066, _820068, _820070] : [-(c_FunDef_Orp__inv__image(_820070, _820066) = c_FunDef_Orp__inv__image(_820068, _820064)), _820070 = _820068, _820066 = _820064], (52518 ^ _781404) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (7972 ^ _781404) ^ [_914171, _914173, _914175, _914177] : [class_Lattices_Olattice(_914171), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914171), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914171), _914173), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_914171), _914175), _914177))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_914171), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914171), _914173), _914175)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914171), _914173), _914177)))))], (7679 ^ _781404) ^ [_907682, _907684, _907686, _907688] : [class_Lattices_Osemilattice__inf(_907682), 7682 ^ _781404 : [(7691 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907682), _907684), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_907682), _907686), _907688)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907682), _907684), _907686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907682), _907684), _907688))], (7683 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907682), _907684), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_907682), _907686), _907688))), 7686 ^ _781404 : [(7689 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907682), _907684), _907688)))], (7687 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907682), _907684), _907686)))]]]]], (44647 ^ _781404) ^ [_1674471, _1674473, _1674475] : [_1674475 = c_List_Olist_ONil(_1674471), -(hAPP(c_List_Orotate(_1674471, _1674473), _1674475) = c_List_Olist_ONil(_1674471))], (18973 ^ _781404) ^ [_1119300] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119300), 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), _1119300)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1119300)))], (43020 ^ _781404) ^ [_1638035, _1638037, _1638039, _1638041, _1638043, _1638045] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1638035, _1638037)), hAPP(hAPP(c_Product__Type_OPair(_1638035, _1638037), _1638039), _1638041)), hAPP(c_List_Oset(tc_prod(_1638035, _1638037)), hAPP(hAPP(c_List_Ozip(_1638035, _1638037), _1638043), _1638045)))), -(hBOOL(hAPP(hAPP(c_member(_1638037), _1638041), hAPP(c_List_Oset(_1638037), _1638045))))], (45617 ^ _781404) ^ [_1695234, _1695236, _1695238] : [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, _1695234), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1695234)), _1695236)))), -(hBOOL(hAPP(hAPP(c_member(_1695234), hAPP(c_Product__Type_Ofst(_1695234, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1695234, _1695236), _1695238))), hAPP(c_List_Oset(_1695234), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1695234), _1695234), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1695234)), _1695236)))))], (15391 ^ _781404) ^ [_1053794, _1053796] : [class_Lattices_Olattice(_1053794), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053794), _1053796)), -(_1053796 = c_Orderings_Obot__class_Obot(tc_fun(_1053794, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053794), c_Big__Operators_Olattice__class_OInf__fin(_1053794, _1053796)), c_Big__Operators_Olattice__class_OSup__fin(_1053794, _1053796))))], (7575 ^ _781404) ^ [_905574, _905576, _905578, _905580] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905574, tc_HOL_Obool)), _905576), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905574, tc_HOL_Obool)), _905578), _905580)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905574, tc_HOL_Obool)), _905578), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905574, tc_HOL_Obool)), _905576), _905580)))], (45774 ^ _781404) ^ [_1698992, _1698994] : [-(hBOOL(hAPP(c_List_Olistsp(_1698992, _1698994), c_List_Olist_ONil(_1698992))))], (24893 ^ _781404) ^ [_1227507, _1227509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227507), _1227509)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1227507, _1227509) = _1227507)], (15032 ^ _781404) ^ [_1046358, _1046360, _1046362, _1046364] : [class_Rings_Ocomm__semiring__1(_1046358), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046358), _1046360), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046358), _1046362), _1046364)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046358), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046358), _1046360), _1046362)), _1046364))], (25883 ^ _781404) ^ [_1243995, _1243997] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1243995))), _1243997) = 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)))), _1243995), _1243997))], (7619 ^ _781404) ^ [_906452, _906454, _906456, _906458, _906460] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906452, tc_HOL_Obool)), hAPP(c_Set_Oimage(_906454, _906452, _906456), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_906454, tc_HOL_Obool)), _906458), _906460))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_906452, tc_HOL_Obool)), hAPP(c_Set_Oimage(_906454, _906452, _906456), _906458)), hAPP(c_Set_Oimage(_906454, _906452, _906456), _906460)))))], (12666 ^ _781404) ^ [_1000388, _1000390, _1000392, _1000394] : [hBOOL(hAPP(hAPP(_1000392, _1000390), _1000394)), -(hBOOL(hAPP(hAPP(c_member(_1000388), _1000390), c_SetInterval_Oord_OatMost(_1000388, _1000392, _1000394))))], (12294 ^ _781404) ^ [_992948, _992950, _992952] : [hBOOL(hAPP(hAPP(c_member(_992948), _992950), hAPP(hAPP(c_Set_Oinsert(_992948), _992952), c_Orderings_Obot__class_Obot(tc_fun(_992948, tc_HOL_Obool))))), -(_992950 = _992952)], (11537 ^ _781404) ^ [_978659, _978661, _978663, _978665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978659, tc_HOL_Obool)), _978661), _978663)), hBOOL(hAPP(hAPP(c_member(_978659), _978665), _978661)), -(hBOOL(hAPP(hAPP(c_member(_978659), _978665), _978663)))], (27459 ^ _781404) ^ [_1271683, _1271685, _1271687, _1271689, _1271691] : [c_Finite__Set_Ofun__left__comm(_1271683, _1271685, _1271687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271683), _1271689)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1271683, _1271685, _1271687, _1271691, _1271689), hAPP(hAPP(c_Finite__Set_Ofold(_1271683, _1271685, _1271687), _1271691), _1271689))))], (17791 ^ _781404) ^ [_1098589, _1098591, _1098593, _1098595, _1098597, _1098599, _1098601, _1098603] : [c_Finite__Set_Ofolding__image__simple__idem(_1098589, _1098591, _1098593, _1098595, _1098597, _1098599), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098591), _1098601)), hBOOL(hAPP(hAPP(c_member(_1098591), _1098603), _1098601)), -(hAPP(hAPP(_1098593, hAPP(_1098597, _1098603)), hAPP(_1098599, _1098601)) = hAPP(_1098599, _1098601))], (8481 ^ _781404) ^ [_924429] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_924429, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_924429, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_924429, tc_HOL_Obool)))], (39027 ^ _781404) ^ [_1527072, _1527074, _1527076] : [-(hAPP(hAPP(c_Set_Oinsert(_1527072), _1527074), hAPP(c_Set_OCollect(_1527072), _1527076)) = hAPP(c_Set_OCollect(_1527072), hAPP(hAPP(c_COMBS(_1527072, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527072), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1527072), c_fNot), hAPP(hAPP(c_COMBC(_1527072, _1527072, tc_HOL_Obool), c_fequal), _1527074)))), _1527076)))], (14544 ^ _781404) ^ [_1036264, _1036266, _1036268] : [_1036264 = _1036268, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036264), _1036266) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036268), _1036266))], (43081 ^ _781404) ^ [_1639437, _1639439, _1639441] : [class_Groups_Omonoid__add(_1639437), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1639437), hAPP(hAPP(c_List_Olist_OCons(_1639437), _1639439), _1639441)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1639437), _1639439), hAPP(c_List_Omonoid__add__class_Olistsum(_1639437), _1639441)))], (47836 ^ _781404) ^ [_1743518, _1743520, _1743522] : [c_List_OdropWhile(_1743518, _1743520, _1743522) = c_List_Olist_ONil(_1743518), 47839 ^ _781404 : [(47840 ^ _781404) ^ [_1743609] : [hBOOL(hAPP(hAPP(c_member(_1743518), _1743609), hAPP(c_List_Oset(_1743518), _1743522))), -(hBOOL(hAPP(_1743520, _1743609)))]]], (24364 ^ _781404) ^ [_1218385, _1218387, _1218389, _1218391] : [_1218385 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218387), _1218389)), _1218391), -(_1218387 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1218385), _1218387) = _1218389), 24371 ^ _781404 : [(24374 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218391), _1218387))], (24372 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218387)))]], 24379 ^ _781404 : [(24382 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218387), _1218391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1218391), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24380 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218387))]]], (17317 ^ _781404) ^ [_1090358, _1090360, _1090362] : [class_Lattices_Olattice(_1090358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090358), _1090360)), -(hBOOL(hAPP(hAPP(c_member(_1090358), _1090362), _1090360))), -(c_Big__Operators_Olattice__class_OInf__fin(_1090358, hAPP(hAPP(c_Set_Oinsert(_1090358), _1090362), _1090360)) = hAPP(hAPP(c_Finite__Set_Ofold(_1090358, _1090358, c_Lattices_Osemilattice__inf__class_Oinf(_1090358)), _1090362), _1090360))], (7537 ^ _781404) ^ [_904715, _904717, _904719, _904721] : [class_Lattices_Olattice(_904715), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904715), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904715), _904717), _904719)), _904721) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904715), _904717), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904715), _904719), _904721)))], (43725 ^ _781404) ^ [_1652782, _1652784] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1652782), tc_List_Olist(_1652782), c_List_Olistrel(_1652782, _1652784)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1652782)), c_List_Olist_ONil(_1652782)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1652782), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1652782)), c_List_Olist_ONil(_1652782)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1652782), tc_HOL_Obool))))], (19691 ^ _781404) ^ [_1131371] : [class_Rings_Osemiring__1(_1131371), -(hBOOL(hAPP(hAPP(c_member(_1131371), c_Groups_Oone__class_Oone(_1131371)), c_Nat_Osemiring__1__class_ONats(_1131371))))], (16531 ^ _781404) ^ [_1075413, _1075415, _1075417, _1075419] : [c_Sum__Type_OPlus(_1075413, _1075415, _1075417, _1075419) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1075413, _1075415), tc_HOL_Obool)), 16534 ^ _781404 : [(16537 ^ _781404) ^ [] : [-(_1075419 = c_Orderings_Obot__class_Obot(tc_fun(_1075415, tc_HOL_Obool)))], (16535 ^ _781404) ^ [] : [-(_1075417 = c_Orderings_Obot__class_Obot(tc_fun(_1075413, tc_HOL_Obool)))]]], (10041 ^ _781404) ^ [_952756, _952758, _952760] : [class_Orderings_Oorder(_952756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952756), _952758), _952760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952756), _952758), _952760))), -(_952758 = _952760)], (37294 ^ _781404) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (12260 ^ _781404) ^ [_992229, _992231, _992233] : [class_Groups_Ocomm__monoid__add(_992229), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_992231, _992229), _992233), c_Orderings_Obot__class_Obot(tc_fun(_992231, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_992229))], (20537 ^ _781404) ^ [] : [-(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))))], (52274 ^ _781404) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (23141 ^ _781404) ^ [_1195679, _1195681, _1195683, _1195685, _1195687, _1195689] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195679), _1195681)), _1195683) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195685), _1195687)), _1195689), 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), _1195685), _1195687)), _1195689)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195683), _1195679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195685), _1195679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195687), _1195681)))], (6452 ^ _781404) ^ [_883998, _884000, _884002, _884004] : [class_Rings_Osemiring__1(_883998), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_883998, _884000, hAPP(c_Nat_OSuc, _884002), _884004) = c_Nat_Osemiring__1__class_Oof__nat__aux(_883998, _884000, _884002, hAPP(_884000, _884004)))], (14436 ^ _781404) ^ [_1034079, _1034081, _1034083, _1034085] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1034079), _1034081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1034079, tc_HOL_Obool)), _1034081), _1034083)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1034079, tc_Nat_Onat), _1034085), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1034079, tc_HOL_Obool)), _1034083), _1034081)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1034079, tc_Nat_Onat), _1034085), _1034083)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1034079, tc_Nat_Onat), _1034085), _1034081)))], (136 ^ _781404) ^ [_783478, _783480, _783482, _783484, _783486, _783488, _783490, _783492, _783494, _783496, _783498, _783500] : [-(c_Finite__Set_Ofolding__image__simple(_783498, _783494, _783490, _783486, _783482, _783478)), c_Finite__Set_Ofolding__image__simple(_783500, _783496, _783492, _783488, _783484, _783480), _783500 = _783498, _783496 = _783494, _783492 = _783490, _783488 = _783486, _783484 = _783482, _783480 = _783478], (25269 ^ _781404) ^ [_1233471] : [class_Int_Onumber__ring(_1233471), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1233471), c_Groups_Oone__class_Oone(_1233471)) = hAPP(c_Int_Onumber__class_Onumber__of(_1233471), c_Int_OMin))], (52606 ^ _781404) ^ [_1840917, _1840919] : [-(class_Finite__Set_Ofinite(tc_prod(_1840917, _1840919))), class_Finite__Set_Ofinite(_1840917), class_Finite__Set_Ofinite(_1840919)], (33786 ^ _781404) ^ [_1398994, _1398996, _1398998, _1399000] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1398994, tc_fun(_1398996, tc_HOL_Obool))), _1398998), _1399000)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1398994, _1398996)), hAPP(hAPP(c_Product__Type_OPair(_1398994, _1398996), _1398998), _1399000)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1398994, _1398996), tc_HOL_Obool)))))], (2540 ^ _781404) ^ [_818786, _818788, _818790, _818792] : [-(c_Divides_Odivmod__nat(_818792, _818788) = c_Divides_Odivmod__nat(_818790, _818786)), _818792 = _818790, _818788 = _818786], (46301 ^ _781404) ^ [_1710527, _1710529, _1710531] : [-(hBOOL(hAPP(hAPP(c_member(_1710527), _1710529), hAPP(c_List_Oset(_1710527), _1710531)))), -(hAPP(c_List_OremoveAll(_1710527, _1710529), _1710531) = _1710531)], (33798 ^ _781404) ^ [_1399338, _1399340, _1399342, _1399344, _1399346] : [hBOOL(hAPP(hAPP(c_member(_1399338), _1399340), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399342, tc_fun(_1399338, tc_HOL_Obool)), _1399344), _1399346))), 33802 ^ _781404 : [(33805 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399338), _1399340), hAPP(_1399346, 33801 ^ [_1399338, _1399340, _1399342, _1399344, _1399346]))))], (33803 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399342), 33801 ^ [_1399338, _1399340, _1399342, _1399344, _1399346]), _1399344)))]]], (15477 ^ _781404) ^ [_1055244, _1055246, _1055248] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055244), _1055246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055244), _1055246)), hAPP(c_Finite__Set_Ocard(_1055244), hAPP(hAPP(c_Set_Oinsert(_1055244), _1055248), _1055246)))))], (41771 ^ _781404) ^ [_1601573, _1601575, _1601577] : [c_Relation_Ototal__on(_1601573, _1601575, _1601577), 41774 ^ _781404 : [(41775 ^ _781404) ^ [_1601717] : [hBOOL(hAPP(hAPP(c_member(_1601573), _1601717), _1601575)), 41778 ^ _781404 : [(41779 ^ _781404) ^ [_1601857] : [hBOOL(hAPP(hAPP(c_member(_1601573), _1601857), _1601575)), -(_1601717 = _1601857), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601573, _1601573)), hAPP(hAPP(c_Product__Type_OPair(_1601573, _1601573), _1601717), _1601857)), _1601577))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601573, _1601573)), hAPP(hAPP(c_Product__Type_OPair(_1601573, _1601573), _1601857), _1601717)), _1601577)))]]]]], (30021 ^ _781404) ^ [_1319502, _1319504, _1319506, _1319508, _1319510] : [class_Groups_Ocomm__monoid__mult(_1319502), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319504), _1319506)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319504), _1319508)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319502), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319504, _1319502), _1319510), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319504, tc_HOL_Obool)), _1319506), _1319508))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319504, _1319502), _1319510), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319504, tc_HOL_Obool)), _1319506), _1319508))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319502), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319504, _1319502), _1319510), _1319506)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319504, _1319502), _1319510), _1319508)))], (25937 ^ _781404) ^ [_1244969, _1244971] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244969)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244969)), _1244971) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244969)), _1244971)))], (48585 ^ _781404) ^ [_1760242, _1760244, _1760246] : [c_List_Olist__ex(_1760242, _1760244, _1760246), -(c_List_Olist__ex(_1760242, _1760244, hAPP(c_List_Orev(_1760242), _1760246)))], (45920 ^ _781404) ^ [_1702361, _1702363, _1702365, _1702367, _1702369, _1702371, _1702373] : [c_List_Olist__all2(_1702361, _1702363, _1702365, _1702367, hAPP(hAPP(c_List_Omap(_1702369, _1702363), _1702371), _1702373)), -(c_List_Olist__all2(_1702361, _1702369, hAPP(hAPP(c_COMBC(_1702361, tc_fun(_1702369, _1702363), tc_fun(_1702369, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1702363, tc_HOL_Obool), tc_fun(tc_fun(_1702369, _1702363), tc_fun(_1702369, tc_HOL_Obool)), _1702361), c_COMBB(_1702363, tc_HOL_Obool, _1702369)), _1702365)), _1702371), _1702367, _1702373))], (14061 ^ _781404) ^ [_1026725, _1026727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026725), _1026727)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026727), _1026725)), _1026725) = _1026727)], (52412 ^ _781404) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (47641 ^ _781404) ^ [_1739327, _1739329] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1739327), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1739327))), _1739329))), 47644 ^ _781404 : [(47651 ^ _781404) ^ [] : [-(_1739329 = c_List_Olist_ONil(tc_List_Olist(_1739327))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1739327))), c_List_Otranspose(_1739327, _1739329)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739327)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1739327)), _1739329), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47645 ^ _781404) ^ [] : [_1739329 = c_List_Olist_ONil(tc_List_Olist(_1739327)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1739327))), c_List_Otranspose(_1739327, _1739329)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (52430 ^ _781404) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (11224 ^ _781404) ^ [_971806, _971808] : [11232 ^ _781404 : [(11235 ^ _781404) ^ [] : [-(hBOOL(hAPP(_971808, 11231 ^ [_971806, _971808])))], (11233 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 11231 ^ [_971806, _971808]), _971806)))]], 11225 ^ _781404 : [(11226 ^ _781404) ^ [_971874] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _971874), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971806))), hBOOL(hAPP(_971808, _971874))]]], (20539 ^ _781404) ^ [_1145748, _1145750] : [class_Rings_Olinordered__idom(_1145748), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145748), c_Groups_Ozero__class_Ozero(_1145748)), hAPP(hAPP(c_Power_Opower__class_Opower(_1145748), _1145750), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (41243 ^ _781404) ^ [_1588953, _1588955, _1588957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588953, _1588953), tc_HOL_Obool)), _1588955), _1588957)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588953, _1588953), tc_HOL_Obool)), _1588957), c_Transitive__Closure_Ortrancl(_1588953, _1588955))), -(c_Transitive__Closure_Ortrancl(_1588953, _1588957) = c_Transitive__Closure_Ortrancl(_1588953, _1588955))], (5674 ^ _781404) ^ [_868149, _868151, _868153, _868155] : [-(tc_fun(_868155, _868151) = tc_fun(_868153, _868149)), _868155 = _868153, _868151 = _868149], (1486 ^ _781404) ^ [_803019, _803021] : [-(class_Lattices_Oboolean__algebra(_803019)), _803021 = _803019, class_Lattices_Oboolean__algebra(_803021)], (33223 ^ _781404) ^ [_1381755, _1381757, _1381759, _1381761] : [class_Groups_Oordered__ab__group__add__abs(_1381755), -(hAPP(c_Groups_Oabs__class_Oabs(_1381755), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1381757, _1381755), hAPP(hAPP(c_COMBB(_1381755, _1381755, _1381757), c_Groups_Oabs__class_Oabs(_1381755)), _1381759)), _1381761)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1381757, _1381755), hAPP(hAPP(c_COMBB(_1381755, _1381755, _1381757), c_Groups_Oabs__class_Oabs(_1381755)), _1381759)), _1381761))], (41718 ^ _781404) ^ [_1600322, _1600324, _1600326] : [c_Relation_Ototal__on(_1600322, _1600324, hAPP(c_Relation_Oconverse(_1600322, _1600322), _1600326)), -(c_Relation_Ototal__on(_1600322, _1600324, _1600326))], (16985 ^ _781404) ^ [_1083672, _1083674] : [class_Rings_Olinordered__idom(_1083672), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083672), _1083674), c_Groups_Ozero__class_Ozero(_1083672))), -(c_Groups_Osgn__class_Osgn(_1083672, _1083674) = hAPP(c_Groups_Ouminus__class_Ouminus(_1083672), c_Groups_Oone__class_Oone(_1083672)))], (37327 ^ _781404) ^ [_1483092, _1483094, _1483096, _1483098, _1483100, _1483102] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1483092, _1483092)), hAPP(hAPP(c_Product__Type_OPair(_1483092, _1483092), _1483094), _1483096)), hAPP(hAPP(c_Relation_Oinv__image(_1483098, _1483092), _1483100), _1483102))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1483098, _1483098)), hAPP(hAPP(c_Product__Type_OPair(_1483098, _1483098), hAPP(_1483102, _1483094)), hAPP(_1483102, _1483096))), _1483100)))], (32428 ^ _781404) ^ [_1365571, _1365573, _1365575] : [class_Orderings_Olinorder(_1365571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365571), _1365573)), hBOOL(hAPP(hAPP(c_member(_1365571), _1365575), _1365573)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365571), _1365575), c_Big__Operators_Olattice_OInf__fin(_1365571, c_Orderings_Oord__class_Omin(_1365571), _1365573)) = _1365575)], (41839 ^ _781404) ^ [_1603424, _1603426] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603424, _1603424)), hAPP(hAPP(c_Product__Type_OPair(_1603424, _1603424), 41840 ^ [_1603424, _1603426]), 41840 ^ [_1603424, _1603426])), c_Transitive__Closure_Otrancl(_1603424, _1603426)))), -(c_Wellfounded_Oacyclic(_1603424, _1603426))], (38773 ^ _781404) ^ [_1520235, _1520237, _1520239, _1520241, _1520243, _1520245] : [class_Groups_Ocomm__monoid__mult(_1520235), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520237), _1520239)), 38783 ^ _781404 : [(38786 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1520241), hAPP(_1520243, 38782 ^ [_1520235, _1520237, _1520239, _1520241, _1520243, _1520245])))], (38784 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1520237), 38782 ^ [_1520235, _1520237, _1520239, _1520241, _1520243, _1520245]), _1520239)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1520235, _1520237, c_Groups_Otimes__class_Otimes(_1520235)), hAPP(hAPP(c_COMBS(_1520237, tc_fun(_1520241, tc_HOL_Obool), _1520235), hAPP(hAPP(c_COMBC(_1520237, _1520235, tc_fun(tc_fun(_1520241, tc_HOL_Obool), _1520235)), hAPP(hAPP(c_COMBB(tc_fun(_1520241, _1520235), tc_fun(_1520235, tc_fun(tc_fun(_1520241, tc_HOL_Obool), _1520235)), _1520237), c_Finite__Set_Ofold__image(_1520235, _1520241, c_Groups_Otimes__class_Otimes(_1520235))), _1520245)), c_Groups_Oone__class_Oone(_1520235))), _1520243)), c_Groups_Oone__class_Oone(_1520235)), _1520239) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1520235, tc_prod(_1520237, _1520241), c_Groups_Otimes__class_Otimes(_1520235)), hAPP(c_Product__Type_Oprod_Oprod__case(_1520237, _1520241, _1520235), _1520245)), c_Groups_Oone__class_Oone(_1520235)), hAPP(hAPP(c_Product__Type_OSigma(_1520237, _1520241), _1520239), _1520243)))], (21075 ^ _781404) ^ [_1155597, _1155599] : [21076 ^ _781404 : [(21079 ^ _781404) ^ [] : [_1155599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21077 ^ _781404) ^ [] : [_1155597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155597), _1155599) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9591 ^ _781404) ^ [_945620, _945622, _945624] : [class_Orderings_Opreorder(_945620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945620), _945622), _945624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945620), _945624), _945622))], (49579 ^ _781404) ^ [_1781428, _1781430, _1781432] : [49581 ^ _781404 : [(49584 ^ _781404) ^ [] : [hBOOL(hAPP(_1781428, 49580 ^ [_1781428, _1781430, _1781432]))], (49582 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 49580 ^ [_1781428, _1781430, _1781432]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1781430, _1781432))))]], -(c_List_Oall__interval__int(_1781428, _1781430, _1781432))], (45914 ^ _781404) ^ [_1702186, _1702188, _1702190, _1702192, _1702194, _1702196, _1702198] : [c_List_Olist__all2(_1702192, _1702188, hAPP(hAPP(c_COMBB(_1702186, tc_fun(_1702188, tc_HOL_Obool), _1702192), _1702190), _1702194), _1702196, _1702198), -(c_List_Olist__all2(_1702186, _1702188, _1702190, hAPP(hAPP(c_List_Omap(_1702192, _1702186), _1702194), _1702196), _1702198))], (34161 ^ _781404) ^ [_1409405, _1409407, _1409409, _1409411, _1409413] : [class_Lattices_Olattice(_1409405), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409407, _1409405)), _1409409), _1409411), _1409413) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1409405), hAPP(_1409409, _1409413)), hAPP(_1409411, _1409413)))], (29317 ^ _781404) ^ [_1306130, _1306132, _1306134, _1306136] : [class_Fields_Olinordered__field(_1306130), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306130), _1306132), _1306134)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306130), _1306136), c_Groups_Ozero__class_Ozero(_1306130))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306130), c_Groups_Ozero__class_Ozero(_1306130)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306130), _1306132), _1306134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306130), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306130), _1306136), _1306132)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306130), _1306136), _1306134))))], (2560 ^ _781404) ^ [_819084, _819086, _819088, _819090, _819092, _819094] : [-(c_Finite__Set_Ofold1Set(_819094, _819090, _819086) = c_Finite__Set_Ofold1Set(_819092, _819088, _819084)), _819094 = _819092, _819090 = _819088, _819086 = _819084], (49059 ^ _781404) ^ [_1770646, _1770648, _1770650, _1770652] : [-(hAPP(hAPP(c_List_Otake(_1770646), _1770648), c_List_Oreplicate(_1770646, _1770650, _1770652)) = c_List_Oreplicate(_1770646, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1770648), _1770650), _1770652))], (2764 ^ _781404) ^ [_822294, _822296] : [_822296 = _822294, -(c_Int_Oint__ge__less__than(_822296) = c_Int_Oint__ge__less__than(_822294))], (51221 ^ _781404) ^ [_1816770, _1816772, _1816774] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1816770, _1816770)), hAPP(hAPP(c_Product__Type_OPair(_1816770, _1816770), hAPP(_1816772, hAPP(c_Nat_OSuc, 51222 ^ [_1816770, _1816772, _1816774]))), hAPP(_1816772, 51222 ^ [_1816770, _1816772, _1816774]))), c_Transitive__Closure_Ortrancl(_1816770, _1816774))), c_Wellfounded_Owf(_1816770, c_Transitive__Closure_Otrancl(_1816770, _1816774)), 51230 ^ _781404 : [(51231 ^ _781404) ^ [_1817036] : [-(hAPP(_1816772, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 51229 ^ [_1816770, _1816772, _1816774]), _1817036)) = hAPP(_1816772, 51229 ^ [_1816770, _1816772, _1816774]))]]], (35512 ^ _781404) ^ [_1444034, _1444036, _1444038] : [hBOOL(hAPP(_1444034, 35513 ^ [_1444034, _1444036, _1444038])), 35516 ^ _781404 : [(35517 ^ _781404) ^ [_1444145, _1444147] : [-(hBOOL(hAPP(_1444034, hAPP(hAPP(c_Product__Type_OPair(_1444036, _1444038), _1444147), _1444145))))]]], (5122 ^ _781404) ^ [_859545, _859547] : [_859547 = _859545, -(c_Orderings_Otop__class_Otop(_859547) = c_Orderings_Otop__class_Otop(_859545))], (13808 ^ _781404) ^ [_1022239, _1022241, _1022243] : [class_Groups_Oordered__comm__monoid__add(_1022239), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022239), _1022241), c_Groups_Ozero__class_Ozero(_1022239))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022239), _1022243), c_Groups_Ozero__class_Ozero(_1022239))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022239), _1022241), _1022243)), c_Groups_Ozero__class_Ozero(_1022239))))], (41612 ^ _781404) ^ [_1597784, _1597786, _1597788, _1597790] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597784, _1597784)), hAPP(hAPP(c_Product__Type_OPair(_1597784, _1597784), _1597786), _1597788)), c_Transitive__Closure_Ortrancl(_1597784, hAPP(c_Relation_Oconverse(_1597784, _1597784), _1597790)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597784, _1597784)), hAPP(hAPP(c_Product__Type_OPair(_1597784, _1597784), _1597788), _1597786)), c_Transitive__Closure_Ortrancl(_1597784, _1597790))))], (39307 ^ _781404) ^ [_1536413] : [-(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)))), _1536413))))], (20225 ^ _781404) ^ [_1140510, _1140512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1140510)), c_Int_OBit0(_1140512))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140510), _1140512)))], (34417 ^ _781404) ^ [_1418892, _1418894, _1418896, _1418898, _1418900] : [class_Groups_Ocomm__monoid__mult(_1418892), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418894), _1418896)), 34424 ^ _781404 : [(34431 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418894), _1418898), _1418896))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1418894, _1418892), hAPP(hAPP(c_COMBC(_1418894, _1418892, _1418892), hAPP(hAPP(c_COMBS(_1418894, _1418892, tc_fun(_1418892, _1418892)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1418892, tc_fun(_1418892, _1418892)), _1418894), c_If(_1418892)), hAPP(hAPP(c_COMBC(_1418894, _1418894, tc_HOL_Obool), c_fequal), _1418898))), _1418900)), c_Groups_Oone__class_Oone(_1418892))), _1418896) = c_Groups_Oone__class_Oone(_1418892))], (34425 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1418894), _1418898), _1418896)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1418894, _1418892), hAPP(hAPP(c_COMBC(_1418894, _1418892, _1418892), hAPP(hAPP(c_COMBS(_1418894, _1418892, tc_fun(_1418892, _1418892)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1418892, tc_fun(_1418892, _1418892)), _1418894), c_If(_1418892)), hAPP(hAPP(c_COMBC(_1418894, _1418894, tc_HOL_Obool), c_fequal), _1418898))), _1418900)), c_Groups_Oone__class_Oone(_1418892))), _1418896) = hAPP(_1418900, _1418898))]]], (42202 ^ _781404) ^ [_1612920, _1612922] : [-(c_List_Olenlex(_1612920, _1612922) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1612920), tc_List_Olist(_1612920))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1612920), tc_List_Olist(_1612920), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1612920), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612920), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool)), tc_List_Olist(_1612920)), c_COMBS(tc_List_Olist(_1612920), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612920), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1612920)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1612920)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1612920), tc_fun(tc_List_Olist(_1612920), tc_Nat_Onat), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1612920), tc_Nat_Onat), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool)), tc_List_Olist(_1612920)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1612920))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1612920)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1612920))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1612920)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1612920), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612920), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool)), tc_List_Olist(_1612920)), c_COMBS(tc_List_Olist(_1612920), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612920), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1612920)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1612920)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1612920), tc_fun(tc_List_Olist(_1612920), tc_Nat_Onat), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1612920), tc_Nat_Onat), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool)), tc_List_Olist(_1612920)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1612920))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1612920)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1612920))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1612920)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1612920), tc_fun(tc_prod(tc_List_Olist(_1612920), tc_List_Olist(_1612920)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612920), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1612920), tc_List_Olist(_1612920)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1612920), tc_List_Olist(_1612920)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612920), tc_HOL_Obool)), tc_List_Olist(_1612920)), c_COMBC(tc_List_Olist(_1612920), tc_fun(tc_prod(tc_List_Olist(_1612920), tc_List_Olist(_1612920)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612920), tc_prod(tc_List_Olist(_1612920), tc_List_Olist(_1612920))), tc_fun(tc_List_Olist(_1612920), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1612920), tc_List_Olist(_1612920)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1612920)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1612920), tc_List_Olist(_1612920)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1612920), tc_List_Olist(_1612920)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1612920)), c_member(tc_prod(tc_List_Olist(_1612920), tc_List_Olist(_1612920))))), c_Product__Type_OPair(tc_List_Olist(_1612920), tc_List_Olist(_1612920))))), c_List_Olex(_1612920, _1612922)))))))], (10273 ^ _781404) ^ [_956048, _956050, _956052] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _956048)), _956050)), hAPP(c_Nat_OSuc, _956052)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956048), _956050)), _956052))], (52186 ^ _781404) ^ [_1836574, _1836576] : [class_Lattices_Olattice(_1836574), -(class_Lattices_Osemilattice__inf(tc_fun(_1836576, _1836574)))], (43473 ^ _781404) ^ [_1648221, _1648223, _1648225] : [hBOOL(hAPP(c_List_Odistinct(_1648221), _1648223)), -(hBOOL(hAPP(c_List_Odistinct(_1648221), c_List_Oremove1(_1648221, _1648225, _1648223))))], (10439 ^ _781404) ^ [_959064, _959066, _959068] : [class_Groups_Oordered__ab__group__add(_959064), 10442 ^ _781404 : [(10449 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959064), _959068), _959066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959064), hAPP(c_Groups_Ouminus__class_Ouminus(_959064), _959066)), hAPP(c_Groups_Ouminus__class_Ouminus(_959064), _959068))))], (10443 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959064), hAPP(c_Groups_Ouminus__class_Ouminus(_959064), _959066)), hAPP(c_Groups_Ouminus__class_Ouminus(_959064), _959068))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959064), _959068), _959066)))]]], (34229 ^ _781404) ^ [_1412477, _1412479, _1412481] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412477, tc_HOL_Obool)), _1412479), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1412477, tc_HOL_Obool), _1412481)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1412477, tc_HOL_Obool), tc_fun(_1412477, tc_HOL_Obool)), _1412481), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412477, tc_HOL_Obool)), _1412479)))], (34237 ^ _781404) ^ [_1412946, _1412948, _1412950, _1412952, _1412954] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412946, tc_HOL_Obool)), _1412948), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412950, tc_fun(_1412946, tc_HOL_Obool)), _1412952), _1412954)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412950, tc_fun(_1412946, tc_HOL_Obool)), _1412952), hAPP(hAPP(c_COMBB(tc_fun(_1412946, tc_HOL_Obool), tc_fun(_1412946, tc_HOL_Obool), _1412950), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412946, tc_HOL_Obool)), _1412948)), _1412954)))], (7531 ^ _781404) ^ [_904572, _904574, _904576, _904578] : [class_Lattices_Osemilattice__inf(_904572), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904572), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904572), _904574), _904576)), _904578) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904572), _904574), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904572), _904576), _904578)))], (32142 ^ _781404) ^ [_1359922, _1359924, _1359926, _1359928] : [class_Orderings_Olinorder(_1359922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359922), _1359924), _1359926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359922), _1359928), _1359926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359922), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359922), _1359924), _1359928)), _1359926)))], (27375 ^ _781404) ^ [_1270276, _1270278] : [-(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), _1270276)), _1270278))))], (11569 ^ _781404) ^ [_979234, _979236, _979238, _979240] : [11570 ^ _781404 : [(11573 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_979234), _979236), _979240))], (11571 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_979234), _979236), _979238))]], -(hBOOL(hAPP(hAPP(c_member(_979234), _979236), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979234, tc_HOL_Obool)), _979240), _979238))))], (4506 ^ _781404) ^ [_849857, _849859] : [_849859 = _849857, -(c_Lazy__Sequence_Oyieldn(_849859) = c_Lazy__Sequence_Oyieldn(_849857))], (33243 ^ _781404) ^ [_1382193, _1382195, _1382197, _1382199, _1382201, _1382203] : [hBOOL(hAPP(hAPP(c_member(_1382193), _1382195), _1382197)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382193, tc_fun(_1382199, tc_HOL_Obool)), _1382197), hAPP(hAPP(c_COMBB(tc_fun(_1382199, tc_HOL_Obool), tc_fun(_1382199, tc_HOL_Obool), _1382193), hAPP(c_Set_Oinsert(_1382199), _1382201)), _1382203)) = hAPP(hAPP(c_Set_Oinsert(_1382199), _1382201), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382193, tc_fun(_1382199, tc_HOL_Obool)), _1382197), _1382203)))], (23069 ^ _781404) ^ [_1194428, _1194430, _1194432] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194428), _1194430)), _1194432) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194430), _1194432)))], (7413 ^ _781404) ^ [_902426, _902428, _902430, _902432] : [hBOOL(hAPP(_902426, _902428)), hBOOL(hAPP(_902430, _902428)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_902432, tc_HOL_Obool)), _902426), _902430), _902428)))], (26123 ^ _781404) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (39157 ^ _781404) ^ [_1530856, _1530858, _1530860, _1530862, _1530864, _1530866] : [-(hAPP(c_Set_Oimage(_1530856, _1530858, hAPP(hAPP(c_COMBS(_1530856, _1530858, _1530858), hAPP(hAPP(c_COMBS(_1530856, _1530858, tc_fun(_1530858, _1530858)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1530858, tc_fun(_1530858, _1530858)), _1530856), c_If(_1530858)), _1530860)), _1530862)), _1530864)), _1530866) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530858, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1530856, _1530858, _1530862), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1530856, tc_HOL_Obool)), _1530866), hAPP(c_Set_OCollect(_1530856), _1530860)))), hAPP(c_Set_Oimage(_1530856, _1530858, _1530864), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1530856, tc_HOL_Obool)), _1530866), hAPP(c_Set_OCollect(_1530856), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1530856), c_fNot), _1530860))))))], (46716 ^ _781404) ^ [_1721233, _1721235, _1721237] : [-(c_List_Osublist(_1721233, _1721235, _1721237) = hAPP(hAPP(c_List_Omap(tc_prod(_1721233, tc_Nat_Onat), _1721233), c_Product__Type_Ofst(_1721233, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1721233, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1721233, 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(_1721233, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1721233, tc_Nat_Onat))), _1721237)), hAPP(hAPP(c_List_Ozip(_1721233, tc_Nat_Onat), _1721235), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721233)), _1721235))))))], (20245 ^ _781404) ^ [_1140880, _1140882] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1140880)), c_Int_OBit1(_1140882)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1140880), _1140882)))], (12640 ^ _781404) ^ [_999996, _999998, _1000000] : [class_Rings_Olinordered__idom(_999996), -(_999998 = _1000000), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999996), _999998), _1000000))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999996), _1000000), _999998)))], (22887 ^ _781404) ^ [_1190672, _1190674] : [-(_1190672 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1190672), _1190674) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1190674), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1190672), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1190674)))], (33780 ^ _781404) ^ [_1398856, _1398858] : [hBOOL(hAPP(hAPP(c_member(_1398856), _1398858), c_Orderings_Obot__class_Obot(tc_fun(_1398856, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1398856, tc_HOL_Obool)), _1398858)))], (49543 ^ _781404) ^ [_1780842, _1780844, _1780846, _1780848] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1780842, _1780844, _1780846, _1780848, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1780844)) = _1780846)], (30450 ^ _781404) ^ [_1328686, _1328688] : [-(c_Random_Olog(_1328686, _1328688) = 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(_1328686, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1328688), _1328686)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1328686), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1328688), _1328686)))], (51650 ^ _781404) ^ [_1827390, _1827392, _1827394, _1827396] : [class_Rings_Ocomm__semiring__1(_1827390), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827390), _1827392), _1827394)), _1827396)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827390), _1827392), _1827396)))], (7926 ^ _781404) ^ [_912872, _912874, _912876, _912878] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912872, tc_HOL_Obool)), _912874), hAPP(hAPP(c_Set_Oinsert(_912872), _912876), _912878)) = hAPP(hAPP(c_Set_Oinsert(_912872), _912876), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912872, tc_HOL_Obool)), _912874), _912878)))], (46818 ^ _781404) ^ [_1723267, _1723269] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723267)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723269)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723267), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723269)) = c_List_Olist_ONil(tc_Nat_Onat))], (34475 ^ _781404) ^ [_1420338, _1420340, _1420342, _1420344, _1420346] : [class_Groups_Ocomm__monoid__mult(_1420338), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420340), _1420342)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1420338, _1420340, c_Groups_Otimes__class_Otimes(_1420338)), hAPP(hAPP(c_COMBS(_1420340, _1420338, _1420338), hAPP(hAPP(c_COMBB(_1420338, tc_fun(_1420338, _1420338), _1420340), c_Groups_Otimes__class_Otimes(_1420338)), _1420344)), _1420346)), c_Groups_Oone__class_Oone(_1420338)), _1420342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420338), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1420338, _1420340, c_Groups_Otimes__class_Otimes(_1420338)), _1420344), c_Groups_Oone__class_Oone(_1420338)), _1420342)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1420338, _1420340, c_Groups_Otimes__class_Otimes(_1420338)), _1420346), c_Groups_Oone__class_Oone(_1420338)), _1420342)))], (6035 ^ _781404) ^ [_876986, _876988, _876990] : [_876986 = _876988, 6038 ^ _781404 : [(6041 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876990, tc_HOL_Obool)), _876988), _876986)))], (6039 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876990, tc_HOL_Obool)), _876986), _876988)))]]], (11373 ^ _781404) ^ [_975083, _975085, _975087, _975089, _975091] : [-(c_Fun_Oinj__on(_975083, _975085, _975087, hAPP(hAPP(c_Set_Oinsert(_975083), _975089), _975091))), c_Fun_Oinj__on(_975083, _975085, _975087, _975091), -(hBOOL(hAPP(hAPP(c_member(_975085), hAPP(_975087, _975089)), hAPP(c_Set_Oimage(_975083, _975085, _975087), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975083, tc_HOL_Obool)), _975091), hAPP(hAPP(c_Set_Oinsert(_975083), _975089), c_Orderings_Obot__class_Obot(tc_fun(_975083, tc_HOL_Obool))))))))], (42631 ^ _781404) ^ [_1626701, _1626703, _1626705, _1626707] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1626701), tc_List_Olist(_1626701))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626701), tc_List_Olist(_1626701)), _1626703), _1626705)), c_List_Olistrel(_1626701, _1626707)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626701)), _1626703) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626701)), _1626705), 42637 ^ _781404 : [(42640 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1626701, _1626701)), hAPP(hAPP(c_Product__Type_OPair(_1626701, _1626701), hAPP(hAPP(c_List_Onth(_1626701), _1626703), 42636 ^ [_1626701, _1626703, _1626705, _1626707])), hAPP(hAPP(c_List_Onth(_1626701), _1626705), 42636 ^ [_1626701, _1626703, _1626705, _1626707]))), _1626707))], (42638 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42636 ^ [_1626701, _1626703, _1626705, _1626707]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626701)), _1626703))))]]], (37288 ^ _781404) ^ [_1481692, _1481694, _1481696, _1481698] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1481692), _1481698) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1481696), _1481694), -(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), _1481692), _1481694)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1481696), _1481698))), c_Int_Ointrel)))], (29513 ^ _781404) ^ [_1309863, _1309865, _1309867, _1309869] : [class_Fields_Olinordered__field__inverse__zero(_1309863), 29516 ^ _781404 : [(29517 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), _1309865), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309863), _1309867), _1309869))), 29520 ^ _781404 : [(29527 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), c_Groups_Ozero__class_Ozero(_1309863)), _1309869))), 29530 ^ _781404 : [(29537 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), _1309869), c_Groups_Ozero__class_Ozero(_1309863)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), _1309865), c_Groups_Ozero__class_Ozero(_1309863))))], (29531 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), _1309869), c_Groups_Ozero__class_Ozero(_1309863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), _1309867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309863), _1309865), _1309869))))]]], (29521 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), c_Groups_Ozero__class_Ozero(_1309863)), _1309869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309863), _1309865), _1309869)), _1309867)))]]], (29543 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), _1309865), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309863), _1309867), _1309869)))), 29546 ^ _781404 : [(29549 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309863), _1309865), _1309869)), _1309867))], (29547 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), c_Groups_Ozero__class_Ozero(_1309863)), _1309869)))]], 29550 ^ _781404 : [(29553 ^ _781404) ^ [] : [29554 ^ _781404 : [(29557 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), _1309867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309863), _1309865), _1309869)))], (29555 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), _1309869), c_Groups_Ozero__class_Ozero(_1309863))))]], 29558 ^ _781404 : [(29561 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), _1309865), c_Groups_Ozero__class_Ozero(_1309863)))], (29559 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), _1309869), c_Groups_Ozero__class_Ozero(_1309863)))]]], (29551 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309863), c_Groups_Ozero__class_Ozero(_1309863)), _1309869))]]]]], (47869 ^ _781404) ^ [_1744133, _1744135, _1744137] : [hBOOL(hAPP(c_List_Odistinct(_1744133), _1744135)), -(hBOOL(hAPP(c_List_Odistinct(_1744133), c_List_OdropWhile(_1744133, _1744137, _1744135))))], (5090 ^ _781404) ^ [_859023, _859025, _859027, _859029, _859031, _859033] : [-(c_Set_Ovimage(_859033, _859029, _859025) = c_Set_Ovimage(_859031, _859027, _859023)), _859033 = _859031, _859029 = _859027, _859025 = _859023], (49626 ^ _781404) ^ [_1782912, _1782914, _1782916, _1782918, _1782920] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1782912), tc_List_Olist(_1782912))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1782912), tc_List_Olist(_1782912)), _1782914), _1782916)), c_List_Olexord(_1782912, _1782918))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1782912), tc_List_Olist(_1782912))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1782912), tc_List_Olist(_1782912)), _1782916), _1782920)), c_List_Olexord(_1782912, _1782918))), c_Relation_Otrans(_1782912, _1782918), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1782912), tc_List_Olist(_1782912))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1782912), tc_List_Olist(_1782912)), _1782914), _1782920)), c_List_Olexord(_1782912, _1782918))))], (31484 ^ _781404) ^ [_1347722, _1347724, _1347726] : [class_Orderings_Olinorder(_1347722), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347722), _1347724)), -(_1347724 = c_Orderings_Obot__class_Obot(tc_fun(_1347722, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347722), _1347726)), -(_1347726 = c_Orderings_Obot__class_Obot(tc_fun(_1347722, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1347722, tc_HOL_Obool)), _1347724), _1347726) = c_Orderings_Obot__class_Obot(tc_fun(_1347722, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1347722, c_Orderings_Oord__class_Omin(_1347722), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1347722, tc_HOL_Obool)), _1347724), _1347726)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1347722), c_Big__Operators_Olattice_OInf__fin(_1347722, c_Orderings_Oord__class_Omin(_1347722), _1347724)), c_Big__Operators_Olattice_OInf__fin(_1347722, c_Orderings_Oord__class_Omin(_1347722), _1347726)))], (26991 ^ _781404) ^ [_1263184, _1263186, _1263188, _1263190] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1263184, _1263186, _1263188, _1263190, c_Orderings_Obot__class_Obot(tc_fun(_1263184, tc_HOL_Obool))), _1263190)))], (3900 ^ _781404) ^ [_839988, _839990] : [_839990 = _839988, -(c_Enum_Oenum__class_Oenum__all(_839990) = c_Enum_Oenum__class_Oenum__all(_839988))], (50801 ^ _781404) ^ [_1808327, _1808329, _1808331] : [c_Fun_Obij__betw(_1808327, _1808329, _1808331, c_Orderings_Otop__class_Otop(tc_fun(_1808327, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808329, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1808329, _1808327, c_Orderings_Otop__class_Otop(tc_fun(_1808329, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1808327, _1808329, c_Orderings_Otop__class_Otop(tc_fun(_1808327, tc_HOL_Obool)), _1808331)) = _1808331)], (37561 ^ _781404) ^ [_1489331, _1489333, _1489335] : [_1489333 = c_Orderings_Obot__class_Obot(tc_fun(_1489331, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1489331), _1489333), _1489335) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1489331, tc_HOL_Obool), tc_HOL_Obool)))], (20751 ^ _781404) ^ [_1149434, _1149436, _1149438, _1149440] : [class_Int_Onumber__ring(_1149434), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149434), hAPP(c_Int_Onumber__class_Onumber__of(_1149434), _1149436)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149434), hAPP(c_Int_Onumber__class_Onumber__of(_1149434), _1149438)), _1149440)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149434), hAPP(c_Int_Onumber__class_Onumber__of(_1149434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1149436), _1149438))), _1149440))], (33774 ^ _781404) ^ [_1398745, _1398747] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1398745, tc_HOL_Obool)), _1398747)), -(hBOOL(hAPP(hAPP(c_member(_1398745), _1398747), c_Orderings_Obot__class_Obot(tc_fun(_1398745, tc_HOL_Obool)))))], (43773 ^ _781404) ^ [_1653868, _1653870, _1653872, _1653874, _1653876] : [-(hAPP(hAPP(c_List_Ozip(_1653868, _1653870), _1653872), hAPP(hAPP(c_List_Olist_OCons(_1653870), _1653874), _1653876)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1653868, _1653870)), _1653868, c_List_Olist_ONil(tc_prod(_1653868, _1653870)), hAPP(hAPP(c_COMBC(_1653868, tc_fun(tc_List_Olist(_1653868), tc_List_Olist(tc_prod(_1653868, _1653870))), tc_fun(tc_List_Olist(_1653868), tc_List_Olist(tc_prod(_1653868, _1653870)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1653868, _1653870)), tc_List_Olist(tc_prod(_1653868, _1653870))), tc_fun(tc_fun(tc_List_Olist(_1653868), tc_List_Olist(tc_prod(_1653868, _1653870))), tc_fun(tc_List_Olist(_1653868), tc_List_Olist(tc_prod(_1653868, _1653870)))), _1653868), c_COMBB(tc_List_Olist(tc_prod(_1653868, _1653870)), tc_List_Olist(tc_prod(_1653868, _1653870)), tc_List_Olist(_1653868))), hAPP(hAPP(c_COMBB(tc_prod(_1653868, _1653870), tc_fun(tc_List_Olist(tc_prod(_1653868, _1653870)), tc_List_Olist(tc_prod(_1653868, _1653870))), _1653868), c_List_Olist_OCons(tc_prod(_1653868, _1653870))), hAPP(hAPP(c_COMBC(_1653868, _1653870, tc_prod(_1653868, _1653870)), c_Product__Type_OPair(_1653868, _1653870)), _1653874)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1653868), tc_List_Olist(_1653870), tc_List_Olist(tc_prod(_1653868, _1653870))), c_List_Ozip(_1653868, _1653870)), _1653876))), _1653872))], (37734 ^ _781404) ^ [_1493615, _1493617, _1493619, _1493621, _1493623, _1493625, _1493627] : [c_Equiv__Relations_Oequiv(_1493615, _1493617, _1493619), hBOOL(hAPP(hAPP(c_member(tc_fun(_1493615, tc_HOL_Obool)), _1493621), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1493615), _1493617), _1493619))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1493615, tc_HOL_Obool)), _1493623), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1493615), _1493617), _1493619))), hBOOL(hAPP(hAPP(c_member(_1493615), _1493625), _1493621)), hBOOL(hAPP(hAPP(c_member(_1493615), _1493627), _1493623)), 37753 ^ _781404 : [(37760 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1493615, _1493615)), hAPP(hAPP(c_Product__Type_OPair(_1493615, _1493615), _1493625), _1493627)), _1493619)), -(_1493621 = _1493623)], (37754 ^ _781404) ^ [] : [_1493621 = _1493623, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1493615, _1493615)), hAPP(hAPP(c_Product__Type_OPair(_1493615, _1493615), _1493625), _1493627)), _1493619)))]]], (41582 ^ _781404) ^ [_1597044, _1597046, _1597048, _1597050, _1597052] : [-(hAPP(c_Relation_Oconverse(_1597044, _1597046), hAPP(hAPP(c_Relation_Orel__comp(_1597044, _1597048, _1597046), _1597050), _1597052)) = hAPP(hAPP(c_Relation_Orel__comp(_1597046, _1597048, _1597044), hAPP(c_Relation_Oconverse(_1597048, _1597046), _1597052)), hAPP(c_Relation_Oconverse(_1597044, _1597048), _1597050)))], (14685 ^ _781404) ^ [_1038897, _1038899, _1038901] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038897), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1038897, tc_HOL_Obool)), _1038899), _1038901)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038897), _1038899)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038897), _1038901))], (43701 ^ _781404) ^ [_1652365, _1652367, _1652369, _1652371] : [_1652365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1652367), _1652365), hAPP(hAPP(c_List_Olist_OCons(_1652367), _1652369), _1652371)) = c_List_Olist_ONil(_1652367))], (14729 ^ _781404) ^ [_1039698, _1039700, _1039702, _1039704, _1039706] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039698), _1039700)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1039702, tc_HOL_Obool)), _1039704), hAPP(c_Set_Oimage(_1039698, _1039702, _1039706), _1039700))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039702), _1039704)))], (51251 ^ _781404) ^ [_1817432, _1817434, _1817436] : [hBOOL(hAPP(hAPP(_1817436, _1817434), _1817434)), -(hBOOL(hAPP(hAPP(c_member(_1817432), _1817434), c_Quotient_ORespects(_1817432, _1817436))))], (42824 ^ _781404) ^ [_1631738, _1631740] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1631738), hAPP(c_List_Oset(_1631738), _1631740))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631738)), _1631740))))], (9210 ^ _781404) ^ [_938536, _938538, _938540] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938536, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938536, tc_HOL_Obool)), _938538), _938540)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938536, tc_HOL_Obool)), _938538), _938540)) = _938538)], (35904 ^ _781404) ^ [_1451492, _1451494, _1451496, _1451498] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451492, _1451494), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1451496), _1451498))), -(_1451494 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1451492, _1451494) = _1451498)], (19941 ^ _781404) ^ [_1135662, _1135664, _1135666] : [class_Rings_Olinordered__idom(_1135662), 19944 ^ _781404 : [(19953 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135662), hAPP(hAPP(c_Power_Opower__class_Opower(_1135662), _1135664), 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(_1135662), _1135666), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1135662)))), _1135664 = c_Groups_Ozero__class_Ozero(_1135662), _1135666 = c_Groups_Ozero__class_Ozero(_1135662)], (19945 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135662), hAPP(hAPP(c_Power_Opower__class_Opower(_1135662), _1135664), 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(_1135662), _1135666), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1135662))), 19948 ^ _781404 : [(19951 ^ _781404) ^ [] : [-(_1135666 = c_Groups_Ozero__class_Ozero(_1135662))], (19949 ^ _781404) ^ [] : [-(_1135664 = c_Groups_Ozero__class_Ozero(_1135662))]]]]], (30674 ^ _781404) ^ [_1332920, _1332922, _1332924, _1332926] : [class_Orderings_Olinorder(_1332920), 30677 ^ _781404 : [(30678 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332920), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332920), _1332922), _1332924)), _1332926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332920), _1332922), _1332926))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332920), _1332924), _1332926)))], (30688 ^ _781404) ^ [] : [30689 ^ _781404 : [(30692 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332920), _1332924), _1332926))], (30690 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332920), _1332922), _1332926))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332920), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332920), _1332922), _1332924)), _1332926)))]]], (19711 ^ _781404) ^ [] : [-(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)))], (12502 ^ _781404) ^ [_997060, _997062, _997064] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_997060, tc_HOL_Obool)), _997062), hAPP(c_Set_OPow(_997060), _997064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997060, tc_HOL_Obool)), _997062), _997064)))], (7561 ^ _781404) ^ [_905235, _905237] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905235, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_905235, tc_HOL_Obool))), _905237) = _905237)], (40877 ^ _781404) ^ [_1578516, _1578518, _1578520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578516, tc_HOL_Obool)), _1578518), hAPP(_1578520, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1578516, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578516, tc_HOL_Obool), tc_fun(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), tc_fun(_1578516, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1578516, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578516, tc_HOL_Obool), tc_fun(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), tc_fun(_1578516, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1578516, tc_HOL_Obool))), _1578520)), _1578518))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1578516, tc_HOL_Obool), _1578520)))))), c_Orderings_Oorder__class_Omono(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool), _1578520), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578516, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1578516, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578516, tc_HOL_Obool), tc_fun(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), tc_fun(_1578516, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1578516, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578516, tc_HOL_Obool), tc_fun(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), tc_fun(_1578516, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1578516, tc_HOL_Obool))), _1578520)), _1578518))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1578516, tc_HOL_Obool), _1578520)))), hAPP(_1578520, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1578516, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578516, tc_HOL_Obool), tc_fun(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), tc_fun(_1578516, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1578516, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578516, tc_HOL_Obool), tc_fun(tc_fun(_1578516, tc_HOL_Obool), tc_fun(_1578516, tc_HOL_Obool)), tc_fun(_1578516, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1578516, tc_HOL_Obool))), _1578520)), _1578518))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1578516, tc_HOL_Obool), _1578520)))))))], (45371 ^ _781404) ^ [_1690122, _1690124, _1690126, _1690128, _1690130, _1690132] : [-(hBOOL(hAPP(hAPP(c_member(_1690122), _1690124), hAPP(c_List_Oset(_1690122), _1690126)))), -(hAPP(hAPP(c_List_Omap(_1690122, _1690128), c_Fun_Ofun__upd(_1690122, _1690128, _1690130, _1690124, _1690132)), _1690126) = hAPP(hAPP(c_List_Omap(_1690122, _1690128), _1690130), _1690126))], (47766 ^ _781404) ^ [_1741932, _1741934, _1741936, _1741938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741932), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741934)), c_List_OtakeWhile(_1741934, _1741936, _1741938)))), -(hAPP(hAPP(c_List_Onth(_1741934), c_List_OtakeWhile(_1741934, _1741936, _1741938)), _1741932) = hAPP(hAPP(c_List_Onth(_1741934), _1741938), _1741932))], (23655 ^ _781404) ^ [_1206318, _1206320, _1206322, _1206324] : [class_Divides_Osemiring__div(_1206318), -(c_Divides_Odiv__class_Omod(_1206318, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206318), _1206320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206318), _1206322), _1206324)), _1206322) = c_Divides_Odiv__class_Omod(_1206318, _1206320, _1206322))], (26491 ^ _781404) ^ [_1253688, _1253690] : [class_Rings_Oring__1(_1253688), -(hAPP(c_Int_Oring__1__class_Oof__int(_1253688), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1253690)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1253688), hAPP(c_Int_Oring__1__class_Oof__int(_1253688), _1253690)))], (19001 ^ _781404) ^ [_1119669, _1119671] : [class_Int_Onumber__ring(_1119669), 19004 ^ _781404 : [(19011 ^ _781404) ^ [] : [-(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), _1119671)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1119669), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1119671)) = c_Groups_Ozero__class_Ozero(_1119669))], (19005 ^ _781404) ^ [] : [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), _1119671))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1119669), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1119671)) = hAPP(c_Int_Onumber__class_Onumber__of(_1119669), _1119671))]]], (11737 ^ _781404) ^ [_982389, _982391] : [-(_982389 = _982391), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982389), _982391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982391), _982389)))], (50777 ^ _781404) ^ [_1807844, _1807846] : [-(c_Fun_Obij__betw(_1807844, _1807844, c_Fun_Oid(_1807844), _1807846, _1807846))], (2642 ^ _781404) ^ [_820383, _820385, _820387, _820389] : [-(c_Nitpick_Onumber__of__frac(_820389, _820385) = c_Nitpick_Onumber__of__frac(_820387, _820383)), _820389 = _820387, _820385 = _820383], (22005 ^ _781404) ^ [_1173273, _1173275] : [class_Rings_Ocomm__semiring__1(_1173273), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173273), _1173275), _1173275) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173273), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173273), c_Groups_Oone__class_Oone(_1173273)), c_Groups_Oone__class_Oone(_1173273))), _1173275))], (9919 ^ _781404) ^ [_950847, _950849, _950851, _950853] : [class_Orderings_Oord(_950847), 9922 ^ _781404 : [(9931 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_950849, _950847)), _950851), _950853))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950849, _950847)), _950851), _950853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950849, _950847)), _950853), _950851)))], (9923 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_950849, _950847)), _950851), _950853)), 9926 ^ _781404 : [(9929 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950849, _950847)), _950853), _950851))], (9927 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950849, _950847)), _950851), _950853)))]]]]], (33287 ^ _781404) ^ [_1383544, _1383546, _1383548, _1383550, _1383552] : [-(_1383544 = c_Orderings_Obot__class_Obot(tc_fun(_1383546, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1383548), _1383550), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383546, tc_fun(_1383548, tc_HOL_Obool)), _1383544), _1383552)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383546, tc_fun(_1383548, tc_HOL_Obool)), _1383544), hAPP(hAPP(c_COMBB(tc_fun(_1383548, tc_HOL_Obool), tc_fun(_1383548, tc_HOL_Obool), _1383546), hAPP(c_Set_Oinsert(_1383548), _1383550)), _1383552)))], (2346 ^ _781404) ^ [_815623, _815625] : [_815625 = _815623, -(c_Int_Opred(_815625) = c_Int_Opred(_815623))], (7966 ^ _781404) ^ [_914072, _914074] : [class_Lattices_Obounded__lattice__top(_914072), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914072), c_Orderings_Otop__class_Otop(_914072)), _914074) = c_Orderings_Otop__class_Otop(_914072))], (4776 ^ _781404) ^ [_854094, _854096, _854098, _854100] : [-(c_Product__Type_Ofst(_854100, _854096) = c_Product__Type_Ofst(_854098, _854094)), _854100 = _854098, _854096 = _854094], (45625 ^ _781404) ^ [_1695515, _1695517] : [-(c_Random_Oselect(_1695515, _1695517) = 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(_1695515, 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(_1695515)), _1695517)))), hAPP(hAPP(c_COMBB(_1695515, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1695515, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1695515, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1695515, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1695515), _1695517)), c_Code__Numeral_Onat__of))))], (24490 ^ _781404) ^ [_1220708, _1220710, _1220712, _1220714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220710)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1220710), _1220712)), -(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), _1220712), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1220714, _1220708))), _1220710)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1220712), _1220708))))], (6667 ^ _781404) ^ [_888050, _888052, _888054, _888056] : [class_Groups_Ouminus(_888050), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_888052, _888050)), _888054), _888056) = hAPP(c_Groups_Ouminus__class_Ouminus(_888050), hAPP(_888054, _888056)))], (20775 ^ _781404) ^ [_1150050, _1150052, _1150054, _1150056, _1150058] : [class_Rings_Ocomm__semiring__1(_1150050), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150050), _1150052), _1150054)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150050), _1150056), _1150058)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150050), _1150056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150050), _1150052), _1150054)), _1150058)))], (20107 ^ _781404) ^ [_1138473] : [_1138473 = c_Int_OPls, -(c_Int_OBit0(_1138473) = c_Int_OPls)], (39059 ^ _781404) ^ [_1527816, _1527818, _1527820] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1527816, tc_HOL_Obool)), _1527818), _1527820) = hAPP(c_Set_OCollect(_1527816), hAPP(hAPP(c_COMBS(_1527816, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527816), c_fdisj), hAPP(hAPP(c_COMBC(_1527816, tc_fun(_1527816, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527816)), _1527818))), hAPP(hAPP(c_COMBC(_1527816, tc_fun(_1527816, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527816)), _1527820))))], (36306 ^ _781404) ^ [_1459266, _1459268, _1459270, _1459272, _1459274, _1459276, _1459278, _1459280] : [c_Finite__Set_Ofolding(_1459266, _1459268, _1459270, _1459272), -(hAPP(c_Fun_Ocomp(_1459268, _1459268, _1459274, hAPP(_1459270, _1459276)), hAPP(c_Fun_Ocomp(_1459268, _1459268, _1459274, hAPP(_1459270, _1459278)), _1459280)) = hAPP(c_Fun_Ocomp(_1459268, _1459268, _1459274, hAPP(_1459270, _1459278)), hAPP(c_Fun_Ocomp(_1459268, _1459268, _1459274, hAPP(_1459270, _1459276)), _1459280)))], (11773 ^ _781404) ^ [_982786, _982788, _982790] : [hBOOL(hAPP(_982790, _982788)), -(hBOOL(hAPP(hAPP(c_member(_982786), _982788), _982790)))], (45734 ^ _781404) ^ [_1697527, _1697529] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1697527), _1697529) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1697527, 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)))), _1697529))))], (34909 ^ _781404) ^ [_1430607, _1430609] : [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(_1430609))), 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), _1430607)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1430607)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430609))))], (50529 ^ _781404) ^ [_1802026, _1802028, _1802030, _1802032, _1802034, _1802036] : [hAPP(c_Hilbert__Choice_Oinv__into(_1802026, _1802028, _1802030, _1802032), _1802034) = hAPP(c_Hilbert__Choice_Oinv__into(_1802026, _1802028, _1802030, _1802032), _1802036), hBOOL(hAPP(hAPP(c_member(_1802028), _1802034), hAPP(c_Set_Oimage(_1802026, _1802028, _1802032), _1802030))), hBOOL(hAPP(hAPP(c_member(_1802028), _1802036), hAPP(c_Set_Oimage(_1802026, _1802028, _1802032), _1802030))), -(_1802034 = _1802036)], (1606 ^ _781404) ^ [_804519, _804521] : [-(class_Rings_Olinordered__semiring__strict(_804519)), _804521 = _804519, class_Rings_Olinordered__semiring__strict(_804521)], (24054 ^ _781404) ^ [_1212915, _1212917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212917), 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), _1212915), _1212917)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (5214 ^ _781404) ^ [_860977, _860979, _860981, _860983] : [-(c_Transitive__Closure_Otrancl(_860983, _860979) = c_Transitive__Closure_Otrancl(_860981, _860977)), _860983 = _860981, _860979 = _860977], (22549 ^ _781404) ^ [_1183697, _1183699, _1183701] : [class_Rings_Olinordered__ring(_1183697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183697), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183697), _1183699), _1183699)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183697), _1183701), _1183701))), c_Groups_Ozero__class_Ozero(_1183697)))], (6861 ^ _781404) ^ [_891346, _891348, _891350] : [class_Lattices_Olattice(_891346), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891346), _891348), _891350) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891346), _891350), _891348))], (52490 ^ _781404) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (19777 ^ _781404) ^ [_1132695, _1132697] : [class_Int_Onumber__ring(_1132695), class_Rings_Olinordered__idom(_1132695), 19784 ^ _781404 : [(19791 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132697), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132695), hAPP(c_Int_Onumber__class_Onumber__of(_1132695), _1132697)), c_Groups_Oone__class_Oone(_1132695))))], (19785 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132695), hAPP(c_Int_Onumber__class_Onumber__of(_1132695), _1132697)), c_Groups_Oone__class_Oone(_1132695))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132697), c_Int_OBit1(c_Int_OPls))))]]], (12798 ^ _781404) ^ [_1003098, _1003100] : [-(hBOOL(hAPP(hAPP(c_member(_1003098), _1003100), c_Orderings_Otop__class_Otop(tc_fun(_1003098, tc_HOL_Obool)))))], (4824 ^ _781404) ^ [_854850, _854852, _854854, _854856] : [-(c_List_Olexord(_854856, _854852) = c_List_Olexord(_854854, _854850)), _854856 = _854854, _854852 = _854850], (40785 ^ _781404) ^ [_1577030, _1577032, _1577034] : [class_Complete__Lattice_Ocomplete__lattice(_1577030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577030), hAPP(_1577032, _1577034)), _1577034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577030), c_Inductive_Ocomplete__lattice__class_Olfp(_1577030, _1577032)), _1577034)))], (44872 ^ _781404) ^ [_1679369, _1679371, _1679373, _1679375, _1679377, _1679379] : [class_Orderings_Olinorder(_1679369), 44875 ^ _781404 : [(44882 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1679369), hAPP(_1679371, _1679373)), hAPP(_1679371, _1679375)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679377, _1679369, _1679371), _1679373), hAPP(hAPP(c_List_Olist_OCons(_1679377), _1679375), _1679379)) = hAPP(hAPP(c_List_Olist_OCons(_1679377), _1679375), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679377, _1679369, _1679371), _1679373), _1679379)))], (44876 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1679369), hAPP(_1679371, _1679373)), hAPP(_1679371, _1679375))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679377, _1679369, _1679371), _1679373), hAPP(hAPP(c_List_Olist_OCons(_1679377), _1679375), _1679379)) = hAPP(hAPP(c_List_Olist_OCons(_1679377), _1679373), hAPP(hAPP(c_List_Olist_OCons(_1679377), _1679375), _1679379)))]]], (34129 ^ _781404) ^ [_1408207, _1408209, _1408211, _1408213, _1408215] : [-(_1408207 = c_Orderings_Obot__class_Obot(tc_fun(_1408209, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408211, tc_HOL_Obool)), _1408213), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408209, tc_fun(_1408211, tc_HOL_Obool)), _1408207), _1408215)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408209, tc_fun(_1408211, tc_HOL_Obool)), _1408207), hAPP(hAPP(c_COMBB(tc_fun(_1408211, tc_HOL_Obool), tc_fun(_1408211, tc_HOL_Obool), _1408209), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408211, tc_HOL_Obool)), _1408213)), _1408215)))], (39489 ^ _781404) ^ [_1545048, _1545050, _1545052, _1545054, _1545056, _1545058] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1545048), _1545050)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545052), _1545054)), 39499 ^ _781404 : [(39502 ^ _781404) ^ [] : [hAPP(c_Finite__Set_Ocard(_1545048), hAPP(c_Set_OCollect(_1545048), hAPP(hAPP(c_COMBS(_1545048, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545048), c_fconj), hAPP(hAPP(c_COMBC(_1545048, tc_fun(_1545048, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545048)), _1545050))), hAPP(hAPP(c_COMBC(_1545048, _1545052, tc_HOL_Obool), _1545056), 39498 ^ [_1545048, _1545050, _1545052, _1545054, _1545056, _1545058])))) = hAPP(_1545058, 39498 ^ [_1545048, _1545050, _1545052, _1545054, _1545056, _1545058])], (39500 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1545052), 39498 ^ [_1545048, _1545050, _1545052, _1545054, _1545056, _1545058]), _1545054)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545048, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1545052, tc_HOL_Obool), tc_Nat_Onat, _1545048), c_Finite__Set_Ocard(_1545052)), hAPP(hAPP(c_COMBB(tc_fun(_1545052, tc_HOL_Obool), tc_fun(_1545052, tc_HOL_Obool), _1545048), c_Set_OCollect(_1545052)), hAPP(hAPP(c_COMBB(tc_fun(_1545052, tc_HOL_Obool), tc_fun(_1545052, tc_HOL_Obool), _1545048), hAPP(c_COMBS(_1545052, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545052), c_fconj), hAPP(hAPP(c_COMBC(_1545052, tc_fun(_1545052, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545052)), _1545054)))), _1545056)))), _1545050) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545052, tc_Nat_Onat), _1545058), _1545054))], (42818 ^ _781404) ^ [_1631584, _1631586, _1631588, _1631590] : [-(hAPP(hAPP(c_List_Otake(_1631584), _1631586), hAPP(hAPP(c_List_Otake(_1631584), _1631588), _1631590)) = hAPP(hAPP(c_List_Otake(_1631584), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1631586), _1631588)), _1631590))], (19987 ^ _781404) ^ [_1136455, _1136457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1136455), _1136457)), -(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)), _1136455)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1136457))))], (45178 ^ _781404) ^ [_1684849, _1684851, _1684853, _1684855] : [-(hAPP(hAPP(c_List_Omap(_1684849, _1684851), _1684853), hAPP(c_List_Otl(_1684849), _1684855)) = hAPP(c_List_Otl(_1684851), hAPP(hAPP(c_List_Omap(_1684849, _1684851), _1684853), _1684855)))], (47529 ^ _781404) ^ [_1737018, _1737020, _1737022] : [hAPP(c_List_Orev(_1737018), _1737020) = _1737022, -(_1737020 = hAPP(c_List_Orev(_1737018), _1737022))], (24692 ^ _781404) ^ [_1224345] : [c_Int_OMin = _1224345, -(c_Int_OMin = c_Int_OBit1(_1224345))], (25744 ^ _781404) ^ [_1241430, _1241432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241430)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1241430)), _1241432) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1241430), _1241432)))], (20357 ^ _781404) ^ [_1142745, _1142747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1142745)), c_Int_OBit0(_1142747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142745), _1142747)))], (44723 ^ _781404) ^ [_1676047, _1676049, _1676051, _1676053] : [class_Groups_Osemigroup__add(_1676047), -(hAPP(c_List_Ofoldl(_1676047, _1676047, c_Groups_Oplus__class_Oplus(_1676047), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1676047), _1676049), _1676051)), _1676053) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1676047), _1676049), hAPP(c_List_Ofoldl(_1676047, _1676047, c_Groups_Oplus__class_Oplus(_1676047), _1676051), _1676053)))], (4932 ^ _781404) ^ [_856556, _856558, _856560, _856562] : [-(c_Relation_Oinv__image(_856562, _856558) = c_Relation_Oinv__image(_856560, _856556)), _856562 = _856560, _856558 = _856556], (12056 ^ _781404) ^ [_988202, _988204, _988206, _988208, _988210] : [hBOOL(hAPP(hAPP(c_member(_988202), _988204), _988206)), -(hBOOL(hAPP(hAPP(c_member(_988208), hAPP(_988210, _988204)), hAPP(c_Set_Oimage(_988202, _988208, _988210), _988206))))], (18743 ^ _781404) ^ [_1115554] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115554) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1115554), c_Int_OPls)))], (31446 ^ _781404) ^ [_1346985, _1346987, _1346989] : [class_Orderings_Olinorder(_1346985), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346985), _1346987)), -(hBOOL(hAPP(hAPP(c_member(_1346985), _1346989), _1346987))), -(_1346987 = c_Orderings_Obot__class_Obot(tc_fun(_1346985, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1346985, c_Orderings_Oord__class_Omin(_1346985), hAPP(hAPP(c_Set_Oinsert(_1346985), _1346989), _1346987)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346985), _1346989), c_Big__Operators_Olattice_OInf__fin(_1346985, c_Orderings_Oord__class_Omin(_1346985), _1346987)))], (342 ^ _781404) ^ [_786619, _786621, _786623, _786625, _786627, _786629, _786631, _786633] : [-(c_Finite__Set_Ofolding__idem(_786631, _786627, _786623, _786619)), c_Finite__Set_Ofolding__idem(_786633, _786629, _786625, _786621), _786633 = _786631, _786629 = _786627, _786625 = _786623, _786621 = _786619], (9352 ^ _781404) ^ [_941625, _941627, _941629, _941631] : [class_Orderings_Olinorder(_941625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941625), _941627), _941629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941625), _941629), _941631)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941625, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_941625, _941627, _941629)), c_SetInterval_Oord__class_OgreaterThanLessThan(_941625, _941629, _941631)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_941625, _941627, _941631))], (50949 ^ _781404) ^ [_1811452, _1811454, _1811456, _1811458] : [c_Fun_Oinj__on(_1811452, _1811454, _1811456, _1811458), -(c_Fun_Obij__betw(_1811452, _1811454, _1811456, _1811458, hAPP(c_Set_Oimage(_1811452, _1811454, _1811456), _1811458)))], (6375 ^ _781404) ^ [_882758, _882760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _882758)), _882760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882758), _882760)))], (33768 ^ _781404) ^ [_1398589, _1398591, _1398593] : [_1398591 = _1398593, -(hAPP(hAPP(c_COMBC(_1398589, tc_fun(_1398589, tc_HOL_Obool), tc_HOL_Obool), c_member(_1398589)), _1398591) = hAPP(hAPP(c_COMBC(_1398589, tc_fun(_1398589, tc_HOL_Obool), tc_HOL_Obool), c_member(_1398589)), _1398593))], (22217 ^ _781404) ^ [_1177303, _1177305, _1177307, _1177309] : [class_Groups_Omonoid__mult(_1177303), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1177303), _1177305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1177307), _1177309)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177303), hAPP(hAPP(c_Power_Opower__class_Opower(_1177303), _1177305), _1177307)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177303), _1177305), _1177309)))], (13720 ^ _781404) ^ [_1020623, _1020625, _1020627, _1020629, _1020631] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1020623), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020623), _1020625), _1020627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020623), _1020629), _1020631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020623), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020623), _1020625), _1020629)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020623), _1020627), _1020631))))], (18839 ^ _781404) ^ [_1117105, _1117107] : [class_Int_Onumber__ring(_1117105), class_Rings_Olinordered__idom(_1117105), 18846 ^ _781404 : [(18853 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1117107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117105), c_Groups_Ozero__class_Ozero(_1117105)), hAPP(c_Int_Onumber__class_Onumber__of(_1117105), _1117107))))], (18847 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117105), c_Groups_Ozero__class_Ozero(_1117105)), hAPP(c_Int_Onumber__class_Onumber__of(_1117105), _1117107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1117107)))]]], (4362 ^ _781404) ^ [_847455, _847457, _847459, _847461, _847463, _847465, _847467, _847469, _847471, _847473] : [-(c_Predicate_Opred__comp(_847473, _847469, _847465, _847461, _847457) = c_Predicate_Opred__comp(_847471, _847467, _847463, _847459, _847455)), _847473 = _847471, _847469 = _847467, _847465 = _847463, _847461 = _847459, _847457 = _847455], (23375 ^ _781404) ^ [_1200558, _1200560, _1200562] : [class_Divides_Osemiring__div(_1200558), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200558), _1200560), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200558), _1200562), _1200560))), c_Divides_Odiv__class_Omod(_1200558, _1200562, _1200560)) = _1200562)], (37392 ^ _781404) ^ [_1484652, _1484654, _1484656, _1484658, _1484660] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484652, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1484654, _1484652, _1484656), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484654, tc_HOL_Obool)), _1484658), _1484660))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484652, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1484654, _1484652, _1484656), _1484658)), hAPP(c_Relation_OImage(_1484654, _1484652, _1484656), _1484660)))))], (47697 ^ _781404) ^ [_1740560, _1740562, _1740564] : [47699 ^ _781404 : [(47702 ^ _781404) ^ [] : [hBOOL(hAPP(_1740562, 47698 ^ [_1740560, _1740562, _1740564]))], (47700 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740560), 47698 ^ [_1740560, _1740562, _1740564]), hAPP(c_List_Oset(_1740560), _1740564))))]], -(c_List_OtakeWhile(_1740560, _1740562, _1740564) = _1740564)], (45120 ^ _781404) ^ [_1683773, _1683775] : [-(_1683773 = c_List_Olist_ONil(_1683775)), -(hAPP(hAPP(c_List_Oappend(_1683775), c_List_Obutlast(_1683775, _1683773)), hAPP(hAPP(c_List_Olist_OCons(_1683775), c_List_Olast(_1683775, _1683773)), c_List_Olist_ONil(_1683775))) = _1683773)], (38462 ^ _781404) ^ [_1511297, _1511299, _1511301] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1511297), _1511299), _1511301) = c_Nitpick_OAbs__Frac(_1511297, c_Nitpick_Onorm__frac(_1511299, _1511301)))], (17230 ^ _781404) ^ [_1088560, _1088562, _1088564] : [class_Int_Onumber(_1088560), class_Orderings_Olinorder(_1088560), 17237 ^ _781404 : [(17244 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088560), hAPP(c_Int_Onumber__class_Onumber__of(_1088560), _1088564)), hAPP(c_Int_Onumber__class_Onumber__of(_1088560), _1088562)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088560), hAPP(c_Int_Onumber__class_Onumber__of(_1088560), _1088562)), hAPP(c_Int_Onumber__class_Onumber__of(_1088560), _1088564))))], (17238 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088560), hAPP(c_Int_Onumber__class_Onumber__of(_1088560), _1088562)), hAPP(c_Int_Onumber__class_Onumber__of(_1088560), _1088564))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088560), hAPP(c_Int_Onumber__class_Onumber__of(_1088560), _1088564)), hAPP(c_Int_Onumber__class_Onumber__of(_1088560), _1088562)))]]], (3558 ^ _781404) ^ [_834587, _834589, _834591, _834593, _834595, _834597] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_834597, _834593, _834589) = c_SetInterval_Oord__class_OgreaterThanAtMost(_834595, _834591, _834587)), _834597 = _834595, _834593 = _834591, _834589 = _834587], (18343 ^ _781404) ^ [_1108303, _1108305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1108303)), -(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), _1108303), _1108305))))], (42563 ^ _781404) ^ [_1624951, _1624953, _1624955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1624951, _1624951), tc_HOL_Obool)), _1624953), hAPP(hAPP(c_Product__Type_OSigma(_1624951, _1624951), _1624955), hAPP(c_COMBK(tc_fun(_1624951, tc_HOL_Obool), _1624951), _1624955)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1624951), tc_List_Olist(_1624951)), tc_HOL_Obool)), c_List_Olistrel(_1624951, _1624953)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1624951), tc_List_Olist(_1624951)), c_List_Olists(_1624951, _1624955)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1624951), tc_HOL_Obool), tc_List_Olist(_1624951)), c_List_Olists(_1624951, _1624955))))))], (9419 ^ _781404) ^ [_942881, _942883] : [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), _942881), _942883))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942883), _942881)))], (7273 ^ _781404) ^ [_899772, _899774, _899776, _899778] : [class_Orderings_Olinorder(_899772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899772), _899774), _899776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899772), _899776), _899778)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899772, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_899772, _899774), _899776)), c_SetInterval_Oord__class_OatLeastAtMost(_899772, _899776, _899778)) = c_SetInterval_Oord__class_OatLeastAtMost(_899772, _899774, _899778))], (49139 ^ _781404) ^ [_1772042, _1772044, _1772046, _1772048, _1772050] : [-(c_List_Oreplicate(_1772042, _1772044, _1772046) = c_List_Oreplicate(_1772042, _1772048, _1772050)), _1772044 = _1772048, 49144 ^ _781404 : [(49147 ^ _781404) ^ [] : [_1772046 = _1772050], (49145 ^ _781404) ^ [] : [_1772044 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (50307 ^ _781404) ^ [_1797750, _1797752] : [c_Equiv__Relations_Opart__equivp(_1797750, _1797752), 50311 ^ _781404 : [(50316 ^ _781404) ^ [] : [-(c_Predicate_Otransp(_1797750, _1797752))], (50314 ^ _781404) ^ [] : [-(c_Predicate_Osymp(_1797750, _1797752))], (50312 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1797752, 50310 ^ [_1797750, _1797752]), 50310 ^ [_1797750, _1797752])))]]], (12832 ^ _781404) ^ [_1003896, _1003898, _1003900, _1003902, _1003904] : [class_Rings_Oring(_1003896), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003898), _1003900)), hBOOL(hAPP(hAPP(c_member(_1003898), _1003902), _1003900)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003898, _1003896), _1003904), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1003898, tc_HOL_Obool)), _1003900), hAPP(hAPP(c_Set_Oinsert(_1003898), _1003902), c_Orderings_Obot__class_Obot(tc_fun(_1003898, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1003896), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003898, _1003896), _1003904), _1003900)), hAPP(_1003904, _1003902)))], (46024 ^ _781404) ^ [_1704571, _1704573, _1704575, _1704577] : [c_List_Olist__all2(_1704571, _1704573, _1704575, c_List_Olist_ONil(_1704571), _1704577), -(_1704577 = c_List_Olist_ONil(_1704573))], (39904 ^ _781404) ^ [_1557124, _1557126] : [-(hAPP(c_Relation_ODomain(_1557124, _1557124), c_Relation_OId__on(_1557124, _1557126)) = _1557126)], (17507 ^ _781404) ^ [_1093579] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1093579)) = _1093579)], (44443 ^ _781404) ^ [_1670020, _1670022, _1670024, _1670026] : [_1670020 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1670022), _1670020), hAPP(hAPP(c_List_Olist_OCons(_1670022), _1670024), _1670026)) = hAPP(hAPP(c_List_Olist_OCons(_1670022), _1670024), _1670026))], (49852 ^ _781404) ^ [_1787815, _1787817, _1787819, _1787821] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1787815, tc_fun(_1787817, tc_HOL_Obool)), _1787819), _1787821) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1787817, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1787817, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1787815, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1787817, tc_HOL_Obool)), c_HOL_OEx(_1787815)), hAPP(hAPP(c_COMBB(tc_fun(_1787815, tc_HOL_Obool), tc_fun(_1787815, tc_HOL_Obool), tc_fun(_1787817, tc_HOL_Obool)), hAPP(c_COMBS(_1787815, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1787815), c_fconj), hAPP(hAPP(c_COMBC(_1787815, tc_fun(_1787815, tc_HOL_Obool), tc_HOL_Obool), c_member(_1787815)), _1787819)))), hAPP(hAPP(c_COMBC(tc_fun(_1787817, tc_HOL_Obool), tc_fun(_1787815, tc_fun(_1787817, tc_HOL_Obool)), tc_fun(_1787815, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1787817, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1787815, tc_fun(_1787817, tc_HOL_Obool)), tc_fun(_1787815, tc_HOL_Obool)), tc_fun(_1787817, tc_HOL_Obool)), c_COMBB(tc_fun(_1787817, tc_HOL_Obool), tc_HOL_Obool, _1787815)), c_fequal)), _1787821))))))], (22795 ^ _781404) ^ [_1188965, _1188967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188965)), 22798 ^ _781404 : [(22807 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1188965), _1188967) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1188965 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1188967 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (22799 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1188965), _1188967) = c_Groups_Oone__class_Oone(tc_Int_Oint), 22802 ^ _781404 : [(22805 ^ _781404) ^ [] : [-(_1188967 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22803 ^ _781404) ^ [] : [-(_1188965 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (24704 ^ _781404) ^ [_1224513] : [_1224513 = c_Int_OMin, -(c_Int_OBit1(_1224513) = c_Int_OMin)], (18913 ^ _781404) ^ [_1118306, _1118308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1118306, _1118308))))], (43097 ^ _781404) ^ [_1639735] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1639735)), -(c_List_Onat__list(_1639735))], (16148 ^ _781404) ^ [_1067902, _1067904] : [class_Lattices_Olattice(_1067902), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067902), _1067904)), -(_1067904 = c_Orderings_Obot__class_Obot(tc_fun(_1067902, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1067902), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067902), 16161 ^ [_1067902, _1067904]), 16162 ^ [_1067902, _1067904])), hAPP(hAPP(c_Set_Oinsert(_1067902), 16161 ^ [_1067902, _1067904]), hAPP(hAPP(c_Set_Oinsert(_1067902), 16162 ^ [_1067902, _1067904]), c_Orderings_Obot__class_Obot(tc_fun(_1067902, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1067902), c_Big__Operators_Olattice__class_OInf__fin(_1067902, _1067904)), _1067904)))], (25239 ^ _781404) ^ [_1232974] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232974))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1232974)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (46487 ^ _781404) ^ [_1715018, _1715020, _1715022, _1715024] : [-(c_List_Otranspose(_1715018, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1715018)), hAPP(hAPP(c_List_Olist_OCons(_1715018), _1715020), _1715022)), _1715024)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1715018)), hAPP(hAPP(c_List_Olist_OCons(_1715018), _1715020), c_List_Oconcat(_1715018, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715018), tc_List_Olist(_1715018)), c_List_Olist_Olist__case(tc_List_Olist(_1715018), _1715018, c_List_Olist_ONil(_1715018), hAPP(hAPP(c_COMBB(tc_List_Olist(_1715018), tc_fun(tc_List_Olist(_1715018), tc_List_Olist(_1715018)), _1715018), c_COMBK(tc_List_Olist(_1715018), tc_List_Olist(_1715018))), hAPP(hAPP(c_COMBC(_1715018, tc_List_Olist(_1715018), tc_List_Olist(_1715018)), c_List_Olist_OCons(_1715018)), c_List_Olist_ONil(_1715018))))), _1715024)))), c_List_Otranspose(_1715018, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1715018)), _1715022), c_List_Oconcat(tc_List_Olist(_1715018), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715018), tc_List_Olist(tc_List_Olist(_1715018))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1715018)), _1715018, c_List_Olist_ONil(tc_List_Olist(_1715018)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1715018), tc_List_Olist(tc_List_Olist(_1715018))), _1715018), hAPP(hAPP(c_COMBC(tc_List_Olist(_1715018), tc_List_Olist(tc_List_Olist(_1715018)), tc_List_Olist(tc_List_Olist(_1715018))), c_List_Olist_OCons(tc_List_Olist(_1715018))), c_List_Olist_ONil(tc_List_Olist(_1715018)))))), _1715024))))))], (8136 ^ _781404) ^ [_917884, _917886, _917888] : [hAPP(c_Set_Oimage(_917886, tc_fun(_917886, tc_HOL_Obool), _917884), _917888) = hAPP(c_Set_OPow(_917886), _917888)], (12272 ^ _781404) ^ [_992447, _992449, _992451, _992453, _992455, _992457] : [c_Fun_Oinj__on(_992447, _992449, _992451, _992453), hBOOL(hAPP(hAPP(c_member(_992449), _992455), hAPP(c_Set_Oimage(_992447, _992449, _992451), _992453))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_992447, tc_HOL_Obool)), _992453), _992457)), -(hBOOL(hAPP(hAPP(c_member(_992447), hAPP(c_Fun_Othe__inv__into(_992447, _992449, _992453, _992451), _992455)), _992457)))], (36870 ^ _781404) ^ [_1471358, _1471360, _1471362, _1471364, _1471366, _1471368] : [class_Groups_Ocomm__monoid__add(_1471358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471360), _1471362)), 36880 ^ _781404 : [(36881 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471360), 36879 ^ [_1471358, _1471360, _1471362, _1471364, _1471366, _1471368]), _1471362)))], (36886 ^ _781404) ^ [] : [36879 ^ [_1471358, _1471360, _1471362, _1471364, _1471366, _1471368] = 36882 ^ [_1471358, _1471360, _1471362, _1471364, _1471366, _1471368]], (36890 ^ _781404) ^ [] : [hAPP(_1471366, hAPP(_1471364, 36879 ^ [_1471358, _1471360, _1471362, _1471364, _1471366, _1471368])) = c_Groups_Ozero__class_Ozero(_1471358)], (36888 ^ _781404) ^ [] : [-(hAPP(_1471364, 36879 ^ [_1471358, _1471360, _1471362, _1471364, _1471366, _1471368]) = hAPP(_1471364, 36882 ^ [_1471358, _1471360, _1471362, _1471364, _1471366, _1471368]))], (36884 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471360), 36882 ^ [_1471358, _1471360, _1471362, _1471364, _1471366, _1471368]), _1471362)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471368, _1471358), _1471366), hAPP(c_Set_Oimage(_1471360, _1471368, _1471364), _1471362)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471360, _1471358), hAPP(c_Fun_Ocomp(_1471368, _1471358, _1471360, _1471366), _1471364)), _1471362))], (42336 ^ _781404) ^ [_1617822, _1617824, _1617826, _1617828] : [-(c_List_Olist_Olist__size(_1617822, _1617824, hAPP(hAPP(c_List_Olist_OCons(_1617822), _1617826), _1617828)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1617824, _1617826)), c_List_Olist_Olist__size(_1617822, _1617824, _1617828))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16628 ^ _781404) ^ [_1077325] : [class_Rings_Oring__1(_1077325), -(hBOOL(hAPP(hAPP(c_member(_1077325), c_Groups_Ozero__class_Ozero(_1077325)), c_Int_Oring__1__class_OInts(_1077325))))], (25973 ^ _781404) ^ [_1245538, _1245540] : [class_Int_Onumber__ring(_1245538), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1245538), hAPP(c_Int_Onumber__class_Onumber__of(_1245538), 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)))), _1245540)) = c_Groups_Oone__class_Oone(_1245538))], (19155 ^ _781404) ^ [_1122265, _1122267] : [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)), _1122265)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1122267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1122265), _1122267)))], (21211 ^ _781404) ^ [_1158364, _1158366] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158364)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158366)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158364), _1158366)))], (30786 ^ _781404) ^ [_1334799, _1334801, _1334803, _1334805] : [class_Orderings_Olinorder(_1334799), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334799), _1334801), _1334803)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334799), _1334801), _1334805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334799), _1334801), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334799), _1334803), _1334805))))], (36713 ^ _781404) ^ [_1468210, _1468212, _1468214] : [-(hAPP(c_Finite__Set_Ofold1(_1468210, _1468212), _1468214) = c_HOL_OThe(_1468210, c_Finite__Set_Ofold1Set(_1468210, _1468212, _1468214)))], (10367 ^ _781404) ^ [_957782, _957784, _957786, _957788] : [class_Lattices_Osemilattice__sup(_957782), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957782), _957784), _957786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957782), _957784), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_957782), _957786), _957788))))], (7033 ^ _781404) ^ [_895177, _895179, _895181, _895183] : [class_Lattices_Osemilattice__sup(_895177), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895177), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895177), _895179), _895181)), _895183)), 7040 ^ _781404 : [(7043 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895177), _895181), _895183)))], (7041 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895177), _895179), _895183)))]]], (32698 ^ _781404) ^ [_1370432, _1370434, _1370436] : [class_Orderings_Olinorder(_1370432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370432), _1370434)), hBOOL(hAPP(hAPP(c_member(_1370432), _1370436), _1370434)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1370432), _1370436), c_Big__Operators_Olattice_OSup__fin(_1370432, c_Orderings_Oord__class_Omax(_1370432), _1370434)) = _1370436)], (12478 ^ _781404) ^ [_996616, _996618, _996620] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_996616, tc_HOL_Obool)), _996618), _996620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_996616, tc_HOL_Obool)), _996618), c_Complete__Lattice_OSup__class_OSup(tc_fun(_996616, tc_HOL_Obool), _996620))))], (39550 ^ _781404) ^ [_1546540, _1546542, _1546544, _1546546] : [-(c_Product__Type_Oapfst(_1546540, _1546542, _1546544, _1546546) = c_Product__Type_Omap__pair(_1546540, _1546542, _1546544, _1546544, _1546546, c_Fun_Oid(_1546544)))], (12414 ^ _781404) ^ [_995508, _995510, _995512, _995514] : [-(hBOOL(hAPP(hAPP(c_member(_995508), _995510), _995512))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995508, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_995508), _995510), _995514)), _995512) = hAPP(hAPP(c_Set_Oinsert(_995508), _995510), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995508, tc_HOL_Obool)), _995514), _995512)))], (49345 ^ _781404) ^ [_1776213, _1776215, _1776217, _1776219, _1776221] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1776213, _1776215, _1776217, _1776219, _1776221) = c_Option_Ooption_Ooption__case(_1776213, tc_prod(_1776215, tc_Lazy__Sequence_Olazy__sequence(_1776215)), _1776217, hAPP(c_Product__Type_Oprod_Oprod__case(_1776215, tc_Lazy__Sequence_Olazy__sequence(_1776215), _1776213), _1776219), hAPP(c_Lazy__Sequence_Oyield(_1776215), _1776221)))], (34141 ^ _781404) ^ [_1408466, _1408468, _1408470, _1408472, _1408474] : [-(_1408466 = c_Orderings_Obot__class_Obot(tc_fun(_1408468, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408470, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408468, tc_fun(_1408470, tc_HOL_Obool)), _1408466), _1408472)), _1408474) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408468, tc_fun(_1408470, tc_HOL_Obool)), _1408466), hAPP(hAPP(c_COMBC(_1408468, tc_fun(_1408470, tc_HOL_Obool), tc_fun(_1408470, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408470, tc_HOL_Obool), tc_fun(tc_fun(_1408470, tc_HOL_Obool), tc_fun(_1408470, tc_HOL_Obool)), _1408468), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408470, tc_HOL_Obool))), _1408472)), _1408474)))], (22207 ^ _781404) ^ [_1177122, _1177124, _1177126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177122), _1177124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1177126), _1177122)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1177126), _1177124))))], (16506 ^ _781404) ^ [_1074823, _1074825, _1074827] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1074823), _1074825)), -(hAPP(c_Finite__Set_Ocard(_1074823), hAPP(hAPP(c_Set_Oinsert(_1074823), _1074827), _1074825)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1074823), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074823, tc_HOL_Obool)), _1074825), hAPP(hAPP(c_Set_Oinsert(_1074823), _1074827), c_Orderings_Obot__class_Obot(tc_fun(_1074823, tc_HOL_Obool)))))))], (11629 ^ _781404) ^ [_980383, _980385, _980387, _980389] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_980383, tc_HOL_Obool)), _980385), _980387)), hBOOL(hAPP(hAPP(c_member(_980383), _980389), _980385)), -(hBOOL(hAPP(hAPP(c_member(_980383), _980389), c_Complete__Lattice_OSup__class_OSup(tc_fun(_980383, tc_HOL_Obool), _980387))))], (32354 ^ _781404) ^ [_1364180, _1364182, _1364184, _1364186, _1364188] : [class_Orderings_Olinorder(_1364180), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364180, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1364180, _1364182, _1364184)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1364180, _1364186, _1364188)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1364180, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364180), _1364182), _1364186), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1364180), _1364184), _1364188)))], (8323 ^ _781404) ^ [_921798, _921800, _921802] : [hBOOL(hAPP(hAPP(c_member(_921800), _921798), c_Orderings_Obot__class_Obot(tc_fun(_921800, tc_HOL_Obool)))), -(hBOOL(hAPP(_921802, _921798)))], (52418 ^ _781404) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (47748 ^ _781404) ^ [_1741578] : [-(c_List_Oreturn__list(_1741578) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1741578))], (16404 ^ _781404) ^ [_1072889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1072889)), -(_1072889 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1072889), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (14111 ^ _781404) ^ [_1027630, _1027632, _1027634, _1027636] : [class_Groups_Ocomm__monoid__add(_1027630), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1027632), _1027634))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027632, _1027630), _1027636), _1027634) = c_Groups_Ozero__class_Ozero(_1027630))], (35537 ^ _781404) ^ [_1444586, _1444588, _1444590, _1444592, _1444594, _1444596] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1444586, _1444588, _1444590), _1444592), hAPP(hAPP(c_Product__Type_OPair(_1444586, _1444588), _1444594), _1444596)) = hAPP(hAPP(_1444592, _1444594), _1444596))], (12897 ^ _781404) ^ [_1005261, _1005263, _1005265, _1005267] : [-(c_Fun_Ofun__upd(_1005261, _1005263, _1005265, _1005267, hAPP(_1005265, _1005267)) = _1005265)], (1166 ^ _781404) ^ [_799019, _799021] : [-(class_Rings_Olinordered__semiring__1__strict(_799019)), _799021 = _799019, class_Rings_Olinordered__semiring__1__strict(_799021)], (41163 ^ _781404) ^ [_1586980, _1586982] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586980, _1586980)), hAPP(hAPP(c_Product__Type_OPair(_1586980, _1586980), _1586982), _1586982)), c_Relation_OId(_1586980))))], (25021 ^ _781404) ^ [_1229503] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1229503))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1229503)) = _1229503)], (35348 ^ _781404) ^ [_1440264, _1440266, _1440268, _1440270, _1440272, _1440274] : [hBOOL(hAPP(hAPP(_1440264, _1440266), _1440268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1440270, tc_fun(_1440272, tc_HOL_Obool))), _1440264), _1440274)), -(hBOOL(hAPP(hAPP(_1440274, _1440266), _1440268)))], (47569 ^ _781404) ^ [_1737896, _1737898] : [-(_1737896 = c_List_Olist_ONil(_1737898)), -(c_List_Olast(_1737898, hAPP(c_List_Orev(_1737898), _1737896)) = hAPP(c_List_Ohd(_1737898), _1737896))], (34631 ^ _781404) ^ [_1423883, _1423885, _1423887] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1423883, tc_HOL_Obool)), _1423887), hAPP(c_Set_OPow(_1423883), _1423885))), -(hBOOL(hAPP(c_Predicate_OPowp(_1423883, hAPP(hAPP(c_COMBC(_1423883, tc_fun(_1423883, tc_HOL_Obool), tc_HOL_Obool), c_member(_1423883)), _1423885)), _1423887)))], (25682 ^ _781404) ^ [_1240348, _1240350] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1240348) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1240350), 25685 ^ _781404 : [(25688 ^ _781404) ^ [] : [-(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), _1240350))))], (25686 ^ _781404) ^ [] : [-(_1240348 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1240350)))]]], (12792 ^ _781404) ^ [_1003007, _1003009, _1003011, _1003013] : [-(hBOOL(hAPP(hAPP(c_member(_1003007), _1003009), _1003011))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003007, tc_Nat_Onat), _1003013), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1003007, tc_HOL_Obool)), _1003011), hAPP(hAPP(c_Set_Oinsert(_1003007), _1003009), c_Orderings_Obot__class_Obot(tc_fun(_1003007, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003007, tc_Nat_Onat), _1003013), _1003011))], (26641 ^ _781404) ^ [_1256184, _1256186, _1256188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256184)), 26647 ^ _781404 : [(26650 ^ _781404) ^ [] : [hBOOL(hAPP(_1256186, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26646 ^ [_1256184, _1256186, _1256188]), _1256184)))], (26648 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1256186, 26646 ^ [_1256184, _1256186, _1256188])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256188)), 26655 ^ _781404 : [(26656 ^ _781404) ^ [_1256473] : [hBOOL(hAPP(_1256186, _1256473)), -(hBOOL(hAPP(_1256186, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1256473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1256188), _1256184)))))]]], (24208 ^ _781404) ^ [_1215521, _1215523] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215521, _1215523) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215521, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1215523)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (38648 ^ _781404) ^ [_1516696, _1516698, _1516700, _1516702, _1516704, _1516706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1516696, _1516698), tc_HOL_Obool)), _1516700), hAPP(hAPP(c_Product__Type_OSigma(_1516696, _1516698), _1516702), hAPP(c_COMBK(tc_fun(_1516698, tc_HOL_Obool), _1516696), _1516704)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1516698, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1516696, _1516698, _1516700), _1516706)), _1516704)))], (45052 ^ _781404) ^ [_1682699, _1682701, _1682703] : [-(_1682699 = c_List_Olist_ONil(_1682701)), -(c_List_Olast(_1682701, hAPP(hAPP(c_List_Olist_OCons(_1682701), _1682703), _1682699)) = c_List_Olast(_1682701, _1682699))], (37629 ^ _781404) ^ [_1491283, _1491285, _1491287, _1491289, _1491291, _1491293] : [c_Equiv__Relations_Oequiv(_1491283, _1491285, _1491287), hBOOL(hAPP(hAPP(c_member(_1491283), _1491289), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491283, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1491283, _1491283, _1491287), hAPP(hAPP(c_Set_Oinsert(_1491283), _1491291), c_Orderings_Obot__class_Obot(tc_fun(_1491283, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1491283, _1491283, _1491287), hAPP(hAPP(c_Set_Oinsert(_1491283), _1491293), c_Orderings_Obot__class_Obot(tc_fun(_1491283, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491283, _1491283)), hAPP(hAPP(c_Product__Type_OPair(_1491283, _1491283), _1491291), _1491293)), _1491287)))], (14027 ^ _781404) ^ [_1026065, _1026067, _1026069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026065), _1026067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026069), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1026067), _1026069)), _1026065))))], (34795 ^ _781404) ^ [_1428045, _1428047, _1428049, _1428051, _1428053, _1428055] : [class_Groups_Ocomm__monoid__add(_1428045), c_Fun_Oinj__on(_1428047, _1428049, _1428051, _1428053), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428049, _1428045), _1428055), hAPP(c_Set_Oimage(_1428047, _1428049, _1428051), _1428053)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428047, _1428045), hAPP(c_Fun_Ocomp(_1428049, _1428045, _1428047, _1428055), _1428051)), _1428053))], (7571 ^ _781404) ^ [_905453, _905455, _905457] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905453, tc_HOL_Obool)), _905455), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905453, tc_HOL_Obool)), _905455), _905457)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905453, tc_HOL_Obool)), _905455), _905457))], (46491 ^ _781404) ^ [_1715387, _1715389, _1715391] : [-(hAPP(c_List_Ofilter(_1715387, _1715389), c_List_Oconcat(_1715387, _1715391)) = c_List_Oconcat(_1715387, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715387), tc_List_Olist(_1715387)), c_List_Ofilter(_1715387, _1715389)), _1715391)))], (3340 ^ _781404) ^ [_831250, _831252] : [_831252 = _831250, -(c_Lazy__Sequence_Ohb__not__seq(_831252) = c_Lazy__Sequence_Ohb__not__seq(_831250))], (42394 ^ _781404) ^ [_1619700, _1619702, _1619704, _1619706, _1619708] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619700, _1619700)), hAPP(hAPP(c_Product__Type_OPair(_1619700, _1619700), _1619702), _1619704)), _1619706)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619700), tc_List_Olist(_1619700))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619700), tc_List_Olist(_1619700)), hAPP(hAPP(c_List_Olist_OCons(_1619700), _1619702), _1619708)), hAPP(hAPP(c_List_Olist_OCons(_1619700), _1619704), _1619708))), c_List_Olistrel1(_1619700, _1619706))))], (19581 ^ _781404) ^ [_1129531, _1129533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1129531)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1129533)))), 19584 ^ _781404 : [(19587 ^ _781404) ^ [] : [-(_1129533 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19585 ^ _781404) ^ [] : [-(_1129531 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (10913 ^ _781404) ^ [_966680, _966682, _966684, _966686, _966688] : [c_Fun_Oinj__on(_966680, _966682, _966684, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_966680, tc_HOL_Obool)), _966686), _966688)), 10916 ^ _781404 : [(10923 ^ _781404) ^ [] : [_966686 = _966688, -(hAPP(c_Set_Oimage(_966680, _966682, _966684), _966686) = hAPP(c_Set_Oimage(_966680, _966682, _966684), _966688))], (10917 ^ _781404) ^ [] : [hAPP(c_Set_Oimage(_966680, _966682, _966684), _966686) = hAPP(c_Set_Oimage(_966680, _966682, _966684), _966688), -(_966686 = _966688)]]], (5694 ^ _781404) ^ [_868447, _868449] : [_868449 = _868447, -(c_member(_868449) = c_member(_868447))], (5014 ^ _781404) ^ [_857847, _857849] : [_857849 = _857847, -(c_Set_OCollect(_857849) = c_Set_OCollect(_857847))], (23091 ^ _781404) ^ [_1194789, _1194791, _1194793, _1194795] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194789), _1194791)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194793), _1194791)), _1194795)) = 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), _1194789), _1194793)), _1194791)), _1194795))], (38140 ^ _781404) ^ [] : [-(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))], (39311 ^ _781404) ^ [_1536601, _1536603, _1536605, _1536607] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1536601, _1536603), _1536605), _1536607) = hAPP(c_Set_OCollect(tc_prod(_1536603, _1536603)), hAPP(c_Product__Type_Oprod_Oprod__case(_1536603, _1536603, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1536603, tc_fun(tc_prod(_1536601, _1536601), tc_HOL_Obool), tc_fun(_1536603, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536603, tc_fun(tc_fun(tc_prod(_1536601, _1536601), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1536601, _1536601), tc_HOL_Obool), tc_fun(_1536603, tc_HOL_Obool)), _1536603), c_COMBC(_1536603, tc_fun(tc_prod(_1536601, _1536601), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536603, tc_prod(_1536601, _1536601)), tc_fun(_1536603, tc_fun(tc_fun(tc_prod(_1536601, _1536601), tc_HOL_Obool), tc_HOL_Obool)), _1536603), hAPP(c_COMBB(tc_prod(_1536601, _1536601), tc_fun(tc_fun(tc_prod(_1536601, _1536601), tc_HOL_Obool), tc_HOL_Obool), _1536603), c_member(tc_prod(_1536601, _1536601)))), hAPP(hAPP(c_COMBC(_1536603, tc_fun(_1536603, _1536601), tc_fun(_1536603, tc_prod(_1536601, _1536601))), hAPP(hAPP(c_COMBB(tc_fun(_1536601, tc_prod(_1536601, _1536601)), tc_fun(tc_fun(_1536603, _1536601), tc_fun(_1536603, tc_prod(_1536601, _1536601))), _1536603), c_COMBB(_1536601, tc_prod(_1536601, _1536601), _1536603)), hAPP(hAPP(c_COMBB(_1536601, tc_fun(_1536601, tc_prod(_1536601, _1536601)), _1536603), c_Product__Type_OPair(_1536601, _1536601)), _1536607))), _1536607)))), _1536605))))], (15974 ^ _781404) ^ [_1064605, _1064607, _1064609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1064605), _1064607)), hBOOL(hAPP(hAPP(c_member(_1064605), _1064609), _1064607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1064605), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064605, tc_HOL_Obool)), _1064607), hAPP(hAPP(c_Set_Oinsert(_1064605), _1064609), c_Orderings_Obot__class_Obot(tc_fun(_1064605, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1064605), _1064607))))], (33029 ^ _781404) ^ [_1376984, _1376986, _1376988, _1376990, _1376992, _1376994] : [hBOOL(hAPP(hAPP(c_member(_1376984), _1376986), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1376988, tc_fun(_1376984, tc_HOL_Obool)), _1376990), _1376992))), hBOOL(hAPP(hAPP(c_member(_1376988), _1376994), _1376990)), -(hBOOL(hAPP(hAPP(c_member(_1376984), _1376986), hAPP(_1376992, _1376994))))], (34247 ^ _781404) ^ [_1413445, _1413447, _1413449, _1413451, _1413453] : [class_Lattices_Olattice(_1413445), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413447, _1413445)), _1413449), _1413451), _1413453) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1413445), hAPP(_1413449, _1413453)), hAPP(_1413451, _1413453)))], (46688 ^ _781404) ^ [_1720585, _1720587, _1720589, _1720591] : [-(c_List_Ofoldr(_1720585, _1720587, _1720589, c_List_Olist_ONil(_1720585), _1720591) = _1720591)], (9985 ^ _781404) ^ [_951942, _951944, _951946, _951948] : [class_Orderings_Oorder(_951942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951942), _951944), _951946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951942), _951948), _951944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951942), _951948), _951946)))], (26166 ^ _781404) ^ [_1248614, _1248616] : [c_Nat__Transfer_Onat__set(_1248614), c_Nat__Transfer_Onat__set(_1248616), 26173 ^ _781404 : [(26180 ^ _781404) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1248614) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1248616), -(_1248614 = _1248616)], (26174 ^ _781404) ^ [] : [_1248614 = _1248616, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1248614) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1248616))]]], (44162 ^ _781404) ^ [_1662688, _1662690, _1662692] : [-(c_List_Obutlast(_1662688, hAPP(hAPP(c_List_Oappend(_1662688), _1662690), hAPP(hAPP(c_List_Olist_OCons(_1662688), _1662692), c_List_Olist_ONil(_1662688)))) = _1662690)], (18673 ^ _781404) ^ [_1114582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114582), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114582)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37091 ^ _781404) ^ [_1476890, _1476892, _1476894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1476890, 37092 ^ [_1476890, _1476892, _1476894])), hAPP(_1476892, 37092 ^ [_1476890, _1476892, _1476894]))), -(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), _1476892), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1476894))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1476890), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1476894))) = 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)), _1476892)), _1476890)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1476894)))], (3906 ^ _781404) ^ [_840073, _840075] : [_840075 = _840073, -(c_Nat_Osemiring__1__class_Oof__nat(_840075) = c_Nat_Osemiring__1__class_Oof__nat(_840073))], (22981 ^ _781404) ^ [_1192381, _1192383, _1192385] : [class_Int_Onumber__ring(_1192381), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1192381), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192381), _1192383), _1192385)), 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(_1192381), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192381), hAPP(hAPP(c_Power_Opower__class_Opower(_1192381), _1192383), 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(_1192381), _1192385), 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(_1192381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192381), hAPP(c_Int_Onumber__class_Onumber__of(_1192381), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1192383)), _1192385)))], (17955 ^ _781404) ^ [_1101593, _1101595] : [class_Groups_Omonoid__mult(_1101593), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1101593), c_Groups_Oone__class_Oone(_1101593)), _1101595) = c_Groups_Oone__class_Oone(_1101593))], (20363 ^ _781404) ^ [_1142846, _1142848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142846), _1142848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1142846)), c_Int_OBit0(_1142848))))], (25307 ^ _781404) ^ [_1234089] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234089, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (41925 ^ _781404) ^ [_1605627, _1605629] : [-(hAPP(hAPP(c_Nat_Ocompow(_1605627, _1605627), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1605629) = c_Fun_Oid(_1605627))], (14498 ^ _781404) ^ [_1035372] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035372), c_Orderings_Obot__class_Obot(tc_fun(_1035372, tc_HOL_Obool)))))], (41431 ^ _781404) ^ [_1593324, _1593326, _1593328, _1593330] : [-(c_Wellfounded_Owf(_1593324, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593324, _1593324)), hAPP(hAPP(c_Product__Type_OPair(_1593324, _1593324), _1593326), _1593328)), _1593330))), c_Wellfounded_Owf(_1593324, _1593330), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593324, _1593324)), hAPP(hAPP(c_Product__Type_OPair(_1593324, _1593324), _1593328), _1593326)), c_Transitive__Closure_Ortrancl(_1593324, _1593330))))], (25845 ^ _781404) ^ [_1243359] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1243359), _1243359)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1243359)], (24921 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45875 ^ _781404) ^ [_1701104, _1701106, _1701108] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1701104)), _1701108), c_List_Olists(_1701104, _1701106))), -(hBOOL(hAPP(c_List_Olistsp(_1701104, hAPP(hAPP(c_COMBC(_1701104, tc_fun(_1701104, tc_HOL_Obool), tc_HOL_Obool), c_member(_1701104)), _1701106)), _1701108)))], (41291 ^ _781404) ^ [_1590123, _1590125, _1590127] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590123, _1590123)), hAPP(hAPP(c_Product__Type_OPair(_1590123, _1590123), _1590125), _1590127)), c_Relation_OId(_1590123))), -(_1590125 = _1590127)], (44709 ^ _781404) ^ [_1675697, _1675699, _1675701, _1675703] : [44710 ^ _781404 : [(44711 ^ _781404) ^ [_1675794, _1675796] : [_1675697 = hAPP(hAPP(c_List_Olist_OCons(_1675699), _1675796), _1675794)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675699), tc_List_Olist(_1675699))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675699), tc_List_Olist(_1675699)), _1675701), hAPP(hAPP(c_List_Oappend(_1675699), _1675701), _1675697))), c_List_Olexord(_1675699, _1675703))))], (23363 ^ _781404) ^ [_1200258, _1200260, _1200262, _1200264] : [class_Divides_Osemiring__div(_1200258), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200258), _1200260), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200258), _1200262), _1200260))), c_Divides_Odiv__class_Omod(_1200258, _1200262, _1200260))), _1200264) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200258), _1200262), _1200264))], (13345 ^ _781404) ^ [_1013309, _1013311, _1013313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013309), _1013311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013309), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013311), _1013313))))], (20231 ^ _781404) ^ [_1140611, _1140613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140611), _1140613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1140611)), c_Int_OBit0(_1140613))))], (19183 ^ _781404) ^ [_1122664] : [class_Rings_Osemiring__1(_1122664), c_Int_Oiszero(_1122664, c_Groups_Oone__class_Oone(_1122664))], (44659 ^ _781404) ^ [_1674692, _1674694, _1674696] : [-(_1674692 = c_List_Olist_ONil(_1674694)), -(hAPP(c_List_Otl(_1674694), hAPP(hAPP(c_List_Oappend(_1674694), _1674692), _1674696)) = hAPP(hAPP(c_List_Oappend(_1674694), hAPP(c_List_Otl(_1674694), _1674692)), _1674696))], (4856 ^ _781404) ^ [_855318, _855320, _855322, _855324] : [-(c_Complete__Lattice_OInf__class_OInf(_855324, _855320) = c_Complete__Lattice_OInf__class_OInf(_855322, _855318)), _855324 = _855322, _855320 = _855318], (12786 ^ _781404) ^ [_1002816, _1002818, _1002820, _1002822] : [hBOOL(hAPP(hAPP(c_member(_1002816), _1002818), _1002820)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1002816, tc_Nat_Onat), _1002822), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002816, tc_HOL_Obool)), _1002820), hAPP(hAPP(c_Set_Oinsert(_1002816), _1002818), c_Orderings_Obot__class_Obot(tc_fun(_1002816, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1002816, tc_Nat_Onat), _1002822), _1002820)), hAPP(_1002822, _1002818)))], (51814 ^ _781404) ^ [_1830380, _1830382, _1830384, _1830386, _1830388] : [class_Rings_Ocomm__semiring__1(_1830380), hBOOL(hAPP(c_Finite__Set_Ofinite(_1830382), _1830384)), hBOOL(hAPP(hAPP(c_member(_1830382), _1830386), _1830384)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830380), hAPP(_1830388, _1830386)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1830382, _1830380), _1830388), _1830384))))], (6265 ^ _781404) ^ [_881065, _881067, _881069] : [class_Orderings_Olinorder(_881065), 6268 ^ _781404 : [(6275 ^ _781404) ^ [] : [_881067 = _881069, -(hAPP(c_SetInterval_Oord__class_OatMost(_881065), _881067) = hAPP(c_SetInterval_Oord__class_OatMost(_881065), _881069))], (6269 ^ _781404) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_881065), _881067) = hAPP(c_SetInterval_Oord__class_OatMost(_881065), _881069), -(_881067 = _881069)]]], (19400 ^ _781404) ^ [_1126424, _1126426, _1126428] : [class_Rings_Olinordered__semidom(_1126424), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126424), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1126424), _1126426)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1126424), _1126428))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126426), _1126428)))], (46997 ^ _781404) ^ [_1726647, _1726649, _1726651] : [class_Orderings_Olinorder(_1726647), 47000 ^ _781404 : [(47007 ^ _781404) ^ [] : [c_List_Olinorder__class_Osorted(_1726647, _1726651), -(c_List_Olinorder__class_Osorted(_1726647, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1726647, _1726647, c_COMBI(_1726647)), _1726649), _1726651)))], (47001 ^ _781404) ^ [] : [c_List_Olinorder__class_Osorted(_1726647, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1726647, _1726647, c_COMBI(_1726647)), _1726649), _1726651)), -(c_List_Olinorder__class_Osorted(_1726647, _1726651))]]], (34637 ^ _781404) ^ [_1424034, _1424036, _1424038, _1424040, _1424042] : [class_Groups_Ocomm__monoid__add(_1424034), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424036), _1424038)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424036, _1424034), _1424040), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424036, tc_HOL_Obool)), _1424038), _1424042)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1424036, _1424034), hAPP(hAPP(c_COMBC(_1424036, _1424034, _1424034), hAPP(hAPP(c_COMBS(_1424036, _1424034, tc_fun(_1424034, _1424034)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1424034, tc_fun(_1424034, _1424034)), _1424036), c_If(_1424034)), hAPP(hAPP(c_COMBC(_1424036, tc_fun(_1424036, tc_HOL_Obool), tc_HOL_Obool), c_member(_1424036)), _1424042))), _1424040)), c_Groups_Ozero__class_Ozero(_1424034))), _1424038))], (882 ^ _781404) ^ [_794671, _794673, _794675, _794677] : [-(c_Relation_Oantisym(_794675, _794671)), c_Relation_Oantisym(_794677, _794673), _794677 = _794675, _794673 = _794671], (43447 ^ _781404) ^ [_1647709, _1647711] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1647709)), c_List_Olist_ONil(_1647709)), c_List_Olists(_1647709, _1647711))))], (50247 ^ _781404) ^ [_1796840, _1796842, _1796844] : [c_Equiv__Relations_Oequiv(_1796840, _1796842, _1796844), 50250 ^ _781404 : [(50255 ^ _781404) ^ [] : [-(c_Relation_Otrans(_1796840, _1796844))], (50253 ^ _781404) ^ [] : [-(c_Relation_Osym(_1796840, _1796844))], (50251 ^ _781404) ^ [] : [-(c_Relation_Orefl__on(_1796840, _1796842, _1796844))]]], (15407 ^ _781404) ^ [_1054009, _1054011] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1054009), _1054011))), -(hAPP(c_Finite__Set_Ocard(_1054009), _1054011) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50177 ^ _781404) ^ [_1795724] : [-(c_Relation_Osym(_1795724, c_Relation_OId(_1795724)))], (51834 ^ _781404) ^ [_1830736] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830736, _1830736) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1830736), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (31840 ^ _781404) ^ [_1354265, _1354267, _1354269, _1354271] : [class_Orderings_Olinorder(_1354265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354265), _1354267)), 31850 ^ _781404 : [(31853 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1354265), _1354269), 31849 ^ [_1354265, _1354267, _1354269, _1354271]))], (31851 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1354265), 31849 ^ [_1354265, _1354267, _1354269, _1354271]), _1354267)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1354265), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1354265), _1354269), _1354271)), hAPP(hAPP(c_Finite__Set_Ofold(_1354265, _1354265, c_Orderings_Oord__class_Omin(_1354265)), _1354271), _1354267))))], (13462 ^ _781404) ^ [_1015590, _1015592, _1015594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015590), _1015592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015590), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015592), _1015594))))], (26271 ^ _781404) ^ [_1250272, _1250274] : [c_Nat__Transfer_Ois__nat(_1250272), c_Nat__Transfer_Ois__nat(_1250274), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1250272, _1250274) = 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, _1250272), hAPP(c_Int_Onat, _1250274))))], (9194 ^ _781404) ^ [_938040, _938042, _938044, _938046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938040, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938040, tc_HOL_Obool)), _938042), _938044)), _938046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938040, tc_HOL_Obool)), _938042), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938040, tc_HOL_Obool)), _938044), _938046))))], (48076 ^ _781404) ^ [_1748476, _1748478] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1748476)), _1748478)), 48082 ^ _781404 : [(48085 ^ _781404) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1748476), 48081 ^ [_1748476, _1748478]))], (48083 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1748476)), 48081 ^ [_1748476, _1748478]), hAPP(c_List_Oset(tc_List_Olist(_1748476)), _1748478))))]], 48089 ^ _781404 : [(48093 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1748476)), 48091 ^ [_1748476, _1748478]), hAPP(c_List_Oset(tc_List_Olist(_1748476)), _1748478))))], (48095 ^ _781404) ^ [] : [48088 ^ [_1748476, _1748478] = 48091 ^ [_1748476, _1748478]], (48097 ^ _781404) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1748476, tc_HOL_Obool)), hAPP(c_List_Oset(_1748476), 48088 ^ [_1748476, _1748478])), hAPP(c_List_Oset(_1748476), 48091 ^ [_1748476, _1748478])) = c_Orderings_Obot__class_Obot(tc_fun(_1748476, tc_HOL_Obool))], (48090 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1748476)), 48088 ^ [_1748476, _1748478]), hAPP(c_List_Oset(tc_List_Olist(_1748476)), _1748478))))]], -(hBOOL(hAPP(c_List_Odistinct(_1748476), c_List_Oconcat(_1748476, _1748478))))], (20113 ^ _781404) ^ [_1138566, _1138568] : [c_Int_OBit0(_1138566) = c_Int_OBit1(_1138568)], (48751 ^ _781404) ^ [_1763447, _1763449, _1763451, _1763453] : [c_List_Olist__all(_1763447, _1763449, hAPP(hAPP(c_List_Olist_OCons(_1763447), _1763451), _1763453)), 48754 ^ _781404 : [(48757 ^ _781404) ^ [] : [-(c_List_Olist__all(_1763447, _1763449, _1763453))], (48755 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1763449, _1763451)))]]], (46868 ^ _781404) ^ [_1724153, _1724155] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1724153, _1724155) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1724153), _1724155)))], (30648 ^ _781404) ^ [_1332348, _1332350, _1332352, _1332354] : [class_Orderings_Olinorder(_1332348), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332348), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332348), _1332350), _1332352)), _1332354) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332348), _1332350), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332348), _1332352), _1332354)))], (38494 ^ _781404) ^ [_1512057, _1512059, _1512061, _1512063] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1512057, _1512059), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1512057, tc_HOL_Obool), _1512061)), _1512063) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1512057, tc_HOL_Obool), tc_fun(tc_prod(_1512057, _1512059), tc_HOL_Obool)), _1512061), hAPP(hAPP(c_COMBC(tc_fun(_1512057, tc_HOL_Obool), tc_fun(_1512057, tc_fun(_1512059, tc_HOL_Obool)), tc_fun(tc_prod(_1512057, _1512059), tc_HOL_Obool)), c_Product__Type_OSigma(_1512057, _1512059)), _1512063)))], (15423 ^ _781404) ^ [_1054241, _1054243, _1054245, _1054247] : [c_Fun_Oinj__on(_1054241, _1054243, _1054245, _1054247), -(hAPP(c_Finite__Set_Ocard(_1054243), hAPP(c_Set_Oimage(_1054241, _1054243, _1054245), _1054247)) = hAPP(c_Finite__Set_Ocard(_1054241), _1054247))], (52238 ^ _781404) ^ [_1837256, _1837258] : [class_Orderings_Oord(_1837256), -(class_Orderings_Oord(tc_fun(_1837258, _1837256)))], (34061 ^ _781404) ^ [_1406720, _1406722, _1406724, _1406726, _1406728] : [class_Complete__Lattice_Ocomplete__lattice(_1406720), hBOOL(hAPP(hAPP(c_member(_1406722), _1406724), _1406726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406720), hAPP(_1406728, _1406724)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406722, _1406720), _1406726), _1406728))))], (4220 ^ _781404) ^ [_845354, _845356, _845358, _845360, _845362, _845364] : [-(c_Predicate_Oconversep(_845364, _845360, _845356) = c_Predicate_Oconversep(_845362, _845358, _845354)), _845364 = _845362, _845360 = _845358, _845356 = _845354], (41313 ^ _781404) ^ [_1590636, _1590638, _1590640, _1590642, _1590644] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590636, _1590636)), hAPP(hAPP(c_Product__Type_OPair(_1590636, _1590636), _1590638), _1590640)), c_Transitive__Closure_Otrancl(_1590636, _1590642))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590636, _1590636)), hAPP(hAPP(c_Product__Type_OPair(_1590636, _1590636), _1590640), _1590644)), c_Transitive__Closure_Ortrancl(_1590636, _1590642))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590636, _1590636)), hAPP(hAPP(c_Product__Type_OPair(_1590636, _1590636), _1590638), _1590644)), c_Transitive__Closure_Otrancl(_1590636, _1590642))))], (43669 ^ _781404) ^ [_1651711, _1651713, _1651715] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651711), tc_List_Olist(_1651711))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651711), tc_List_Olist(_1651711)), c_List_Olist_ONil(_1651711)), _1651713)), c_List_Olex(_1651711, _1651715)))], (42338 ^ _781404) ^ [_1617882, _1617884, _1617886, _1617888] : [hBOOL(hAPP(hAPP(c_member(_1617882), _1617884), c_Wellfounded_Oacc(_1617882, _1617886))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1617882)), _1617888), c_Wellfounded_Oacc(tc_List_Olist(_1617882), c_List_Olistrel1(_1617882, _1617886)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1617882)), hAPP(hAPP(c_List_Olist_OCons(_1617882), _1617884), _1617888)), c_Wellfounded_Oacc(tc_List_Olist(_1617882), c_List_Olistrel1(_1617882, _1617886)))))], (3804 ^ _781404) ^ [_838468, _838470, _838472, _838474, _838476, _838478, _838480, _838482] : [-(c_List_Ofoldl(_838482, _838478, _838474, _838470) = c_List_Ofoldl(_838480, _838476, _838472, _838468)), _838482 = _838480, _838478 = _838476, _838474 = _838472, _838470 = _838468], (41441 ^ _781404) ^ [_1593571, _1593573, _1593575, _1593577] : [c_Wellfounded_Oacyclic(_1593571, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593571, _1593571)), hAPP(hAPP(c_Product__Type_OPair(_1593571, _1593571), _1593573), _1593575)), _1593577)), 41444 ^ _781404 : [(41447 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593571, _1593571)), hAPP(hAPP(c_Product__Type_OPair(_1593571, _1593571), _1593575), _1593573)), c_Transitive__Closure_Ortrancl(_1593571, _1593577)))], (41445 ^ _781404) ^ [] : [-(c_Wellfounded_Oacyclic(_1593571, _1593577))]]], (45845 ^ _781404) ^ [_1700478, _1700480, _1700482, _1700484] : [hBOOL(hAPP(c_List_Olistsp(_1700478, _1700480), hAPP(hAPP(c_List_Oappend(_1700478), _1700482), _1700484))), 45848 ^ _781404 : [(45851 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1700478, _1700480), _1700484)))], (45849 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1700478, _1700480), _1700482)))]]], (18195 ^ _781404) ^ [_1105540, _1105542, _1105544] : [class_Rings_Olinordered__semidom(_1105540), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105540), c_Groups_Oone__class_Oone(_1105540)), _1105542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105540), c_Groups_Oone__class_Oone(_1105540)), hAPP(hAPP(c_Power_Opower__class_Opower(_1105540), _1105542), hAPP(c_Nat_OSuc, _1105544)))))], (52380 ^ _781404) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (43429 ^ _781404) ^ [_1647319, _1647321, _1647323] : [hBOOL(hAPP(c_List_Odistinct(_1647319), _1647321)), -(hAPP(c_List_Oset(_1647319), c_List_Oremove1(_1647319, _1647323, _1647321)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1647319, tc_HOL_Obool)), hAPP(c_List_Oset(_1647319), _1647321)), hAPP(hAPP(c_Set_Oinsert(_1647319), _1647323), c_Orderings_Obot__class_Obot(tc_fun(_1647319, tc_HOL_Obool)))))], (51100 ^ _781404) ^ [_1814301, _1814303, _1814305, _1814307, _1814309] : [c_Fun_Obij__betw(_1814301, _1814303, _1814305, c_Orderings_Otop__class_Otop(tc_fun(_1814301, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1814303, tc_HOL_Obool))), 51103 ^ _781404 : [(51110 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814303, tc_HOL_Obool)), _1814307), hAPP(c_Set_Oimage(_1814301, _1814303, _1814305), _1814309))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814301, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1814301, _1814303, _1814305), _1814307)), _1814309)))], (51104 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814301, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1814301, _1814303, _1814305), _1814307)), _1814309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814303, tc_HOL_Obool)), _1814307), hAPP(c_Set_Oimage(_1814301, _1814303, _1814305), _1814309))))]]], (6777 ^ _781404) ^ [_890047, _890049, _890051] : [class_Lattices_Oboolean__algebra(_890047), 6780 ^ _781404 : [(6787 ^ _781404) ^ [] : [_890049 = _890051, -(hAPP(c_Groups_Ouminus__class_Ouminus(_890047), _890049) = hAPP(c_Groups_Ouminus__class_Ouminus(_890047), _890051))], (6781 ^ _781404) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_890047), _890049) = hAPP(c_Groups_Ouminus__class_Ouminus(_890047), _890051), -(_890049 = _890051)]]], (1386 ^ _781404) ^ [_801769, _801771] : [-(class_Rings_Oring(_801769)), _801771 = _801769, class_Rings_Oring(_801771)], (6933 ^ _781404) ^ [_892934, _892936, _892938, _892940] : [hBOOL(hAPP(_892934, _892936)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892938, tc_HOL_Obool)), _892940), _892934), _892936)))], (19348 ^ _781404) ^ [_1125560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125560), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1125560)), c_Int_OPls)))], (23439 ^ _781404) ^ [_1202004, _1202006, _1202008, _1202010] : [class_Divides_Osemiring__div(_1202004), -(c_Divides_Odiv__class_Omod(_1202004, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202004), _1202006), _1202008), _1202010) = c_Divides_Odiv__class_Omod(_1202004, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202004), c_Divides_Odiv__class_Omod(_1202004, _1202006, _1202010)), c_Divides_Odiv__class_Omod(_1202004, _1202008, _1202010)), _1202010))], (50043 ^ _781404) ^ [_1792807, _1792809] : [-(c_Relation_Oantisym(_1792807, c_Relation_OId__on(_1792807, _1792809)))], (35734 ^ _781404) ^ [_1448403, _1448405, _1448407, _1448409] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1448403, _1448405), _1448407)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1448403, _1448405), _1448409)), -(_1448407 = _1448409)], (41385 ^ _781404) ^ [] : [-(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))))], (12752 ^ _781404) ^ [_1002138, _1002140, _1002142, _1002144, _1002146, _1002148] : [-(hBOOL(hAPP(hAPP(c_member(_1002138), _1002140), c_SetInterval_Oord_OatLeastLessThan(_1002138, _1002142, _1002144, _1002146, _1002148)))), hBOOL(hAPP(hAPP(_1002142, _1002146), _1002140)), hBOOL(hAPP(hAPP(_1002144, _1002140), _1002148))], (32782 ^ _781404) ^ [_1371962, _1371964, _1371966] : [class_Orderings_Olinorder(_1371962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371962), _1371964)), -(_1371964 = c_Orderings_Obot__class_Obot(tc_fun(_1371962, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371962), _1371966)), -(_1371966 = c_Orderings_Obot__class_Obot(tc_fun(_1371962, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371962, tc_HOL_Obool)), _1371964), _1371966) = c_Orderings_Obot__class_Obot(tc_fun(_1371962, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1371962, c_Orderings_Oord__class_Omax(_1371962), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1371962, tc_HOL_Obool)), _1371964), _1371966)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371962), c_Big__Operators_Olattice_OSup__fin(_1371962, c_Orderings_Oord__class_Omax(_1371962), _1371964)), c_Big__Operators_Olattice_OSup__fin(_1371962, c_Orderings_Oord__class_Omax(_1371962), _1371966)))], (31722 ^ _781404) ^ [_1352356, _1352358] : [class_Groups_Olinordered__ab__group__add(_1352356), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352356), _1352358)), -(_1352358 = c_Orderings_Obot__class_Obot(tc_fun(_1352356, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1352356), c_Big__Operators_Olinorder__class_OMin(_1352356, _1352358)) = c_Big__Operators_Olinorder__class_OMax(_1352356, hAPP(c_Set_Oimage(_1352356, _1352356, c_Groups_Ouminus__class_Ouminus(_1352356)), _1352358)))], (20005 ^ _781404) ^ [_1136771, _1136773] : [_1136771 = _1136773, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136771) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136773))], (45070 ^ _781404) ^ [_1682928, _1682930, _1682932] : [_1682928 = c_List_Olist_ONil(_1682930), -(c_List_Olast(_1682930, hAPP(hAPP(c_List_Oappend(_1682930), _1682932), _1682928)) = c_List_Olast(_1682930, _1682932))], (43771 ^ _781404) ^ [_1653820, _1653822, _1653824] : [-(c_List_Olistset(_1653820, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1653820, tc_HOL_Obool)), _1653822), _1653824)) = c_List_Oset__Cons(_1653820, _1653822, c_List_Olistset(_1653820, _1653824)))], (42143 ^ _781404) ^ [_1611685, _1611687, _1611689] : [c_Nitpick_Oless__frac(_1611685, _1611687, _1611689), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1611685), c_Nitpick_Oplus__frac(_1611685, _1611687, c_Nitpick_Ouminus__frac(_1611685, _1611689)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (1576 ^ _781404) ^ [_804144, _804146] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_804144)), _804146 = _804144, class_Groups_Oordered__ab__semigroup__add__imp__le(_804146)], (52198 ^ _781404) ^ [_1836732, _1836734] : [class_Lattices_Oboolean__algebra(_1836732), -(class_Lattices_Oboolean__algebra(tc_fun(_1836734, _1836732)))], (52672 ^ _781404) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52722 ^ _781404) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (37530 ^ _781404) ^ [_1488512, _1488514, _1488516] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1488512), _1488514), _1488516) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1488512, tc_fun(tc_fun(_1488512, tc_HOL_Obool), tc_HOL_Obool)), _1488514), hAPP(hAPP(c_COMBC(_1488512, tc_fun(tc_fun(_1488512, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1488512, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488512, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1488512, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1488512, tc_HOL_Obool), tc_HOL_Obool)), _1488512), c_Set_Oinsert(tc_fun(_1488512, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1488512, tc_HOL_Obool), tc_fun(_1488512, tc_HOL_Obool), _1488512), c_Relation_OImage(_1488512, _1488512, _1488516)), hAPP(hAPP(c_COMBC(_1488512, tc_fun(_1488512, tc_HOL_Obool), tc_fun(_1488512, tc_HOL_Obool)), c_Set_Oinsert(_1488512)), c_Orderings_Obot__class_Obot(tc_fun(_1488512, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1488512, tc_HOL_Obool), tc_HOL_Obool)))))], (32278 ^ _781404) ^ [_1362476, _1362478, _1362480, _1362482] : [class_Orderings_Olinorder(_1362476), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362476), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362476), _1362478), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1362476), _1362480), _1362482))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1362476), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362476), _1362478), _1362480)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362476), _1362478), _1362482)))))], (44461 ^ _781404) ^ [_1670416, _1670418, _1670420, _1670422, _1670424] : [hAPP(hAPP(c_List_Oappend(_1670416), _1670418), _1670420) = hAPP(hAPP(c_List_Oappend(_1670416), _1670422), _1670424), 44464 ^ _781404 : [(44473 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670416)), _1670418)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670416)), _1670422)))), 44476 ^ _781404 : [(44479 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1670416), hAPP(hAPP(c_List_Odrop(_1670416), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670416)), _1670422)), _1670418)), _1670420) = _1670424)], (44477 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1670416), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670416)), _1670422)), _1670418) = _1670422)]]], (44465 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670416)), _1670418)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670416)), _1670422))), 44468 ^ _781404 : [(44471 ^ _781404) ^ [] : [-(_1670420 = hAPP(hAPP(c_List_Oappend(_1670416), hAPP(hAPP(c_List_Odrop(_1670416), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670416)), _1670418)), _1670422)), _1670424))], (44469 ^ _781404) ^ [] : [-(_1670418 = hAPP(hAPP(c_List_Otake(_1670416), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670416)), _1670418)), _1670422))]]]]], (29663 ^ _781404) ^ [_1312593, _1312595, _1312597] : [class_Fields_Olinordered__field(_1312593), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312593), _1312595), _1312597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312593), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312593), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1312593), _1312595), _1312597)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1312593), c_Groups_Oone__class_Oone(_1312593)), c_Groups_Oone__class_Oone(_1312593)))), _1312597)))], (20503 ^ _781404) ^ [] : [-(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))))], (45337 ^ _781404) ^ [_1689359, _1689361, _1689363, _1689365, _1689367] : [-(c_List_Olist_Olist__size(_1689359, _1689361, hAPP(hAPP(c_List_Omap(_1689363, _1689359), _1689365), _1689367)) = c_List_Olist_Olist__size(_1689363, hAPP(c_Fun_Ocomp(_1689359, tc_Nat_Onat, _1689363, _1689361), _1689365), _1689367))], (12905 ^ _781404) ^ [_1005391] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1005391))))], (17495 ^ _781404) ^ [_1093508, _1093510] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093508), _1093510))), -(_1093508 = _1093510), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093510), _1093508)))], (35646 ^ _781404) ^ [_1446724, _1446726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1446724), _1446726)), -(c_Divides_Odivmod__nat(_1446724, _1446726) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1446724))], (36221 ^ _781404) ^ [_1457544, _1457546] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1457544, _1457546) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1457544, _1457546)))], (49491 ^ _781404) ^ [_1779665, _1779667, _1779669] : [-(c_FunDef_OTHE__default(_1779667, _1779669, _1779665) = _1779669), 49493 ^ _781404 : [(49496 ^ _781404) ^ [_1779787] : [hBOOL(hAPP(_1779665, _1779787)), -(_1779787 = 49492 ^ [_1779665, _1779667, _1779669])], (49494 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1779665, 49492 ^ [_1779665, _1779667, _1779669])))]]], (50051 ^ _781404) ^ [_1792935, _1792937] : [c_Relation_Oantisym(_1792935, _1792937), -(c_Relation_Oantisym(_1792935, hAPP(c_Relation_Oconverse(_1792935, _1792935), _1792937)))], (44928 ^ _781404) ^ [_1680588, _1680590, _1680592, _1680594, _1680596] : [class_Orderings_Olinorder(_1680588), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680590, _1680588, _1680592), _1680594), _1680596) = c_List_Olist_ONil(_1680590)], (8870 ^ _781404) ^ [_931276, _931278, _931280] : [class_Orderings_Oorder(_931276), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931276, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_931276), _931278)), c_SetInterval_Oord__class_OatLeastAtMost(_931276, _931278, _931280)) = c_Orderings_Obot__class_Obot(tc_fun(_931276, tc_HOL_Obool)))], (52408 ^ _781404) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (37804 ^ _781404) ^ [_1495140, _1495142, _1495144, _1495146, _1495148] : [c_Equiv__Relations_Oequiv(_1495140, _1495142, _1495144), 37807 ^ _781404 : [(37818 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1495140, _1495140)), hAPP(hAPP(c_Product__Type_OPair(_1495140, _1495140), _1495146), _1495148)), _1495144))), hAPP(c_Relation_OImage(_1495140, _1495140, _1495144), hAPP(hAPP(c_Set_Oinsert(_1495140), _1495146), c_Orderings_Obot__class_Obot(tc_fun(_1495140, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1495140, _1495140, _1495144), hAPP(hAPP(c_Set_Oinsert(_1495140), _1495148), c_Orderings_Obot__class_Obot(tc_fun(_1495140, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1495140), _1495146), _1495142)), hBOOL(hAPP(hAPP(c_member(_1495140), _1495148), _1495142))], (37808 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1495140, _1495140)), hAPP(hAPP(c_Product__Type_OPair(_1495140, _1495140), _1495146), _1495148)), _1495144)), 37811 ^ _781404 : [(37816 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1495140), _1495148), _1495142)))], (37814 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1495140), _1495146), _1495142)))], (37812 ^ _781404) ^ [] : [-(hAPP(c_Relation_OImage(_1495140, _1495140, _1495144), hAPP(hAPP(c_Set_Oinsert(_1495140), _1495146), c_Orderings_Obot__class_Obot(tc_fun(_1495140, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1495140, _1495140, _1495144), hAPP(hAPP(c_Set_Oinsert(_1495140), _1495148), c_Orderings_Obot__class_Obot(tc_fun(_1495140, tc_HOL_Obool)))))]]]]], (43170 ^ _781404) ^ [_1641423, _1641425, _1641427] : [hBOOL(hAPP(hAPP(c_member(_1641423), _1641425), hAPP(c_List_Oset(_1641423), c_List_Obutlast(_1641423, _1641427)))), -(hBOOL(hAPP(hAPP(c_member(_1641423), _1641425), hAPP(c_List_Oset(_1641423), _1641427))))], (7946 ^ _781404) ^ [_913613, _913615, _913617] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_913613, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_913613, tc_HOL_Obool), tc_HOL_Obool)), _913615), _913617)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913613, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_913613, tc_HOL_Obool), _913615)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_913613, tc_HOL_Obool), _913617)))], (414 ^ _781404) ^ [_787711, _787713] : [-(c_Nitpick_Ounknown(_787711)), _787713 = _787711, c_Nitpick_Ounknown(_787713)], (46742 ^ _781404) ^ [_1721925, _1721927, _1721929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1721925), _1721927)), -(c_List_Oupt(_1721925, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1721927), _1721929)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1721925, _1721927)), c_List_Oupt(_1721927, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1721927), _1721929))))], (45311 ^ _781404) ^ [_1688689, _1688691, _1688693, _1688695] : [-(hAPP(c_List_Oset(_1688689), hAPP(hAPP(c_List_Omap(_1688691, _1688689), _1688693), _1688695)) = hAPP(c_Set_Oimage(_1688691, _1688689, _1688693), hAPP(c_List_Oset(_1688691), _1688695)))], (34099 ^ _781404) ^ [_1407548] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1407548)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407548)), 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))))], (39705 ^ _781404) ^ [_1551029, _1551031, _1551033, _1551035, _1551037] : [-(hAPP(c_Relation_ORange(_1551029, _1551031), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1551029, _1551031)), hAPP(hAPP(c_Product__Type_OPair(_1551029, _1551031), _1551033), _1551035)), _1551037)) = hAPP(hAPP(c_Set_Oinsert(_1551031), _1551035), hAPP(c_Relation_ORange(_1551029, _1551031), _1551037)))], (15026 ^ _781404) ^ [_1046215, _1046217, _1046219, _1046221] : [class_Rings_Ocomm__semiring__1(_1046215), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046215), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046215), _1046217), _1046219)), _1046221) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046215), _1046217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046215), _1046219), _1046221)))], (6401 ^ _781404) ^ [_883185] : [_883185 = hAPP(c_Nat_OSuc, _883185)], (46381 ^ _781404) ^ [_1712026] : [-(c_List_Oconcat(_1712026, c_List_Olist_ONil(tc_List_Olist(_1712026))) = c_List_Olist_ONil(_1712026))], (26003 ^ _781404) ^ [] : [-(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))))], (26202 ^ _781404) ^ [_1249115] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1249115)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1249115)], (41864 ^ _781404) ^ [_1603890, _1603892, _1603894] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1603890, _1603890, _1603890), _1603892), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603890, _1603890), tc_HOL_Obool), _1603894), _1603892)) = hAPP(hAPP(c_Relation_Orel__comp(_1603890, _1603890, _1603890), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603890, _1603890), tc_HOL_Obool), _1603894), _1603892)), _1603892))], (43785 ^ _781404) ^ [_1654302, _1654304, _1654306] : [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), _1654302), _1654304))), -(hBOOL(hAPP(hAPP(_1654306, _1654302), _1654304))), 43792 ^ _781404 : [(43795 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 43790 ^ [_1654302, _1654304, _1654306]), 43791 ^ [_1654302, _1654304, _1654306])), -(hBOOL(hAPP(hAPP(_1654306, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43790 ^ [_1654302, _1654304, _1654306]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 43791 ^ [_1654302, _1654304, _1654306])))], (43801 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1654306, 43790 ^ [_1654302, _1654304, _1654306]), 43791 ^ [_1654302, _1654304, _1654306]))], (43793 ^ _781404) ^ [] : [-(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), 43790 ^ [_1654302, _1654304, _1654306]), 43791 ^ [_1654302, _1654304, _1654306]))))]]], (51233 ^ _781404) ^ [_1817113, _1817115, _1817117] : [hBOOL(hAPP(c_Quotient_ORespects(_1817113, _1817115), _1817117)), -(hBOOL(hAPP(hAPP(_1817115, _1817117), _1817117)))], (8487 ^ _781404) ^ [] : [-(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))))], (50703 ^ _781404) ^ [_1806521, _1806523] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1806521), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1806523, hAPP(c_Code__Numeral_Onat__of, 50708 ^ [_1806521, _1806523]))), -(hBOOL(hAPP(_1806523, _1806521)))], (48117 ^ _781404) ^ [_1749660, _1749662, _1749664, _1749666, _1749668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1749660, _1749662)), hAPP(_1749660, _1749664))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1749666, _1749666)), hAPP(hAPP(c_Product__Type_OPair(_1749666, _1749666), _1749662), _1749664)), c_List_Omeasures(_1749666, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1749666, tc_Nat_Onat)), _1749660), _1749668)))))], (44699 ^ _781404) ^ [_1675537, _1675539] : [class_Lattices_Oab__semigroup__idem__mult(_1675537), -(_1675539 = c_List_Olist_ONil(_1675537)), -(hAPP(c_Finite__Set_Ofold1(_1675537, c_Groups_Otimes__class_Otimes(_1675537)), hAPP(c_List_Oset(_1675537), _1675539)) = hAPP(c_List_Ofoldl(_1675537, _1675537, c_Groups_Otimes__class_Otimes(_1675537), hAPP(c_List_Ohd(_1675537), _1675539)), hAPP(c_List_Otl(_1675537), _1675539)))], (16206 ^ _781404) ^ [_1069226, _1069228, _1069230] : [-(hAPP(c_Finite__Set_Ocard(_1069226), _1069228) = hAPP(c_Nat_OSuc, _1069230)), 16207 ^ _781404 : [(16208 ^ _781404) ^ [_1069326, _1069328] : [_1069228 = hAPP(hAPP(c_Set_Oinsert(_1069226), _1069328), _1069326), -(hBOOL(hAPP(hAPP(c_member(_1069226), _1069328), _1069326))), hAPP(c_Finite__Set_Ocard(_1069226), _1069326) = _1069230, 16219 ^ _781404 : [(16222 ^ _781404) ^ [] : [_1069326 = c_Orderings_Obot__class_Obot(tc_fun(_1069226, tc_HOL_Obool))], (16220 ^ _781404) ^ [] : [-(_1069230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (22437 ^ _781404) ^ [_1181598, _1181600, _1181602, _1181604, _1181606] : [class_Rings_Olinordered__semiring__strict(_1181598), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181598), _1181600), _1181602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181598), _1181604), _1181606)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181598), c_Groups_Ozero__class_Ozero(_1181598)), _1181602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181598), c_Groups_Ozero__class_Ozero(_1181598)), _1181604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181598), _1181600), _1181604)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181598), _1181602), _1181606))))], (32650 ^ _781404) ^ [_1369604, _1369606] : [class_Orderings_Olinorder(_1369604), -(c_Big__Operators_Olattice_OSup__fin(_1369604, c_Orderings_Oord__class_Omax(_1369604), hAPP(hAPP(c_Set_Oinsert(_1369604), _1369606), c_Orderings_Obot__class_Obot(tc_fun(_1369604, tc_HOL_Obool)))) = _1369606)], (24945 ^ _781404) ^ [_1228334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1228334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1228334))))], (11847 ^ _781404) ^ [_984149, _984151, _984153, _984155] : [_984149 = _984151, hBOOL(hAPP(hAPP(c_member(_984153), _984151), _984155)), -(hBOOL(hAPP(hAPP(c_member(_984153), _984149), _984155)))], (1596 ^ _781404) ^ [_804394, _804396] : [-(class_Groups_Olinordered__ab__semigroup__add(_804394)), _804396 = _804394, class_Groups_Olinordered__ab__semigroup__add(_804396)], (37003 ^ _781404) ^ [_1475129, _1475131, _1475133, _1475135, _1475137, _1475139] : [c_Finite__Set_Ofolding__idem(_1475129, _1475131, _1475133, _1475135), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475129), _1475137)), hBOOL(hAPP(hAPP(c_member(_1475129), _1475139), _1475137)), -(hAPP(c_Fun_Ocomp(_1475131, _1475131, _1475131, hAPP(_1475135, _1475137)), hAPP(_1475133, _1475139)) = hAPP(_1475135, _1475137))], (19887 ^ _781404) ^ [_1134669, _1134671] : [class_Int_Onumber__ring(_1134669), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1134669), c_Groups_Oone__class_Oone(_1134669)), hAPP(c_Int_Onumber__class_Onumber__of(_1134669), _1134671)) = hAPP(c_Int_Onumber__class_Onumber__of(_1134669), 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), _1134671))))], (24184 ^ _781404) ^ [_1215101, _1215103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215101), 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, _1215103, _1215101)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52476 ^ _781404) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (27843 ^ _781404) ^ [_1279611, _1279613, _1279615, _1279617] : [class_Rings_Odivision__ring(_1279611), -(_1279613 = c_Groups_Ozero__class_Ozero(_1279611)), _1279615 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279611), _1279617), _1279613), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279611), _1279615), _1279613) = _1279617)], (6721 ^ _781404) ^ [_889016, _889018, _889020] : [class_Lattices_Oboolean__algebra(_889016), 6724 ^ _781404 : [(6731 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889016), _889020), _889018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889016), hAPP(c_Groups_Ouminus__class_Ouminus(_889016), _889018)), hAPP(c_Groups_Ouminus__class_Ouminus(_889016), _889020))))], (6725 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889016), hAPP(c_Groups_Ouminus__class_Ouminus(_889016), _889018)), hAPP(c_Groups_Ouminus__class_Ouminus(_889016), _889020))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889016), _889020), _889018)))]]], (48853 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9030 ^ _781404) ^ [_934502, _934504, _934506, _934508, _934510] : [class_Groups_Oordered__ab__group__add(_934502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_934502), _934504), _934506) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_934502), _934508), _934510), 9037 ^ _781404 : [(9044 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934502), _934508), _934510)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934502), _934504), _934506)))], (9038 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934502), _934504), _934506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934502), _934508), _934510)))]]], (3996 ^ _781404) ^ [_841722, _841724, _841726, _841728, _841730, _841732, _841734, _841736] : [-(c_New__DSequence_Opos__decr__bind(_841736, _841732, _841728, _841724) = c_New__DSequence_Opos__decr__bind(_841734, _841730, _841726, _841722)), _841736 = _841734, _841732 = _841730, _841728 = _841726, _841724 = _841722], (44916 ^ _781404) ^ [_1680342, _1680344, _1680346, _1680348, _1680350] : [class_Orderings_Olinorder(_1680342), -(hAPP(c_List_Oset(_1680344), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680344, _1680342, _1680346), _1680348), _1680350)) = hAPP(hAPP(c_Set_Oinsert(_1680344), _1680348), hAPP(c_List_Oset(_1680344), _1680350)))], (51349 ^ _781404) ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1820430, _1820432), tc_prod(_1820430, _1820432))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1820430, _1820432), tc_prod(_1820430, _1820432)), hAPP(hAPP(c_Product__Type_OPair(_1820430, _1820432), _1820434), _1820436)), hAPP(hAPP(c_Product__Type_OPair(_1820430, _1820432), _1820438), _1820440))), c_Transitive__Closure_Ortrancl(tc_prod(_1820430, _1820432), _1820442))), hBOOL(hAPP(hAPP(_1820444, _1820434), _1820436)), 51360 ^ _781404 : [(51365 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1820430, _1820432), tc_prod(_1820430, _1820432))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1820430, _1820432), tc_prod(_1820430, _1820432)), hAPP(hAPP(c_Product__Type_OPair(_1820430, _1820432), 51358 ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444]), 51359 ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444])), hAPP(hAPP(c_Product__Type_OPair(_1820430, _1820432), 51362 ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444]), 51363 ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444]))), _1820442)))], (51367 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1820444, 51358 ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444]), 51359 ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444])))], (51369 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1820444, 51362 ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444]), 51363 ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444]))], (51361 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1820430, _1820432), tc_prod(_1820430, _1820432))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1820430, _1820432), tc_prod(_1820430, _1820432)), hAPP(hAPP(c_Product__Type_OPair(_1820430, _1820432), _1820434), _1820436)), hAPP(hAPP(c_Product__Type_OPair(_1820430, _1820432), 51358 ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444]), 51359 ^ [_1820430, _1820432, _1820434, _1820436, _1820438, _1820440, _1820442, _1820444]))), c_Transitive__Closure_Ortrancl(tc_prod(_1820430, _1820432), _1820442))))]], -(hBOOL(hAPP(hAPP(_1820444, _1820438), _1820440)))], (26204 ^ _781404) ^ [_1249146] : [c_Nat__Transfer_Onat__set(_1249146), -(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), _1249146)) = _1249146)], (25457 ^ _781404) ^ [_1236541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1236541))))], (51162 ^ _781404) ^ [_1815535, _1815537, _1815539, _1815541, _1815543, _1815545] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1815535, _1815537, _1815539, _1815541), _1815543), _1815545) = hAPP(_1815541, hAPP(hAPP(c_Product__Type_OPair(_1815535, _1815537), _1815543), _1815545)))], (17577 ^ _781404) ^ [_1094794, _1094796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094794), _1094796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1094794)), _1094796)))], (42364 ^ _781404) ^ [_1618632, _1618634, _1618636, _1618638, _1618640] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618632), tc_List_Olist(_1618632))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618632), tc_List_Olist(_1618632)), _1618634), _1618636)), c_List_Olistrel1(_1618632, _1618638))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618632), tc_List_Olist(_1618632))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618632), tc_List_Olist(_1618632)), hAPP(hAPP(c_List_Olist_OCons(_1618632), _1618640), _1618634)), hAPP(hAPP(c_List_Olist_OCons(_1618632), _1618640), _1618636))), c_List_Olistrel1(_1618632, _1618638))))], (39672 ^ _781404) ^ [_1550101, _1550103, _1550105, _1550107, _1550109, _1550111, _1550113, _1550115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1550101, _1550103), tc_HOL_Obool)), _1550105), hAPP(hAPP(c_Product__Type_OSigma(_1550101, _1550103), _1550107), hAPP(c_COMBK(tc_fun(_1550103, tc_HOL_Obool), _1550101), _1550109)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1550103, _1550111), tc_HOL_Obool)), _1550113), hAPP(hAPP(c_Product__Type_OSigma(_1550103, _1550111), _1550109), hAPP(c_COMBK(tc_fun(_1550111, tc_HOL_Obool), _1550103), _1550115)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1550101, _1550111), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1550101, _1550103, _1550111), _1550105), _1550113)), hAPP(hAPP(c_Product__Type_OSigma(_1550101, _1550111), _1550107), hAPP(c_COMBK(tc_fun(_1550111, tc_HOL_Obool), _1550101), _1550115)))))], (33105 ^ _781404) ^ [_1378685, _1378687, _1378689, _1378691] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1378685, tc_HOL_Obool), hAPP(c_Set_Oimage(_1378687, tc_fun(_1378685, tc_HOL_Obool), _1378689), _1378691)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378687, tc_fun(_1378685, tc_HOL_Obool)), _1378691), _1378689))], (8118 ^ _781404) ^ [_917530, _917532] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _917530), _917532))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _917530), hAPP(c_Nat_OSuc, _917532)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51952 ^ _781404) ^ [_1832688, _1832690] : [51953 ^ _781404 : [(51956 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832690), _1832688))], (51954 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832688), _1832690)))]], -(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)))), _1832688, _1832690) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (6427 ^ _781404) ^ [_883531, _883533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883531), _883533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883533), _883531)), -(_883531 = _883533)], (13454 ^ _781404) ^ [_1015443, _1015445] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015443), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015445), _1015443))))], (33261 ^ _781404) ^ [_1382863, _1382865, _1382867, _1382869, _1382871] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1382863), hAPP(c_Set_Oimage(_1382865, _1382863, _1382867), c_Orderings_Otop__class_Otop(tc_fun(_1382865, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1382869), hAPP(c_Set_Oimage(_1382865, _1382869, hAPP(hAPP(c_COMBB(_1382863, _1382869, _1382865), _1382871), _1382867)), c_Orderings_Otop__class_Otop(tc_fun(_1382865, tc_HOL_Obool))))))], (44824 ^ _781404) ^ [_1678171, _1678173, _1678175, _1678177] : [class_Complete__Lattice_Ocomplete__lattice(_1678171), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1678173, _1678171), hAPP(c_List_Oset(_1678173), _1678175)), _1678177) = hAPP(c_List_Ofoldl(_1678171, _1678173, hAPP(c_COMBC(_1678173, _1678171, _1678171), hAPP(hAPP(c_COMBB(_1678171, tc_fun(_1678171, _1678171), _1678173), c_Lattices_Osemilattice__sup__class_Osup(_1678171)), _1678177)), c_Orderings_Obot__class_Obot(_1678171)), _1678175))], (12881 ^ _781404) ^ [_1004925, _1004927, _1004929, _1004931] : [class_Groups_Ocomm__monoid__add(_1004925), 12884 ^ _781404 : [(12891 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1004927)), _1004929))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1004925), _1004931), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1004929, hAPP(c_Nat_OSuc, _1004927))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004925), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1004925), _1004931), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1004929, _1004927))), hAPP(_1004931, hAPP(c_Nat_OSuc, _1004927))))], (12885 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1004927)), _1004929)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1004925), _1004931), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1004929, hAPP(c_Nat_OSuc, _1004927))) = c_Groups_Ozero__class_Ozero(_1004925))]]], (33609 ^ _781404) ^ [_1393933, _1393935, _1393937, _1393939, _1393941, _1393943] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393933, tc_fun(_1393935, tc_HOL_Obool)), _1393937), hAPP(hAPP(c_COMBC(_1393933, tc_fun(_1393939, tc_fun(_1393935, tc_HOL_Obool)), tc_fun(_1393935, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393939, tc_HOL_Obool), tc_fun(tc_fun(_1393939, tc_fun(_1393935, tc_HOL_Obool)), tc_fun(_1393935, tc_HOL_Obool)), _1393933), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393939, tc_fun(_1393935, tc_HOL_Obool))), _1393941)), _1393943)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393939, tc_fun(_1393935, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393933, tc_fun(_1393939, tc_HOL_Obool)), _1393937), _1393941)), _1393943))], (24090 ^ _781404) ^ [_1213491, _1213493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213491), 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)), _1213493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213491), _1213493)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41179 ^ _781404) ^ [_1587371, _1587373] : [-(c_Transitive__Closure_Otrancl(_1587371, c_Transitive__Closure_Ortrancl(_1587371, _1587373)) = c_Transitive__Closure_Ortrancl(_1587371, _1587373))], (50999 ^ _781404) ^ [_1812329, _1812331, _1812333, _1812335] : [c_Fun_Obij__betw(_1812329, _1812331, _1812333, _1812335, c_Orderings_Obot__class_Obot(tc_fun(_1812331, tc_HOL_Obool))), -(_1812335 = c_Orderings_Obot__class_Obot(tc_fun(_1812329, tc_HOL_Obool)))], (3222 ^ _781404) ^ [_829365, _829367, _829369, _829371] : [-(c_Big__Operators_Olinorder__class_OMax(_829371, _829367) = c_Big__Operators_Olinorder__class_OMax(_829369, _829365)), _829371 = _829369, _829367 = _829365], (35888 ^ _781404) ^ [_1451332, _1451334] : [-(_1451332 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451334, _1451332), c_Divides_Odivmod__int(_1451334, _1451332))))], (47714 ^ _781404) ^ [_1740915, _1740917, _1740919, _1740921, _1740923] : [-(hAPP(hAPP(c_List_Ozip(_1740915, _1740917), _1740919), c_List_OtakeWhile(_1740917, _1740921, _1740923)) = c_List_OtakeWhile(tc_prod(_1740915, _1740917), hAPP(c_Fun_Ocomp(_1740917, tc_HOL_Obool, tc_prod(_1740915, _1740917), _1740921), c_Product__Type_Osnd(_1740915, _1740917)), hAPP(hAPP(c_List_Ozip(_1740915, _1740917), _1740919), _1740923)))], (43571 ^ _781404) ^ [_1649839] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649839)), c_List_Olist_ONil(_1649839)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8164 ^ _781404) ^ [_918491, _918493, _918495] : [class_Orderings_Obot(_918491), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_918493, _918491)), _918495) = c_Orderings_Obot__class_Obot(_918491))], (11141 ^ _781404) ^ [_970570, _970572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _970570)), _970572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970570), _970572)))], (43304 ^ _781404) ^ [_1644493, _1644495, _1644497] : [hBOOL(hAPP(c_List_Odistinct(_1644493), hAPP(hAPP(c_List_Olist_OCons(_1644493), _1644495), _1644497))), 43307 ^ _781404 : [(43310 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1644493), _1644497)))], (43308 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1644493), _1644495), hAPP(c_List_Oset(_1644493), _1644497)))]]], (52820 ^ _781404) ^ [_1843362, _1843364] : [hBOOL(hAPP(hAPP(c_fimplies, _1843362), _1843364)), hBOOL(_1843362), -(hBOOL(_1843364))], (35131 ^ _781404) ^ [_1435921, _1435923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1435921)), 35134 ^ _781404 : [(35141 ^ _781404) ^ [] : [-(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), _1435923), _1435921)))), -(c_Divides_OnegDivAlg(_1435923, _1435921) = hAPP(c_Divides_Oadjust(_1435921), c_Divides_OnegDivAlg(_1435923, 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)))), _1435921))))], (35135 ^ _781404) ^ [] : [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), _1435923), _1435921))), -(c_Divides_OnegDivAlg(_1435923, _1435921) = 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), _1435923), _1435921)))]]], (41287 ^ _781404) ^ [_1590032, _1590034, _1590036] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1590032, _1590032, _1590034), c_Relation_OId(_1590032)), _1590036) = _1590036)], (3488 ^ _781404) ^ [_833512, _833514, _833516, _833518, _833520, _833522, _833524, _833526] : [-(c_List_Olist_Olist__case(_833526, _833522, _833518, _833514) = c_List_Olist_Olist__case(_833524, _833520, _833516, _833512)), _833526 = _833524, _833522 = _833520, _833518 = _833516, _833514 = _833512], (29683 ^ _781404) ^ [_1313009, _1313011, _1313013, _1313015] : [class_Fields_Olinordered__field__inverse__zero(_1313009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313009), _1313011), _1313013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313009), _1313015), c_Groups_Ozero__class_Ozero(_1313009))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1313009), c_Groups_Ozero__class_Ozero(_1313009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313009), _1313011), _1313013))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313009), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313009), _1313015), _1313011)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313009), _1313015), _1313013))))], (26983 ^ _781404) ^ [_1263033, _1263035, _1263037, _1263039, _1263041] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1263033, _1263035, _1263037, _1263039, c_Orderings_Obot__class_Obot(tc_fun(_1263033, tc_HOL_Obool))), _1263041)), -(_1263041 = _1263039)], (30316 ^ _781404) ^ [_1325883, _1325885, _1325887] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1325883, _1325885) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1325887, _1325885), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1325887), _1325883)), -(_1325883 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1325887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1325885), 30323 ^ [_1325883, _1325885, _1325887])))], (40238 ^ _781404) ^ [_1564892, _1564894] : [c_Wellfounded_OwfP(_1564892, _1564894), 40241 ^ _781404 : [(40242 ^ _781404) ^ [_1564956] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1564892, _1564894), _1564956)))]]], (15483 ^ _781404) ^ [_1055377, _1055379, _1055381] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055377), _1055379)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1055377, tc_HOL_Obool)), _1055381), _1055379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055377), _1055381)), hAPP(c_Finite__Set_Ocard(_1055377), _1055379))))], (46684 ^ _781404) ^ [_1720319, _1720321] : [-(c_List_Ofoldr(tc_List_Olist(_1720319), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1720319)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1720319))), c_List_Otranspose(_1720319, _1720321), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1720319))), hAPP(c_List_Ofilter(tc_List_Olist(_1720319), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1720319)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1720319), tc_List_Olist(_1720319), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1720319)))), _1720321)))], (1476 ^ _781404) ^ [_802894, _802896] : [-(class_Lattices_Odistrib__lattice(_802894)), _802896 = _802894, class_Lattices_Odistrib__lattice(_802896)], (40964 ^ _781404) ^ [_1581251, _1581253, _1581255, _1581257, _1581259] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1581251, _1581253, _1581251, _1581255), hAPP(c_Product__Type_OPair(_1581253, _1581251), _1581257)), _1581259) = hAPP(_1581259, _1581257))], (52474 ^ _781404) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (39009 ^ _781404) ^ [_1526648, _1526650, _1526652] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526648), hAPP(c_Set_OCollect(_1526648), hAPP(hAPP(c_COMBS(_1526648, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526648), c_fdisj), _1526650)), _1526652)))), 39012 ^ _781404 : [(39015 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1526648), hAPP(c_Set_OCollect(_1526648), _1526652))))], (39013 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1526648), hAPP(c_Set_OCollect(_1526648), _1526650))))]]], (25718 ^ _781404) ^ [_1240994, _1240996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240994)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1240994), _1240996)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1240996), _1240994)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1240996)), hAPP(c_Int_Onat, _1240994)))], (21993 ^ _781404) ^ [_1172983, _1172985, _1172987] : [class_Rings_Ocomm__semiring__1(_1172983), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172983), _1172985), _1172987)), _1172987) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172983), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172983), _1172985), c_Groups_Oone__class_Oone(_1172983))), _1172987))], (34451 ^ _781404) ^ [_1419830, _1419832, _1419834, _1419836] : [hBOOL(hAPP(hAPP(c_member(_1419830), _1419832), _1419834)), -(hAPP(c_Set_Ovimage(_1419836, _1419830, hAPP(c_COMBK(_1419830, _1419836), _1419832)), _1419834) = c_Orderings_Otop__class_Otop(tc_fun(_1419836, tc_HOL_Obool)))], (26226 ^ _781404) ^ [_1249451] : [c_Nat__Transfer_Onat__set(_1249451), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1249451) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1249451)))], (39656 ^ _781404) ^ [_1549744, _1549746, _1549748] : [-(hAPP(c_Relation_ORange(_1549744, _1549746), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1549744, _1549746), tc_HOL_Obool), _1549748)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1549744, _1549746), tc_HOL_Obool), tc_fun(_1549746, tc_HOL_Obool)), _1549748), c_Relation_ORange(_1549744, _1549746)))], (25815 ^ _781404) ^ [_1242778, _1242780, _1242782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242778)), 25818 ^ _781404 : [(25819 ^ _781404) ^ [] : [-(_1242780 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242782), _1242778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242778), _1242780)), _1242782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1242782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242778), hAPP(c_Nat_OSuc, _1242780))))], (25829 ^ _781404) ^ [] : [_1242780 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242782), _1242778), 25832 ^ _781404 : [(25835 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1242782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242778), hAPP(c_Nat_OSuc, _1242780)))))], (25833 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242778), _1242780)), _1242782)))]]]]], (45932 ^ _781404) ^ [_1702761, _1702763, _1702765, _1702767, _1702769, _1702771] : [c_List_Olist__all2(_1702761, _1702763, _1702765, _1702767, _1702769), -(c_List_Olist__all2(_1702761, _1702763, _1702765, hAPP(hAPP(c_List_Odrop(_1702761), _1702771), _1702767), hAPP(hAPP(c_List_Odrop(_1702763), _1702771), _1702769)))], (37992 ^ _781404) ^ [_1499534, _1499536, _1499538, _1499540] : [c_Equiv__Relations_Ocongruent(_1499534, _1499536, _1499538, _1499540), 37995 ^ _781404 : [(37996 ^ _781404) ^ [_1499679] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1499534, _1499534)), _1499679), _1499538)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1499534, _1499534, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1499534, tc_fun(_1499534, _1499536), tc_fun(_1499534, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499536, tc_HOL_Obool), tc_fun(tc_fun(_1499534, _1499536), tc_fun(_1499534, tc_HOL_Obool)), _1499534), c_COMBB(_1499536, tc_HOL_Obool, _1499534)), hAPP(hAPP(c_COMBB(_1499536, tc_fun(_1499536, tc_HOL_Obool), _1499534), c_fequal), _1499540))), _1499540)), _1499679)))]]], (32917 ^ _781404) ^ [_1374681, _1374683, _1374685] : [class_Orderings_Olinorder(_1374681), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374681), _1374683)), 32927 ^ _781404 : [(32930 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374681), _1374685), 32926 ^ [_1374681, _1374683, _1374685]))], (32928 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1374681), 32926 ^ [_1374681, _1374683, _1374685]), _1374683)))]], hBOOL(hAPP(hAPP(c_member(_1374681), _1374685), _1374683)), -(c_Big__Operators_Olinorder__class_OMin(_1374681, _1374683) = _1374685)], (34245 ^ _781404) ^ [_1413324, _1413326, _1413328, _1413330, _1413332] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413324, tc_fun(_1413326, tc_HOL_Obool)), _1413328), hAPP(hAPP(c_COMBS(_1413324, tc_fun(_1413326, tc_HOL_Obool), tc_fun(_1413326, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1413326, tc_HOL_Obool), tc_fun(tc_fun(_1413326, tc_HOL_Obool), tc_fun(_1413326, tc_HOL_Obool)), _1413324), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413326, tc_HOL_Obool))), _1413330)), _1413332)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413326, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413324, tc_fun(_1413326, tc_HOL_Obool)), _1413328), _1413330)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413324, tc_fun(_1413326, tc_HOL_Obool)), _1413328), _1413332)))], (39940 ^ _781404) ^ [_1557662, _1557664, _1557666] : [c_Wellfounded_Owf(_1557662, _1557664), c_Wellfounded_Owf(_1557662, _1557666), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1557662, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1557662, _1557662), _1557664)), hAPP(c_Relation_ORange(_1557662, _1557662), _1557666)) = c_Orderings_Obot__class_Obot(tc_fun(_1557662, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1557662, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1557662, _1557662), tc_HOL_Obool)), _1557664), _1557666)))], (46493 ^ _781404) ^ [_1715442, _1715444, _1715446, _1715448, _1715450] : [class_Orderings_Olinorder(_1715442), -(hAPP(c_List_Ofilter(_1715444, _1715446), c_List_Olinorder__class_Osort__key(_1715444, _1715442, _1715448, _1715450)) = c_List_Olinorder__class_Osort__key(_1715444, _1715442, _1715448, hAPP(c_List_Ofilter(_1715444, _1715446), _1715450)))], (39554 ^ _781404) ^ [_1546626, _1546628] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1546626, _1546628, tc_prod(_1546626, _1546628)), c_Product__Type_OPair(_1546626, _1546628)) = c_Fun_Oid(tc_prod(_1546626, _1546628)))], (5706 ^ _781404) ^ [_871398, _871400] : [hAPP(_871398, 5707 ^ [_871398, _871400]) = hAPP(_871400, 5707 ^ [_871398, _871400]), -(_871398 = _871400)], (37571 ^ _781404) ^ [_1489587, _1489589, _1489591] : [-(hAPP(c_Relation_OImage(_1489587, _1489587, c_Relation_OId__on(_1489587, _1489589)), _1489591) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489587, tc_HOL_Obool)), _1489589), _1489591))], (44667 ^ _781404) ^ [_1674814, _1674816, _1674818] : [-(hAPP(c_List_Orotate(_1674814, _1674816), _1674818) = hAPP(c_List_Orotate(_1674814, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1674816, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674814)), _1674818))), _1674818))], (50215 ^ _781404) ^ [_1796314, _1796316] : [c_Relation_Osym(_1796314, _1796316), -(hAPP(c_Relation_Oconverse(_1796314, _1796314), _1796316) = _1796316)], (23950 ^ _781404) ^ [_1211331, _1211333] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211331), _1211333) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1211333 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23959 ^ _781404 : [(23962 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211331), _1211333)))], (23960 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211331)))]], 23963 ^ _781404 : [(23966 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211333), _1211331)))], (23964 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211331), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (1746 ^ _781404) ^ [_806269, _806271] : [-(class_Groups_Ocomm__monoid__add(_806269)), _806271 = _806269, class_Groups_Ocomm__monoid__add(_806271)], (9903 ^ _781404) ^ [_950559, _950561, _950563, _950565, _950567] : [c_Fun_Oinj__on(_950559, _950561, _950563, _950565), c_Fun_Oinj__on(_950559, _950561, _950563, _950567), -(c_Fun_Oinj__on(_950559, _950561, _950563, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_950559, tc_HOL_Obool)), _950565), _950567)))], (44976 ^ _781404) ^ [_1681424, _1681426, _1681428, _1681430, _1681432] : [class_Orderings_Olinorder(_1681424), hBOOL(hAPP(c_List_Odistinct(_1681426), _1681428)), -(hBOOL(hAPP(c_List_Odistinct(_1681426), c_List_Olinorder__class_Oinsort__insert__key(_1681426, _1681424, _1681430, _1681432, _1681428))))], (15275 ^ _781404) ^ [_1051118, _1051120, _1051122] : [class_Lattices_Olattice(_1051118), hBOOL(hAPP(c_Finite__Set_Ofinite(_1051118), _1051120)), hBOOL(hAPP(hAPP(c_member(_1051118), _1051122), _1051120)), 15286 ^ _781404 : [(15293 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051118, tc_HOL_Obool)), _1051120), hAPP(hAPP(c_Set_Oinsert(_1051118), _1051122), c_Orderings_Obot__class_Obot(tc_fun(_1051118, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1051118, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1051118, _1051120) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1051118), _1051122), c_Big__Operators_Olattice__class_OSup__fin(_1051118, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051118, tc_HOL_Obool)), _1051120), hAPP(hAPP(c_Set_Oinsert(_1051118), _1051122), c_Orderings_Obot__class_Obot(tc_fun(_1051118, tc_HOL_Obool)))))))], (15287 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051118, tc_HOL_Obool)), _1051120), hAPP(hAPP(c_Set_Oinsert(_1051118), _1051122), c_Orderings_Obot__class_Obot(tc_fun(_1051118, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1051118, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1051118, _1051120) = _1051122)]]], (38961 ^ _781404) ^ [_1525599] : [-(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)), _1525599)))))], (36747 ^ _781404) ^ [_1469003, _1469005, _1469007, _1469009, _1469011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1469003, _1469005)), hAPP(_1469003, _1469007))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1469009, _1469009)), hAPP(hAPP(c_Product__Type_OPair(_1469009, _1469009), _1469005), _1469007)), c_Wellfounded_Omlex__prod(_1469009, _1469003, _1469011))))], (22677 ^ _781404) ^ [_1186764, _1186766, _1186768] : [class_Rings_Olinordered__semidom(_1186764), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186764), c_Groups_Oone__class_Oone(_1186764)), _1186766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186764), hAPP(hAPP(c_Power_Opower__class_Opower(_1186764), _1186766), _1186768)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186764), _1186766), hAPP(hAPP(c_Power_Opower__class_Opower(_1186764), _1186766), _1186768)))))], (43066 ^ _781404) ^ [_1639160] : [43068 ^ _781404 : [(43071 ^ _781404) ^ [] : [43067 ^ [_1639160] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43069 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43067 ^ [_1639160]), hAPP(c_List_Oset(tc_Nat_Onat), _1639160))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1639160) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3436 ^ _781404) ^ [_832700, _832702, _832704, _832706, _832708, _832710] : [-(c_Finite__Set_Ofold(_832710, _832706, _832702) = c_Finite__Set_Ofold(_832708, _832704, _832700)), _832710 = _832708, _832706 = _832704, _832702 = _832700], (32410 ^ _781404) ^ [_1365257, _1365259, _1365261] : [class_Orderings_Olinorder(_1365257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365257), _1365259)), -(_1365261 = c_Orderings_Obot__class_Obot(tc_fun(_1365257, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1365257, tc_HOL_Obool)), _1365261), _1365259)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365257), c_Big__Operators_Olinorder__class_OMax(_1365257, _1365261)), c_Big__Operators_Olinorder__class_OMax(_1365257, _1365259)) = c_Big__Operators_Olinorder__class_OMax(_1365257, _1365259))], (30253 ^ _781404) ^ [_1324724, _1324726, _1324728, _1324730, _1324732, _1324734, _1324736] : [c_Finite__Set_Ofun__left__comm(_1324724, _1324726, _1324728), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1324724, _1324726, _1324728, _1324730, hAPP(hAPP(c_Set_Oinsert(_1324724), _1324732), _1324734)), _1324736)), -(hBOOL(hAPP(hAPP(c_member(_1324724), _1324732), _1324734))), 30265 ^ _781404 : [(30268 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1324724, _1324726, _1324728, _1324730, _1324734), 30264 ^ [_1324724, _1324726, _1324728, _1324730, _1324732, _1324734, _1324736])))], (30266 ^ _781404) ^ [] : [-(_1324736 = hAPP(hAPP(_1324728, _1324732), 30264 ^ [_1324724, _1324726, _1324728, _1324730, _1324732, _1324734, _1324736]))]]], (8144 ^ _781404) ^ [_918076, _918078] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918076, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_918076, tc_HOL_Obool))), _918078)))], (43968 ^ _781404) ^ [_1658686, _1658688, _1658690, _1658692] : [hAPP(hAPP(c_List_Oappend(_1658686), _1658688), _1658690) = hAPP(hAPP(c_List_Oappend(_1658686), _1658688), _1658692), -(_1658690 = _1658692)], (39993 ^ _781404) ^ [_1558879, _1558881, _1558883] : [hAPP(c_Relation_ODomain(_1558879, _1558881), _1558883) = c_Orderings_Obot__class_Obot(tc_fun(_1558879, tc_HOL_Obool)), -(_1558883 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1558879, _1558881), tc_HOL_Obool)))], (37522 ^ _781404) ^ [_1488279, _1488281] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1488279, _1488279)), _1488281)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1488279), hAPP(c_Relation_OField(_1488279), _1488281))))], (6984 ^ _781404) ^ [_894084, _894086, _894088, _894090] : [6985 ^ _781404 : [(6986 ^ _781404) ^ [_894194] : [hBOOL(hAPP(hAPP(c_member(_894084), _894194), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894084, tc_HOL_Obool)), _894086), _894088))), hBOOL(hAPP(_894090, _894194))]], 6994 ^ _781404 : [(6997 ^ _781404) ^ [] : [-(hBOOL(hAPP(_894090, 6993 ^ [_894084, _894086, _894088, _894090])))], (6995 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894084), 6993 ^ [_894084, _894086, _894088, _894090]), _894086)))]], 6999 ^ _781404 : [(7002 ^ _781404) ^ [] : [-(hBOOL(hAPP(_894090, 6998 ^ [_894084, _894086, _894088, _894090])))], (7000 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894084), 6998 ^ [_894084, _894086, _894088, _894090]), _894088)))]]], (38756 ^ _781404) ^ [_1519748, _1519750, _1519752, _1519754] : [-(c_Fun_Oinj__on(_1519748, tc_prod(_1519750, _1519748), 38754 ^ [_1519748, _1519750, _1519752, _1519754], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519750, tc_fun(_1519748, tc_HOL_Obool)), _1519752), _1519754)))], (47621 ^ _781404) ^ [_1739013, _1739015, _1739017] : [class_Orderings_Olinorder(_1739013), c_List_Olinorder__class_Osorted(_1739013, hAPP(c_List_Orev(_1739013), _1739015)), 47628 ^ _781404 : [(47635 ^ _781404) ^ [] : [-(_1739015 = c_List_Olist_ONil(_1739013)), -(c_List_Ofoldr(_1739013, _1739013, c_Orderings_Oord__class_Omax(_1739013), _1739015, _1739017) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1739013), hAPP(hAPP(c_List_Onth(_1739013), _1739015), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1739017))], (47629 ^ _781404) ^ [] : [_1739015 = c_List_Olist_ONil(_1739013), -(c_List_Ofoldr(_1739013, _1739013, c_Orderings_Oord__class_Omax(_1739013), _1739015, _1739017) = _1739017)]]], (38053 ^ _781404) ^ [_1501248, _1501250, _1501252, _1501254, _1501256, _1501258, _1501260] : [c_Equiv__Relations_Oequiv(_1501248, _1501250, _1501252), c_Equiv__Relations_Ocongruent(_1501248, tc_fun(_1501254, tc_HOL_Obool), _1501252, _1501256), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501248, tc_fun(_1501254, tc_HOL_Obool)), _1501258), _1501256) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501248, tc_fun(_1501254, tc_HOL_Obool)), _1501260), _1501256), hBOOL(hAPP(hAPP(c_member(tc_fun(_1501248, tc_HOL_Obool)), _1501258), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1501248), _1501250), _1501252))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1501248, tc_HOL_Obool)), _1501260), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1501248), _1501250), _1501252))), 38075 ^ _781404 : [(38079 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501248), 38077 ^ [_1501248, _1501250, _1501252, _1501254, _1501256, _1501258, _1501260]), _1501250)))], (38081 ^ _781404) ^ [] : [-(hAPP(_1501256, 38074 ^ [_1501248, _1501250, _1501252, _1501254, _1501256, _1501258, _1501260]) = hAPP(_1501256, 38077 ^ [_1501248, _1501250, _1501252, _1501254, _1501256, _1501258, _1501260]))], (38083 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1501248, _1501248)), hAPP(hAPP(c_Product__Type_OPair(_1501248, _1501248), 38074 ^ [_1501248, _1501250, _1501252, _1501254, _1501256, _1501258, _1501260]), 38077 ^ [_1501248, _1501250, _1501252, _1501254, _1501256, _1501258, _1501260])), _1501252))], (38076 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501248), 38074 ^ [_1501248, _1501250, _1501252, _1501254, _1501256, _1501258, _1501260]), _1501250)))]], -(_1501258 = _1501260)], (37508 ^ _781404) ^ [_1487872, _1487874, _1487876, _1487878] : [-(hAPP(c_Relation_OField(_1487872), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1487872, _1487872)), hAPP(hAPP(c_Product__Type_OPair(_1487872, _1487872), _1487874), _1487876)), _1487878)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1487872, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1487872), _1487874), hAPP(hAPP(c_Set_Oinsert(_1487872), _1487876), c_Orderings_Obot__class_Obot(tc_fun(_1487872, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1487872), _1487878)))], (5562 ^ _781404) ^ [_866465, _866467] : [_866467 = _866465, -(tc_List_Olist(_866467) = tc_List_Olist(_866465))], (43543 ^ _781404) ^ [_1649352, _1649354, _1649356, _1649358] : [-(c_List_Oremove1(_1649352, _1649354, c_List_Oremove1(_1649352, _1649356, _1649358)) = c_List_Oremove1(_1649352, _1649356, c_List_Oremove1(_1649352, _1649354, _1649358)))], (50785 ^ _781404) ^ [_1807979, _1807981, _1807983, _1807985, _1807987, _1807989] : [c_Fun_Obij__betw(_1807979, _1807981, _1807983, _1807985, _1807987), hBOOL(hAPP(hAPP(c_member(_1807979), _1807989), _1807985)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1807981, _1807979, _1807987, c_Hilbert__Choice_Oinv__into(_1807979, _1807981, _1807985, _1807983)), _1807989) = hAPP(_1807983, _1807989))], (23794 ^ _781404) ^ [_1208576, _1208578] : [23795 ^ _781404 : [(23796 ^ _781404) ^ [_1208625] : [_1208576 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1208578), _1208625)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208576, _1208578) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (39566 ^ _781404) ^ [_1546862, _1546864, _1546866, _1546868] : [class_Groups_Ocomm__monoid__mult(_1546862), c_Fun_Oinj__on(_1546864, _1546862, _1546866, _1546868), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1546864, _1546862), _1546866), _1546868) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1546862, _1546862), c_Fun_Oid(_1546862)), hAPP(c_Set_Oimage(_1546864, _1546862, _1546866), _1546868)))], (44421 ^ _781404) ^ [_1669432, _1669434, _1669436, _1669438] : [-(hAPP(hAPP(c_List_Odrop(_1669432), _1669434), hAPP(hAPP(c_List_Oappend(_1669432), _1669436), _1669438)) = hAPP(hAPP(c_List_Oappend(_1669432), hAPP(hAPP(c_List_Odrop(_1669432), _1669434), _1669436)), hAPP(hAPP(c_List_Odrop(_1669432), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1669434), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669432)), _1669436))), _1669438)))], (46466 ^ _781404) ^ [_1714170, _1714172, _1714174] : [c_List_Oconcat(_1714170, _1714172) = c_List_Oconcat(_1714170, _1714174), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714170))), _1714172) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714170))), _1714174), 46476 ^ _781404 : [(46479 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1714170), tc_List_Olist(_1714170), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714170), tc_fun(tc_List_Olist(_1714170), tc_Nat_Onat), tc_fun(tc_List_Olist(_1714170), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1714170), tc_Nat_Onat), tc_fun(tc_List_Olist(_1714170), tc_HOL_Obool)), tc_List_Olist(_1714170)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714170))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1714170)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1714170))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1714170)))), 46475 ^ [_1714170, _1714172, _1714174]))], (46477 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714170), tc_List_Olist(_1714170))), 46475 ^ [_1714170, _1714172, _1714174]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1714170), tc_List_Olist(_1714170))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1714170), tc_List_Olist(_1714170)), _1714172), _1714174)))))]], -(_1714172 = _1714174)], (12222 ^ _781404) ^ [_991489, _991491, _991493, _991495] : [-(hAPP(c_Set_Ovimage(_991489, _991491, _991493), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_991491, tc_HOL_Obool)), _991495)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_991489, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_991489, _991491, _991493), _991495)))], (6399 ^ _781404) ^ [_883150] : [hAPP(c_Nat_OSuc, _883150) = _883150], (16837 ^ _781404) ^ [_1081327, _1081329] : [class_Groups_Osgn__if(_1081327), 16840 ^ _781404 : [(16847 ^ _781404) ^ [] : [-(_1081329 = c_Groups_Ozero__class_Ozero(_1081327)), 16850 ^ _781404 : [(16857 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081327), c_Groups_Ozero__class_Ozero(_1081327)), _1081329))), -(c_Groups_Osgn__class_Osgn(_1081327, _1081329) = hAPP(c_Groups_Ouminus__class_Ouminus(_1081327), c_Groups_Oone__class_Oone(_1081327)))], (16851 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081327), c_Groups_Ozero__class_Ozero(_1081327)), _1081329)), -(c_Groups_Osgn__class_Osgn(_1081327, _1081329) = c_Groups_Oone__class_Oone(_1081327))]]], (16841 ^ _781404) ^ [] : [_1081329 = c_Groups_Ozero__class_Ozero(_1081327), -(c_Groups_Osgn__class_Osgn(_1081327, _1081329) = c_Groups_Ozero__class_Ozero(_1081327))]]], (3010 ^ _781404) ^ [_826073, _826075] : [_826075 = _826073, -(c_Nitpick_Odenom(_826075) = c_Nitpick_Odenom(_826073))], (52422 ^ _781404) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (8656 ^ _781404) ^ [_927337, _927339, _927341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927337, tc_HOL_Obool)), _927339), hAPP(hAPP(c_Set_Oinsert(_927337), _927341), c_Orderings_Obot__class_Obot(tc_fun(_927337, tc_HOL_Obool))))), -(_927339 = c_Orderings_Obot__class_Obot(tc_fun(_927337, tc_HOL_Obool))), -(_927339 = hAPP(hAPP(c_Set_Oinsert(_927337), _927341), c_Orderings_Obot__class_Obot(tc_fun(_927337, tc_HOL_Obool))))], (13588 ^ _781404) ^ [_1018209, _1018211] : [class_Groups_Olinordered__ab__group__add(_1018209), 13591 ^ _781404 : [(13598 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018209), c_Groups_Ozero__class_Ozero(_1018209)), _1018211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018209), c_Groups_Ozero__class_Ozero(_1018209)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018209), _1018211), _1018211))))], (13592 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018209), c_Groups_Ozero__class_Ozero(_1018209)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018209), _1018211), _1018211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018209), c_Groups_Ozero__class_Ozero(_1018209)), _1018211)))]]], (15008 ^ _781404) ^ [_1045786, _1045788, _1045790, _1045792, _1045794, _1045796] : [c_Finite__Set_Ofolding__image__simple(_1045786, _1045788, _1045790, _1045792, _1045794, _1045796), -(hAPP(_1045796, c_Orderings_Obot__class_Obot(tc_fun(_1045788, tc_HOL_Obool))) = _1045792)], (9581 ^ _781404) ^ [_945460, _945462, _945464] : [class_Orderings_Oorder(_945460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945460), _945462), _945464)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945460), _945464), _945462))], (40232 ^ _781404) ^ [_1564788, _1564790, _1564792] : [c_Wellfounded_OwfP(_1564788, _1564790), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1564788, _1564790), _1564792)))], (29575 ^ _781404) ^ [_1310994, _1310996, _1310998, _1311000] : [class_Fields_Ofield(_1310994), -(_1310996 = c_Groups_Ozero__class_Ozero(_1310994)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1310994), _1310998), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310994), _1311000), _1310996)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310994), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1310994), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1310994), _1310996), _1310998)), _1311000)), _1310996))], (39465 ^ _781404) ^ [_1543474] : [-(c_Int_Oint__ge__less__than2(_1543474) = 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), _1543474)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (47740 ^ _781404) ^ [_1741425, _1741427, _1741429] : [-(c_List_OtakeWhile(_1741425, _1741427, _1741429) = hAPP(hAPP(c_List_Otake(_1741425), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741425)), c_List_OtakeWhile(_1741425, _1741427, _1741429))), _1741429))], (19518 ^ _781404) ^ [_1128492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1128492)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1128492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42036 ^ _781404) ^ [_1608850, _1608852, _1608854, _1608856, _1608858] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608850, _1608850)), hAPP(hAPP(c_Product__Type_OPair(_1608850, _1608850), _1608852), _1608854)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608850, _1608850), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1608856)), _1608858))), 42040 ^ _781404 : [(42043 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608850, _1608850)), hAPP(hAPP(c_Product__Type_OPair(_1608850, _1608850), 42039 ^ [_1608850, _1608852, _1608854, _1608856, _1608858]), _1608854)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608850, _1608850), tc_HOL_Obool), _1608856), _1608858))))], (42041 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608850, _1608850)), hAPP(hAPP(c_Product__Type_OPair(_1608850, _1608850), _1608852), 42039 ^ [_1608850, _1608852, _1608854, _1608856, _1608858])), _1608858)))]]], (11163 ^ _781404) ^ [_970900, _970902, _970904] : [class_Orderings_Oorder(_970900), 11166 ^ _781404 : [(11173 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970900), _970902), _970904))), -(c_Orderings_Obot__class_Obot(tc_fun(_970900, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_970900, _970902), _970904))], (11167 ^ _781404) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_970900, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_970900, _970902), _970904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970900), _970902), _970904))]]], (6915 ^ _781404) ^ [_892511, _892513, _892515, _892517] : [class_Lattices_Olattice(_892511), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892511), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892511), _892513), _892515)), _892517) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892511), _892513), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892511), _892515), _892517)))], (49077 ^ _781404) ^ [_1770925, _1770927, _1770929, _1770931] : [49084 ^ _781404 : [(49087 ^ _781404) ^ [] : [_1770927 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49085 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1770931, _1770929)))]], 49078 ^ _781404 : [(49079 ^ _781404) ^ [_1770997] : [hBOOL(hAPP(hAPP(c_member(_1770925), _1770997), hAPP(c_List_Oset(_1770925), c_List_Oreplicate(_1770925, _1770927, _1770929)))), hBOOL(hAPP(_1770931, _1770997))]]], (41602 ^ _781404) ^ [_1597513, _1597515, _1597517] : [-(hAPP(c_Relation_ODomain(_1597513, _1597515), hAPP(c_Relation_Oconverse(_1597515, _1597513), _1597517)) = hAPP(c_Relation_ORange(_1597515, _1597513), _1597517))], (38431 ^ _781404) ^ [_1510573, _1510575, _1510577, _1510579] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1510573), _1510575)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510573), _1510577)), -(_1510577 = c_Orderings_Obot__class_Obot(tc_fun(_1510573, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1510573, tc_HOL_Obool), tc_fun(_1510573, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1510573, tc_HOL_Obool), tc_fun(_1510573, tc_HOL_Obool)), _1510575), _1510577)), c_Wellfounded_Omax__ext(_1510573, _1510579)))), 38445 ^ _781404 : [(38448 ^ _781404) ^ [_1510978] : [hBOOL(hAPP(hAPP(c_member(_1510573), _1510978), _1510577)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1510573, _1510573)), hAPP(hAPP(c_Product__Type_OPair(_1510573, _1510573), 38444 ^ [_1510573, _1510575, _1510577, _1510579]), _1510978)), _1510579))], (38446 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1510573), 38444 ^ [_1510573, _1510575, _1510577, _1510579]), _1510575)))]]], (15889 ^ _781404) ^ [_1062755, _1062757, _1062759] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062755), _1062757)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062755), _1062759)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062755, tc_HOL_Obool)), _1062757), _1062759) = c_Orderings_Obot__class_Obot(tc_fun(_1062755, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1062755), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062755, tc_HOL_Obool)), _1062757), _1062759)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1062755), _1062757)), hAPP(c_Finite__Set_Ocard(_1062755), _1062759)))], (19478 ^ _781404) ^ [_1127751, _1127753, _1127755] : [class_Rings_Osemiring__1(_1127751), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127751), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1127753), _1127755)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1127751), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127751), _1127753)), _1127755))], (40209 ^ _781404) ^ [_1564130, _1564132, _1564134, _1564136] : [40211 ^ _781404 : [(40214 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1564132, hAPP(_1564134, 40210 ^ [_1564130, _1564132, _1564134, _1564136]))), hAPP(_1564132, 40210 ^ [_1564130, _1564132, _1564134, _1564136])))], (40212 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1564130, 40210 ^ [_1564130, _1564132, _1564134, _1564136])))]], -(c_Wellfounded_Owf(_1564136, hAPP(c_Set_OCollect(tc_prod(_1564136, _1564136)), hAPP(c_Product__Type_Oprod_Oprod__case(_1564136, _1564136, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1564136, tc_HOL_Obool), tc_fun(_1564136, tc_HOL_Obool), _1564136), hAPP(c_COMBS(_1564136, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1564136), c_fconj), _1564130))), hAPP(hAPP(c_COMBC(_1564136, tc_fun(_1564136, _1564136), tc_fun(_1564136, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1564136, tc_HOL_Obool), tc_fun(tc_fun(_1564136, _1564136), tc_fun(_1564136, tc_HOL_Obool)), _1564136), c_COMBB(_1564136, tc_HOL_Obool, _1564136)), c_fequal)), _1564134))))))], (32322 ^ _781404) ^ [_1363428, _1363430, _1363432, _1363434, _1363436] : [class_Lattices_Osemilattice__sup(_1363428), class_Orderings_Olinorder(_1363430), c_Orderings_Oorder__class_Omono(_1363430, _1363428, _1363432), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363428), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1363428), hAPP(_1363432, _1363434)), hAPP(_1363432, _1363436))), hAPP(_1363432, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363430), _1363434), _1363436)))))], (45142 ^ _781404) ^ [_1684136, _1684138, _1684140] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1684136)), _1684138), c_List_Olists(_1684136, _1684140)))), 45143 ^ _781404 : [(45146 ^ _781404) ^ [_1684264, _1684266] : [_1684138 = hAPP(hAPP(c_List_Olist_OCons(_1684136), _1684266), _1684264), hBOOL(hAPP(hAPP(c_member(_1684136), _1684266), _1684140)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1684136)), _1684264), c_List_Olists(_1684136, _1684140)))], (45144 ^ _781404) ^ [] : [_1684138 = c_List_Olist_ONil(_1684136)]]], (6614 ^ _781404) ^ [] : [-(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc))], (13928 ^ _781404) ^ [_1024207, _1024209] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1024207), _1024209) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 13929 ^ _781404 : [(13936 ^ _781404) ^ [] : [_1024207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1024209 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13930 ^ _781404) ^ [] : [_1024207 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024209 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (2770 ^ _781404) ^ [_822379, _822381, _822383, _822385, _822387, _822389, _822391, _822393] : [-(c_Recdef_Osame__fst(_822393, _822389, _822385, _822381) = c_Recdef_Osame__fst(_822391, _822387, _822383, _822379)), _822393 = _822391, _822389 = _822387, _822385 = _822383, _822381 = _822379], (30618 ^ _781404) ^ [_1331669, _1331671, _1331673] : [class_Orderings_Olinorder(_1331669), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331669), _1331671), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331669), _1331671), _1331673)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331669), _1331671), _1331673))], (52550 ^ _781404) ^ [_1840203] : [class_Lazy__Sequence_Osmall__lazy(_1840203), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1840203)))], (36318 ^ _781404) ^ [_1459592, _1459594, _1459596, _1459598, _1459600, _1459602, _1459604, _1459606, _1459608, _1459610, _1459612] : [c_Finite__Set_Ofolding(_1459592, _1459594, _1459596, _1459598), -(hAPP(c_Fun_Ocomp(_1459600, _1459602, _1459604, _1459606), hAPP(c_Fun_Ocomp(_1459608, _1459600, _1459604, _1459610), _1459612)) = hAPP(c_Fun_Ocomp(_1459608, _1459602, _1459604, hAPP(c_Fun_Ocomp(_1459600, _1459602, _1459608, _1459606), _1459610)), _1459612))], (41921 ^ _781404) ^ [_1605501, _1605503, _1605505] : [-(hAPP(hAPP(c_Nat_Ocompow(_1605501, _1605501), hAPP(c_Nat_OSuc, _1605503)), _1605505) = hAPP(c_Fun_Ocomp(_1605501, _1605501, _1605501, _1605505), hAPP(hAPP(c_Nat_Ocompow(_1605501, _1605501), _1605503), _1605505)))], (92 ^ _781404) ^ [_782740, _782742, _782744, _782746, _782748, _782750, _782752, _782754, _782756, _782758, _782760, _782762] : [-(c_Finite__Set_Ofolding__image__simple__idem(_782760, _782756, _782752, _782748, _782744, _782740)), c_Finite__Set_Ofolding__image__simple__idem(_782762, _782758, _782754, _782750, _782746, _782742), _782762 = _782760, _782758 = _782756, _782754 = _782752, _782750 = _782748, _782746 = _782744, _782742 = _782740], (33970 ^ _781404) ^ [_1404726, _1404728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1404726)), _1404728)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1404726), _1404728)))], (41548 ^ _781404) ^ [_1596074, _1596076, _1596078] : [c_Relation_Orefl__on(_1596074, _1596076, _1596078), -(c_Relation_Orefl__on(_1596074, _1596076, hAPP(c_Relation_Oconverse(_1596074, _1596074), _1596078)))], (8335 ^ _781404) ^ [_921996, _921998] : [class_Groups_Ogroup__add(_921996), 8338 ^ _781404 : [(8345 ^ _781404) ^ [] : [c_Groups_Ozero__class_Ozero(_921996) = _921998, -(c_Groups_Ozero__class_Ozero(_921996) = hAPP(c_Groups_Ouminus__class_Ouminus(_921996), _921998))], (8339 ^ _781404) ^ [] : [c_Groups_Ozero__class_Ozero(_921996) = hAPP(c_Groups_Ouminus__class_Ouminus(_921996), _921998), -(c_Groups_Ozero__class_Ozero(_921996) = _921998)]]], (9611 ^ _781404) ^ [_945926, _945928, _945930] : [class_Orderings_Oorder(_945926), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945926), _945928), _945930)), _945928 = _945930], (26043 ^ _781404) ^ [] : [-(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))], (20135 ^ _781404) ^ [_1138941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138941), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1138941)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7567 ^ _781404) ^ [_905353, _905355, _905357] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905353, tc_HOL_Obool)), _905355), _905357) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905353, tc_HOL_Obool)), _905357), _905355))], (39838 ^ _781404) ^ [_1555858, _1555860, _1555862, _1555864, _1555866] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1555858, _1555860)), hAPP(hAPP(c_Product__Type_OPair(_1555858, _1555860), _1555862), _1555864)), _1555866)), -(hBOOL(hAPP(hAPP(c_member(_1555858), _1555862), hAPP(c_Relation_ODomain(_1555858, _1555860), _1555866))))], (52692 ^ _781404) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (44381 ^ _781404) ^ [_1668589, _1668591, _1668593] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1668589, tc_HOL_Obool)), hAPP(c_List_Oset(_1668589), hAPP(hAPP(c_List_Odrop(_1668589), _1668591), _1668593))), hAPP(c_List_Oset(_1668589), _1668593))))], (23405 ^ _781404) ^ [_1201227, _1201229, _1201231, _1201233] : [class_Divides_Oring__div(_1201227), -(c_Divides_Odiv__class_Omod(_1201227, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201227), _1201229), _1201231), _1201233) = c_Divides_Odiv__class_Omod(_1201227, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201227), c_Divides_Odiv__class_Omod(_1201227, _1201229, _1201233)), c_Divides_Odiv__class_Omod(_1201227, _1201231, _1201233)), _1201233))], (52360 ^ _781404) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (2234 ^ _781404) ^ [_813869, _813871, _813873, _813875, _813877, _813879, _813881, _813883, _813885, _813887] : [-(c_Nitpick_Opair__box_Opair__box__size(_813887, _813883, _813879, _813875, _813871) = c_Nitpick_Opair__box_Opair__box__size(_813885, _813881, _813877, _813873, _813869)), _813887 = _813885, _813883 = _813881, _813879 = _813877, _813875 = _813873, _813871 = _813869], (34151 ^ _781404) ^ [_1408804, _1408806, _1408808, _1408810, _1408812] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408804, tc_fun(_1408806, tc_HOL_Obool)), _1408808), hAPP(hAPP(c_COMBC(_1408804, tc_fun(_1408806, tc_HOL_Obool), tc_fun(_1408806, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408806, tc_HOL_Obool), tc_fun(tc_fun(_1408806, tc_HOL_Obool), tc_fun(_1408806, tc_HOL_Obool)), _1408804), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408806, tc_HOL_Obool))), _1408810)), _1408812)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408806, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408804, tc_fun(_1408806, tc_HOL_Obool)), _1408808), _1408810)), _1408812))], (47824 ^ _781404) ^ [_1743311, _1743313, _1743315] : [class_Orderings_Olinorder(_1743311), c_List_Olinorder__class_Osorted(_1743311, _1743313), -(c_List_Olinorder__class_Osorted(_1743311, c_List_OdropWhile(_1743311, _1743315, _1743313)))], (7543 ^ _781404) ^ [_904858, _904860, _904862, _904864] : [class_Lattices_Osemilattice__inf(_904858), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904858), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904858), _904860), _904862)), _904864) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904858), _904860), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_904858), _904862), _904864)))], (19109 ^ _781404) ^ [_1121486, _1121488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1121486)), c_Int_OBit1(_1121488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121486), _1121488)))], (4570 ^ _781404) ^ [_850801, _850803, _850805, _850807, _850809, _850811] : [-(c_FunDef_OTHE__default(_850811, _850807, _850803) = c_FunDef_OTHE__default(_850809, _850805, _850801)), _850811 = _850809, _850807 = _850805, _850803 = _850801], (25377 ^ _781404) ^ [_1235090] : [-(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)), _1235090)) = hAPP(c_Int_Onat, _1235090))], (4274 ^ _781404) ^ [_846149, _846151, _846153, _846155] : [-(c_List_Ozip(_846155, _846151) = c_List_Ozip(_846153, _846149)), _846155 = _846153, _846151 = _846149], (18749 ^ _781404) ^ [_1115641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1115641), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115641) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35768 ^ _781404) ^ [_1449000, _1449002] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1449000, _1449002), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1449000), _1449002)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1449000, _1449002)))))], (43412 ^ _781404) ^ [_1646902, _1646904, _1646906, _1646908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1646902), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646904)), _1646906))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1646902), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646904)), _1646908))), 43422 ^ _781404 : [(43425 ^ _781404) ^ [] : [hAPP(hAPP(c_List_Onth(_1646904), _1646906), 43421 ^ [_1646902, _1646904, _1646906, _1646908]) = hAPP(hAPP(c_List_Onth(_1646904), _1646908), 43421 ^ [_1646902, _1646904, _1646906, _1646908])], (43423 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43421 ^ [_1646902, _1646904, _1646906, _1646908]), _1646902)))]], -(hAPP(hAPP(c_List_Otake(_1646904), _1646902), _1646906) = hAPP(hAPP(c_List_Otake(_1646904), _1646902), _1646908))], (34121 ^ _781404) ^ [_1407973, _1407975, _1407977] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407973, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1407973, tc_HOL_Obool), _1407975)), _1407977) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1407973, tc_HOL_Obool), tc_fun(_1407973, tc_HOL_Obool)), _1407975), hAPP(hAPP(c_COMBC(tc_fun(_1407973, tc_HOL_Obool), tc_fun(_1407973, tc_HOL_Obool), tc_fun(_1407973, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407973, tc_HOL_Obool))), _1407977)))], (49588 ^ _781404) ^ [_1781604, _1781606, _1781608, _1781610] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1781604, _1781606, _1781608, c_Code__Numeral_OSuc__code__numeral(_1781610)) = hAPP(hAPP(_1781608, _1781610), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1781604, _1781606, _1781608, _1781610)))], (43675 ^ _781404) ^ [_1651942, _1651944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1651942), _1651944)), -(c_List_Oupto(_1651942, _1651944) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1651942), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1651942), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1651944)))], (17643 ^ _781404) ^ [_1095794, _1095796, _1095798] : [class_Rings_Oring__1(_1095794), hBOOL(hAPP(hAPP(c_member(_1095794), _1095796), c_Int_Oring__1__class_OInts(_1095794))), -(hBOOL(hAPP(hAPP(c_member(_1095794), hAPP(hAPP(c_Power_Opower__class_Opower(_1095794), _1095796), _1095798)), c_Int_Oring__1__class_OInts(_1095794))))], (27097 ^ _781404) ^ [_1265029, _1265031, _1265033] : [class_Groups_Oordered__ab__group__add__abs(_1265029), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265029), hAPP(c_Groups_Oabs__class_Oabs(_1265029), _1265031)), hAPP(c_Groups_Oabs__class_Oabs(_1265029), _1265033))), hAPP(c_Groups_Oabs__class_Oabs(_1265029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265029), _1265033), _1265031)))))], (17653 ^ _781404) ^ [_1095977, _1095979, _1095981] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1095977), _1095979)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1095977, tc_HOL_Obool)), _1095979), _1095981) = hAPP(hAPP(c_Finite__Set_Ofold(_1095977, tc_fun(_1095977, tc_HOL_Obool), c_Set_Oinsert(_1095977)), _1095981), _1095979))], (30177 ^ _781404) ^ [_1323066, _1323068, _1323070, _1323072, _1323074] : [class_Groups_Ocomm__monoid__mult(_1323066), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323068), _1323070)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323068), _1323072)), 30191 ^ _781404 : [(30194 ^ _781404) ^ [] : [hAPP(_1323074, 30190 ^ [_1323066, _1323068, _1323070, _1323072, _1323074]) = c_Groups_Oone__class_Oone(_1323066)], (30192 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1323068), 30190 ^ [_1323066, _1323068, _1323070, _1323072, _1323074]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323068, tc_HOL_Obool)), _1323070), _1323072))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1323068, _1323066), _1323074), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1323068, tc_HOL_Obool)), _1323070), _1323072)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1323066), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1323068, _1323066), _1323074), _1323070)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1323068, _1323066), _1323074), _1323072)))], (1446 ^ _781404) ^ [_802519, _802521] : [-(class_Lattices_Obounded__lattice__bot(_802519)), _802521 = _802519, class_Lattices_Obounded__lattice__bot(_802521)], (52388 ^ _781404) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (41057 ^ _781404) ^ [_1583557, _1583559] : [-(hAPP(c_Relation_ODomain(_1583557, _1583557), c_Transitive__Closure_Otrancl(_1583557, _1583559)) = hAPP(c_Relation_ODomain(_1583557, _1583557), _1583559))], (7467 ^ _781404) ^ [_903332, _903334, _903336] : [class_Lattices_Osemilattice__inf(_903332), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903332), _903334), _903336) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903332), _903336), _903334))], (25371 ^ _781404) ^ [_1235032] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235032)))), -(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), _1235032)) = 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), _1235032))))], (27723 ^ _781404) ^ [_1276820, _1276822, _1276824, _1276826, _1276828] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1276820, _1276822, hAPP(hAPP(c_Set_Oinsert(_1276820), _1276824), _1276826)), _1276828)), 27728 ^ _781404 : [(27733 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1276820), 27726 ^ [_1276820, _1276822, _1276824, _1276826, _1276828]), 27727 ^ [_1276820, _1276822, _1276824, _1276826, _1276828]))], (27731 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1276820, _1276820, _1276822, 27726 ^ [_1276820, _1276822, _1276824, _1276826, _1276828], 27727 ^ [_1276820, _1276822, _1276824, _1276826, _1276828]), _1276828)))], (27729 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1276820), _1276824), _1276826) = hAPP(hAPP(c_Set_Oinsert(_1276820), 27726 ^ [_1276820, _1276822, _1276824, _1276826, _1276828]), 27727 ^ [_1276820, _1276822, _1276824, _1276826, _1276828]))]]], (22393 ^ _781404) ^ [_1180752, _1180754, _1180756, _1180758, _1180760] : [class_Rings_Olinordered__semiring__strict(_1180752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180752), _1180754), _1180756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180752), _1180758), _1180760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180752), c_Groups_Ozero__class_Ozero(_1180752)), _1180754)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180752), c_Groups_Ozero__class_Ozero(_1180752)), _1180758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180752), _1180754), _1180758)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180752), _1180756), _1180760))))], (52500 ^ _781404) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (50582 ^ _781404) ^ [_1803382, _1803384, _1803386, _1803388, _1803390] : [c_Fun_Oinj__on(_1803382, _1803384, _1803386, c_Orderings_Otop__class_Otop(tc_fun(_1803382, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1803384, _1803388, _1803382, hAPP(c_Fun_Ocomp(_1803382, _1803388, _1803384, _1803390), c_Hilbert__Choice_Oinv__into(_1803382, _1803384, c_Orderings_Otop__class_Otop(tc_fun(_1803382, tc_HOL_Obool)), _1803386))), _1803386) = _1803390)], (2428 ^ _781404) ^ [_817008, _817010, _817012, _817014] : [-(c_Divides_Odivmod__int__rel(_817014, _817010) = c_Divides_Odivmod__int__rel(_817012, _817008)), _817014 = _817012, _817010 = _817008], (15585 ^ _781404) ^ [_1057239, _1057241, _1057243] : [class_Lattices_Olattice(_1057239), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057239), _1057241)), hBOOL(hAPP(hAPP(c_member(_1057239), _1057243), _1057241)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1057239), _1057243), c_Big__Operators_Olattice__class_OSup__fin(_1057239, _1057241)) = _1057243)], (16897 ^ _781404) ^ [_1082225, _1082227] : [class_Rings_Olinordered__idom(_1082225), 16900 ^ _781404 : [(16907 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082225), _1082227), c_Groups_Ozero__class_Ozero(_1082225))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082225), c_Groups_Osgn__class_Osgn(_1082225, _1082227)), c_Groups_Ozero__class_Ozero(_1082225))))], (16901 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082225), c_Groups_Osgn__class_Osgn(_1082225, _1082227)), c_Groups_Ozero__class_Ozero(_1082225))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082225), _1082227), c_Groups_Ozero__class_Ozero(_1082225))))]]], (50817 ^ _781404) ^ [_1808757, _1808759, _1808761, _1808763, _1808765] : [c_Fun_Obij__betw(_1808757, _1808759, _1808761, c_Orderings_Otop__class_Otop(tc_fun(_1808757, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808759, tc_HOL_Obool))), c_Fun_Obij__betw(_1808759, _1808763, _1808765, c_Orderings_Otop__class_Otop(tc_fun(_1808759, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808763, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1808757, _1808763, hAPP(c_Fun_Ocomp(_1808759, _1808763, _1808757, _1808765), _1808761), c_Orderings_Otop__class_Otop(tc_fun(_1808757, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808763, tc_HOL_Obool))))], (40088 ^ _781404) ^ [_1561070, _1561072] : [-(c_FunDef_Oreduction__pair(_1561070, _1561072)), c_Wellfounded_Owf(_1561070, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1561070, _1561070), tc_HOL_Obool), tc_fun(tc_prod(_1561070, _1561070), tc_HOL_Obool)), _1561072)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561070, _1561070), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1561070, _1561070, _1561070), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1561070, _1561070), tc_HOL_Obool), tc_fun(tc_prod(_1561070, _1561070), tc_HOL_Obool)), _1561072)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1561070, _1561070), tc_HOL_Obool), tc_fun(tc_prod(_1561070, _1561070), tc_HOL_Obool)), _1561072))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1561070, _1561070), tc_HOL_Obool), tc_fun(tc_prod(_1561070, _1561070), tc_HOL_Obool)), _1561072)))], (8329 ^ _781404) ^ [_921905] : [class_Groups_Ogroup__add(_921905), -(hAPP(c_Groups_Ouminus__class_Ouminus(_921905), c_Groups_Ozero__class_Ozero(_921905)) = c_Groups_Ozero__class_Ozero(_921905))], (31702 ^ _781404) ^ [_1351953, _1351955, _1351957] : [class_Orderings_Olinorder(_1351953), hAPP(_1351955, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1351953), 31707 ^ [_1351953, _1351955, _1351957]), 31708 ^ [_1351953, _1351955, _1351957])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1351953), hAPP(_1351955, 31707 ^ [_1351953, _1351955, _1351957])), hAPP(_1351955, 31708 ^ [_1351953, _1351955, _1351957])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351953), _1351957)), -(_1351957 = c_Orderings_Obot__class_Obot(tc_fun(_1351953, tc_HOL_Obool))), -(hAPP(_1351955, c_Big__Operators_Olinorder__class_OMin(_1351953, _1351957)) = c_Big__Operators_Olinorder__class_OMin(_1351953, hAPP(c_Set_Oimage(_1351953, _1351953, _1351955), _1351957)))], (9743 ^ _781404) ^ [_947571, _947573] : [class_Orderings_Opreorder(_947571), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947571), _947573), _947573))], (38272 ^ _781404) ^ [_1507138, _1507140, _1507142] : [hBOOL(hAPP(hAPP(c_member(_1507138), _1507142), c_Wellfounded_Oacc(_1507138, _1507140))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1507138, hAPP(hAPP(c_COMBC(_1507138, tc_fun(tc_prod(_1507138, _1507138), tc_HOL_Obool), tc_fun(_1507138, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507138, tc_fun(tc_fun(tc_prod(_1507138, _1507138), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1507138, _1507138), tc_HOL_Obool), tc_fun(_1507138, tc_HOL_Obool)), _1507138), c_COMBC(_1507138, tc_fun(tc_prod(_1507138, _1507138), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507138, tc_prod(_1507138, _1507138)), tc_fun(_1507138, tc_fun(tc_fun(tc_prod(_1507138, _1507138), tc_HOL_Obool), tc_HOL_Obool)), _1507138), hAPP(c_COMBB(tc_prod(_1507138, _1507138), tc_fun(tc_fun(tc_prod(_1507138, _1507138), tc_HOL_Obool), tc_HOL_Obool), _1507138), c_member(tc_prod(_1507138, _1507138)))), c_Product__Type_OPair(_1507138, _1507138)))), _1507140)), _1507142)))], (50549 ^ _781404) ^ [_1802487, _1802489, _1802491] : [hAPP(_1802491, hAPP(c_Hilbert__Choice_Oinv__into(_1802487, _1802489, c_Orderings_Otop__class_Otop(tc_fun(_1802487, tc_HOL_Obool)), _1802491), 50550 ^ [_1802487, _1802489, _1802491])) = 50550 ^ [_1802487, _1802489, _1802491], -(hAPP(c_Set_Oimage(_1802487, _1802489, _1802491), c_Orderings_Otop__class_Otop(tc_fun(_1802487, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1802489, tc_HOL_Obool)))], (33904 ^ _781404) ^ [_1402544, _1402546, _1402548, _1402550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool)), _1402548), _1402550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402544, tc_fun(_1402546, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1402544, tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_fun(_1402546, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1402546, tc_fun(tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_fun(_1402546, tc_HOL_Obool)), _1402544), c_COMBC(_1402546, tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1402546, tc_prod(_1402544, _1402546)), tc_fun(_1402546, tc_fun(tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_HOL_Obool)), _1402544), hAPP(c_COMBB(tc_prod(_1402544, _1402546), tc_fun(tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_HOL_Obool), _1402546), c_member(tc_prod(_1402544, _1402546)))), c_Product__Type_OPair(_1402544, _1402546)))), _1402548)), hAPP(hAPP(c_COMBC(_1402544, tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_fun(_1402546, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1402546, tc_fun(tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_fun(_1402546, tc_HOL_Obool)), _1402544), c_COMBC(_1402546, tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1402546, tc_prod(_1402544, _1402546)), tc_fun(_1402546, tc_fun(tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_HOL_Obool)), _1402544), hAPP(c_COMBB(tc_prod(_1402544, _1402546), tc_fun(tc_fun(tc_prod(_1402544, _1402546), tc_HOL_Obool), tc_HOL_Obool), _1402546), c_member(tc_prod(_1402544, _1402546)))), c_Product__Type_OPair(_1402544, _1402546)))), _1402550))))], (24730 ^ _781404) ^ [_1224964, _1224966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224964)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224966)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1224964, _1224966)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1224964), hAPP(c_Int_Onat, _1224966)))], (48798 ^ _781404) ^ [_1764335, _1764337, _1764339] : [48800 ^ _781404 : [(48803 ^ _781404) ^ [] : [hBOOL(hAPP(_1764337, 48799 ^ [_1764335, _1764337, _1764339]))], (48801 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1764335), 48799 ^ [_1764335, _1764337, _1764339]), hAPP(c_List_Oset(_1764335), _1764339))))]], -(c_List_Olist__all(_1764335, _1764337, _1764339))], (32474 ^ _781404) ^ [_1366340, _1366342, _1366344] : [class_Orderings_Olinorder(_1366340), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366340), _1366342)), -(hBOOL(hAPP(hAPP(c_member(_1366340), _1366344), _1366342))), -(_1366342 = c_Orderings_Obot__class_Obot(tc_fun(_1366340, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1366340, hAPP(hAPP(c_Set_Oinsert(_1366340), _1366344), _1366342)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366340), _1366344), c_Big__Operators_Olinorder__class_OMax(_1366340, _1366342)))], (19619 ^ _781404) ^ [_1130145, _1130147] : [class_Int_Onumber__ring(_1130145), 19622 ^ _781404 : [(19629 ^ _781404) ^ [] : [c_Int_Oiszero(_1130145, hAPP(c_Int_Onumber__class_Onumber__of(_1130145), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1130147), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1130145), _1130147) = c_Groups_Oone__class_Oone(_1130145))], (19623 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1130145), _1130147) = c_Groups_Oone__class_Oone(_1130145), -(c_Int_Oiszero(_1130145, hAPP(c_Int_Onumber__class_Onumber__of(_1130145), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1130147), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (52516 ^ _781404) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (42206 ^ _781404) ^ [_1613542, _1613544, _1613546] : [-(hAPP(c_List_Olexn(_1613542, _1613544), hAPP(c_Nat_OSuc, _1613546)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1613542), tc_List_Olist(_1613542)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1613542, tc_List_Olist(_1613542)), tc_prod(_1613542, tc_List_Olist(_1613542))), tc_prod(tc_List_Olist(_1613542), tc_List_Olist(_1613542)), c_Product__Type_Omap__pair(tc_prod(_1613542, tc_List_Olist(_1613542)), tc_List_Olist(_1613542), tc_prod(_1613542, tc_List_Olist(_1613542)), tc_List_Olist(_1613542), hAPP(c_Product__Type_Oprod_Oprod__case(_1613542, tc_List_Olist(_1613542), tc_List_Olist(_1613542)), c_List_Olist_OCons(_1613542)), hAPP(c_Product__Type_Oprod_Oprod__case(_1613542, tc_List_Olist(_1613542), tc_List_Olist(_1613542)), c_List_Olist_OCons(_1613542)))), c_Wellfounded_Olex__prod(_1613542, tc_List_Olist(_1613542), _1613544, hAPP(c_List_Olexn(_1613542, _1613544), _1613546)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1613542), tc_List_Olist(_1613542))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1613542), tc_List_Olist(_1613542), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613542), tc_fun(tc_List_Olist(_1613542), tc_HOL_Obool), tc_fun(tc_List_Olist(_1613542), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1613542), tc_HOL_Obool), tc_fun(tc_List_Olist(_1613542), tc_HOL_Obool)), tc_List_Olist(_1613542)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1613542))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1613542)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613542), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1613542)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1613542)))), hAPP(c_Nat_OSuc, _1613546))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613542), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1613542)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1613542)))), hAPP(c_Nat_OSuc, _1613546)))))))], (38967 ^ _781404) ^ [_1525786, _1525788, _1525790, _1525792] : [-(hAPP(c_Set_OCollect(tc_prod(_1525786, _1525788)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525786, _1525788, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1525786, tc_fun(_1525788, tc_HOL_Obool), tc_fun(_1525788, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1525788, tc_HOL_Obool), tc_fun(_1525788, tc_HOL_Obool)), _1525786), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1525788)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525786), c_fconj), _1525790))), _1525792))) = hAPP(hAPP(c_Product__Type_OSigma(_1525786, _1525788), hAPP(c_Set_OCollect(_1525786), _1525790)), hAPP(c_COMBK(tc_fun(_1525788, tc_HOL_Obool), _1525786), hAPP(c_Set_OCollect(_1525788), _1525792))))], (38158 ^ _781404) ^ [_1504386, _1504388, _1504390] : [-(c_Relation_Orefl__on(_1504386, _1504388, _1504390)), 38162 ^ _781404 : [(38165 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1504386, _1504386, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1504386, tc_fun(_1504386, tc_HOL_Obool), tc_fun(_1504386, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1504386, tc_HOL_Obool), tc_fun(_1504386, tc_HOL_Obool)), _1504386), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1504386)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1504386), c_fconj), hAPP(hAPP(c_COMBC(_1504386, tc_fun(_1504386, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504386)), _1504388)))), hAPP(hAPP(c_COMBC(_1504386, tc_fun(_1504386, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504386)), _1504388))), 38161 ^ [_1504386, _1504388, _1504390]))], (38163 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504386, _1504386)), 38161 ^ [_1504386, _1504388, _1504390]), _1504390)))]], 38167 ^ _781404 : [(38170 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504386, _1504386)), hAPP(hAPP(c_Product__Type_OPair(_1504386, _1504386), 38166 ^ [_1504386, _1504388, _1504390]), 38166 ^ [_1504386, _1504388, _1504390])), _1504390))], (38168 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504386), 38166 ^ [_1504386, _1504388, _1504390]), _1504388)))]]], (13914 ^ _781404) ^ [_1024023, _1024025] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1024023), _1024025) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 13919 ^ _781404 : [(13922 ^ _781404) ^ [] : [-(_1024025 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13920 ^ _781404) ^ [] : [-(_1024023 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 13923 ^ _781404 : [(13926 ^ _781404) ^ [] : [-(_1024025 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13924 ^ _781404) ^ [] : [-(_1024023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42252 ^ _781404) ^ [_1614885, _1614887, _1614889, _1614891, _1614893, _1614895] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614885), tc_List_Olist(_1614885))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614885), tc_List_Olist(_1614885)), hAPP(hAPP(c_List_Olist_OCons(_1614885), _1614887), _1614889)), hAPP(hAPP(c_List_Olist_OCons(_1614885), _1614891), _1614893))), c_List_Olex(_1614885, _1614895)))), 42253 ^ _781404 : [(42260 ^ _781404) ^ [] : [_1614887 = _1614891, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614885), tc_List_Olist(_1614885))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614885), tc_List_Olist(_1614885)), _1614889), _1614893)), c_List_Olex(_1614885, _1614895)))], (42254 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614885, _1614885)), hAPP(hAPP(c_Product__Type_OPair(_1614885, _1614885), _1614887), _1614891)), _1614895)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614885)), _1614889) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614885)), _1614893)]]], (13057 ^ _781404) ^ [_1007979, _1007981, _1007983, _1007985] : [class_Groups_Oordered__ab__semigroup__add(_1007979), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007979), _1007981), _1007983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007979), _1007981), _1007985)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007979), _1007983), _1007985))))], (22301 ^ _781404) ^ [_1178984, _1178986, _1178988, _1178990] : [class_Rings_Olinordered__semiring__strict(_1178984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178984), _1178986), _1178988)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178984), _1178990), _1178988))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178984), c_Groups_Ozero__class_Ozero(_1178984)), _1178988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178984), _1178986), _1178990)))], (17049 ^ _781404) ^ [_1084973, _1084975, _1084977] : [17051 ^ _781404 : [(17054 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1084973), _1084977), 17050 ^ [_1084973, _1084975, _1084977]))], (17052 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1084973, tc_HOL_Obool)), 17050 ^ [_1084973, _1084975, _1084977]), _1084975)))]], -(hBOOL(hAPP(hAPP(c_member(_1084973), _1084977), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1084973, tc_HOL_Obool), _1084975))))], (23751 ^ _781404) ^ [_1207911] : [-(_1207911 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1207911), _1207911) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (37236 ^ _781404) ^ [] : [-(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)))))], (8158 ^ _781404) ^ [_918398] : [class_Complete__Lattice_Ocomplete__lattice(_918398), -(c_Complete__Lattice_OSup__class_OSup(_918398, c_Orderings_Obot__class_Obot(tc_fun(_918398, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_918398))], (46656 ^ _781404) ^ [_1718999, _1719001, _1719003] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718999)), hAPP(c_List_Ofilter(_1718999, _1719001), _1719003)) = 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(_1718999)), _1719003)))), hAPP(hAPP(c_COMBB(_1718999, tc_HOL_Obool, tc_Nat_Onat), _1719001), hAPP(c_List_Onth(_1718999), _1719003))))))], (45708 ^ _781404) ^ [_1697103] : [-(hAPP(c_Code__Numeral_Onat__of, _1697103) = c_Code__Numeral_Onat__of__aux(_1697103, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18091 ^ _781404) ^ [_1103795, _1103797] : [18092 ^ _781404 : [(18095 ^ _781404) ^ [] : [_1103795 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18093 ^ _781404) ^ [] : [_1103797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1103795), _1103797) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26869 ^ _781404) ^ [_1260950, _1260952, _1260954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1260952), 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), _1260952), _1260954))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1260950))), _1260954)))], (34829 ^ _781404) ^ [_1428792, _1428794, _1428796, _1428798, _1428800, _1428802] : [class_Groups_Ocomm__monoid__mult(_1428792), c_Fun_Oinj__on(_1428794, _1428796, _1428798, _1428800), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1428796, _1428792), _1428802), hAPP(c_Set_Oimage(_1428794, _1428796, _1428798), _1428800)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1428794, _1428792), hAPP(c_Fun_Ocomp(_1428796, _1428792, _1428794, _1428802), _1428798)), _1428800))], (13489 ^ _781404) ^ [_1016127] : [13491 ^ _781404 : [(13494 ^ _781404) ^ [_1016237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13490 ^ [_1016127, _1016237]), _1016237))], (13492 ^ _781404) ^ [_1016203] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 13490 ^ [_1016127, _1016203]), _1016127)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1016127)))], (31210 ^ _781404) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (26662 ^ _781404) ^ [_1256596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1256596), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1256596 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 26665 ^ [_1256596]))))], (36868 ^ _781404) ^ [_1471304, _1471306, _1471308, _1471310, _1471312, _1471314] : [-(c_Product__Type_Oprod_Oprod__rec(_1471304, _1471306, _1471308, _1471310, hAPP(hAPP(c_Product__Type_OPair(_1471304, _1471306), _1471312), _1471314)) = hAPP(hAPP(_1471310, _1471312), _1471314))], (49033 ^ _781404) ^ [_1769779, _1769781, _1769783, _1769785, _1769787] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1769781, _1769779)), hAPP(hAPP(c_Product__Type_OPair(_1769781, _1769779), _1769785), _1769787)), hAPP(c_Relation_Oconverse(_1769779, _1769781), _1769783))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1769779, _1769781, hAPP(hAPP(c_COMBC(_1769779, tc_fun(tc_prod(_1769779, _1769781), tc_HOL_Obool), tc_fun(_1769781, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769781, tc_fun(tc_fun(tc_prod(_1769779, _1769781), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1769779, _1769781), tc_HOL_Obool), tc_fun(_1769781, tc_HOL_Obool)), _1769779), c_COMBC(_1769781, tc_fun(tc_prod(_1769779, _1769781), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769781, tc_prod(_1769779, _1769781)), tc_fun(_1769781, tc_fun(tc_fun(tc_prod(_1769779, _1769781), tc_HOL_Obool), tc_HOL_Obool)), _1769779), hAPP(c_COMBB(tc_prod(_1769779, _1769781), tc_fun(tc_fun(tc_prod(_1769779, _1769781), tc_HOL_Obool), tc_HOL_Obool), _1769781), c_member(tc_prod(_1769779, _1769781)))), c_Product__Type_OPair(_1769779, _1769781)))), _1769783)), _1769785), _1769787)))], (12180 ^ _781404) ^ [_990779, _990781, _990783, _990785, _990787, _990789] : [c_Fun_Oinj__on(_990779, _990781, _990783, _990785), hBOOL(hAPP(hAPP(c_member(_990779), _990787), _990785)), hBOOL(hAPP(hAPP(c_member(_990779), _990789), _990785)), 12191 ^ _781404 : [(12198 ^ _781404) ^ [] : [_990787 = _990789, -(hAPP(_990783, _990787) = hAPP(_990783, _990789))], (12192 ^ _781404) ^ [] : [hAPP(_990783, _990787) = hAPP(_990783, _990789), -(_990787 = _990789)]]], (31118 ^ _781404) ^ [_1340961] : [class_Orderings_Oord(_1340961), -(c_Orderings_Oord__class_Omin(_1340961) = c_Orderings_Oord_Omin(_1340961, c_Orderings_Oord__class_Oless__eq(_1340961)))], (51325 ^ _781404) ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1819370, _1819372), tc_prod(_1819370, _1819372))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1819370, _1819372), tc_prod(_1819370, _1819372)), hAPP(hAPP(c_Product__Type_OPair(_1819370, _1819372), _1819374), _1819376)), hAPP(hAPP(c_Product__Type_OPair(_1819370, _1819372), _1819378), _1819380))), c_Transitive__Closure_Ortrancl(tc_prod(_1819370, _1819372), _1819382))), hBOOL(hAPP(hAPP(_1819384, _1819378), _1819380)), 51338 ^ _781404 : [(51341 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1819370, _1819372), tc_prod(_1819370, _1819372))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1819370, _1819372), tc_prod(_1819370, _1819372)), hAPP(hAPP(c_Product__Type_OPair(_1819370, _1819372), 51336 ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384]), 51337 ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384])), hAPP(hAPP(c_Product__Type_OPair(_1819370, _1819372), _1819378), _1819380))), c_Transitive__Closure_Ortrancl(tc_prod(_1819370, _1819372), _1819382))))], (51343 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1819384, 51336 ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384]), 51337 ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384])))], (51345 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1819384, 51334 ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384]), 51335 ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384]))], (51339 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1819370, _1819372), tc_prod(_1819370, _1819372))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1819370, _1819372), tc_prod(_1819370, _1819372)), hAPP(hAPP(c_Product__Type_OPair(_1819370, _1819372), 51334 ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384]), 51335 ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384])), hAPP(hAPP(c_Product__Type_OPair(_1819370, _1819372), 51336 ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384]), 51337 ^ [_1819370, _1819372, _1819374, _1819376, _1819378, _1819380, _1819382, _1819384]))), _1819382)))]], -(hBOOL(hAPP(hAPP(_1819384, _1819374), _1819376)))], (8032 ^ _781404) ^ [_915674, _915676, _915678] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_915674, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915674, tc_HOL_Obool)), _915676), _915678)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915674, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_915674, tc_HOL_Obool)), _915676)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_915674, tc_HOL_Obool)), _915678)))], (40435 ^ _781404) ^ [_1569194, _1569196, _1569198] : [-(c_Hilbert__Choice_OEps(tc_prod(_1569194, _1569196), hAPP(c_Product__Type_Oprod_Oprod__case(_1569194, _1569196, tc_HOL_Obool), _1569198)) = c_Hilbert__Choice_OEps(tc_prod(_1569194, _1569196), hAPP(hAPP(c_COMBS(tc_prod(_1569194, _1569196), _1569196, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1569194, tc_fun(_1569196, tc_HOL_Obool), tc_prod(_1569194, _1569196)), _1569198), c_Product__Type_Ofst(_1569194, _1569196))), c_Product__Type_Osnd(_1569194, _1569196))))], (5536 ^ _781404) ^ [_866074, _866076, _866078, _866080, _866082, _866084] : [-(c_Divides_Odiv__class_Omod(_866084, _866080, _866076) = c_Divides_Odiv__class_Omod(_866082, _866078, _866074)), _866084 = _866082, _866080 = _866078, _866076 = _866074], (46925 ^ _781404) ^ [_1725613] : [class_Orderings_Olinorder(_1725613), -(c_List_Olinorder__class_Osorted(_1725613, c_List_Olist_ONil(_1725613)))], (9621 ^ _781404) ^ [_946072, _946074, _946076] : [class_Orderings_Opreorder(_946072), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946072), _946074), _946076)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946072), _946076), _946074))], (39309 ^ _781404) ^ [_1536441] : [-(c_Wellfounded_Ofinite__psubset(_1536441) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1536441, tc_HOL_Obool), tc_fun(_1536441, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1536441, tc_HOL_Obool), tc_fun(_1536441, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1536441, tc_HOL_Obool), tc_fun(tc_fun(_1536441, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1536441, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1536441, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1536441, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1536441, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1536441, tc_HOL_Obool)), c_COMBS(tc_fun(_1536441, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1536441, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1536441, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1536441, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1536441, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1536441, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1536441)))))], (15439 ^ _781404) ^ [_1054579, _1054581] : [class_Lattices_Olattice(_1054579), -(c_Big__Operators_Olattice__class_OInf__fin(_1054579, hAPP(hAPP(c_Set_Oinsert(_1054579), _1054581), c_Orderings_Obot__class_Obot(tc_fun(_1054579, tc_HOL_Obool)))) = _1054581)], (42167 ^ _781404) ^ [_1612159] : [-(c_Nitpick_Odenom(_1612159) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1612159, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1612159)))], (23800 ^ _781404) ^ [_1208687, _1208689] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1208687), _1208689) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208687, _1208689) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (21741 ^ _781404) ^ [_1167989, _1167991, _1167993] : [class_Rings_Olinordered__semiring__strict(_1167989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167989), c_Groups_Ozero__class_Ozero(_1167989)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167989), _1167991), _1167993))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167989), c_Groups_Ozero__class_Ozero(_1167989)), _1167991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167989), c_Groups_Ozero__class_Ozero(_1167989)), _1167993)))], (24961 ^ _781404) ^ [_1228572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228572), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1228572)), c_Int_OMin)))], (32038 ^ _781404) ^ [_1358143, _1358145, _1358147] : [class_Orderings_Olinorder(_1358143), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358143), _1358145), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358143), _1358145), _1358147))))], (4172 ^ _781404) ^ [_844598, _844600, _844602, _844604, _844606, _844608, _844610, _844612] : [-(c_New__Random__Sequence_Opos__bind(_844612, _844608, _844604, _844600) = c_New__Random__Sequence_Opos__bind(_844610, _844606, _844602, _844598)), _844612 = _844610, _844608 = _844606, _844604 = _844602, _844600 = _844598], (22723 ^ _781404) ^ [_1187611, _1187613] : [class_Int_Onumber__ring(_1187611), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187611), _1187613), hAPP(c_Int_Onumber__class_Onumber__of(_1187611), c_Int_OBit1(c_Int_OPls))) = _1187613)], (12027 ^ _781404) ^ [_987591, _987593, _987595, _987597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987591, tc_HOL_Obool)), _987593), _987595)), hBOOL(hAPP(hAPP(c_member(_987591), _987597), _987593)), -(hBOOL(hAPP(hAPP(c_member(_987591), _987597), _987595)))], (24788 ^ _781404) ^ [_1225849, _1225851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1225851, _1225849)), _1225849)))], (9953 ^ _781404) ^ [_951421] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _951421), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _951421)], (19115 ^ _781404) ^ [_1121587, _1121589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121587), _1121589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1121587)), c_Int_OBit1(_1121589))))], (35934 ^ _781404) ^ [_1451903, _1451905] : [-(_1451903 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451905, _1451903), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1451905), _1451903)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1451905, _1451903)))))], (17268 ^ _781404) ^ [_1089334, _1089336] : [class_Int_Onumber__ring(_1089334), -(hAPP(c_Int_Onumber__class_Onumber__of(_1089334), c_Int_Opred(_1089336)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089334), hAPP(c_Groups_Ouminus__class_Ouminus(_1089334), c_Groups_Oone__class_Oone(_1089334))), hAPP(c_Int_Onumber__class_Onumber__of(_1089334), _1089336)))], (42523 ^ _781404) ^ [_1624013, _1624015, _1624017, _1624019, _1624021, _1624023] : [c_List_Olistrelp(_1624013, _1624015, hAPP(hAPP(c_List_Olist_OCons(_1624013), _1624017), _1624019), hAPP(hAPP(c_List_Olist_OCons(_1624013), _1624021), _1624023)), 42526 ^ _781404 : [(42529 ^ _781404) ^ [] : [-(c_List_Olistrelp(_1624013, _1624015, _1624019, _1624023))], (42527 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1624015, _1624017), _1624021)))]]], (8520 ^ _781404) ^ [_925154, _925156] : [class_Orderings_Obot(_925154), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925154), c_Orderings_Obot__class_Obot(_925154)), _925156)))], (38496 ^ _781404) ^ [_1512147, _1512149, _1512151] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1512147, _1512149), c_Orderings_Obot__class_Obot(tc_fun(_1512147, tc_HOL_Obool))), _1512151) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1512147, _1512149), tc_HOL_Obool)))], (49545 ^ _781404) ^ [_1780897, _1780899, _1780901] : [c_List_Olist__all(tc_Int_Oint, _1780897, c_List_Oupto(_1780899, _1780901)), -(c_List_Oall__interval__int(_1780897, _1780899, _1780901))], (42430 ^ _781404) ^ [_1620738, _1620740, _1620742, _1620744] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1620738), tc_List_Olist(_1620738), c_List_Olistrel(_1620738, _1620740)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1620738)), hAPP(hAPP(c_List_Olist_OCons(_1620738), _1620742), _1620744)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1620738), tc_HOL_Obool)))) = c_List_Oset__Cons(_1620738, hAPP(c_Relation_OImage(_1620738, _1620738, _1620740), hAPP(hAPP(c_Set_Oinsert(_1620738), _1620742), c_Orderings_Obot__class_Obot(tc_fun(_1620738, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1620738), tc_List_Olist(_1620738), c_List_Olistrel(_1620738, _1620740)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1620738)), _1620744), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1620738), tc_HOL_Obool))))))], (34347 ^ _781404) ^ [_1417110, _1417112, _1417114] : [-(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)), _1417110)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1417112, _1417114)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1417112), _1417110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1417114), _1417110)))], (51882 ^ _781404) ^ [_1831492, _1831494] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831492), _1831494))), -(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), _1831492, _1831494))], (42619 ^ _781404) ^ [_1626293, _1626295, _1626297, _1626299] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1626293), tc_List_Olist(_1626293))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626293), tc_List_Olist(_1626293)), _1626295), _1626297)), c_List_Olistrel(_1626293, _1626299))), 42622 ^ _781404 : [(42625 ^ _781404) ^ [_1626522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1626522), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626293)), _1626295))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1626293, _1626293)), hAPP(hAPP(c_Product__Type_OPair(_1626293, _1626293), hAPP(hAPP(c_List_Onth(_1626293), _1626295), _1626522)), hAPP(hAPP(c_List_Onth(_1626293), _1626297), _1626522))), _1626299)))], (42623 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626293)), _1626295) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626293)), _1626297))]]], (16869 ^ _781404) ^ [_1081819, _1081821] : [class_Rings_Olinordered__idom(_1081819), -(c_Groups_Osgn__class_Osgn(_1081819, c_Groups_Osgn__class_Osgn(_1081819, _1081821)) = c_Groups_Osgn__class_Osgn(_1081819, _1081821))], (44782 ^ _781404) ^ [_1677270, _1677272] : [class_Complete__Lattice_Ocomplete__lattice(_1677270), -(c_Complete__Lattice_OInf__class_OInf(_1677270, hAPP(c_List_Oset(_1677270), _1677272)) = hAPP(c_List_Ofoldl(_1677270, _1677270, c_Lattices_Osemilattice__inf__class_Oinf(_1677270), c_Orderings_Otop__class_Otop(_1677270)), _1677272))], (19085 ^ _781404) ^ [_1121040, _1121042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1121040)), c_Int_OBit1(_1121042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121040), _1121042)))], (42882 ^ _781404) ^ [_1633076, _1633078, _1633080] : [42884 ^ _781404 : [(42887 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1633076), 42883 ^ [_1633076, _1633078, _1633080]), _1633080))], (42885 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633076), 42883 ^ [_1633076, _1633078, _1633080]), hAPP(c_List_Oset(_1633076), _1633078))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1633076)), _1633078), c_List_Olists(_1633076, _1633080))))], (44142 ^ _781404) ^ [_1662238, _1662240, _1662242, _1662244] : [hBOOL(hAPP(hAPP(c_member(_1662238), _1662240), hAPP(c_List_Oset(_1662238), _1662242))), -(c_List_Oremove1(_1662238, _1662240, hAPP(hAPP(c_List_Oappend(_1662238), _1662242), _1662244)) = hAPP(hAPP(c_List_Oappend(_1662238), c_List_Oremove1(_1662238, _1662240, _1662242)), _1662244))], (43974 ^ _781404) ^ [_1658795, _1658797, _1658799, _1658801] : [_1658799 = _1658801, -(hAPP(hAPP(c_List_Oappend(_1658795), _1658797), _1658799) = hAPP(hAPP(c_List_Oappend(_1658795), _1658797), _1658801))], (6833 ^ _781404) ^ [_890925, _890927, _890929, _890931] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890925, tc_HOL_Obool)), _890927), _890929), _890931)), -(hBOOL(hAPP(_890927, _890931))), -(hBOOL(hAPP(_890929, _890931)))], (44431 ^ _781404) ^ [_1669714, _1669716, _1669718, _1669720] : [-(hAPP(hAPP(c_List_Oappend(_1669714), _1669716), _1669718) = _1669720), _1669716 = hAPP(hAPP(c_List_Otake(_1669714), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669714)), _1669716)), _1669720), _1669718 = hAPP(hAPP(c_List_Odrop(_1669714), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669714)), _1669716)), _1669720)], (42826 ^ _781404) ^ [_1631803, _1631805, _1631807] : [42828 ^ _781404 : [(42831 ^ _781404) ^ [] : [hBOOL(hAPP(_1631807, 42827 ^ [_1631803, _1631805, _1631807]))], (42829 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1631803), 42827 ^ [_1631803, _1631805, _1631807]), hAPP(c_List_Oset(_1631803), _1631805))))]], 42832 ^ _781404 : [(42833 ^ _781404) ^ [_1631987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631987), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631803)), _1631805))), -(hBOOL(hAPP(_1631807, hAPP(hAPP(c_List_Onth(_1631803), _1631805), _1631987))))]]], (1666 ^ _781404) ^ [_805269, _805271] : [-(class_Groups_Ocancel__semigroup__add(_805269)), _805271 = _805269, class_Groups_Ocancel__semigroup__add(_805271)], (48471 ^ _781404) ^ [_1757885, _1757887, _1757889, _1757891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757885), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757887)), _1757889))), 48477 ^ _781404 : [(48480 ^ _781404) ^ [] : [hBOOL(hAPP(_1757891, 48476 ^ [_1757885, _1757887, _1757889, _1757891]))], (48478 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757887), 48476 ^ [_1757885, _1757887, _1757889, _1757891]), hAPP(c_List_Oset(_1757887), _1757889))))]], -(hBOOL(hAPP(_1757891, hAPP(hAPP(c_List_Onth(_1757887), _1757889), _1757885))))], (35543 ^ _781404) ^ [_1444770, _1444772, _1444774, _1444776, _1444778, _1444780, _1444782, _1444784] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1444770, _1444772, _1444774), _1444776), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1444778, _1444780, tc_prod(_1444770, _1444772)), _1444782), _1444784)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1444778, _1444780, _1444774), hAPP(hAPP(c_COMBB(tc_fun(_1444780, tc_prod(_1444770, _1444772)), tc_fun(_1444780, _1444774), _1444778), hAPP(c_COMBB(tc_prod(_1444770, _1444772), _1444774, _1444780), hAPP(c_Product__Type_Oprod_Oprod__case(_1444770, _1444772, _1444774), _1444776))), _1444782)), _1444784))], (52664 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (47798 ^ _781404) ^ [_1742609, _1742611] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1742609), _1742611) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1742609)), c_List_Oembed__list(_1742611))))], (20213 ^ _781404) ^ [_1140287, _1140289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1140287)), c_Int_OBit0(_1140289))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140287), _1140289)))], (20647 ^ _781404) ^ [_1147474, _1147476] : [class_Rings_Oring__1__no__zero__divisors(_1147474), 20650 ^ _781404 : [(20651 ^ _781404) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1147474), _1147476), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1147474), -(_1147476 = c_Groups_Oone__class_Oone(_1147474)), -(_1147476 = hAPP(c_Groups_Ouminus__class_Ouminus(_1147474), c_Groups_Oone__class_Oone(_1147474)))], (20661 ^ _781404) ^ [] : [20662 ^ _781404 : [(20665 ^ _781404) ^ [] : [_1147476 = hAPP(c_Groups_Ouminus__class_Ouminus(_1147474), c_Groups_Oone__class_Oone(_1147474))], (20663 ^ _781404) ^ [] : [_1147476 = c_Groups_Oone__class_Oone(_1147474)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1147474), _1147476), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1147474))]]], (3426 ^ _781404) ^ [_832551, _832553, _832555, _832557] : [-(c_Enum_Oenum__the(_832557, _832553) = c_Enum_Oenum__the(_832555, _832551)), _832557 = _832555, _832553 = _832551], (6757 ^ _781404) ^ [_889657, _889659, _889661] : [class_Orderings_Olinorder(_889657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889657), _889659), _889661)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889657, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_889657, _889659, _889661)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_889657), _889661)) = hAPP(c_SetInterval_Oord__class_OatLeast(_889657), _889659))], (43631 ^ _781404) ^ [_1650948, _1650950, _1650952, _1650954] : [-(hBOOL(hAPP(hAPP(c_member(_1650948), _1650950), hAPP(c_List_Oset(_1650948), _1650952)))), hBOOL(hAPP(hAPP(c_member(_1650948), _1650950), hAPP(c_List_Oset(_1650948), c_List_Oremove1(_1650948, _1650954, _1650952))))], (6217 ^ _781404) ^ [_880342, _880344, _880346] : [class_Orderings_Olinorder(_880342), 6220 ^ _781404 : [(6227 ^ _781404) ^ [] : [_880344 = _880346, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_880342), _880344) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_880342), _880346))], (6221 ^ _781404) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_880342), _880344) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_880342), _880346), -(_880344 = _880346)]]], (52162 ^ _781404) ^ [_1836258, _1836260] : [class_Complete__Lattice_Ocomplete__lattice(_1836258), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1836260, _1836258)))], (39534 ^ _781404) ^ [_1546259, _1546261] : [-(c_Product__Type_Omap__pair(_1546259, _1546259, _1546261, _1546261, c_Fun_Oid(_1546259), c_Fun_Oid(_1546261)) = c_Fun_Oid(tc_prod(_1546259, _1546261)))], (10027 ^ _781404) ^ [_952582, _952584, _952586] : [class_Orderings_Oorder(_952582), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952582), _952584), _952586)), -(_952584 = _952586), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952582), _952584), _952586)))], (52432 ^ _781404) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (31678 ^ _781404) ^ [_1351449, _1351451] : [-(c_Nitpick_Oint__lcm(_1351449, _1351451) = 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), _1351449)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1351451)))))], (52276 ^ _781404) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (7221 ^ _781404) ^ [_898677, _898679, _898681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898677, tc_HOL_Obool)), _898679), _898681)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898677, tc_HOL_Obool)), _898679), _898681) = _898681)], (5310 ^ _781404) ^ [_862465, _862467, _862469, _862471] : [-(c_Lazy__Sequence_Oflat(_862471, _862467) = c_Lazy__Sequence_Oflat(_862469, _862465)), _862471 = _862469, _862467 = _862465], (42388 ^ _781404) ^ [_1619465, _1619467, _1619469, _1619471] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619465), tc_List_Olist(_1619465))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619465), tc_List_Olist(_1619465)), _1619467), _1619469)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1619465), tc_List_Olist(_1619465)), c_List_Olistrel1(_1619465, _1619471)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619465), tc_List_Olist(_1619465))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619465), tc_List_Olist(_1619465)), _1619467), _1619469)), c_List_Olistrel1(_1619465, hAPP(c_Relation_Oconverse(_1619465, _1619465), _1619471)))))], (51383 ^ _781404) ^ [_1821818, _1821820, _1821822, _1821824, _1821826, _1821828] : [51386 ^ _781404 : [(51393 ^ _781404) ^ [] : [hAPP(hAPP(_1821826, 51384 ^ [_1821818, _1821820, _1821822, _1821824, _1821826, _1821828]), 51388 ^ [_1821818, _1821820, _1821822, _1821824, _1821826, _1821828]) = hAPP(hAPP(_1821826, 51385 ^ [_1821818, _1821820, _1821822, _1821824, _1821826, _1821828]), 51389 ^ [_1821818, _1821820, _1821822, _1821824, _1821826, _1821828])], (51391 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1821822, _1821822)), hAPP(hAPP(c_Product__Type_OPair(_1821822, _1821822), 51388 ^ [_1821818, _1821820, _1821822, _1821824, _1821826, _1821828]), 51389 ^ [_1821818, _1821820, _1821822, _1821824, _1821826, _1821828])), _1821824)))], (51387 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1821818, _1821818)), hAPP(hAPP(c_Product__Type_OPair(_1821818, _1821818), 51384 ^ [_1821818, _1821820, _1821822, _1821824, _1821826, _1821828]), 51385 ^ [_1821818, _1821820, _1821822, _1821824, _1821826, _1821828])), _1821820)))]], -(c_Equiv__Relations_Ocongruent2(_1821818, _1821822, _1821828, _1821820, _1821824, _1821826))], (23391 ^ _781404) ^ [_1200944, _1200946, _1200948, _1200950, _1200952, _1200954] : [class_Divides_Oring__div(_1200944), c_Divides_Odiv__class_Omod(_1200944, _1200946, _1200948) = c_Divides_Odiv__class_Omod(_1200944, _1200950, _1200948), c_Divides_Odiv__class_Omod(_1200944, _1200952, _1200948) = c_Divides_Odiv__class_Omod(_1200944, _1200954, _1200948), -(c_Divides_Odiv__class_Omod(_1200944, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1200944), _1200946), _1200952), _1200948) = c_Divides_Odiv__class_Omod(_1200944, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1200944), _1200950), _1200954), _1200948))], (19281 ^ _781404) ^ [_1124306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1124306), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1124306)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13954 ^ _781404) ^ [_1024741, _1024743] : [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), _1024741), _1024743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024741))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024743)))], (44715 ^ _781404) ^ [_1675893, _1675895, _1675897, _1675899] : [-(hAPP(c_List_Ofoldl(_1675893, _1675895, _1675897, _1675899), c_List_Olist_ONil(_1675895)) = _1675899)], (33079 ^ _781404) ^ [_1378070, _1378072, _1378074, _1378076, _1378078, _1378080] : [hBOOL(hAPP(hAPP(c_member(_1378070), _1378072), _1378074)), hBOOL(hAPP(hAPP(c_member(_1378076), _1378078), hAPP(_1378080, _1378072))), -(hBOOL(hAPP(hAPP(c_member(_1378076), _1378078), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378070, tc_fun(_1378076, tc_HOL_Obool)), _1378074), _1378080))))], (45684 ^ _781404) ^ [_1696680, _1696682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1696680)), hAPP(c_Code__Numeral_Onat__of, _1696682))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1696680), _1696682)))], (35784 ^ _781404) ^ [_1449407, _1449409, _1449411, _1449413] : [-(hAPP(c_Nat_Onat_Onat__rec(_1449407, _1449409, _1449411), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1449413)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1449407), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1449413))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1449407, _1449407), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1449407, tc_fun(_1449407, _1449407)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1449407, tc_fun(_1449407, _1449407)), tc_Int_Oint), c_If(_1449407)), c_Nat__Numeral_Oneg)), _1449409)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1449407, _1449407), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1449407, _1449407), tc_Int_Oint), _1449411), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1449407, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1449407, _1449409, _1449411)), c_Int_Onat)))))], (46414 ^ _781404) ^ [_1712742, _1712744] : [46416 ^ _781404 : [(46419 ^ _781404) ^ [] : [46415 ^ [_1712742, _1712744] = c_List_Olist_ONil(_1712742)], (46417 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1712742)), 46415 ^ [_1712742, _1712744]), hAPP(c_List_Oset(tc_List_Olist(_1712742)), _1712744))))]], -(c_List_Oconcat(_1712742, _1712744) = c_List_Olist_ONil(_1712742))], (7245 ^ _781404) ^ [_899232, _899234, _899236, _899238, _899240] : [class_Lattices_Osemilattice__sup(_899232), class_Lattices_Osemilattice__sup(_899234), c_Orderings_Oorder__class_Omono(_899234, _899232, _899236), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899232), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899232), hAPP(_899236, _899238)), hAPP(_899236, _899240))), hAPP(_899236, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899234), _899238), _899240)))))], (2190 ^ _781404) ^ [_813201, _813203, _813205, _813207] : [-(c_Random_Olog(_813207, _813203) = c_Random_Olog(_813205, _813201)), _813207 = _813205, _813203 = _813201], (36524 ^ _781404) ^ [_1463969, _1463971, _1463973, _1463975, _1463977] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1463969, _1463971, _1463973), _1463975), _1463977) = hAPP(hAPP(_1463975, hAPP(c_Product__Type_Ofst(_1463969, _1463971), _1463977)), hAPP(c_Product__Type_Osnd(_1463969, _1463971), _1463977)))], (13634 ^ _781404) ^ [_1019030, _1019032, _1019034] : [class_Groups_Oordered__comm__monoid__add(_1019030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019030), c_Groups_Ozero__class_Ozero(_1019030)), _1019032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019030), c_Groups_Ozero__class_Ozero(_1019030)), _1019034)), 13645 ^ _781404 : [(13654 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019030), _1019032), _1019034) = c_Groups_Ozero__class_Ozero(_1019030)), _1019032 = c_Groups_Ozero__class_Ozero(_1019030), _1019034 = c_Groups_Ozero__class_Ozero(_1019030)], (13646 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019030), _1019032), _1019034) = c_Groups_Ozero__class_Ozero(_1019030), 13649 ^ _781404 : [(13652 ^ _781404) ^ [] : [-(_1019034 = c_Groups_Ozero__class_Ozero(_1019030))], (13650 ^ _781404) ^ [] : [-(_1019032 = c_Groups_Ozero__class_Ozero(_1019030))]]]]], (44613 ^ _781404) ^ [_1673814, _1673816, _1673818] : [hBOOL(hAPP(c_List_Odistinct(_1673814), hAPP(c_List_Orotate(_1673814, _1673816), _1673818))), -(hBOOL(hAPP(c_List_Odistinct(_1673814), _1673818)))], (4240 ^ _781404) ^ [_845660, _845662] : [_845662 = _845660, -(c_List_Orev(_845662) = c_List_Orev(_845660))], (34327 ^ _781404) ^ [_1416615, _1416617, _1416619, _1416621, _1416623] : [hBOOL(hAPP(hAPP(c_member(_1416615), _1416617), _1416619)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1416621, tc_HOL_Obool)), hAPP(_1416623, _1416617)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416615, tc_fun(_1416621, tc_HOL_Obool)), _1416619), _1416623)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416615, tc_fun(_1416621, tc_HOL_Obool)), _1416619), _1416623))], (9957 ^ _781404) ^ [_951476, _951478, _951480, _951482] : [class_Orderings_Oorder(_951476), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951476), _951478), _951480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951476), _951482), _951478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951476), _951482), _951480)))], (45499 ^ _781404) ^ [_1692899, _1692901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1692899)), hAPP(c_Code__Numeral_Oof__nat, _1692901))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692899), _1692901)))], (44140 ^ _781404) ^ [_1662144, _1662146, _1662148, _1662150, _1662152] : [-(hAPP(hAPP(c_List_Olist__update(_1662144, hAPP(hAPP(c_List_Oappend(_1662144), _1662146), hAPP(hAPP(c_List_Olist_OCons(_1662144), _1662148), _1662150))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662144)), _1662146)), _1662152) = hAPP(hAPP(c_List_Oappend(_1662144), _1662146), hAPP(hAPP(c_List_Olist_OCons(_1662144), _1662152), _1662150)))], (49798 ^ _781404) ^ [_1786701] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1786701, tc_HOL_Obool) = c_Set_OBex(_1786701))], (35035 ^ _781404) ^ [_1433719, _1433721] : [-(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), _1433719)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1433721), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1433719))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (40962 ^ _781404) ^ [_1581178, _1581180, _1581182, _1581184, _1581186, _1581188, _1581190] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1581178, _1581180, _1581182, _1581184), _1581186), _1581188), _1581190) = hAPP(hAPP(_1581188, hAPP(c_Product__Type_Ofst(_1581180, _1581182), hAPP(_1581186, _1581190))), hAPP(c_Product__Type_Osnd(_1581180, _1581182), hAPP(_1581186, _1581190))))], (40391 ^ _781404) ^ [_1567985, _1567987] : [40393 ^ _781404 : [(40396 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1567987), 40392 ^ [_1567985, _1567987]))], (40394 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 40392 ^ [_1567985, _1567987]), _1567985)))]], -(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)), _1567987), _1567985))], (36283 ^ _781404) ^ [_1458723, _1458725, _1458727] : [36285 ^ _781404 : [(36288 ^ _781404) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1458727, 36284 ^ [_1458723, _1458725, _1458727]))], (36286 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458723), 36284 ^ [_1458723, _1458725, _1458727]), _1458725)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458723, tc_Int_Oint), _1458727), _1458725) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458723, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1458723), c_Int_Onat), _1458727)), _1458725)))], (46556 ^ _781404) ^ [_1716747, _1716749, _1716751, _1716753, _1716755] : [-(hAPP(c_List_Ofilter(_1716747, _1716749), hAPP(hAPP(c_List_Omap(_1716751, _1716747), _1716753), _1716755)) = hAPP(hAPP(c_List_Omap(_1716751, _1716747), _1716753), hAPP(c_List_Ofilter(_1716751, hAPP(c_Fun_Ocomp(_1716747, tc_HOL_Obool, _1716751, _1716749), _1716753)), _1716755)))], (48919 ^ _781404) ^ [_1766680, _1766682, _1766684, _1766686, _1766688, _1766690, _1766692] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1766680, _1766682, _1766684, _1766686, _1766688, _1766690, _1766692) = c_New__DSequence_Oneg__decr__bind(_1766680, _1766682, hAPP(hAPP(hAPP(_1766684, _1766688), _1766690), _1766692), hAPP(hAPP(c_COMBC(_1766680, 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(_1766682)))), hAPP(hAPP(c_COMBC(_1766680, 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(_1766682))))), hAPP(hAPP(c_COMBC(_1766680, 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(_1766682)))))), _1766686), _1766688)), _1766690)), _1766692)))], (30075 ^ _781404) ^ [_1320691, _1320693, _1320695, _1320697, _1320699] : [class_Groups_Ocomm__monoid__mult(_1320691), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320693), _1320695)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1320693, _1320691), _1320697), hAPP(hAPP(c_Set_Oinsert(_1320693), _1320699), _1320695)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1320691), hAPP(_1320697, _1320699)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1320693, _1320691), _1320697), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320693, tc_HOL_Obool)), _1320695), hAPP(hAPP(c_Set_Oinsert(_1320693), _1320699), c_Orderings_Obot__class_Obot(tc_fun(_1320693, tc_HOL_Obool)))))))], (34823 ^ _781404) ^ [_1428663, _1428665] : [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(_1428665))), 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)), _1428663))))), -(hAPP(c_Nat_OSuc, _1428663) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428665))], (48999 ^ _781404) ^ [_1768806, _1768808, _1768810, _1768812, _1768814] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1768806, _1768808, _1768810), _1768812), _1768814)), -(hBOOL(hAPP(hAPP(_1768810, _1768814), _1768812)))], (35662 ^ _781404) ^ [_1447007, _1447009] : [-(c_Divides_Odivmod__nat(_1447009, _1447007) = 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), _1447009), _1447007), _1447007))), -(_1447007 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1447009), _1447007)))], (14500 ^ _781404) ^ [_1035404, _1035406, _1035408, _1035410] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1035404), _1035406)), c_Fun_Oinj__on(_1035408, _1035404, _1035410, c_Orderings_Otop__class_Otop(tc_fun(_1035408, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035408), hAPP(c_Set_Ovimage(_1035408, _1035404, _1035410), _1035406))))], (37617 ^ _781404) ^ [_1490847, _1490849, _1490851] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490847), hAPP(hAPP(c_Set_Oinsert(_1490847), _1490849), c_Orderings_Obot__class_Obot(tc_fun(_1490847, tc_HOL_Obool)))), _1490851) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1490847, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1490847, _1490847, _1490851), hAPP(hAPP(c_Set_Oinsert(_1490847), _1490849), c_Orderings_Obot__class_Obot(tc_fun(_1490847, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1490847, tc_HOL_Obool), tc_HOL_Obool))))], (45676 ^ _781404) ^ [] : [-(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))))], (52376 ^ _781404) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (43659 ^ _781404) ^ [_1651362, _1651364, _1651366] : [-(hAPP(hAPP(c_List_Otake(_1651362), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1651362), _1651364), _1651366)) = hAPP(hAPP(c_List_Olist_OCons(_1651362), _1651364), c_List_Olist_ONil(_1651362)))], (51173 ^ _781404) ^ [_1815859, _1815861, _1815863, _1815865, _1815867] : [hBOOL(hAPP(_1815859, hAPP(hAPP(c_Product__Type_OPair(_1815861, _1815863), _1815865), _1815867))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1815861, _1815863, tc_HOL_Obool, _1815859), _1815865), _1815867)))], (43858 ^ _781404) ^ [_1656141, _1656143, _1656145, _1656147, _1656149] : [-(hAPP(hAPP(c_List_Olist_OCons(_1656141), _1656143), _1656145) = hAPP(hAPP(c_List_Oappend(_1656141), _1656147), _1656149)), 43859 ^ _781404 : [(43866 ^ _781404) ^ [_1656324] : [hAPP(hAPP(c_List_Olist_OCons(_1656141), _1656143), _1656324) = _1656147, _1656145 = hAPP(hAPP(c_List_Oappend(_1656141), _1656324), _1656149)], (43860 ^ _781404) ^ [] : [_1656147 = c_List_Olist_ONil(_1656141), hAPP(hAPP(c_List_Olist_OCons(_1656141), _1656143), _1656145) = _1656149]]], (19438 ^ _781404) ^ [] : [-(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)))], (38371 ^ _781404) ^ [_1509351, _1509353, _1509355, _1509357, _1509359, _1509361] : [c_Typedef_Otype__definition(_1509351, _1509353, _1509355, _1509357, _1509359), -(hBOOL(hAPP(hAPP(c_member(_1509353), hAPP(_1509355, _1509361)), _1509359)))], (10841 ^ _781404) ^ [_965504, _965506, _965508, _965510] : [class_Orderings_Oorder(_965504), class_Orderings_Olinorder(_965506), c_Orderings_Oorder__class_Ostrict__mono(_965506, _965504, _965508), -(c_Fun_Oinj__on(_965506, _965504, _965508, _965510))], (50033 ^ _781404) ^ [_1792646, _1792648] : [c_Relation_Otrans(_1792646, _1792648), c_Relation_Oantisym(_1792646, _1792648), -(c_Relation_Otrans(_1792646, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1792646, _1792646), tc_HOL_Obool)), _1792648), c_Relation_OId(_1792646))))], (12364 ^ _781404) ^ [_994434, _994436, _994438, _994440] : [hBOOL(hAPP(hAPP(c_member(_994434), _994436), _994438)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994434, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_994434), _994436), _994440)), _994438) = hAPP(hAPP(c_Set_Oinsert(_994434), _994436), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994434, tc_HOL_Obool)), _994440), _994438)))], (46866 ^ _781404) ^ [_1724112, _1724114] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1724112, _1724114) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1724112), hAPP(c_Nat_OSuc, _1724114))))], (22753 ^ _781404) ^ [_1188124, _1188126, _1188128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188124), _1188126)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188128), _1188126))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1188124), _1188128)))], (9254 ^ _781404) ^ [_939522, _939524, _939526, _939528] : [class_Orderings_Oorder(_939522), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939522, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_939522, _939524, _939526)), c_SetInterval_Oord__class_OgreaterThanLessThan(_939522, _939526, _939528)) = c_Orderings_Obot__class_Obot(tc_fun(_939522, tc_HOL_Obool)))], (52446 ^ _781404) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (45926 ^ _781404) ^ [_1702558, _1702560, _1702562, _1702564, _1702566, _1702568, _1702570] : [c_List_Olist__all2(_1702558, _1702566, hAPP(hAPP(c_COMBC(_1702558, tc_fun(_1702566, _1702560), tc_fun(_1702566, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1702560, tc_HOL_Obool), tc_fun(tc_fun(_1702566, _1702560), tc_fun(_1702566, tc_HOL_Obool)), _1702558), c_COMBB(_1702560, tc_HOL_Obool, _1702566)), _1702562)), _1702568), _1702564, _1702570), -(c_List_Olist__all2(_1702558, _1702560, _1702562, _1702564, hAPP(hAPP(c_List_Omap(_1702566, _1702560), _1702568), _1702570)))], (47685 ^ _781404) ^ [_1740296, _1740298, _1740300] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740296)), c_List_OtakeWhile(_1740296, _1740298, _1740300))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740296)), _1740300))))], (44934 ^ _781404) ^ [_1680694, _1680696, _1680698, _1680700, _1680702] : [class_Orderings_Olinorder(_1680694), 44937 ^ _781404 : [(44946 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1680696), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680696, _1680694, _1680698), _1680700), _1680702)))), -(hBOOL(hAPP(hAPP(c_member(_1680696), _1680700), hAPP(c_List_Oset(_1680696), _1680702)))), hBOOL(hAPP(c_List_Odistinct(_1680696), _1680702))], (44938 ^ _781404) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1680696), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680696, _1680694, _1680698), _1680700), _1680702))), 44941 ^ _781404 : [(44944 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1680696), _1680702)))], (44942 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1680696), _1680700), hAPP(c_List_Oset(_1680696), _1680702)))]]]]], (1006 ^ _781404) ^ [_796451, _796453, _796455, _796457, _796459, _796461, _796463, _796465, _796467, _796469] : [-(c_Fun_Obij__betw(_796467, _796463, _796459, _796455, _796451)), c_Fun_Obij__betw(_796469, _796465, _796461, _796457, _796453), _796469 = _796467, _796465 = _796463, _796461 = _796459, _796457 = _796455, _796453 = _796451], (33059 ^ _781404) ^ [_1377645, _1377647, _1377649, _1377651] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1377649), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377645, tc_fun(_1377649, tc_HOL_Obool)), _1377647), _1377651)))), 33060 ^ _781404 : [(33061 ^ _781404) ^ [_1377719] : [hBOOL(hAPP(hAPP(c_member(_1377645), _1377719), _1377647)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377649), hAPP(_1377651, _1377719)))]]], (39099 ^ _781404) ^ [_1528831, _1528833, _1528835] : [-(hBOOL(hAPP(_1528831, _1528833))), -(hAPP(c_Set_OCollect(_1528835), hAPP(hAPP(c_COMBS(_1528835, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1528835), c_fconj), hAPP(c_fequal, _1528833))), _1528831)) = c_Orderings_Obot__class_Obot(tc_fun(_1528835, tc_HOL_Obool)))], (43537 ^ _781404) ^ [_1649255, _1649257] : [-(c_List_Olist_Olist__size(_1649255, _1649257, c_List_Olist_ONil(_1649255)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34309 ^ _781404) ^ [_1416229, _1416231, _1416233, _1416235, _1416237] : [-(_1416229 = c_Orderings_Obot__class_Obot(tc_fun(_1416231, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1416233, tc_HOL_Obool)), _1416235), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416231, tc_fun(_1416233, tc_HOL_Obool)), _1416229), _1416237)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416231, tc_fun(_1416233, tc_HOL_Obool)), _1416229), hAPP(hAPP(c_COMBB(tc_fun(_1416233, tc_HOL_Obool), tc_fun(_1416233, tc_HOL_Obool), _1416231), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1416233, tc_HOL_Obool)), _1416235)), _1416237)))], (1986 ^ _781404) ^ [_809269, _809271] : [-(hBOOL(_809269)), _809271 = _809269, hBOOL(_809271)], (51181 ^ _781404) ^ [_1816025, _1816027, _1816029, _1816031] : [-(c_Product__Type_Ocurry(_1816025, _1816027, _1816029, hAPP(c_Product__Type_Oprod_Oprod__case(_1816025, _1816027, _1816029), _1816031)) = _1816031)], (1876 ^ _781404) ^ [_807894, _807896] : [-(class_Rings_Omult__zero(_807894)), _807896 = _807894, class_Rings_Omult__zero(_807896)], (46812 ^ _781404) ^ [_1723114, _1723116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723114)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723116))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723114), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723116)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723114)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723114)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1723116))))], (49705 ^ _781404) ^ [_1784842, _1784844] : [c_Relation_Otrans(_1784842, _1784844), -(c_Transitive__Closure_Otrancl(_1784842, _1784844) = _1784844)], (36412 ^ _781404) ^ [_1461612, _1461614, _1461616, _1461618, _1461620, _1461622] : [c_Finite__Set_Ofolding(_1461612, _1461614, _1461616, _1461618), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461612), _1461620)), -(hAPP(_1461618, hAPP(hAPP(c_Set_Oinsert(_1461612), _1461622), _1461620)) = hAPP(c_Fun_Ocomp(_1461614, _1461614, _1461614, hAPP(_1461618, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461612, tc_HOL_Obool)), _1461620), hAPP(hAPP(c_Set_Oinsert(_1461612), _1461622), c_Orderings_Obot__class_Obot(tc_fun(_1461612, tc_HOL_Obool)))))), hAPP(_1461616, _1461622)))], (42969 ^ _781404) ^ [_1636669, _1636671, _1636673, _1636675, _1636677, _1636679] : [-(hAPP(hAPP(c_List_Ozip(_1636669, _1636671), hAPP(hAPP(c_List_Olist_OCons(_1636669), _1636673), _1636675)), hAPP(hAPP(c_List_Olist_OCons(_1636671), _1636677), _1636679)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1636669, _1636671)), hAPP(hAPP(c_Product__Type_OPair(_1636669, _1636671), _1636673), _1636677)), hAPP(hAPP(c_List_Ozip(_1636669, _1636671), _1636675), _1636679)))], (34227 ^ _781404) ^ [_1412388, _1412390, _1412392, _1412394, _1412396] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412388, tc_fun(_1412390, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412388, tc_HOL_Obool)), _1412392), _1412394)), _1412396) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412390, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412388, tc_fun(_1412390, tc_HOL_Obool)), _1412392), _1412396)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412388, tc_fun(_1412390, tc_HOL_Obool)), _1412394), _1412396)))], (13117 ^ _781404) ^ [_1009125, _1009127] : [class_Groups_Ocomm__monoid__add(_1009125), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009125), c_Groups_Ozero__class_Ozero(_1009125)), _1009127) = _1009127)], (18111 ^ _781404) ^ [_1104071, _1104073] : [18112 ^ _781404 : [(18115 ^ _781404) ^ [] : [_1104073 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18113 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1104071))]], -(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), _1104071), _1104073))))], (26339 ^ _781404) ^ [_1251286, _1251288] : [c_Nat__Transfer_Ois__nat(_1251286), c_Nat__Transfer_Ois__nat(_1251288), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1251286), _1251288)))], (18319 ^ _781404) ^ [_1107703, _1107705, _1107707, _1107709, _1107711, _1107713] : [c_Finite__Set_Ofun__left__comm(_1107703, _1107705, _1107707), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107703), _1107709)), hBOOL(hAPP(hAPP(c_member(_1107703), _1107711), _1107709)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1107703, _1107705, _1107707), _1107713), _1107709) = hAPP(hAPP(_1107707, _1107711), hAPP(hAPP(c_Finite__Set_Ofold(_1107703, _1107705, _1107707), _1107713), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1107703, tc_HOL_Obool)), _1107709), hAPP(hAPP(c_Set_Oinsert(_1107703), _1107711), c_Orderings_Obot__class_Obot(tc_fun(_1107703, tc_HOL_Obool)))))))], (33167 ^ _781404) ^ [_1380346, _1380348, _1380350, _1380352] : [class_Rings_Osemiring__1(_1380346), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1380346), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1380348, tc_Nat_Onat), _1380350), _1380352)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1380348, _1380346), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1380346, _1380348), c_Nat_Osemiring__1__class_Oof__nat(_1380346)), _1380350)), _1380352))], (43727 ^ _781404) ^ [_1652859, _1652861] : [-(c_List_Oset__Cons(_1652859, _1652861, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1652859)), c_List_Olist_ONil(_1652859)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1652859), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1652859, tc_List_Olist(_1652859), hAPP(hAPP(c_COMBC(_1652859, tc_List_Olist(_1652859), tc_List_Olist(_1652859)), c_List_Olist_OCons(_1652859)), c_List_Olist_ONil(_1652859))), _1652861))], (43545 ^ _781404) ^ [_1649397, _1649399] : [-(c_List_Olistrelp(_1649397, _1649399, c_List_Olist_ONil(_1649397), c_List_Olist_ONil(_1649397)))], (1956 ^ _781404) ^ [_808894, _808896] : [-(class_Groups_Oone(_808894)), _808896 = _808894, class_Groups_Oone(_808896)], (46637 ^ _781404) ^ [_1718594, _1718596] : [c_List_Otranspose(_1718594, _1718596) = c_List_Olist_ONil(tc_List_Olist(_1718594)), 46640 ^ _781404 : [(46641 ^ _781404) ^ [_1718689] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1718594)), _1718689), hAPP(c_List_Oset(tc_List_Olist(_1718594)), _1718596))), -(_1718689 = c_List_Olist_ONil(_1718594))]]], (35545 ^ _781404) ^ [] : [-(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)))))], (2278 ^ _781404) ^ [_814577, _814579, _814581, _814583] : [-(c_Orderings_Oord_Omin(_814583, _814579) = c_Orderings_Oord_Omin(_814581, _814577)), _814583 = _814581, _814579 = _814577], (20513 ^ _781404) ^ [_1145316] : [class_Rings_Osemiring__1(_1145316), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1145316), c_Groups_Oone__class_Oone(_1145316)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1145316))], (35358 ^ _781404) ^ [_1440455, _1440457, _1440459, _1440461, _1440463, _1440465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1440455, tc_fun(_1440457, tc_HOL_Obool))), _1440459), _1440461)), hBOOL(hAPP(hAPP(_1440459, _1440463), _1440465)), -(hBOOL(hAPP(hAPP(_1440461, _1440463), _1440465)))], (46267 ^ _781404) ^ [_1709917, _1709919] : [c_List_Oremdups(_1709917, _1709919) = c_List_Olist_ONil(_1709917), -(_1709919 = c_List_Olist_ONil(_1709917))], (14711 ^ _781404) ^ [_1039356, _1039358] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039356), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1039356, tc_HOL_Obool), _1039358))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1039356, tc_HOL_Obool)), _1039358)))], (52724 ^ _781404) ^ [_1842072] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1842072)))], (13664 ^ _781404) ^ [_1019501, _1019503, _1019505, _1019507] : [class_Groups_Oordered__comm__monoid__add(_1019501), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019501), c_Groups_Ozero__class_Ozero(_1019501)), _1019503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019501), _1019505), _1019507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019501), _1019505), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019501), _1019503), _1019507))))], (44236 ^ _781404) ^ [_1664557, _1664559, _1664561, _1664563, _1664565, _1664567, _1664569, _1664571] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1664557, _1664557)), hAPP(hAPP(c_Product__Type_OPair(_1664557, _1664557), _1664559), _1664561)), _1664563)), _1664565 = hAPP(hAPP(c_List_Oappend(_1664557), _1664567), hAPP(hAPP(c_List_Olist_OCons(_1664557), _1664559), _1664569)), _1664571 = hAPP(hAPP(c_List_Oappend(_1664557), _1664567), hAPP(hAPP(c_List_Olist_OCons(_1664557), _1664561), _1664569)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664557), tc_List_Olist(_1664557))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664557), tc_List_Olist(_1664557)), _1664565), _1664571)), c_List_Olistrel1(_1664557, _1664563))))], (43935 ^ _781404) ^ [_1657861, _1657863, _1657865, _1657867] : [-(hAPP(hAPP(c_List_Oappend(_1657861), hAPP(hAPP(c_List_Oappend(_1657861), _1657863), _1657865)), _1657867) = hAPP(hAPP(c_List_Oappend(_1657861), _1657863), hAPP(hAPP(c_List_Oappend(_1657861), _1657865), _1657867)))], (2126 ^ _781404) ^ [_812211, _812213, _812215, _812217, _812219, _812221] : [-(c_Power_Opower_Opower(_812221, _812217, _812213) = c_Power_Opower_Opower(_812219, _812215, _812211)), _812221 = _812219, _812217 = _812215, _812213 = _812211], (35996 ^ _781404) ^ [_1453112, _1453114, _1453116, _1453118, _1453120] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1453112, _1453114), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1453116), _1453118))), -(_1453114 = 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), _1453120), _1453112), _1453114), 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), _1453120), _1453116)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1453120), _1453118)), _1453114))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1453120), _1453118), _1453114)))))], (41636 ^ _781404) ^ [_1598566, _1598568, _1598570, _1598572, _1598574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598568, tc_HOL_Obool)), _1598572), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598568, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598566, _1598568, hAPP(c_Relation_Oconverse(_1598568, _1598566), _1598570)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598566, tc_HOL_Obool)), _1598574))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598566, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598568, _1598566, _1598570), _1598572)), _1598574)))], (35299 ^ _781404) ^ [_1439140, _1439142, _1439144, _1439146, _1439148, _1439150, _1439152] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1439140, tc_fun(_1439142, tc_fun(_1439144, tc_HOL_Obool))), _1439146), _1439148), _1439150), _1439152)), 35303 ^ _781404 : [(35306 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1439148, 35302 ^ [_1439140, _1439142, _1439144, _1439146, _1439148, _1439150, _1439152]), _1439150), _1439152)))], (35304 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1439140), 35302 ^ [_1439140, _1439142, _1439144, _1439146, _1439148, _1439150, _1439152]), _1439146)))]]], (46182 ^ _781404) ^ [_1708225, _1708227, _1708229, _1708231] : [46184 ^ _781404 : [(46187 ^ _781404) ^ [] : [hBOOL(hAPP(_1708229, hAPP(hAPP(c_List_Onth(_1708225), _1708227), 46183 ^ [_1708225, _1708227, _1708229, _1708231])))], (46185 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46183 ^ [_1708225, _1708227, _1708229, _1708231]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708225)), _1708227))))]], hBOOL(hAPP(hAPP(c_member(_1708225), _1708231), hAPP(c_List_Oset(_1708225), _1708227))), -(hBOOL(hAPP(_1708229, _1708231)))], (50562 ^ _781404) ^ [_1802834, _1802836, _1802838, _1802840] : [hAPP(c_Set_Oimage(_1802834, _1802836, _1802838), c_Orderings_Otop__class_Otop(tc_fun(_1802834, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1802836, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1802834, _1802836, _1802838), hAPP(c_Set_Oimage(_1802836, _1802834, c_Hilbert__Choice_Oinv__into(_1802834, _1802836, c_Orderings_Otop__class_Otop(tc_fun(_1802834, tc_HOL_Obool)), _1802838)), _1802840)) = _1802840)], (46070 ^ _781404) ^ [_1705572, _1705574, _1705576, _1705578, _1705580] : [-(c_List_Olist__all2(_1705572, _1705574, _1705576, _1705578, _1705580)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705572)), _1705578) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705574)), _1705580), 46076 ^ _781404 : [(46079 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1705576, hAPP(hAPP(c_List_Onth(_1705572), _1705578), 46075 ^ [_1705572, _1705574, _1705576, _1705578, _1705580])), hAPP(hAPP(c_List_Onth(_1705574), _1705580), 46075 ^ [_1705572, _1705574, _1705576, _1705578, _1705580])))], (46077 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46075 ^ [_1705572, _1705574, _1705576, _1705578, _1705580]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705572)), _1705578))))]]], (26833 ^ _781404) ^ [_1260299, _1260301, _1260303, _1260305, _1260307, _1260309, _1260311] : [c_Big__Operators_Ocomm__monoid__big(_1260299, _1260301, _1260303, _1260305, _1260307), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260301), _1260309))), -(hAPP(hAPP(_1260307, _1260311), _1260309) = _1260305)], (2636 ^ _781404) ^ [_820298, _820300] : [_820300 = _820298, -(c_Nitpick_Oone__frac(_820300) = c_Nitpick_Oone__frac(_820298))], (35029 ^ _781404) ^ [_1433562, _1433564] : [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), _1433562))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1433564), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1433562))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1433564), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433562))), 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), _1433564))), c_COMBI(tc_Int_Oint))))], (31990 ^ _781404) ^ [_1357212, _1357214, _1357216, _1357218] : [class_Orderings_Olinorder(_1357212), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357212), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357212), _1357214), _1357216)), _1357218) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357212), _1357214), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357212), _1357216), _1357218)))], (19575 ^ _781404) ^ [_1129427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1129427)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1129427))))], (40845 ^ _781404) ^ [_1577962, _1577964, _1577966, _1577968] : [class_Complete__Lattice_Ocomplete__lattice(_1577962), _1577964 = c_Inductive_Ocomplete__lattice__class_Olfp(_1577962, _1577966), c_Orderings_Oorder__class_Omono(_1577962, _1577962, _1577966), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577962), hAPP(_1577966, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1577962), _1577964), _1577968))), _1577968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577962), _1577964), _1577968)))], (49223 ^ _781404) ^ [_1773565, _1773567, _1773569] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1773565), hAPP(c_COMBK(_1773565, tc_Nat_Onat), _1773567)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1773569)) = c_List_Oreplicate(_1773565, _1773569, _1773567))], (38632 ^ _781404) ^ [_1516274, _1516276, _1516278, _1516280, _1516282, _1516284] : [hBOOL(hAPP(hAPP(c_member(_1516274), _1516276), _1516278)), 38635 ^ _781404 : [(38642 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1516280, tc_HOL_Obool)), _1516282), _1516284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1516280, _1516274), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1516280, _1516274), _1516282), hAPP(c_COMBK(tc_fun(_1516274, tc_HOL_Obool), _1516280), _1516278))), hAPP(hAPP(c_Product__Type_OSigma(_1516280, _1516274), _1516284), hAPP(c_COMBK(tc_fun(_1516274, tc_HOL_Obool), _1516280), _1516278)))))], (38636 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1516280, _1516274), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1516280, _1516274), _1516282), hAPP(c_COMBK(tc_fun(_1516274, tc_HOL_Obool), _1516280), _1516278))), hAPP(hAPP(c_Product__Type_OSigma(_1516280, _1516274), _1516284), hAPP(c_COMBK(tc_fun(_1516274, tc_HOL_Obool), _1516280), _1516278)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1516280, tc_HOL_Obool)), _1516282), _1516284)))]]], (44363 ^ _781404) ^ [_1668137, _1668139] : [-(hAPP(hAPP(c_List_Odrop(_1668137), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1668139) = _1668139)], (23537 ^ _781404) ^ [_1203853, _1203855, _1203857] : [class_Divides_Osemiring__div(_1203853), -(c_Divides_Odiv__class_Omod(_1203853, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1203853), _1203855), _1203857), _1203855) = c_Divides_Odiv__class_Omod(_1203853, _1203857, _1203855))], (40098 ^ _781404) ^ [_1561391, _1561393, _1561395, _1561397] : [c_FunDef_Oreduction__pair(_1561391, _1561393), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561391, _1561391), tc_HOL_Obool)), _1561395), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1561391, _1561391), tc_HOL_Obool), tc_fun(tc_prod(_1561391, _1561391), tc_HOL_Obool)), _1561393))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561391, _1561391), tc_HOL_Obool)), _1561397), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1561391, _1561391), tc_HOL_Obool), tc_fun(tc_prod(_1561391, _1561391), tc_HOL_Obool)), _1561393))), c_Wellfounded_Owf(_1561391, _1561397), -(c_Wellfounded_Owf(_1561391, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1561391, _1561391), tc_HOL_Obool)), _1561395), _1561397)))], (47597 ^ _781404) ^ [_1738477, _1738479, _1738481, _1738483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738477), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738479)), _1738481))), -(hAPP(c_List_Orev(_1738479), hAPP(hAPP(c_List_Olist__update(_1738479, _1738481), _1738477), _1738483)) = hAPP(hAPP(c_List_Olist__update(_1738479, hAPP(c_List_Orev(_1738479), _1738481)), 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(_1738479)), _1738481)), _1738477)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1738483))], (26087 ^ _781404) ^ [_1247430, _1247432] : [c_Nat__Transfer_Onat__set(_1247430), c_Nat__Transfer_Onat__set(_1247432), 26094 ^ _781404 : [(26101 ^ _781404) ^ [] : [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), _1247430)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1247432))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1247430), _1247432)))], (26095 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1247430), _1247432)), -(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), _1247430)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1247432))))]]], (42862 ^ _781404) ^ [_1632632, _1632634, _1632636, _1632638, _1632640] : [hBOOL(hAPP(hAPP(c_member(_1632632), _1632634), hAPP(c_List_Oset(_1632632), _1632636))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1632638), hAPP(_1632640, _1632634))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1632638), c_List_Olist_Olist__size(_1632632, _1632640, _1632636))))], (35233 ^ _781404) ^ [_1437489, _1437491, _1437493, _1437495, _1437497, _1437499] : [35234 ^ _781404 : [(35237 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1437495, _1437491), _1437493))], (35235 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1437489, _1437491), _1437493))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437497, tc_fun(_1437499, tc_HOL_Obool))), _1437495), _1437489), _1437491), _1437493)))], (18791 ^ _781404) ^ [_1116325, _1116327] : [18792 ^ _781404 : [(18795 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116325), c_Int_OPls))], (18793 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116325), _1116327))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1116325)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1116327))))], (17539 ^ _781404) ^ [_1094206, _1094208, _1094210, _1094212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094206), _1094208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094210), _1094212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094206), _1094210)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094208), _1094212))))], (8447 ^ _781404) ^ [_923845, _923847] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923845, tc_HOL_Obool)), _923847), c_Orderings_Obot__class_Obot(tc_fun(_923845, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_923845, tc_HOL_Obool)))], (2120 ^ _781404) ^ [_812126, _812128] : [_812128 = _812126, -(c_Int_Osucc(_812128) = c_Int_Osucc(_812126))], (30286 ^ _781404) ^ [_1325394] : [-(c_Finite__Set_Ofun__left__comm__idem(_1325394, tc_fun(_1325394, tc_HOL_Obool), c_Set_Oinsert(_1325394)))], (48819 ^ _781404) ^ [_1764732, _1764734, _1764736, _1764738] : [c_List_Olist__ex1(_1764732, _1764734, hAPP(hAPP(c_List_Olist_OCons(_1764732), _1764736), _1764738)), 48822 ^ _781404 : [(48829 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1764734, _1764736))), -(c_List_Olist__ex1(_1764732, _1764734, _1764738))], (48823 ^ _781404) ^ [] : [hBOOL(hAPP(_1764734, _1764736)), -(c_List_Olist__all(_1764732, hAPP(hAPP(c_COMBS(_1764732, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1764732), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1764732), c_fNot), _1764734))), hAPP(c_fequal, _1764736)), _1764738))]]], (8485 ^ _781404) ^ [_924503, _924505] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_924503, _924505, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_924503), tc_HOL_Obool))))], (30850 ^ _781404) ^ [_1335970, _1335972, _1335974, _1335976] : [class_Orderings_Olinorder(_1335970), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335970), _1335972), _1335974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335970), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1335970), _1335976), _1335972)), _1335974)))], (39107 ^ _781404) ^ [_1528959, _1528961] : [-(hAPP(c_Set_OCollect(_1528959), hAPP(c_fequal, _1528961)) = hAPP(hAPP(c_Set_Oinsert(_1528959), _1528961), c_Orderings_Obot__class_Obot(tc_fun(_1528959, tc_HOL_Obool))))], (14220 ^ _781404) ^ [_1029748, _1029750, _1029752, _1029754] : [class_Groups_Oordered__comm__monoid__add(_1029748), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029748), c_Groups_Ozero__class_Ozero(_1029748)), _1029750)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029748), _1029752), _1029754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029748), _1029752), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029748), _1029750), _1029754))))], (25925 ^ _781404) ^ [_1244785, _1244787] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244785)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244785)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244787)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244785)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244787))))], (20271 ^ _781404) ^ [_1141276] : [-(c_Int_Osucc(c_Int_OBit0(_1141276)) = c_Int_OBit1(_1141276))], (52420 ^ _781404) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (31784 ^ _781404) ^ [_1353270, _1353272, _1353274] : [class_Orderings_Olinorder(_1353270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1353270, tc_HOL_Obool)), _1353272), _1353274)), -(_1353272 = c_Orderings_Obot__class_Obot(tc_fun(_1353270, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353270), _1353274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1353270), c_Big__Operators_Olinorder__class_OMax(_1353270, _1353272)), c_Big__Operators_Olinorder__class_OMax(_1353270, _1353274))))], (45046 ^ _781404) ^ [_1682600, _1682602, _1682604] : [_1682600 = c_List_Olist_ONil(_1682602), -(c_List_Olast(_1682602, hAPP(hAPP(c_List_Olist_OCons(_1682602), _1682604), _1682600)) = _1682604)], (13123 ^ _781404) ^ [_1009220, _1009222] : [class_Groups_Olinordered__ab__group__add(_1009220), 13126 ^ _781404 : [(13133 ^ _781404) ^ [] : [_1009222 = c_Groups_Ozero__class_Ozero(_1009220), -(c_Groups_Ozero__class_Ozero(_1009220) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009220), _1009222), _1009222))], (13127 ^ _781404) ^ [] : [c_Groups_Ozero__class_Ozero(_1009220) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009220), _1009222), _1009222), -(_1009222 = c_Groups_Ozero__class_Ozero(_1009220))]]], (44770 ^ _781404) ^ [_1677010, _1677012, _1677014, _1677016, _1677018] : [c_Finite__Set_Ofun__left__comm__idem(_1677010, _1677012, _1677014), -(hAPP(hAPP(c_Finite__Set_Ofold(_1677010, _1677012, _1677014), _1677016), hAPP(c_List_Oset(_1677010), _1677018)) = hAPP(c_List_Ofoldl(_1677012, _1677010, hAPP(c_COMBC(_1677010, _1677012, _1677012), _1677014), _1677016), _1677018))], (2550 ^ _781404) ^ [_818935, _818937, _818939, _818941] : [-(c_Divides_Odivmod__nat__rel(_818941, _818937) = c_Divides_Odivmod__nat__rel(_818939, _818935)), _818941 = _818939, _818937 = _818935], (19141 ^ _781404) ^ [_1122016, _1122018] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1122016)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1122018))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1122016), _1122018)))], (26321 ^ _781404) ^ [_1251058] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1251058)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1251058))], (20577 ^ _781404) ^ [_1146427, _1146429] : [class_Rings_Olinordered__idom(_1146427), 20580 ^ _781404 : [(20587 ^ _781404) ^ [] : [-(_1146429 = c_Groups_Ozero__class_Ozero(_1146427)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146427), c_Groups_Ozero__class_Ozero(_1146427)), hAPP(hAPP(c_Power_Opower__class_Opower(_1146427), _1146429), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20581 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146427), c_Groups_Ozero__class_Ozero(_1146427)), hAPP(hAPP(c_Power_Opower__class_Opower(_1146427), _1146429), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1146429 = c_Groups_Ozero__class_Ozero(_1146427)]]], (30035 ^ _781404) ^ [_1319863, _1319865, _1319867, _1319869, _1319871] : [class_Groups_Ocomm__monoid__mult(_1319863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319865), _1319867)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319865), _1319869)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319863), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319865, _1319863), _1319871), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319865, tc_HOL_Obool)), _1319867), _1319869))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319865, _1319863), _1319871), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319865, tc_HOL_Obool)), _1319867), _1319869))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319863), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319865, _1319863), _1319871), _1319867)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319865, _1319863), _1319871), _1319869)))], (43585 ^ _781404) ^ [_1650101, _1650103] : [c_Orderings_Obot__class_Obot(tc_fun(_1650101, tc_HOL_Obool)) = hAPP(c_List_Oset(_1650101), _1650103), -(_1650103 = c_List_Olist_ONil(_1650101))], (25853 ^ _781404) ^ [_1243491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1243491)), -(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, _1243491))))], (35593 ^ _781404) ^ [_1445603, _1445605] : [c_Nitpick_Orefl_H(_1445603, _1445605), 35596 ^ _781404 : [(35597 ^ _781404) ^ [_1445681] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1445603, _1445603)), hAPP(hAPP(c_Product__Type_OPair(_1445603, _1445603), _1445681), _1445681)), _1445605)))]]], (5272 ^ _781404) ^ [_861874, _861876, _861878, _861880] : [-(c_Product__Type_OPair(_861880, _861876) = c_Product__Type_OPair(_861878, _861874)), _861880 = _861878, _861876 = _861874], (48635 ^ _781404) ^ [_1761128, _1761130, _1761132] : [hBOOL(hAPP(hAPP(c_member(_1761128), _1761130), hAPP(c_List_Oset(_1761128), _1761132))), 48640 ^ _781404 : [(48643 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1761128), _1761130), hAPP(c_List_Oset(_1761128), 48639 ^ [_1761128, _1761130, _1761132])))], (48641 ^ _781404) ^ [] : [-(_1761132 = hAPP(hAPP(c_List_Oappend(_1761128), 48638 ^ [_1761128, _1761130, _1761132]), hAPP(hAPP(c_List_Olist_OCons(_1761128), _1761130), 48639 ^ [_1761128, _1761130, _1761132])))]]], (43441 ^ _781404) ^ [_1647620, _1647622, _1647624, _1647626] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647620) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1647622), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647620)), hAPP(hAPP(c_List_Olist_OCons(_1647622), _1647624), _1647626)) = hAPP(hAPP(c_List_Olist_OCons(_1647622), _1647624), hAPP(hAPP(c_List_Otake(_1647622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647620)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1647626)))], (27811 ^ _781404) ^ [_1279024, _1279026] : [class_Rings_Odivision__ring__inverse__zero(_1279024), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279024), _1279026), c_Groups_Ozero__class_Ozero(_1279024)) = c_Groups_Ozero__class_Ozero(_1279024))], (51283 ^ _781404) ^ [_1818012, _1818014, _1818016, _1818018, _1818020] : [hBOOL(hAPP(hAPP(c_member(_1818012), _1818014), _1818016)), -(hAPP(c_Quotient_OBabs(_1818012, _1818018, _1818016, _1818020), _1818014) = hAPP(_1818020, _1818014))], (49868 ^ _781404) ^ [_1789069, _1789071, _1789073, _1789075] : [class_Complete__Lattice_Ocomplete__lattice(_1789069), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1789071, _1789069), _1789073), _1789075) = c_Complete__Lattice_OInf__class_OInf(_1789069, hAPP(c_Set_OCollect(_1789069), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1789071, _1789069), tc_HOL_Obool), tc_HOL_Obool, _1789069), c_HOL_OEx(tc_fun(_1789071, _1789069))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1789071, _1789069), tc_HOL_Obool), tc_fun(tc_fun(_1789071, _1789069), tc_HOL_Obool), _1789069), hAPP(c_COMBS(tc_fun(_1789071, _1789069), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1789071, _1789069)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1789071, _1789069), tc_fun(tc_fun(_1789071, _1789069), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1789071, _1789069))), _1789073)))), hAPP(hAPP(c_COMBC(_1789069, tc_fun(tc_fun(_1789071, _1789069), _1789069), tc_fun(tc_fun(_1789071, _1789069), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1789069, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1789071, _1789069), _1789069), tc_fun(tc_fun(_1789071, _1789069), tc_HOL_Obool)), _1789069), c_COMBB(_1789069, tc_HOL_Obool, tc_fun(_1789071, _1789069))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1789071, _1789069), _1789071, _1789069), c_COMBI(tc_fun(_1789071, _1789069))), _1789075)))))))], (23589 ^ _781404) ^ [_1205011] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1205011) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13111 ^ _781404) ^ [_1009030, _1009032] : [class_Groups_Omonoid__add(_1009030), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009030), c_Groups_Ozero__class_Ozero(_1009030)), _1009032) = _1009032)], (38880 ^ _781404) ^ [_1523247, _1523249, _1523251, _1523253, _1523255, _1523257, _1523259] : [-(hAPP(c_Product__Type_Ofst(_1523247, _1523249), hAPP(c_Product__Type_Omap__pair(_1523251, _1523247, _1523253, _1523249, _1523255, _1523257), _1523259)) = hAPP(_1523255, hAPP(c_Product__Type_Ofst(_1523251, _1523253), _1523259)))], (39111 ^ _781404) ^ [_1529108, _1529110] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529108), hAPP(c_Set_OCollect(_1529108), _1529110))), 39114 ^ _781404 : [(39121 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529108), c_Orderings_Otop__class_Otop(tc_fun(_1529108, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1529108), hAPP(c_Set_OCollect(_1529108), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1529108), c_fNot), _1529110)))))], (39115 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529108), hAPP(c_Set_OCollect(_1529108), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1529108), c_fNot), _1529110)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1529108), c_Orderings_Otop__class_Otop(tc_fun(_1529108, tc_HOL_Obool)))))]]], (50203 ^ _781404) ^ [_1796123, _1796125] : [c_Relation_Osym(_1796123, hAPP(c_Relation_Oconverse(_1796123, _1796123), _1796125)), -(c_Relation_Osym(_1796123, _1796125))], (24680 ^ _781404) ^ [] : [c_Int_OMin = c_Int_OPls], (47541 ^ _781404) ^ [_1737214, _1737216] : [-(hAPP(c_List_Orev(_1737214), hAPP(c_List_Orev(_1737214), _1737216)) = _1737216)], (16698 ^ _781404) ^ [_1078509, _1078511] : [class_Int_Oring__char__0(_1078509), hBOOL(hAPP(hAPP(c_member(_1078509), _1078511), c_Int_Oring__1__class_OInts(_1078509))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078509), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078509), c_Groups_Oone__class_Oone(_1078509)), _1078511)), _1078511) = c_Groups_Ozero__class_Ozero(_1078509)], (25289 ^ _781404) ^ [_1233792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1233792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1233792))))], (48955 ^ _781404) ^ [_1767838, _1767840, _1767842] : [-(hAPP(c_New__DSequence_Opos__single(_1767838, _1767840), _1767842) = hAPP(c_Lazy__Sequence_Osingle(_1767838), _1767840))], (50111 ^ _781404) ^ [_1794186, _1794188] : [c_Relation_Oantisym(_1794186, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1794186, _1794186), tc_HOL_Obool)), _1794188), c_Relation_OId(_1794186))), -(c_Relation_Oantisym(_1794186, _1794188))], (39129 ^ _781404) ^ [_1529478, _1529480] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1529478, tc_HOL_Obool)), _1529480) = hAPP(c_Set_OCollect(_1529478), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1529478), c_fNot), hAPP(hAPP(c_COMBC(_1529478, tc_fun(_1529478, tc_HOL_Obool), tc_HOL_Obool), c_member(_1529478)), _1529480))))], (2110 ^ _781404) ^ [_811977, _811979, _811981, _811983] : [-(c_SMT_Oz3mod(_811983, _811979) = c_SMT_Oz3mod(_811981, _811977)), _811983 = _811981, _811979 = _811977], (28781 ^ _781404) ^ [_1296511, _1296513, _1296515, _1296517] : [class_Fields_Olinordered__field(_1296511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296511), c_Groups_Ozero__class_Ozero(_1296511)), _1296513)), 28788 ^ _781404 : [(28795 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296511), _1296515), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296511), _1296517), _1296513))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296511), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296511), _1296515), _1296513)), _1296517)))], (28789 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296511), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296511), _1296515), _1296513)), _1296517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296511), _1296515), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296511), _1296517), _1296513))))]]], (19342 ^ _781404) ^ [_1125465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1125465)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125465), c_Int_OPls)))], (34541 ^ _781404) ^ [_1421917, _1421919, _1421921] : [class_Groups_Ocomm__monoid__add(_1421917), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1421917), _1421919), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421921))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1421917), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1421917), _1421919), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1421921))), hAPP(_1421919, _1421921)))], (7637 ^ _781404) ^ [_906957] : [-(hAPP(c_Set_OPow(_906957), c_Orderings_Otop__class_Otop(tc_fun(_906957, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_906957, tc_HOL_Obool), tc_HOL_Obool)))], (3094 ^ _781404) ^ [_827417, _827419, _827421, _827423] : [-(c_Wellfounded_Oacc(_827423, _827419) = c_Wellfounded_Oacc(_827421, _827417)), _827423 = _827421, _827419 = _827417], (928 ^ _781404) ^ [_795326, _795328, _795330, _795332] : [-(c_Relation_Osym(_795330, _795326)), c_Relation_Osym(_795332, _795328), _795332 = _795330, _795328 = _795326], (39017 ^ _781404) ^ [_1526843, _1526845, _1526847] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1526843), hAPP(c_Set_OCollect(_1526843), hAPP(hAPP(c_COMBS(_1526843, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526843), c_fdisj), _1526845)), _1526847))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526843), hAPP(c_Set_OCollect(_1526843), _1526845))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526843), hAPP(c_Set_OCollect(_1526843), _1526847)))], (18143 ^ _781404) ^ [_1104658, _1104660, _1104662, _1104664] : [class_Rings_Olinordered__semidom(_1104658), hAPP(hAPP(c_Power_Opower__class_Opower(_1104658), _1104660), hAPP(c_Nat_OSuc, _1104662)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1104658), _1104664), hAPP(c_Nat_OSuc, _1104662)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104658), c_Groups_Ozero__class_Ozero(_1104658)), _1104660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104658), c_Groups_Ozero__class_Ozero(_1104658)), _1104664)), -(_1104660 = _1104664)], (24770 ^ _781404) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18951 ^ _781404) ^ [_1118944, _1118946] : [class_Int_Onumber__ring(_1118944), 18954 ^ _781404 : [(18961 ^ _781404) ^ [] : [c_Int_Oiszero(_1118944, hAPP(c_Int_Onumber__class_Onumber__of(_1118944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1118946), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1118944), _1118946) = c_Groups_Ozero__class_Ozero(_1118944))], (18955 ^ _781404) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1118944), _1118946) = c_Groups_Ozero__class_Ozero(_1118944), -(c_Int_Oiszero(_1118944, hAPP(c_Int_Onumber__class_Onumber__of(_1118944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1118946), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (14677 ^ _781404) ^ [_1038750, _1038752, _1038754] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1038750), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1038750, tc_HOL_Obool)), _1038752), _1038754))), 14680 ^ _781404 : [(14683 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038750), _1038754)))], (14681 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038750), _1038752)))]]], (47543 ^ _781404) ^ [_1737249, _1737251] : [class_Groups_Ocomm__monoid__add(_1737249), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1737249), hAPP(c_List_Orev(_1737249), _1737251)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1737249), _1737251))], (6387 ^ _781404) ^ [_882965, _882967] : [hAPP(c_Nat_OSuc, _882965) = hAPP(c_Nat_OSuc, _882967), -(_882965 = _882967)], (33319 ^ _781404) ^ [_1384371, _1384373, _1384375, _1384377, _1384379] : [_1384371 = c_Orderings_Obot__class_Obot(tc_fun(_1384373, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384375, tc_HOL_Obool)), _1384377), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384373, tc_fun(_1384375, tc_HOL_Obool)), _1384371), _1384379)) = _1384377)], (27319 ^ _781404) ^ [_1269395, _1269397, _1269399, _1269401] : [c_Finite__Set_Ofolding__one(_1269395, _1269397, _1269399), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269395), _1269401)), -(hAPP(_1269399, _1269401) = hAPP(c_Finite__Set_Ofold1(_1269395, _1269397), _1269401))], (8912 ^ _781404) ^ [_932173] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _932173), hAPP(c_Nat_OSuc, _932173)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _932173), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (29719 ^ _781404) ^ [_1313727, _1313729, _1313731, _1313733] : [class_Fields_Olinordered__field(_1313727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1313727), _1313729), c_Groups_Ozero__class_Ozero(_1313727))), 29726 ^ _781404 : [(29733 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313727), _1313733), _1313729)), _1313731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313727), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313727), _1313731), _1313729)), _1313733)))], (29727 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313727), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313727), _1313731), _1313729)), _1313733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313727), _1313733), _1313729)), _1313731)))]]], (24750 ^ _781404) ^ [_1225306] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1225306), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1225306)], (4092 ^ _781404) ^ [_843312, _843314, _843316, _843318, _843320, _843322, _843324, _843326] : [-(c_New__Random__Sequence_Oneg__bind(_843326, _843322, _843318, _843314) = c_New__Random__Sequence_Oneg__bind(_843324, _843320, _843316, _843312)), _843326 = _843324, _843322 = _843320, _843318 = _843316, _843314 = _843312], (4834 ^ _781404) ^ [_854999, _855001] : [_855001 = _854999, -(c_Set_OBex(_855001) = c_Set_OBex(_854999))], (47583 ^ _781404) ^ [_1738040, _1738042] : [-(hAPP(c_List_Orev(_1738040), _1738042) = hAPP(c_List_Ofoldl(tc_List_Olist(_1738040), _1738040, hAPP(c_COMBC(_1738040, tc_List_Olist(_1738040), tc_List_Olist(_1738040)), c_List_Olist_OCons(_1738040)), c_List_Olist_ONil(_1738040)), _1738042))], (11577 ^ _781404) ^ [_979419, _979421, _979423, _979425] : [hBOOL(hAPP(hAPP(c_member(_979419), _979421), _979423)), hBOOL(hAPP(hAPP(c_member(_979419), _979421), _979425)), -(hBOOL(hAPP(hAPP(c_member(_979419), _979421), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979419, tc_HOL_Obool)), _979423), _979425))))], (42149 ^ _781404) ^ [_1611796, _1611798, _1611800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1611796), c_Nitpick_Oplus__frac(_1611796, _1611798, c_Nitpick_Ouminus__frac(_1611796, _1611800)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1611796, _1611798, _1611800))], (36251 ^ _781404) ^ [_1458034, _1458036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1458034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1458036), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1458034, _1458036) = 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), _1458034), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1458036)))))], (52384 ^ _781404) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (41868 ^ _781404) ^ [_1604016, _1604018, _1604020] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604016, _1604016)), _1604018), c_Transitive__Closure_Ortrancl(_1604016, _1604020))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604016, _1604016)), _1604018), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604016, _1604016), tc_HOL_Obool), 41871 ^ [_1604016, _1604018, _1604020]), _1604020))))], (16444 ^ _781404) ^ [_1073561, _1073563, _1073565, _1073567] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1073561, _1073563)), c_Sum__Type_OPlus(_1073561, _1073563, _1073565, _1073567))), 16447 ^ _781404 : [(16450 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1073563), _1073567)))], (16448 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1073561), _1073565)))]]], (17583 ^ _781404) ^ [_1094891, _1094893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1094891)), _1094893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094891), _1094893)))], (9008 ^ _781404) ^ [_934129, _934131, _934133, _934135, _934137] : [class_Groups_Oab__group__add(_934129), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_934129), _934131), _934133) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_934129), _934135), _934137), 9015 ^ _781404 : [(9022 ^ _781404) ^ [] : [_934135 = _934137, -(_934131 = _934133)], (9016 ^ _781404) ^ [] : [_934131 = _934133, -(_934135 = _934137)]]], (15539 ^ _781404) ^ [_1056413, _1056415, _1056417, _1056419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1056413), hAPP(c_Set_Oimage(_1056415, _1056413, _1056417), _1056419))), hAPP(c_Finite__Set_Ocard(_1056415), _1056419))), c_Fun_Oinj__on(_1056415, _1056413, _1056417, _1056419)], (22181 ^ _781404) ^ [_1176615, _1176617, _1176619] : [class_Rings_Ocomm__semiring__1(_1176615), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176615), _1176617), hAPP(hAPP(c_Power_Opower__class_Opower(_1176615), _1176617), _1176619)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1176615), _1176617), hAPP(c_Nat_OSuc, _1176619)))], (6149 ^ _781404) ^ [_879114, _879116, _879118] : [class_Orderings_Olinorder(_879114), 6152 ^ _781404 : [(6159 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879114), _879116), _879118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879114, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_879114), _879116)), hAPP(c_SetInterval_Oord__class_OlessThan(_879114), _879118))))], (6153 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879114, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_879114), _879116)), hAPP(c_SetInterval_Oord__class_OlessThan(_879114), _879118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879114), _879116), _879118)))]]], (12812 ^ _781404) ^ [_1003426, _1003428, _1003430, _1003432, _1003434] : [class_Groups_Oab__group__add(_1003426), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003428), _1003430)), 12819 ^ _781404 : [(12826 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1003428), _1003432), _1003430))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003428, _1003426), _1003434), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1003428, tc_HOL_Obool)), _1003430), hAPP(hAPP(c_Set_Oinsert(_1003428), _1003432), c_Orderings_Obot__class_Obot(tc_fun(_1003428, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003428, _1003426), _1003434), _1003430))], (12820 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1003428), _1003432), _1003430)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003428, _1003426), _1003434), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1003428, tc_HOL_Obool)), _1003430), hAPP(hAPP(c_Set_Oinsert(_1003428), _1003432), c_Orderings_Obot__class_Obot(tc_fun(_1003428, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1003426), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003428, _1003426), _1003434), _1003430)), hAPP(_1003434, _1003432)))]]], (40200 ^ _781404) ^ [_1563945, _1563947, _1563949, _1563951] : [40202 ^ _781404 : [(40205 ^ _781404) ^ [] : [c_Wellfounded_Owf(_1563947, hAPP(_1563949, 40201 ^ [_1563945, _1563947, _1563949, _1563951]))], (40203 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1563945, 40201 ^ [_1563945, _1563947, _1563949, _1563951])))]], -(c_Wellfounded_Owf(tc_prod(_1563951, _1563947), c_Recdef_Osame__fst(_1563951, _1563947, _1563945, _1563949)))], (26186 ^ _781404) ^ [_1248887, _1248889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248887)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1248887, _1248889)))], (33101 ^ _781404) ^ [_1378589, _1378591] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1378589), hAPP(c_Nat_OSuc, _1378591)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1378591), 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)), _1378591)), _1378589))], (15238 ^ _781404) ^ [_1050353, _1050355] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1050353, tc_HOL_Obool)), _1050355)), 15244 ^ _781404 : [(15247 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050353), 15243 ^ [_1050353, _1050355]))], (15245 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1050353, tc_HOL_Obool)), 15243 ^ [_1050353, _1050355]), _1050355)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050353), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1050353, tc_HOL_Obool), _1050355))))], (17036 ^ _781404) ^ [_1084773, _1084775] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1084773), _1084775)), 17042 ^ _781404 : [(17045 ^ _781404) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17043 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1084773), 17041 ^ [_1084773, _1084775]), _1084775)))]], -(hAPP(c_Finite__Set_Ocard(_1084773), _1084775) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51302 ^ _781404) ^ [_1818528, _1818530, _1818532, _1818534, _1818536] : [51304 ^ _781404 : [(51307 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1818532, tc_HOL_Obool)), _1818534), hAPP(_1818536, 51303 ^ [_1818528, _1818530, _1818532, _1818534, _1818536])))], (51305 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1818528), 51303 ^ [_1818528, _1818530, _1818532, _1818534, _1818536]), _1818530)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1818532, tc_HOL_Obool)), _1818534), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1818528, tc_fun(_1818532, tc_HOL_Obool)), _1818530), _1818536))))], (2156 ^ _781404) ^ [_812666, _812668, _812670, _812672] : [-(c_Nat__Transfer_Otsub(_812672, _812668) = c_Nat__Transfer_Otsub(_812670, _812666)), _812672 = _812670, _812668 = _812666], (23563 ^ _781404) ^ [_1204458, _1204460, _1204462, _1204464] : [class_Divides_Osemiring__div(_1204458), -(c_Divides_Odiv__class_Omod(_1204458, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204458), _1204460), c_Divides_Odiv__class_Omod(_1204458, _1204462, _1204464)), _1204464) = c_Divides_Odiv__class_Omod(_1204458, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204458), _1204460), _1204462), _1204464))], (7407 ^ _781404) ^ [_902321, _902323] : [class_Lattices_Oboolean__algebra(_902321), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902321), hAPP(c_Groups_Ouminus__class_Ouminus(_902321), _902323)), _902323) = c_Orderings_Otop__class_Otop(_902321))], (36346 ^ _781404) ^ [_1460256, _1460258, _1460260, _1460262, _1460264, _1460266] : [c_Finite__Set_Ofolding(_1460256, _1460258, _1460260, _1460262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460256), _1460264)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460256), _1460266)), -(hAPP(c_Fun_Ocomp(_1460258, _1460258, _1460258, hAPP(_1460262, _1460266)), hAPP(_1460262, _1460264)) = hAPP(c_Fun_Ocomp(_1460258, _1460258, _1460258, hAPP(_1460262, _1460264)), hAPP(_1460262, _1460266)))], (17085 ^ _781404) ^ [_1085796, _1085798, _1085800, _1085802, _1085804, _1085806, _1085808, _1085810] : [class_Groups_Ocomm__monoid__add(_1085796), class_Orderings_Oord(_1085798), _1085800 = _1085802, _1085804 = _1085806, 17103 ^ _781404 : [(17108 ^ _781404) ^ [] : [hAPP(_1085808, 17102 ^ [_1085796, _1085798, _1085800, _1085802, _1085804, _1085806, _1085808, _1085810]) = hAPP(_1085810, 17102 ^ [_1085796, _1085798, _1085800, _1085802, _1085804, _1085806, _1085808, _1085810])], (17106 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085798), 17102 ^ [_1085796, _1085798, _1085800, _1085802, _1085804, _1085806, _1085808, _1085810]), _1085806)))], (17104 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085798), _1085802), 17102 ^ [_1085796, _1085798, _1085800, _1085802, _1085804, _1085806, _1085808, _1085810])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085798, _1085796), _1085808), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1085798, _1085800), _1085804)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085798, _1085796), _1085810), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1085798, _1085802), _1085806)))], (5819 ^ _781404) ^ [_873680, _873682, _873684, _873686] : [hBOOL(hAPP(_873680, _873682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873684, tc_HOL_Obool)), _873680), _873686)), -(hBOOL(hAPP(_873686, _873682)))], (36211 ^ _781404) ^ [_1457333, _1457335, _1457337] : [-(hAPP(c_Product__Type_Osnd(_1457333, _1457335), _1457337) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1457333, _1457335, _1457335), hAPP(c_COMBK(tc_fun(_1457335, _1457335), _1457333), c_COMBI(_1457335))), _1457337))], (19589 ^ _781404) ^ [_1129658, _1129660] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1129658)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1129660))))), _1129658 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1129660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2816 ^ _781404) ^ [_823122, _823124, _823126, _823128, _823130, _823132] : [-(c_Predicate_ORangeP(_823132, _823128, _823124) = c_Predicate_ORangeP(_823130, _823126, _823122)), _823132 = _823130, _823128 = _823126, _823124 = _823122], (5616 ^ _781404) ^ [_867252, _867254, _867256, _867258] : [-(c_COMBK(_867258, _867254) = c_COMBK(_867256, _867252)), _867258 = _867256, _867254 = _867252], (27528 ^ _781404) ^ [_1272955, _1272957, _1272959] : [class_Lattices_Oab__semigroup__idem__mult(_1272955), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272955), _1272957)), -(_1272957 = c_Orderings_Obot__class_Obot(tc_fun(_1272955, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272955), _1272959)), -(_1272959 = c_Orderings_Obot__class_Obot(tc_fun(_1272955, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1272955, c_Groups_Otimes__class_Otimes(_1272955)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272955, tc_HOL_Obool)), _1272957), _1272959)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272955), hAPP(c_Finite__Set_Ofold1(_1272955, c_Groups_Otimes__class_Otimes(_1272955)), _1272957)), hAPP(c_Finite__Set_Ofold1(_1272955, c_Groups_Otimes__class_Otimes(_1272955)), _1272959)))], (37376 ^ _781404) ^ [_1484218, _1484220, _1484222] : [-(hAPP(c_Relation_OImage(_1484218, _1484220, _1484222), c_Orderings_Obot__class_Obot(tc_fun(_1484218, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1484220, tc_HOL_Obool)))], (52486 ^ _781404) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (28339 ^ _781404) ^ [_1288038, _1288040, _1288042, _1288044] : [class_Fields_Olinordered__field__inverse__zero(_1288038), class_Int_Onumber(_1288038), 28346 ^ _781404 : [(28347 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288038), _1288040), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042))), _1288044)), 28350 ^ _781404 : [(28357 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), c_Groups_Ozero__class_Ozero(_1288038)), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042)))), 28360 ^ _781404 : [(28367 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042)), c_Groups_Ozero__class_Ozero(_1288038)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), c_Groups_Ozero__class_Ozero(_1288038)), _1288044)))], (28361 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042)), c_Groups_Ozero__class_Ozero(_1288038))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288038), _1288044), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042))), _1288040)))]]], (28351 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), c_Groups_Ozero__class_Ozero(_1288038)), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), _1288040), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288038), _1288044), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042)))))]]], (28373 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288038), _1288040), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042))), _1288044))), 28376 ^ _781404 : [(28379 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), _1288040), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288038), _1288044), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042))))], (28377 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), c_Groups_Ozero__class_Ozero(_1288038)), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042))))]], 28380 ^ _781404 : [(28383 ^ _781404) ^ [] : [28384 ^ _781404 : [(28387 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288038), _1288044), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042))), _1288040))], (28385 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042)), c_Groups_Ozero__class_Ozero(_1288038))))]], 28388 ^ _781404 : [(28391 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), c_Groups_Ozero__class_Ozero(_1288038)), _1288044))], (28389 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042)), c_Groups_Ozero__class_Ozero(_1288038)))]]], (28381 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288038), c_Groups_Ozero__class_Ozero(_1288038)), hAPP(c_Int_Onumber__class_Onumber__of(_1288038), _1288042)))]]]]], (30288 ^ _781404) ^ [_1325423] : [class_Lattices_Oab__semigroup__idem__mult(_1325423), -(c_Finite__Set_Ofun__left__comm__idem(_1325423, _1325423, c_Groups_Otimes__class_Otimes(_1325423)))], (4428 ^ _781404) ^ [_848630, _848632, _848634, _848636, _848638, _848640] : [-(c_New__DSequence_Opos__union(_848640, _848636, _848632) = c_New__DSequence_Opos__union(_848638, _848634, _848630)), _848640 = _848638, _848636 = _848634, _848632 = _848630], (24874 ^ _781404) ^ [_1227230, _1227232] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1227230, _1227232) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1227230 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227232), 24877 ^ [_1227230, _1227232]))], (10325 ^ _781404) ^ [_957022, _957024, _957026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957022), _957024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957022), _957026)), 10332 ^ _781404 : [(10339 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957024), _957026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957024), _957022)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957026), _957022))))], (10333 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957024), _957022)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957026), _957022))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957024), _957026)))]]], (35290 ^ _781404) ^ [_1438850, _1438852, _1438854, _1438856, _1438858, _1438860, _1438862] : [35292 ^ _781404 : [(35295 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1438858, 35291 ^ [_1438850, _1438852, _1438854, _1438856, _1438858, _1438860, _1438862]), _1438860), _1438862))], (35293 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438850), 35291 ^ [_1438850, _1438852, _1438854, _1438856, _1438858, _1438860, _1438862]), _1438856)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1438850, tc_fun(_1438852, tc_fun(_1438854, tc_HOL_Obool))), _1438856), _1438858), _1438860), _1438862)))], (13313 ^ _781404) ^ [_1012703, _1012705, _1012707, _1012709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012703), _1012705)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012707), _1012705) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012703), _1012709), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012707), _1012709)))], (3300 ^ _781404) ^ [_830646, _830648, _830650, _830652, _830654, _830656] : [-(c_List_Olist_Olist__size(_830656, _830652, _830648) = c_List_Olist_Olist__size(_830654, _830650, _830646)), _830656 = _830654, _830652 = _830650, _830648 = _830646], (26895 ^ _781404) ^ [_1261426, _1261428] : [class_Rings_Olinordered__idom(_1261426), -(hAPP(c_Groups_Oabs__class_Oabs(_1261426), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1261426), _1261428)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1261426), _1261428))], (2954 ^ _781404) ^ [_825235, _825237] : [_825237 = _825235, -(c_Int_Oring__1__class_Oof__int(_825237) = c_Int_Oring__1__class_Oof__int(_825235))], (5568 ^ _781404) ^ [_866550, _866552, _866554, _866556] : [-(tc_sum(_866556, _866552) = tc_sum(_866554, _866550)), _866556 = _866554, _866552 = _866550], (32002 ^ _781404) ^ [_1357498, _1357500] : [class_Orderings_Olinorder(_1357498), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357498), _1357500), _1357500) = _1357500)], (20453 ^ _781404) ^ [_1144287, _1144289, _1144291] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1144287))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144287)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144289)), _1144291)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144289)), _1144291))], (14021 ^ _781404) ^ [_1025940, _1025942, _1025944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025940), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025944), _1025942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025940), _1025942)), _1025944)))], (42762 ^ _781404) ^ [_1630320, _1630322, _1630324] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630320, tc_HOL_Obool)), hAPP(c_List_Oset(_1630320), _1630322)), hAPP(c_List_Oset(_1630320), hAPP(hAPP(c_List_Olist_OCons(_1630320), _1630324), _1630322)))))], (25716 ^ _781404) ^ [_1240948, _1240950] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1240948), _1240950) = 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)), _1240948)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1240950))))], (19131 ^ _781404) ^ [] : [-(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))))], (33574 ^ _781404) ^ [_1392697, _1392699, _1392701, _1392703, _1392705, _1392707] : [class_Groups_Ocomm__monoid__add(_1392697), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1392699, _1392697), hAPP(hAPP(c_COMBC(_1392699, tc_fun(_1392701, tc_HOL_Obool), _1392697), hAPP(hAPP(c_COMBB(tc_fun(_1392701, _1392697), tc_fun(tc_fun(_1392701, tc_HOL_Obool), _1392697), _1392699), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1392701, _1392697)), _1392703)), _1392705)), _1392707) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1392701, _1392697), hAPP(hAPP(c_COMBC(_1392701, tc_fun(_1392699, tc_HOL_Obool), _1392697), hAPP(hAPP(c_COMBB(tc_fun(_1392699, _1392697), tc_fun(tc_fun(_1392699, tc_HOL_Obool), _1392697), _1392701), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1392699, _1392697)), hAPP(c_COMBC(_1392699, _1392701, _1392697), _1392703))), _1392707)), _1392705))], (44088 ^ _781404) ^ [_1661099, _1661101, _1661103] : [_1661103 = c_List_Olist_ONil(_1661101), -(_1661099 = hAPP(hAPP(c_List_Oappend(_1661101), _1661099), _1661103))], (45279 ^ _781404) ^ [_1688051, _1688053, _1688055, _1688057, _1688059] : [c_Fun_Oinj__on(_1688051, _1688053, _1688055, c_Orderings_Otop__class_Otop(tc_fun(_1688051, tc_HOL_Obool))), 45282 ^ _781404 : [(45289 ^ _781404) ^ [] : [_1688057 = _1688059, -(hAPP(hAPP(c_List_Omap(_1688051, _1688053), _1688055), _1688057) = hAPP(hAPP(c_List_Omap(_1688051, _1688053), _1688055), _1688059))], (45283 ^ _781404) ^ [] : [hAPP(hAPP(c_List_Omap(_1688051, _1688053), _1688055), _1688057) = hAPP(hAPP(c_List_Omap(_1688051, _1688053), _1688055), _1688059), -(_1688057 = _1688059)]]], (43541 ^ _781404) ^ [_1649319, _1649321] : [-(c_List_Oremove1(_1649319, _1649321, c_List_Olist_ONil(_1649319)) = c_List_Olist_ONil(_1649319))], (49862 ^ _781404) ^ [_1788626, _1788628, _1788630, _1788632] : [class_Complete__Lattice_Ocomplete__lattice(_1788626), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1788628, _1788626), _1788630), _1788632) = c_Complete__Lattice_OSup__class_OSup(_1788626, hAPP(c_Set_OCollect(_1788626), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1788628, _1788626), tc_HOL_Obool), tc_HOL_Obool, _1788626), c_HOL_OEx(tc_fun(_1788628, _1788626))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1788628, _1788626), tc_HOL_Obool), tc_fun(tc_fun(_1788628, _1788626), tc_HOL_Obool), _1788626), hAPP(c_COMBS(tc_fun(_1788628, _1788626), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1788628, _1788626)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1788628, _1788626), tc_fun(tc_fun(_1788628, _1788626), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1788628, _1788626))), _1788630)))), hAPP(hAPP(c_COMBC(_1788626, tc_fun(tc_fun(_1788628, _1788626), _1788626), tc_fun(tc_fun(_1788628, _1788626), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788626, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1788628, _1788626), _1788626), tc_fun(tc_fun(_1788628, _1788626), tc_HOL_Obool)), _1788626), c_COMBB(_1788626, tc_HOL_Obool, tc_fun(_1788628, _1788626))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1788628, _1788626), _1788628, _1788626), c_COMBI(tc_fun(_1788628, _1788626))), _1788632)))))))], (8495 ^ _781404) ^ [_924688, _924690, _924692] : [-(c_Nat_Onat_Onat__case(_924688, _924690, _924692, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _924690)], (34951 ^ _781404) ^ [_1431619, _1431621] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1431619)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431621)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1431621))), 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, _1431619))), 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), _1431619)), c_Int_Onat)))))], (52122 ^ _781404) ^ [_1835640, _1835642, _1835644, _1835646] : [class_Divides_Osemiring__div(_1835640), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835640), _1835642), _1835644)), 52129 ^ _781404 : [(52136 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835640), _1835642), _1835646)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835640), _1835642), c_Divides_Odiv__class_Omod(_1835640, _1835646, _1835644))))], (52130 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835640), _1835642), c_Divides_Odiv__class_Omod(_1835640, _1835646, _1835644))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835640), _1835642), _1835646)))]]], (24672 ^ _781404) ^ [_1224068, _1224070, _1224072] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1224068, _1224070)), _1224072) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1224068), _1224072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1224070), _1224072)))], (30840 ^ _781404) ^ [_1335791, _1335793, _1335795, _1335797] : [class_Orderings_Olinorder(_1335791), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335791), _1335793), _1335795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335791), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1335791), _1335793), _1335797)), _1335795)))], (31252 ^ _781404) ^ [_1343778, _1343780] : [class_Orderings_Olinorder(_1343778), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343778), _1343780)), -(_1343780 = c_Orderings_Obot__class_Obot(tc_fun(_1343778, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1343778), c_Big__Operators_Olinorder__class_OMin(_1343778, _1343780)), _1343780)))], (5610 ^ _781404) ^ [_867167, _867169] : [_867169 = _867167, -(c_COMBI(_867169) = c_COMBI(_867167))], (10465 ^ _781404) ^ [_959544, _959546, _959548, _959550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_959544, tc_HOL_Obool)), _959546), _959548)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959544, tc_HOL_Obool)), _959548), _959550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_959544, tc_HOL_Obool)), _959546), _959550)))], (49557 ^ _781404) ^ [_1781091, _1781093, _1781095] : [c_List_Olist__ex(tc_Int_Oint, _1781091, c_List_Oupto(_1781093, _1781095)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1781091), _1781093, _1781095)], (49159 ^ _781404) ^ [_1772417, _1772419, _1772421, _1772423] : [-(c_List_Oreplicate(_1772417, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1772419), _1772421), _1772423) = hAPP(hAPP(c_List_Oappend(_1772417), c_List_Oreplicate(_1772417, _1772419, _1772423)), c_List_Oreplicate(_1772417, _1772421, _1772423)))], (11907 ^ _781404) ^ [_985354, _985356, _985358, _985360, _985362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_985354, tc_HOL_Obool)), _985356), _985358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_985360, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_985360, _985354, _985362), _985356)), hAPP(c_Set_Ovimage(_985360, _985354, _985362), _985358))))], (42571 ^ _781404) ^ [_1625234, _1625236, _1625238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1625234, tc_HOL_Obool)), _1625236), _1625238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1625234), tc_HOL_Obool)), c_List_Olists(_1625234, _1625236)), c_List_Olists(_1625234, _1625238))))], (44830 ^ _781404) ^ [_1678342, _1678344, _1678346, _1678348] : [class_Complete__Lattice_Ocomplete__lattice(_1678342), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1678344, _1678342), hAPP(c_List_Oset(_1678344), _1678346)), _1678348) = hAPP(c_List_Ofoldl(_1678342, _1678344, hAPP(c_COMBC(_1678344, _1678342, _1678342), hAPP(hAPP(c_COMBB(_1678342, tc_fun(_1678342, _1678342), _1678344), c_Lattices_Osemilattice__inf__class_Oinf(_1678342)), _1678348)), c_Orderings_Otop__class_Otop(_1678342)), _1678346))], (26335 ^ _781404) ^ [_1251243] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1251243)))], (48072 ^ _781404) ^ [_1748380, _1748382, _1748384] : [-(c_List_Omaps(_1748380, _1748382, _1748384, c_List_Olist_ONil(_1748380)) = c_List_Olist_ONil(_1748382))], (46872 ^ _781404) ^ [_1724226, _1724228] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1724226), hAPP(c_List_Onth(_1724226), _1724228)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724226)), _1724228))) = _1724228)], (7804 ^ _781404) ^ [_909962, _909964, _909966, _909968, _909970] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909962, tc_HOL_Obool)), _909964), hAPP(c_Set_Oimage(_909966, _909962, _909968), _909970)))), 7805 ^ _781404 : [(7806 ^ _781404) ^ [_910042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909966, tc_HOL_Obool)), _910042), _909970)), _909964 = hAPP(c_Set_Oimage(_909966, _909962, _909968), _910042)]]], (38862 ^ _781404) ^ [_1522672, _1522674, _1522676, _1522678, _1522680, _1522682] : [hAPP(c_Set_Oimage(_1522672, _1522674, _1522676), c_Orderings_Otop__class_Otop(tc_fun(_1522672, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1522674, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1522678, _1522680, _1522682), c_Orderings_Otop__class_Otop(tc_fun(_1522678, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1522680, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1522672, _1522678), tc_prod(_1522674, _1522680), c_Product__Type_Omap__pair(_1522672, _1522674, _1522678, _1522680, _1522676, _1522682)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1522672, _1522678), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1522674, _1522680), tc_HOL_Obool)))], (22591 ^ _781404) ^ [_1184487, _1184489, _1184491] : [class_Rings_Ocomm__semiring__1(_1184487), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184487), _1184489), 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)))), _1184491))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184487), _1184489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184487), hAPP(hAPP(c_Power_Opower__class_Opower(_1184487), _1184489), _1184491)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184487), _1184489), _1184491))))], (24758 ^ _781404) ^ [_1225446, _1225448, _1225450] : [_1225446 = 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), _1225446), _1225448)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1225446), _1225450)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48064 ^ _781404) ^ [_1748194, _1748196, _1748198] : [-(hAPP(c_List_Oset(_1748194), c_List_Oinsert(_1748194, _1748196, _1748198)) = hAPP(hAPP(c_Set_Oinsert(_1748194), _1748196), hAPP(c_List_Oset(_1748194), _1748198)))], (48665 ^ _781404) ^ [_1761887, _1761889, _1761891] : [48667 ^ _781404 : [(48670 ^ _781404) ^ [] : [hBOOL(hAPP(_1761889, hAPP(hAPP(c_List_Onth(_1761887), _1761891), 48666 ^ [_1761887, _1761889, _1761891])))], (48668 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48666 ^ [_1761887, _1761889, _1761891]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761887)), _1761891))))]], -(c_List_Olist__all(_1761887, _1761889, _1761891))], (5640 ^ _781404) ^ [_867622, _867624, _867626, _867628, _867630, _867632] : [-(c_COMBC(_867632, _867628, _867624) = c_COMBC(_867630, _867626, _867622)), _867632 = _867630, _867628 = _867626, _867624 = _867622], (41594 ^ _781404) ^ [_1597355, _1597357, _1597359] : [c_Equiv__Relations_Oequiv(_1597355, _1597357, _1597359), -(hAPP(hAPP(c_Relation_Orel__comp(_1597355, _1597355, _1597355), hAPP(c_Relation_Oconverse(_1597355, _1597355), _1597359)), _1597359) = _1597359)], (34279 ^ _781404) ^ [_1415449, _1415451, _1415453, _1415455, _1415457] : [_1415449 = c_Orderings_Obot__class_Obot(tc_fun(_1415451, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415451, tc_fun(_1415453, tc_HOL_Obool)), _1415449), hAPP(hAPP(c_COMBB(tc_fun(_1415453, tc_HOL_Obool), tc_fun(_1415453, tc_HOL_Obool), _1415451), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415453, tc_HOL_Obool)), _1415455)), _1415457)) = c_Orderings_Obot__class_Obot(tc_fun(_1415453, tc_HOL_Obool)))], (7087 ^ _781404) ^ [_896169, _896171, _896173] : [class_Lattices_Osemilattice__sup(_896169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896169), _896171), _896173)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896169), _896173), _896171) = _896173)], (7814 ^ _781404) ^ [_910207, _910209, _910211, _910213, _910215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910207, tc_HOL_Obool)), _910209), _910211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910213, tc_HOL_Obool)), hAPP(c_Set_Oimage(_910207, _910213, _910215), _910209)), hAPP(c_Set_Oimage(_910207, _910213, _910215), _910211))))], (30582 ^ _781404) ^ [_1331056, _1331058, _1331060, _1331062, _1331064] : [class_Orderings_Olinorder(_1331056), class_Orderings_Olinorder(_1331058), c_Orderings_Oorder__class_Omono(_1331058, _1331056, _1331060), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331056), hAPP(_1331060, _1331062)), hAPP(_1331060, _1331064)) = hAPP(_1331060, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331058), _1331062), _1331064)))], (17331 ^ _781404) ^ [_1090572, _1090574, _1090576] : [class_Lattices_Olattice(_1090572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090572), _1090574)), -(hBOOL(hAPP(hAPP(c_member(_1090572), _1090576), _1090574))), -(c_Big__Operators_Olattice__class_OSup__fin(_1090572, hAPP(hAPP(c_Set_Oinsert(_1090572), _1090576), _1090574)) = hAPP(hAPP(c_Finite__Set_Ofold(_1090572, _1090572, c_Lattices_Osemilattice__sup__class_Osup(_1090572)), _1090576), _1090574))], (33113 ^ _781404) ^ [_1378973, _1378975] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1378973), hAPP(c_Nat_OSuc, _1378975)) = 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)), _1378975)), _1378973))], (3028 ^ _781404) ^ [_826328, _826330, _826332, _826334, _826336, _826338] : [-(c_Product__Type_Ointernal__split(_826338, _826334, _826330) = c_Product__Type_Ointernal__split(_826336, _826332, _826328)), _826338 = _826336, _826334 = _826332, _826330 = _826328], (34973 ^ _781404) ^ [_1432233, _1432235, _1432237, _1432239, _1432241, _1432243] : [class_Groups_Ocomm__monoid__mult(_1432233), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432235), _1432237)), 34980 ^ _781404 : [(34987 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1432235), _1432239), _1432237))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432235, _1432233), hAPP(hAPP(c_COMBC(_1432235, _1432233, _1432233), hAPP(hAPP(c_COMBS(_1432235, _1432233, tc_fun(_1432233, _1432233)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1432233, tc_fun(_1432233, _1432233)), _1432235), c_If(_1432233)), hAPP(hAPP(c_COMBC(_1432235, _1432235, tc_HOL_Obool), c_fequal), _1432239))), _1432241)), _1432243)), _1432237) = hAPP(hAPP(c_Power_Opower__class_Opower(_1432233), _1432243), hAPP(c_Finite__Set_Ocard(_1432235), _1432237)))], (34981 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1432235), _1432239), _1432237)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432235, _1432233), hAPP(hAPP(c_COMBC(_1432235, _1432233, _1432233), hAPP(hAPP(c_COMBS(_1432235, _1432233, tc_fun(_1432233, _1432233)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1432233, tc_fun(_1432233, _1432233)), _1432235), c_If(_1432233)), hAPP(hAPP(c_COMBC(_1432235, _1432235, tc_HOL_Obool), c_fequal), _1432239))), _1432241)), _1432243)), _1432237) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432233), hAPP(_1432241, _1432239)), hAPP(hAPP(c_Power_Opower__class_Opower(_1432233), _1432243), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1432235), _1432237)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (43004 ^ _781404) ^ [_1637619, _1637621, _1637623, _1637625] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1637619, _1637619)), hAPP(hAPP(c_Product__Type_OPair(_1637619, _1637619), _1637621), _1637623)), hAPP(c_List_Oset(tc_prod(_1637619, _1637619)), hAPP(hAPP(c_List_Ozip(_1637619, _1637619), _1637625), _1637625))))), hBOOL(hAPP(hAPP(c_member(_1637619), _1637621), hAPP(c_List_Oset(_1637619), _1637625))), _1637621 = _1637623], (38522 ^ _781404) ^ [_1512928, _1512930, _1512932, _1512934, _1512936, _1512938] : [class_Groups_Ocomm__monoid__add(_1512928), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512930, _1512928), hAPP(hAPP(c_COMBC(_1512930, tc_fun(_1512932, tc_HOL_Obool), _1512928), hAPP(hAPP(c_COMBB(tc_fun(_1512932, _1512928), tc_fun(tc_fun(_1512932, tc_HOL_Obool), _1512928), _1512930), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512932, _1512928)), _1512934)), _1512936)), _1512938) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1512930, _1512932), _1512928), hAPP(c_Product__Type_Oprod_Oprod__case(_1512930, _1512932, _1512928), _1512934)), hAPP(hAPP(c_Product__Type_OSigma(_1512930, _1512932), _1512938), hAPP(c_COMBK(tc_fun(_1512932, tc_HOL_Obool), _1512930), _1512936))))], (34239 ^ _781404) ^ [_1413036, _1413038, _1413040, _1413042, _1413044] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413036, tc_fun(_1413038, tc_HOL_Obool)), _1413040), hAPP(hAPP(c_COMBC(_1413036, tc_fun(_1413038, tc_HOL_Obool), tc_fun(_1413038, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1413038, tc_HOL_Obool), tc_fun(tc_fun(_1413038, tc_HOL_Obool), tc_fun(_1413038, tc_HOL_Obool)), _1413036), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413038, tc_HOL_Obool))), _1413042)), _1413044)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413038, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413036, tc_fun(_1413038, tc_HOL_Obool)), _1413040), _1413042)), _1413044))], (39159 ^ _781404) ^ [_1531004, _1531006, _1531008, _1531010] : [_1531004 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1531006, _1531008), 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)), _1531010))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1531006), _1531004)))], (38807 ^ _781404) ^ [_1521269, _1521271, _1521273, _1521275, _1521277, _1521279] : [class_Groups_Ocomm__monoid__add(_1521269), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521271), _1521273)), 38817 ^ _781404 : [(38820 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521275), hAPP(_1521277, 38816 ^ [_1521269, _1521271, _1521273, _1521275, _1521277, _1521279])))], (38818 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1521271), 38816 ^ [_1521269, _1521271, _1521273, _1521275, _1521277, _1521279]), _1521273)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1521271, _1521269), hAPP(hAPP(c_COMBS(_1521271, tc_fun(_1521275, tc_HOL_Obool), _1521269), hAPP(hAPP(c_COMBB(tc_fun(_1521275, _1521269), tc_fun(tc_fun(_1521275, tc_HOL_Obool), _1521269), _1521271), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1521275, _1521269)), _1521279)), _1521277)), _1521273) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1521271, _1521275), _1521269), hAPP(c_Product__Type_Oprod_Oprod__case(_1521271, _1521275, _1521269), _1521279)), hAPP(hAPP(c_Product__Type_OSigma(_1521271, _1521275), _1521273), _1521277)))], (6127 ^ _781404) ^ [_878717, _878719, _878721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_878717), tc_HOL_Obool)), _878719), _878721)), -(c_Hoare__Mirabelle_Ohoare__derivs(_878717, _878721, _878719))], (37130 ^ _781404) ^ [_1477985, _1477987, _1477989, _1477991, _1477993, _1477995] : [-(hAPP(c_Product__Type_Oapfst(_1477985, _1477987, _1477989, _1477991), hAPP(hAPP(c_Product__Type_OPair(_1477985, _1477989), _1477993), _1477995)) = hAPP(hAPP(c_Product__Type_OPair(_1477987, _1477989), hAPP(_1477991, _1477993)), _1477995))], (20389 ^ _781404) ^ [_1143267] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143267)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143267)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143267))], (20033 ^ _781404) ^ [_1137221, _1137223] : [_1137221 = _1137223, -(c_Int_OBit0(_1137221) = c_Int_OBit0(_1137223))], (16130 ^ _781404) ^ [_1067554, _1067556, _1067558] : [class_Lattices_Olattice(_1067554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067554), _1067556)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067554), _1067558)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1067554, tc_HOL_Obool)), _1067556), _1067558) = c_Orderings_Obot__class_Obot(tc_fun(_1067554, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067554), c_Big__Operators_Olattice__class_OInf__fin(_1067554, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1067554, tc_HOL_Obool)), _1067556), _1067558))), c_Big__Operators_Olattice__class_OInf__fin(_1067554, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1067554, tc_HOL_Obool)), _1067556), _1067558))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067554), c_Big__Operators_Olattice__class_OInf__fin(_1067554, _1067556)), c_Big__Operators_Olattice__class_OInf__fin(_1067554, _1067558)))], (20013 ^ _781404) ^ [_1136911] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1136911)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136911))))], (24939 ^ _781404) ^ [_1228251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1228251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1228251)))], (2960 ^ _781404) ^ [_825320, _825322, _825324, _825326] : [-(c_Nitpick_Oinverse__frac(_825326, _825322) = c_Nitpick_Oinverse__frac(_825324, _825320)), _825326 = _825324, _825322 = _825320], (4544 ^ _781404) ^ [_850418, _850420] : [_850420 = _850418, -(c_List_Omember(_850420) = c_List_Omember(_850418))], (35591 ^ _781404) ^ [_1445545, _1445547] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1445545), _1445547)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1445545), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445547)))], (6468 ^ _781404) ^ [_884318, _884320, _884322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884318, tc_HOL_Obool)), _884320), _884322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_884318, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_884318), _884320)), hAPP(c_Set_OPow(_884318), _884322))))], (35720 ^ _781404) ^ [_1448096, _1448098, _1448100, _1448102, _1448104] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1448096, _1448098), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1448100), _1448102))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1448098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1448104)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1448096, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1448098), _1448104)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1448100), _1448104)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1448098), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1448100, _1448104))), _1448102)))))], (31948 ^ _781404) ^ [_1356367, _1356369] : [class_Orderings_Olinorder(_1356367), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356367), _1356369), _1356369) = _1356369)], (14611 ^ _781404) ^ [_1037473, _1037475, _1037477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1037473, tc_HOL_Obool)), _1037475), _1037477)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1037473), _1037477)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1037473), _1037475)))], (23167 ^ _781404) ^ [_1196184, _1196186, _1196188, _1196190, _1196192] : [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), _1196184), _1196186)), _1196188)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1196184), _1196190)), _1196192))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1196192), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196184), _1196192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196184), _1196188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1196190), _1196186)))], (26543 ^ _781404) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (44633 ^ _781404) ^ [_1674159, _1674161, _1674163, _1674165] : [-(hAPP(c_List_Orotate(_1674159, _1674161), hAPP(c_List_Orotate(_1674159, _1674163), _1674165)) = hAPP(c_List_Orotate(_1674159, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1674161), _1674163)), _1674165))], (11147 ^ _781404) ^ [_970675, _970677, _970679] : [class_Orderings_Oorder(_970675), 11150 ^ _781404 : [(11157 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970675), _970677), _970679))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_970675, _970677), _970679) = c_Orderings_Obot__class_Obot(tc_fun(_970675, tc_HOL_Obool)))], (11151 ^ _781404) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_970675, _970677), _970679) = c_Orderings_Obot__class_Obot(tc_fun(_970675, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970675), _970677), _970679))]]], (45853 ^ _781404) ^ [_1700627, _1700629, _1700631, _1700633] : [-(hBOOL(hAPP(c_List_Olistsp(_1700627, _1700629), hAPP(hAPP(c_List_Oappend(_1700627), _1700631), _1700633)))), hBOOL(hAPP(c_List_Olistsp(_1700627, _1700629), _1700631)), hBOOL(hAPP(c_List_Olistsp(_1700627, _1700629), _1700633))], (43647 ^ _781404) ^ [_1651219, _1651221] : [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(_1651219)), _1651221))), _1651221 = c_List_Olist_ONil(_1651219)], (34999 ^ _781404) ^ [_1433009, _1433011, _1433013] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1433009), _1433011))), 35002 ^ _781404 : [(35009 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1433013), _1433011))), -(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)), _1433009)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1433013), _1433011)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (35003 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1433013), _1433011)), -(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)), _1433009)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1433013), _1433011)) = 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))))]]], (43194 ^ _781404) ^ [_1641994, _1641996, _1641998, _1642000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641994), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641996)), _1641998))), 43197 ^ _781404 : [(43204 ^ _781404) ^ [] : [hAPP(hAPP(c_List_Onth(_1641996), _1641998), _1641994) = _1642000, -(hAPP(hAPP(c_List_Olist__update(_1641996, _1641998), _1641994), _1642000) = _1641998)], (43198 ^ _781404) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1641996, _1641998), _1641994), _1642000) = _1641998, -(hAPP(hAPP(c_List_Onth(_1641996), _1641998), _1641994) = _1642000)]]], (32634 ^ _781404) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (22789 ^ _781404) ^ [_1188820, _1188822, _1188824] : [class_Int_Onumber__ring(_1188820), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188820), hAPP(c_Groups_Ouminus__class_Ouminus(_1188820), hAPP(c_Int_Onumber__class_Onumber__of(_1188820), _1188822))), _1188824) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188820), hAPP(c_Int_Onumber__class_Onumber__of(_1188820), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1188822))), _1188824))], (24925 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (27483 ^ _781404) ^ [_1272107, _1272109, _1272111] : [class_Lattices_Osemilattice__inf(_1272107), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272107), _1272109)), -(_1272109 = c_Orderings_Obot__class_Obot(tc_fun(_1272107, tc_HOL_Obool))), 27494 ^ _781404 : [(27495 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272107), _1272111), hAPP(c_Finite__Set_Ofold1(_1272107, c_Lattices_Osemilattice__inf__class_Oinf(_1272107)), _1272109))), 27498 ^ _781404 : [(27499 ^ _781404) ^ [_1272400] : [hBOOL(hAPP(hAPP(c_member(_1272107), _1272400), _1272109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272107), _1272111), _1272400)))]]], (27505 ^ _781404) ^ [] : [27507 ^ _781404 : [(27510 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272107), _1272111), 27506 ^ [_1272107, _1272109, _1272111]))], (27508 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1272107), 27506 ^ [_1272107, _1272109, _1272111]), _1272109)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272107), _1272111), hAPP(c_Finite__Set_Ofold1(_1272107, c_Lattices_Osemilattice__inf__class_Oinf(_1272107)), _1272109))))]]], (52294 ^ _781404) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (18879 ^ _781404) ^ [_1117736] : [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), _1117736))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1117736)))], (27683 ^ _781404) ^ [_1275998, _1276000, _1276002] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1275998, _1276000, c_Orderings_Obot__class_Obot(tc_fun(_1275998, tc_HOL_Obool))), _1276002))], (40045 ^ _781404) ^ [_1559989, _1559991, _1559993] : [c_Wellfounded_Owf(_1559989, _1559991), c_Wellfounded_Owf(_1559989, _1559993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559989, _1559989), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1559989, _1559989, _1559989), _1559991), _1559993)), _1559991)), -(c_Wellfounded_Owf(_1559989, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1559989, _1559989), tc_HOL_Obool)), _1559991), _1559993)))], (13227 ^ _781404) ^ [_1011121, _1011123, _1011125, _1011127] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1011121), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011121), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011121), _1011123), _1011125)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011121), _1011123), _1011127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011121), _1011125), _1011127)))], (34089 ^ _781404) ^ [_1407357, _1407359, _1407361, _1407363, _1407365] : [class_Complete__Lattice_Ocomplete__lattice(_1407357), hBOOL(hAPP(hAPP(c_member(_1407359), _1407361), _1407363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1407357), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1407359, _1407357), _1407363), _1407365)), hAPP(_1407365, _1407361))))], (9631 ^ _781404) ^ [_946232, _946234, _946236] : [class_Orderings_Opreorder(_946232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946232), _946234), _946236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946232), _946236), _946234))], (39479 ^ _781404) ^ [_1543771, _1543773, _1543775, _1543777, _1543779, _1543781, _1543783] : [class_Rings_Osemiring__0(_1543771), c_Fun_Oinj__on(tc_prod(_1543773, _1543775), _1543771, hAPP(c_Product__Type_Oprod_Oprod__case(_1543773, _1543775, _1543771), hAPP(hAPP(c_COMBC(_1543773, tc_fun(_1543775, _1543771), tc_fun(_1543775, _1543771)), hAPP(hAPP(c_COMBB(tc_fun(_1543771, _1543771), tc_fun(tc_fun(_1543775, _1543771), tc_fun(_1543775, _1543771)), _1543773), c_COMBB(_1543771, _1543771, _1543775)), hAPP(hAPP(c_COMBB(_1543771, tc_fun(_1543771, _1543771), _1543773), c_Groups_Otimes__class_Otimes(_1543771)), _1543777))), _1543779)), hAPP(hAPP(c_Product__Type_OSigma(_1543773, _1543775), _1543781), hAPP(c_COMBK(tc_fun(_1543775, tc_HOL_Obool), _1543773), _1543783))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1543771), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543773, _1543771), _1543777), _1543781)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543775, _1543771), _1543779), _1543783)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543771, _1543771), c_Fun_Oid(_1543771)), hAPP(c_Set_OCollect(_1543771), hAPP(hAPP(c_COMBB(tc_fun(_1543773, tc_HOL_Obool), tc_HOL_Obool, _1543771), c_HOL_OEx(_1543773)), hAPP(hAPP(c_COMBB(tc_fun(_1543773, tc_fun(_1543775, tc_HOL_Obool)), tc_fun(_1543773, tc_HOL_Obool), _1543771), hAPP(c_COMBB(tc_fun(_1543775, tc_HOL_Obool), tc_HOL_Obool, _1543773), c_HOL_OEx(_1543775))), hAPP(hAPP(c_COMBC(_1543771, tc_fun(_1543773, tc_fun(_1543775, tc_HOL_Obool)), tc_fun(_1543773, tc_fun(_1543775, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1543773, tc_fun(tc_fun(_1543775, tc_HOL_Obool), tc_fun(_1543775, tc_HOL_Obool))), tc_fun(tc_fun(_1543773, tc_fun(_1543775, tc_HOL_Obool)), tc_fun(_1543773, tc_fun(_1543775, tc_HOL_Obool))), _1543771), c_COMBS(_1543773, tc_fun(_1543775, tc_HOL_Obool), tc_fun(_1543775, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1543773, tc_fun(_1543775, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1543773, tc_fun(tc_fun(_1543775, tc_HOL_Obool), tc_fun(_1543775, tc_HOL_Obool))), _1543771), hAPP(c_COMBB(tc_fun(_1543775, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1543775, tc_HOL_Obool), tc_fun(_1543775, tc_HOL_Obool)), _1543773), c_COMBS(_1543775, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1543773, tc_fun(_1543775, tc_HOL_Obool)), tc_fun(_1543773, tc_fun(_1543775, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1543771), hAPP(c_COMBB(tc_fun(_1543775, tc_HOL_Obool), tc_fun(_1543775, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1543773), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543775), c_fconj))), hAPP(hAPP(c_COMBC(_1543771, tc_fun(_1543773, tc_fun(_1543775, _1543771)), tc_fun(_1543773, tc_fun(_1543775, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1543775, _1543771), tc_fun(_1543775, tc_HOL_Obool)), tc_fun(tc_fun(_1543773, tc_fun(_1543775, _1543771)), tc_fun(_1543773, tc_fun(_1543775, tc_HOL_Obool))), _1543771), c_COMBB(tc_fun(_1543775, _1543771), tc_fun(_1543775, tc_HOL_Obool), _1543773)), hAPP(hAPP(c_COMBB(tc_fun(_1543771, tc_HOL_Obool), tc_fun(tc_fun(_1543775, _1543771), tc_fun(_1543775, tc_HOL_Obool)), _1543771), c_COMBB(_1543771, tc_HOL_Obool, _1543775)), c_fequal))), hAPP(hAPP(c_COMBC(_1543773, tc_fun(_1543775, _1543771), tc_fun(_1543775, _1543771)), hAPP(hAPP(c_COMBB(tc_fun(_1543771, _1543771), tc_fun(tc_fun(_1543775, _1543771), tc_fun(_1543775, _1543771)), _1543773), c_COMBB(_1543771, _1543771, _1543775)), hAPP(hAPP(c_COMBB(_1543771, tc_fun(_1543771, _1543771), _1543773), c_Groups_Otimes__class_Otimes(_1543771)), _1543777))), _1543779)))))), hAPP(hAPP(c_COMBC(_1543773, tc_fun(_1543775, tc_HOL_Obool), tc_fun(_1543775, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1543775, tc_HOL_Obool), tc_fun(_1543775, tc_HOL_Obool)), _1543773), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1543775)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543773), c_fconj), hAPP(hAPP(c_COMBC(_1543773, tc_fun(_1543773, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543773)), _1543781)))), hAPP(hAPP(c_COMBC(_1543775, tc_fun(_1543775, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543775)), _1543783))))))))], (21147 ^ _781404) ^ [_1156919, _1156921, _1156923] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1156919), _1156921)), _1156923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156919), _1156923)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156921), _1156923)))], (6964 ^ _781404) ^ [_893599, _893601, _893603, _893605] : [6968 ^ _781404 : [(6971 ^ _781404) ^ [] : [hBOOL(hAPP(_893605, 6967 ^ [_893599, _893601, _893603, _893605]))], (6969 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893599), 6967 ^ [_893599, _893601, _893603, _893605]), _893601)))]], 6973 ^ _781404 : [(6976 ^ _781404) ^ [] : [hBOOL(hAPP(_893605, 6972 ^ [_893599, _893601, _893603, _893605]))], (6974 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893599), 6972 ^ [_893599, _893601, _893603, _893605]), _893603)))]], 6977 ^ _781404 : [(6978 ^ _781404) ^ [_893932] : [hBOOL(hAPP(hAPP(c_member(_893599), _893932), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_893599, tc_HOL_Obool)), _893601), _893603))), -(hBOOL(hAPP(_893605, _893932)))]]], (26369 ^ _781404) ^ [_1251687, _1251689] : [c_Nat__Transfer_Ois__nat(_1251687), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1251687), _1251689)))], (31996 ^ _781404) ^ [_1357355, _1357357, _1357359, _1357361] : [class_Orderings_Olinorder(_1357355), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357355), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357355), _1357357), _1357359)), _1357361) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357355), _1357357), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357355), _1357359), _1357361)))], (3314 ^ _781404) ^ [_830867, _830869, _830871, _830873] : [-(c_Random_Oselect(_830873, _830869) = c_Random_Oselect(_830871, _830867)), _830873 = _830871, _830869 = _830867], (45082 ^ _781404) ^ [_1683085, _1683087] : [-(_1683085 = c_List_Olist_ONil(_1683087)), -(hBOOL(hAPP(hAPP(c_member(_1683087), c_List_Olast(_1683087, _1683085)), hAPP(c_List_Oset(_1683087), _1683085))))], (14797 ^ _781404) ^ [_1041043, _1041045, _1041047] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041043), _1041045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1041043, tc_HOL_Obool)), _1041045), hAPP(c_Set_Oimage(_1041043, _1041043, _1041047), _1041045))), -(c_Fun_Oinj__on(_1041043, _1041043, _1041047, _1041045))], (14089 ^ _781404) ^ [_1027232, _1027234, _1027236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027232), _1027234)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027234), _1027232)), _1027236) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027234), _1027236)), _1027232))], (38941 ^ _781404) ^ [_1525104, _1525106] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1525104)), -(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)), _1525104))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1525106))))) = 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)), _1525104))), 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, _1525106))))))], (7834 ^ _781404) ^ [_910750, _910752, _910754, _910756] : [class_Lattices_Odistrib__lattice(_910750), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910750), _910752), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_910750), _910754), _910756)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_910750), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910750), _910752), _910754)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910750), _910752), _910756)))], (41175 ^ _781404) ^ [_1587277, _1587279] : [-(c_Transitive__Closure_Otrancl(_1587277, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587277, _1587277), tc_HOL_Obool)), _1587279), c_Relation_OId(_1587277))) = c_Transitive__Closure_Ortrancl(_1587277, _1587279))], (51005 ^ _781404) ^ [_1812436, _1812438, _1812440, _1812442] : [c_Fun_Obij__betw(_1812436, _1812438, _1812440, c_Orderings_Obot__class_Obot(tc_fun(_1812436, tc_HOL_Obool)), _1812442), -(_1812442 = c_Orderings_Obot__class_Obot(tc_fun(_1812438, tc_HOL_Obool)))], (43390 ^ _781404) ^ [_1646434, _1646436] : [class_Groups_Ocomm__monoid__add(_1646434), hBOOL(hAPP(c_List_Odistinct(_1646434), _1646436)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1646434), _1646436) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1646434, _1646434), c_COMBI(_1646434)), hAPP(c_List_Oset(_1646434), _1646436)))], (19287 ^ _781404) ^ [_1124422, _1124424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124422)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124424))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124422), _1124424)))], (37228 ^ _781404) ^ [_1479866] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1479866)), -(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))), _1479866)), c_FunDef_Omax__weak)))], (43637 ^ _781404) ^ [_1651068, _1651070, _1651072] : [-(hBOOL(hAPP(hAPP(c_member(_1651068), _1651070), hAPP(c_List_Oset(_1651068), _1651072)))), -(c_List_Oremove1(_1651068, _1651070, _1651072) = _1651072)], (51257 ^ _781404) ^ [_1817543, _1817545, _1817547, _1817549] : [c_Equiv__Relations_Oequivp(_1817543, _1817545), 51263 ^ _781404 : [(51266 ^ _781404) ^ [] : [hBOOL(hAPP(_1817549, 51262 ^ [_1817543, _1817545, _1817547, _1817549]))], (51264 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1817547, 51262 ^ [_1817543, _1817545, _1817547, _1817549])))]], 51269 ^ _781404 : [(51270 ^ _781404) ^ [_1817802] : [hBOOL(hAPP(_1817547, _1817802))]], 51272 ^ _781404 : [(51275 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1817549, 51271 ^ [_1817543, _1817545, _1817547, _1817549])))], (51273 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1817543), 51271 ^ [_1817543, _1817545, _1817547, _1817549]), c_Quotient_ORespects(_1817543, _1817545))))]]], (7287 ^ _781404) ^ [_900041, _900043, _900045] : [class_Orderings_Olinorder(_900041), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900041), _900043), _900045)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900041, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_900041), _900043)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_900041, _900043), _900045)) = hAPP(c_SetInterval_Oord__class_OlessThan(_900041), _900045))], (8042 ^ _781404) ^ [_915956] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _915956)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _915956)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _915956)))], (43188 ^ _781404) ^ [_1641855, _1641857, _1641859, _1641861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641855), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641857)), _1641859))), -(hAPP(hAPP(c_List_Onth(_1641857), hAPP(hAPP(c_List_Olist__update(_1641857, _1641859), _1641855), _1641861)), _1641855) = _1641861)], (41936 ^ _781404) ^ [_1605879, _1605881, _1605883] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605879, _1605879)), _1605881), c_Transitive__Closure_Otrancl(_1605879, _1605883)))), 41937 ^ _781404 : [(41938 ^ _781404) ^ [_1605958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1605958)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1605879, _1605879)), _1605881), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605879, _1605879), tc_HOL_Obool), _1605958), _1605883)))]]], (33731 ^ _781404) ^ [_1396820, _1396822, _1396824, _1396826, _1396828] : [hBOOL(hAPP(hAPP(c_member(_1396820), _1396822), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396824, tc_fun(_1396820, tc_HOL_Obool)), _1396826), _1396828))), 33734 ^ _781404 : [(33735 ^ _781404) ^ [_1396944] : [hBOOL(hAPP(hAPP(c_member(_1396824), _1396944), _1396826)), -(hBOOL(hAPP(hAPP(c_member(_1396820), _1396822), hAPP(_1396828, _1396944))))]]], (8700 ^ _781404) ^ [_928008, _928010, _928012] : [class_Orderings_Oorder(_928008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928008), _928010), _928012)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_928008, _928012), _928010) = c_Orderings_Obot__class_Obot(tc_fun(_928008, tc_HOL_Obool)))], (50889 ^ _781404) ^ [_1810149, _1810151, _1810153, _1810155] : [c_Fun_Obij__betw(_1810149, _1810151, _1810153, c_Orderings_Otop__class_Otop(tc_fun(_1810149, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1810151, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1810149, _1810151, _1810153), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1810149, tc_HOL_Obool)), _1810155)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1810151, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1810149, _1810151, _1810153), _1810155)))], (9094 ^ _781404) ^ [_935529, _935531, _935533] : [class_Groups_Oab__group__add(_935529), -(hAPP(c_Groups_Ouminus__class_Ouminus(_935529), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_935529), _935531), _935533)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_935529), _935533), _935531))], (5809 ^ _781404) ^ [_873505, _873507, _873509] : [-(_873505 = _873507), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873509, tc_HOL_Obool)), _873505), _873507)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873509, tc_HOL_Obool)), _873507), _873505))], (52458 ^ _781404) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (45255 ^ _781404) ^ [_1687309, _1687311, _1687313, _1687315, _1687317] : [class_Groups_Ocomm__monoid__add(_1687309), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687309), hAPP(hAPP(c_List_Omap(_1687311, _1687309), hAPP(hAPP(c_COMBS(_1687311, _1687309, _1687309), hAPP(hAPP(c_COMBB(_1687309, tc_fun(_1687309, _1687309), _1687311), c_Groups_Oplus__class_Oplus(_1687309)), _1687313)), _1687315)), _1687317)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1687309), hAPP(c_List_Omonoid__add__class_Olistsum(_1687309), hAPP(hAPP(c_List_Omap(_1687311, _1687309), _1687313), _1687317))), hAPP(c_List_Omonoid__add__class_Olistsum(_1687309), hAPP(hAPP(c_List_Omap(_1687311, _1687309), _1687315), _1687317))))], (37200 ^ _781404) ^ [_1479304, _1479306, _1479308, _1479310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1479304), _1479306)), 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)), _1479308), _1479304)), 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)), _1479310), _1479306)), 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)), _1479308), _1479310)), _1479306)), c_FunDef_Omax__weak)))], (51397 ^ _781404) ^ [_1822382, _1822384, _1822386] : [-(c_Lazy__Sequence_Oflat(_1822382, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1822382), _1822384, _1822386)) = c_Lazy__Sequence_Oappend(_1822382, _1822384, c_Lazy__Sequence_Oflat(_1822382, _1822386)))], (1556 ^ _781404) ^ [_803894, _803896] : [-(class_Enum_Oenum(_803894)), _803896 = _803894, class_Enum_Oenum(_803896)], (18533 ^ _781404) ^ [_1111984, _1111986, _1111988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1111984)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1111986), _1111988)), 18540 ^ _781404 : [(18541 ^ _781404) ^ [_1112180] : [18543 ^ _781404 : [(18549 ^ _781404) ^ [] : [-(_1112180 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 18545 ^ [_1111984, _1111986, _1111988, _1112180]), 18542 ^ [_1111984, _1111986, _1111988, _1112180]))], (18547 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18545 ^ [_1111984, _1111986, _1111988, _1112180]), _1111988)))], (18544 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18542 ^ [_1111984, _1111986, _1111988, _1112180]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1111984))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111986), _1112180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111986), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1112180), _1111984))))]]], (23617 ^ _781404) ^ [_1205581, _1205583] : [class_Divides_Osemiring__div(_1205581), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1205581), c_Groups_Ozero__class_Ozero(_1205581)), _1205583) = c_Groups_Ozero__class_Ozero(_1205581))], (2150 ^ _781404) ^ [_812581, _812583] : [_812583 = _812581, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_812583) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_812581))], (24064 ^ _781404) ^ [_1213080, _1213082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213080)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213080), _1213082)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213080), _1213082) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31606 ^ _781404) ^ [_1349993, _1349995, _1349997] : [class_Orderings_Olinorder(_1349993), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349993), _1349995)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349993), _1349997)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349993, tc_HOL_Obool)), _1349995), _1349997) = c_Orderings_Obot__class_Obot(tc_fun(_1349993, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349993), c_Big__Operators_Olinorder__class_OMin(_1349993, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1349993, tc_HOL_Obool)), _1349995), _1349997))), c_Big__Operators_Olinorder__class_OMin(_1349993, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349993, tc_HOL_Obool)), _1349995), _1349997))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1349993), c_Big__Operators_Olinorder__class_OMin(_1349993, _1349995)), c_Big__Operators_Olinorder__class_OMin(_1349993, _1349997)))], (48050 ^ _781404) ^ [_1747939, _1747941, _1747943] : [-(c_List_Oinsert(_1747939, _1747941, c_List_Oremdups(_1747939, _1747943)) = c_List_Oremdups(_1747939, c_List_Oinsert(_1747939, _1747941, _1747943)))], (26831 ^ _781404) ^ [_1260260, _1260262, _1260264, _1260266] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1260260, _1260262, _1260264, c_Code__Numeral_OSuc__code__numeral(_1260266)) = hAPP(_1260264, _1260266))], (40491 ^ _781404) ^ [_1570222, _1570224, _1570226] : [-(c_Hilbert__Choice_OEps(tc_prod(_1570222, _1570224), _1570226) = c_Hilbert__Choice_OEps(tc_prod(_1570222, _1570224), hAPP(c_Product__Type_Oprod_Oprod__case(_1570222, _1570224, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1570224, tc_prod(_1570222, _1570224)), tc_fun(_1570224, tc_HOL_Obool), _1570222), hAPP(c_COMBB(tc_prod(_1570222, _1570224), tc_HOL_Obool, _1570224), _1570226)), c_Product__Type_OPair(_1570222, _1570224)))))], (23623 ^ _781404) ^ [_1205680, _1205682] : [class_Divides_Osemiring__div(_1205680), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1205680), _1205682), c_Groups_Oone__class_Oone(_1205680)) = _1205682)], (38600 ^ _781404) ^ [_1515424, _1515426, _1515428, _1515430, _1515432, _1515434] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515424, _1515426)), hAPP(hAPP(c_Product__Type_OPair(_1515424, _1515426), _1515428), _1515430)), hAPP(hAPP(c_Product__Type_OSigma(_1515424, _1515426), _1515432), _1515434))), -(hBOOL(hAPP(hAPP(c_member(_1515426), _1515430), hAPP(_1515434, _1515428))))], (44739 ^ _781404) ^ [_1676463] : [class_Groups_Omonoid__add(_1676463), -(c_List_Omonoid__add__class_Olistsum(_1676463) = c_List_Ofoldl(_1676463, _1676463, c_Groups_Oplus__class_Oplus(_1676463), c_Groups_Ozero__class_Ozero(_1676463)))], (8152 ^ _781404) ^ [_918257] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_918257, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_918257, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_918257, tc_HOL_Obool)))], (44116 ^ _781404) ^ [_1661592, _1661594, _1661596] : [_1661592 = c_List_Olist_ONil(_1661594), -(c_List_Obutlast(_1661594, hAPP(hAPP(c_List_Oappend(_1661594), _1661596), _1661592)) = c_List_Obutlast(_1661594, _1661596))], (38590 ^ _781404) ^ [_1515158, _1515160] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1515158, _1515160), c_Orderings_Otop__class_Otop(tc_fun(_1515158, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1515160, tc_HOL_Obool), _1515158), c_Orderings_Otop__class_Otop(tc_fun(_1515160, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1515158, _1515160), tc_HOL_Obool)))], (26515 ^ _781404) ^ [_1254112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254112)), -(c_Nat__Transfer_Ois__nat(_1254112))], (39960 ^ _781404) ^ [_1558050, _1558052] : [hBOOL(hAPP(hAPP(c_member(_1558050), 39961 ^ [_1558050, _1558052]), c_Wellfounded_Oacc(_1558050, _1558052))), -(c_Wellfounded_Owf(_1558050, _1558052))], (22131 ^ _781404) ^ [_1175574, _1175576, _1175578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1175574), _1175576)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175578)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175574), _1175578)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175576), _1175578))))], (3400 ^ _781404) ^ [_832168, _832170] : [_832170 = _832168, -(c_Set_OPow(_832170) = c_Set_OPow(_832168))], (33617 ^ _781404) ^ [_1394261, _1394263, _1394265, _1394267, _1394269] : [-(hAPP(hAPP(c_Set_Oinsert(_1394261), _1394263), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394265, tc_fun(_1394261, tc_HOL_Obool)), _1394267), _1394269)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394265, tc_fun(_1394261, tc_HOL_Obool)), _1394267), hAPP(hAPP(c_COMBB(tc_fun(_1394261, tc_HOL_Obool), tc_fun(_1394261, tc_HOL_Obool), _1394265), hAPP(c_Set_Oinsert(_1394261), _1394263)), _1394269)))], (52312 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (45599 ^ _781404) ^ [_1694866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1694866)), _1694866 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10207 ^ _781404) ^ [_955133, _955135, _955137] : [class_Orderings_Oorder(_955133), 10210 ^ _781404 : [(10219 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955133), _955135), _955137))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955133), _955135), _955137)), -(_955135 = _955137)], (10211 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955133), _955135), _955137)), 10214 ^ _781404 : [(10217 ^ _781404) ^ [] : [_955135 = _955137], (10215 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955133), _955135), _955137)))]]]]], (38142 ^ _781404) ^ [_1503767, _1503769, _1503771] : [c_Relation_Orefl__on(_1503767, _1503769, _1503771), 38145 ^ _781404 : [(38152 ^ _781404) ^ [_1504251] : [hBOOL(hAPP(hAPP(c_member(_1503767), _1504251), _1503769)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1503767, _1503767)), hAPP(hAPP(c_Product__Type_OPair(_1503767, _1503767), _1504251), _1504251)), _1503771)))], (38146 ^ _781404) ^ [_1503978] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1503767, _1503767)), _1503978), _1503771)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1503767, _1503767, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1503767, tc_fun(_1503767, tc_HOL_Obool), tc_fun(_1503767, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1503767, tc_HOL_Obool), tc_fun(_1503767, tc_HOL_Obool)), _1503767), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1503767)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1503767), c_fconj), hAPP(hAPP(c_COMBC(_1503767, tc_fun(_1503767, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503767)), _1503769)))), hAPP(hAPP(c_COMBC(_1503767, tc_fun(_1503767, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503767)), _1503769))), _1503978)))]]], (15613 ^ _781404) ^ [_1057703, _1057705] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1057703, _1057705)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057705), hAPP(c_Nat_OSuc, _1057703)))], (41497 ^ _781404) ^ [_1594900, _1594902, _1594904, _1594906, _1594908] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594900, _1594900)), hAPP(hAPP(c_Product__Type_OPair(_1594900, _1594900), hAPP(_1594902, hAPP(c_Nat_OSuc, 41498 ^ [_1594900, _1594902, _1594904, _1594906, _1594908]))), hAPP(_1594902, 41498 ^ [_1594900, _1594902, _1594904, _1594906, _1594908]))), c_Transitive__Closure_Ortrancl(_1594900, _1594904))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594900, _1594900)), hAPP(hAPP(c_Product__Type_OPair(_1594900, _1594900), hAPP(_1594902, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1594906), _1594908))), hAPP(_1594902, _1594906))), c_Transitive__Closure_Ortrancl(_1594900, _1594904))))], (43671 ^ _781404) ^ [_1651785, _1651787, _1651789] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651785), tc_List_Olist(_1651785))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651785), tc_List_Olist(_1651785)), _1651787), c_List_Olist_ONil(_1651785))), c_List_Olex(_1651785, _1651789)))], (52642 ^ _781404) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (43833 ^ _781404) ^ [_1655609, _1655611, _1655613, _1655615, _1655617] : [-(hAPP(hAPP(c_List_Oappend(_1655609), _1655611), hAPP(hAPP(c_List_Olist_OCons(_1655609), _1655613), c_List_Olist_ONil(_1655609))) = hAPP(hAPP(c_List_Oappend(_1655609), _1655615), hAPP(hAPP(c_List_Olist_OCons(_1655609), _1655617), c_List_Olist_ONil(_1655609)))), _1655611 = _1655615, _1655613 = _1655617], (20159 ^ _781404) ^ [_1139345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1139345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1139345))))], (37264 ^ _781404) ^ [_1480902, _1480904, _1480906, _1480908] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480902, tc_HOL_Obool), tc_fun(_1480902, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480902, tc_HOL_Obool), tc_fun(_1480902, tc_HOL_Obool)), _1480906), _1480908)), c_Wellfounded_Omax__ext(_1480902, _1480904))), -(c_Wellfounded_Omax__extp(_1480902, hAPP(hAPP(c_COMBC(_1480902, tc_fun(tc_prod(_1480902, _1480902), tc_HOL_Obool), tc_fun(_1480902, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1480902, tc_fun(tc_fun(tc_prod(_1480902, _1480902), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1480902, _1480902), tc_HOL_Obool), tc_fun(_1480902, tc_HOL_Obool)), _1480902), c_COMBC(_1480902, tc_fun(tc_prod(_1480902, _1480902), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1480902, tc_prod(_1480902, _1480902)), tc_fun(_1480902, tc_fun(tc_fun(tc_prod(_1480902, _1480902), tc_HOL_Obool), tc_HOL_Obool)), _1480902), hAPP(c_COMBB(tc_prod(_1480902, _1480902), tc_fun(tc_fun(tc_prod(_1480902, _1480902), tc_HOL_Obool), tc_HOL_Obool), _1480902), c_member(tc_prod(_1480902, _1480902)))), c_Product__Type_OPair(_1480902, _1480902)))), _1480904), _1480906, _1480908))], (34277 ^ _781404) ^ [_1415354, _1415356, _1415358, _1415360, _1415362] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415354, tc_fun(_1415356, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1415354), _1415358), _1415360)), _1415362) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415356, tc_HOL_Obool)), hAPP(_1415362, _1415358)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415354, tc_fun(_1415356, tc_HOL_Obool)), _1415360), _1415362)))], (41901 ^ _781404) ^ [_1604875, _1604877, _1604879, _1604881, _1604883, _1604885] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604875, _1604875)), hAPP(hAPP(c_Product__Type_OPair(_1604875, _1604875), _1604877), _1604879)), _1604881)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604875, _1604875)), hAPP(hAPP(c_Product__Type_OPair(_1604875, _1604875), _1604879), _1604883)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604875, _1604875), tc_HOL_Obool), _1604885), _1604881))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604875, _1604875)), hAPP(hAPP(c_Product__Type_OPair(_1604875, _1604875), _1604877), _1604883)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604875, _1604875), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1604885)), _1604881))))], (4134 ^ _781404) ^ [_843999, _844001, _844003, _844005] : [-(c_New__DSequence_Oneg__single(_844005, _844001) = c_New__DSequence_Oneg__single(_844003, _843999)), _844005 = _844003, _844001 = _843999], (45696 ^ _781404) ^ [_1696887, _1696889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1696887), _1696889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1696887)), hAPP(c_Code__Numeral_Onat__of, _1696889))))], (38477 ^ _781404) ^ [_1511717] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1511717), c_Int_OInteg)), -(_1511717 = hAPP(c_Int_ORep__Integ, 38480 ^ [_1511717]))], (8953 ^ _781404) ^ [_932981, _932983] : [8961 ^ _781404 : [(8964 ^ _781404) ^ [] : [-(hBOOL(hAPP(_932983, 8960 ^ [_932981, _932983])))], (8962 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 8960 ^ [_932981, _932983]), _932981)))]], 8954 ^ _781404 : [(8955 ^ _781404) ^ [_933050] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _933050), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _932981))), hBOOL(hAPP(_932983, _933050))]]], (17757 ^ _781404) ^ [_1097997, _1097999, _1098001] : [class_Lattices_Olattice(_1097997), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097997), _1097999)), -(c_Big__Operators_Olattice__class_OSup__fin(_1097997, hAPP(hAPP(c_Set_Oinsert(_1097997), _1098001), _1097999)) = hAPP(hAPP(c_Finite__Set_Ofold(_1097997, _1097997, c_Lattices_Osemilattice__sup__class_Osup(_1097997)), _1098001), _1097999))], (52438 ^ _781404) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (52706 ^ _781404) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (6165 ^ _781404) ^ [_879406, _879408, _879410] : [class_Orderings_Oorder(_879406), 6168 ^ _781404 : [(6175 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879406), _879410), _879408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879406, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_879406), _879408)), hAPP(c_SetInterval_Oord__class_OatLeast(_879406), _879410))))], (6169 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879406, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_879406), _879408)), hAPP(c_SetInterval_Oord__class_OatLeast(_879406), _879410))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879406), _879410), _879408)))]]], (39087 ^ _781404) ^ [_1528578, _1528580, _1528582] : [-(hBOOL(hAPP(_1528578, _1528580))), -(hAPP(c_Set_OCollect(_1528582), hAPP(hAPP(c_COMBS(_1528582, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1528582), c_fconj), hAPP(hAPP(c_COMBC(_1528582, _1528582, tc_HOL_Obool), c_fequal), _1528580))), _1528578)) = c_Orderings_Obot__class_Obot(tc_fun(_1528582, tc_HOL_Obool)))], (40825 ^ _781404) ^ [_1577640, _1577642] : [class_Complete__Lattice_Ocomplete__lattice(_1577640), c_Orderings_Oorder__class_Omono(_1577640, _1577640, _1577642), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577640), hAPP(_1577642, c_Inductive_Ocomplete__lattice__class_Olfp(_1577640, _1577642))), c_Inductive_Ocomplete__lattice__class_Olfp(_1577640, _1577642))))], (39666 ^ _781404) ^ [_1549982, _1549984, _1549986] : [_1549986 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549982, _1549984), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1549982, _1549984), _1549986) = c_Orderings_Obot__class_Obot(tc_fun(_1549984, tc_HOL_Obool)))], (20845 ^ _781404) ^ [_1151623, _1151625] : [class_Rings_Omult__zero(_1151623), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151623), c_Groups_Ozero__class_Ozero(_1151623)), _1151625) = c_Groups_Ozero__class_Ozero(_1151623))], (33792 ^ _781404) ^ [_1399151, _1399153, _1399155, _1399157] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1399151, _1399153)), hAPP(hAPP(c_Product__Type_OPair(_1399151, _1399153), _1399155), _1399157)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1399151, _1399153), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1399151, tc_fun(_1399153, tc_HOL_Obool))), _1399155), _1399157)))], (33039 ^ _781404) ^ [_1377201, _1377203, _1377205, _1377207, _1377209, _1377211] : [hBOOL(hAPP(hAPP(c_member(_1377201), _1377203), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377205, tc_fun(_1377201, tc_HOL_Obool)), _1377207), _1377209))), -(hBOOL(hAPP(hAPP(c_member(_1377201), _1377203), hAPP(_1377209, _1377211)))), hBOOL(hAPP(hAPP(c_member(_1377205), _1377211), _1377207))], (4246 ^ _781404) ^ [_845745, _845747] : [_845747 = _845745, -(c_List_Otake(_845747) = c_List_Otake(_845745))], (24646 ^ _781404) ^ [_1223503, _1223505] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223503), _1223505)), _1223505) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223503), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223503, _1223505)))], (11934 ^ _781404) ^ [_985962, _985964] : [11935 ^ _781404 : [(11936 ^ _781404) ^ [_986015] : [hBOOL(hAPP(hAPP(c_member(_985962), _986015), _985964))]], _985964 = c_Orderings_Obot__class_Obot(tc_fun(_985962, tc_HOL_Obool))], (50131 ^ _781404) ^ [_1794698, _1794700] : [c_Relation_Osym(_1794698, _1794700), c_Relation_Otrans(_1794698, _1794700), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1794698, _1794698), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1794698, _1794698, _1794698), hAPP(c_Relation_Oconverse(_1794698, _1794698), _1794700)), _1794700)), _1794700)))], (49905 ^ _781404) ^ [_1790481, _1790483] : [c_Predicate_Otransp(_1790481, _1790483), -(c_Relation_Otrans(_1790481, hAPP(c_Set_OCollect(tc_prod(_1790481, _1790481)), hAPP(c_Product__Type_Oprod_Oprod__case(_1790481, _1790481, tc_HOL_Obool), _1790483))))], (27877 ^ _781404) ^ [_1280169, _1280171, _1280173, _1280175] : [class_Rings_Odivision__ring(_1280169), -(_1280171 = c_Groups_Ozero__class_Ozero(_1280169)), 27884 ^ _781404 : [(27891 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1280169), _1280173), _1280171) = _1280175, -(_1280173 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280169), _1280175), _1280171))], (27885 ^ _781404) ^ [] : [_1280173 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280169), _1280175), _1280171), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1280169), _1280173), _1280171) = _1280175)]]], (9102 ^ _781404) ^ [_935694, _935696] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935694, tc_HOL_Obool)), _935696), c_Orderings_Obot__class_Obot(tc_fun(_935694, tc_HOL_Obool))) = _935696)], (8493 ^ _781404) ^ [_924646] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_924646, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_924646, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_924646, tc_HOL_Obool)))], (45431 ^ _781404) ^ [_1691425, _1691427, _1691429, _1691431] : [class_Groups_Ocomm__monoid__add(_1691425), hBOOL(hAPP(c_List_Odistinct(_1691427), _1691429)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1691425), hAPP(hAPP(c_List_Omap(_1691427, _1691425), _1691431), _1691429)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1691427, _1691425), _1691431), hAPP(c_List_Oset(_1691427), _1691429)))], (36546 ^ _781404) ^ [_1464528, _1464530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1464528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1464530)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1464528), _1464530) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1464528, _1464530)))], (8455 ^ _781404) ^ [_924016] : [hAPP(c_Nat_OSuc, _924016) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49522 ^ _781404) ^ [_1780410, _1780412] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1780410)), _1780412)), 49526 ^ _781404 : [(49527 ^ _781404) ^ [_1780511] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1780410)), _1780511), _1780412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780410)), _1780511)), 49525 ^ [_1780410, _1780412])))]]], (17363 ^ _781404) ^ [_1091162, _1091164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091162)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091162), _1091164)))], (52556 ^ _781404) ^ [_1840278] : [-(class_Nat_Osize(tc_List_Olist(_1840278)))], (49287 ^ _781404) ^ [_1774904, _1774906, _1774908, _1774910, _1774912, _1774914] : [-(c_New__Random__Sequence_Opos__union(_1774904, _1774906, _1774908, _1774910, _1774912, _1774914) = c_New__DSequence_Opos__union(_1774904, hAPP(hAPP(hAPP(_1774906, _1774910), _1774912), _1774914), hAPP(hAPP(hAPP(_1774908, _1774910), _1774912), _1774914)))], (14009 ^ _781404) ^ [_1025666, _1025668, _1025670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025666), _1025668)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025670), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1025668), _1025666)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025670), _1025666)), _1025668))], (19354 ^ _781404) ^ [_1125661, _1125663] : [class_Rings_Olinordered__semidom(_1125661), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125661), c_Groups_Ozero__class_Ozero(_1125661)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1125661), _1125663))))], (44894 ^ _781404) ^ [_1679926] : [class_Orderings_Olinorder(_1679926), -(c_Finite__Set_Ofun__left__comm(_1679926, tc_List_Olist(_1679926), c_List_Olinorder__class_Oinsort__key(_1679926, _1679926, c_COMBI(_1679926))))], (51600 ^ _781404) ^ [_1826489, _1826491, _1826493] : [class_Rings_Ocomm__semiring__1(_1826489), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826489), _1826491), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826489), _1826493), _1826491))))], (37258 ^ _781404) ^ [_1480517, _1480519, _1480521, _1480523] : [c_Wellfounded_Omax__extp(_1480517, hAPP(hAPP(c_COMBC(_1480517, tc_fun(tc_prod(_1480517, _1480517), tc_HOL_Obool), tc_fun(_1480517, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1480517, tc_fun(tc_fun(tc_prod(_1480517, _1480517), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1480517, _1480517), tc_HOL_Obool), tc_fun(_1480517, tc_HOL_Obool)), _1480517), c_COMBC(_1480517, tc_fun(tc_prod(_1480517, _1480517), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1480517, tc_prod(_1480517, _1480517)), tc_fun(_1480517, tc_fun(tc_fun(tc_prod(_1480517, _1480517), tc_HOL_Obool), tc_HOL_Obool)), _1480517), hAPP(c_COMBB(tc_prod(_1480517, _1480517), tc_fun(tc_fun(tc_prod(_1480517, _1480517), tc_HOL_Obool), tc_HOL_Obool), _1480517), c_member(tc_prod(_1480517, _1480517)))), c_Product__Type_OPair(_1480517, _1480517)))), _1480519), _1480521, _1480523), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480517, tc_HOL_Obool), tc_fun(_1480517, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480517, tc_HOL_Obool), tc_fun(_1480517, tc_HOL_Obool)), _1480521), _1480523)), c_Wellfounded_Omax__ext(_1480517, _1480519))))], (4512 ^ _781404) ^ [_849942, _849944, _849946, _849948, _849950, _849952] : [-(c_Lazy__Sequence_Oanamorph(_849952, _849948, _849944) = c_Lazy__Sequence_Oanamorph(_849950, _849946, _849942)), _849952 = _849950, _849948 = _849946, _849944 = _849942], (24040 ^ _781404) ^ [_1212676, _1212678, _1212680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212678), _1212680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1212676), _1212680)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1212676), _1212678))))], (45232 ^ _781404) ^ [_1686618, _1686620, _1686622, _1686624, _1686626] : [45234 ^ _781404 : [(45237 ^ _781404) ^ [] : [hAPP(_1686622, 45233 ^ [_1686618, _1686620, _1686622, _1686624, _1686626]) = hAPP(_1686626, 45233 ^ [_1686618, _1686620, _1686622, _1686624, _1686626])], (45235 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1686618), 45233 ^ [_1686618, _1686620, _1686622, _1686624, _1686626]), hAPP(c_List_Oset(_1686618), _1686624))))]], -(hAPP(hAPP(c_List_Omap(_1686618, _1686620), _1686622), _1686624) = hAPP(hAPP(c_List_Omap(_1686618, _1686620), _1686626), _1686624))], (8004 ^ _781404) ^ [_914972, _914974, _914976, _914978, _914980] : [class_Lattices_Osemilattice__inf(_914972), class_Lattices_Osemilattice__inf(_914974), c_Orderings_Oorder__class_Omono(_914974, _914972, _914976), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914972), hAPP(_914976, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_914974), _914978), _914980))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_914972), hAPP(_914976, _914978)), hAPP(_914976, _914980)))))], (51444 ^ _781404) ^ [_1823343] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1823343)))], (7345 ^ _781404) ^ [_901065, _901067, _901069] : [class_Orderings_Olinorder(_901065), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901065), _901067), _901069)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901065, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_901065), _901067)), c_SetInterval_Oord__class_OgreaterThanAtMost(_901065, _901067, _901069)) = hAPP(c_SetInterval_Oord__class_OatMost(_901065), _901069))], (52712 ^ _781404) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (8812 ^ _781404) ^ [_930133] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _930133) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _930133))], (19456 ^ _781404) ^ [_1127364, _1127366, _1127368] : [class_Rings_Osemiring__1(_1127364), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127364), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1127366), _1127368)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127364), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127364), _1127366)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127364), _1127368)))], (17188 ^ _781404) ^ [_1087623, _1087625, _1087627] : [class_Int_Onumber__ring(_1087623), -(hAPP(c_Int_Onumber__class_Onumber__of(_1087623), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1087625), _1087627)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087623), hAPP(c_Int_Onumber__class_Onumber__of(_1087623), _1087625)), hAPP(c_Int_Onumber__class_Onumber__of(_1087623), _1087627)))], (18383 ^ _781404) ^ [_1109048, _1109050, _1109052, _1109054, _1109056, _1109058] : [c_Finite__Set_Ofun__left__comm(_1109048, _1109050, _1109052), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109048), _1109054)), -(hBOOL(hAPP(hAPP(c_member(_1109048), _1109056), _1109054))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1109048, _1109050, _1109052), _1109058), hAPP(hAPP(c_Set_Oinsert(_1109048), _1109056), _1109054)) = hAPP(hAPP(c_Finite__Set_Ofold(_1109048, _1109050, _1109052), hAPP(hAPP(_1109052, _1109056), _1109058)), _1109054))], (50795 ^ _781404) ^ [_1808176, _1808178, _1808180] : [c_Fun_Obij__betw(_1808176, _1808178, _1808180, c_Orderings_Otop__class_Otop(tc_fun(_1808176, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808178, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1808178, _1808176, c_Hilbert__Choice_Oinv__into(_1808176, _1808178, c_Orderings_Otop__class_Otop(tc_fun(_1808176, tc_HOL_Obool)), _1808180), c_Orderings_Otop__class_Otop(tc_fun(_1808178, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1808176, tc_HOL_Obool))))], (1236 ^ _781404) ^ [_799894, _799896] : [-(class_Groups_Oordered__ab__group__add(_799894)), _799896 = _799894, class_Groups_Oordered__ab__group__add(_799896)], (38406 ^ _781404) ^ [_1510060, _1510062, _1510064, _1510066] : [-(c_Wellfounded_Omax__extp(_1510060, _1510062, _1510064, _1510066)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510060), _1510064)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510060), _1510066)), -(_1510066 = c_Orderings_Obot__class_Obot(tc_fun(_1510060, tc_HOL_Obool))), 38420 ^ _781404 : [(38423 ^ _781404) ^ [_1510405] : [hBOOL(hAPP(hAPP(c_member(_1510060), _1510405), _1510066)), hBOOL(hAPP(hAPP(_1510062, 38419 ^ [_1510060, _1510062, _1510064, _1510066]), _1510405))], (38421 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1510060), 38419 ^ [_1510060, _1510062, _1510064, _1510066]), _1510064)))]]], (27287 ^ _781404) ^ [_1268869, _1268871] : [class_Groups_Oordered__ab__group__add__abs(_1268869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268869), _1268871), c_Groups_Ozero__class_Ozero(_1268869))), -(hAPP(c_Groups_Oabs__class_Oabs(_1268869), _1268871) = hAPP(c_Groups_Ouminus__class_Ouminus(_1268869), _1268871))], (6528 ^ _781404) ^ [_885462, _885464] : [class_Orderings_Olinorder(_885462), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_885462, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_885462), _885464)) = hAPP(c_SetInterval_Oord__class_OatMost(_885462), _885464))], (7573 ^ _781404) ^ [_905513, _905515, _905517, _905519] : [-(hAPP(hAPP(c_Set_Oinsert(_905513), _905515), hAPP(hAPP(c_Set_Oinsert(_905513), _905517), _905519)) = hAPP(hAPP(c_Set_Oinsert(_905513), _905517), hAPP(hAPP(c_Set_Oinsert(_905513), _905515), _905519)))], (20727 ^ _781404) ^ [_1148929, _1148931] : [class_Rings_Oring__1(_1148929), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1148929), hAPP(c_Groups_Ouminus__class_Ouminus(_1148929), c_Groups_Oone__class_Oone(_1148929))), 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)))), _1148931)) = c_Groups_Oone__class_Oone(_1148929))], (12312 ^ _781404) ^ [_993302, _993304, _993306, _993308] : [-(hBOOL(hAPP(hAPP(c_member(_993302), _993304), _993306))), 12315 ^ _781404 : [(12322 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993302, tc_HOL_Obool)), _993306), _993308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993302, tc_HOL_Obool)), _993306), hAPP(hAPP(c_Set_Oinsert(_993302), _993304), _993308))))], (12316 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993302, tc_HOL_Obool)), _993306), hAPP(hAPP(c_Set_Oinsert(_993302), _993304), _993308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993302, tc_HOL_Obool)), _993306), _993308)))]]], (46647 ^ _781404) ^ [_1718804, _1718806] : [46649 ^ _781404 : [(46652 ^ _781404) ^ [] : [46648 ^ [_1718804, _1718806] = c_List_Olist_ONil(_1718804)], (46650 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1718804)), 46648 ^ [_1718804, _1718806]), hAPP(c_List_Oset(tc_List_Olist(_1718804)), _1718806))))]], -(c_List_Otranspose(_1718804, _1718806) = c_List_Olist_ONil(tc_List_Olist(_1718804)))], (26561 ^ _781404) ^ [_1254780, _1254782] : [class_Rings_Olinordered__idom(_1254780), 26564 ^ _781404 : [(26571 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254780), c_Groups_Ozero__class_Ozero(_1254780)), hAPP(c_Int_Oring__1__class_Oof__int(_1254780), _1254782))))], (26565 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254780), c_Groups_Ozero__class_Ozero(_1254780)), hAPP(c_Int_Oring__1__class_Oof__int(_1254780), _1254782))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254782)))]]], (20519 ^ _781404) ^ [_1145413, _1145415] : [class_Rings_Oring__1(_1145413), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1145413), hAPP(c_Groups_Ouminus__class_Ouminus(_1145413), _1145415)), 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(_1145413), _1145415), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (16040 ^ _781404) ^ [_1065782, _1065784, _1065786] : [class_Lattices_Olattice(_1065782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065782), _1065784)), 16047 ^ _781404 : [(16054 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065782, tc_HOL_Obool)), _1065784), hAPP(hAPP(c_Set_Oinsert(_1065782), _1065786), c_Orderings_Obot__class_Obot(tc_fun(_1065782, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1065782, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1065782, hAPP(hAPP(c_Set_Oinsert(_1065782), _1065786), _1065784)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065782), _1065786), c_Big__Operators_Olattice__class_OInf__fin(_1065782, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065782, tc_HOL_Obool)), _1065784), hAPP(hAPP(c_Set_Oinsert(_1065782), _1065786), c_Orderings_Obot__class_Obot(tc_fun(_1065782, tc_HOL_Obool)))))))], (16048 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1065782, tc_HOL_Obool)), _1065784), hAPP(hAPP(c_Set_Oinsert(_1065782), _1065786), c_Orderings_Obot__class_Obot(tc_fun(_1065782, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1065782, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1065782, hAPP(hAPP(c_Set_Oinsert(_1065782), _1065786), _1065784)) = _1065786)]]], (9441 ^ _781404) ^ [_943244, _943246] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _943244), _943246)), hAPP(c_Nat_OSuc, _943244))))], (25891 ^ _781404) ^ [_1244140, _1244142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1244140), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244140), _1244142)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1244140))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1244142))))], (40686 ^ _781404) ^ [_1574605, _1574607, _1574609] : [class_Complete__Lattice_Ocomplete__lattice(_1574605), c_Orderings_Oorder__class_Omono(_1574605, _1574605, _1574607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1574605), _1574609), hAPP(_1574607, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1574605), _1574609), c_Inductive_Ocomplete__lattice__class_Ogfp(_1574605, _1574607))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1574605), _1574609), c_Inductive_Ocomplete__lattice__class_Ogfp(_1574605, _1574607))))], (2034 ^ _781404) ^ [_810779, _810781, _810783, _810785, _810787, _810789] : [-(c_SetInterval_Oord_OatLeast(_810789, _810785, _810781) = c_SetInterval_Oord_OatLeast(_810787, _810783, _810779)), _810789 = _810787, _810785 = _810783, _810781 = _810779], (24002 ^ _781404) ^ [_1212098, _1212100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212098)), 24005 ^ _781404 : [(24012 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212098), _1212100)), -(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), _1212100), _1212098))))], (24006 ^ _781404) ^ [] : [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), _1212100), _1212098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212098), _1212100)))]]], (48923 ^ _781404) ^ [_1766908, _1766910, _1766912, _1766914, _1766916] : [-(hAPP(c_New__DSequence_Oneg__bind(_1766908, _1766910, _1766912, _1766914), _1766916) = c_Lazy__Sequence_Ohb__bind(_1766908, _1766910, hAPP(_1766912, _1766916), hAPP(hAPP(c_COMBC(_1766908, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1766910))), _1766914), _1766916)))], (45883 ^ _781404) ^ [_1701351, _1701353, _1701355, _1701357, _1701359] : [c_List_Olist__all2(_1701351, _1701353, _1701355, _1701357, _1701359), 45886 ^ _781404 : [(45889 ^ _781404) ^ [_1701517] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1701351, _1701353)), _1701517), hAPP(c_List_Oset(tc_prod(_1701351, _1701353)), hAPP(hAPP(c_List_Ozip(_1701351, _1701353), _1701357), _1701359)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1701351, _1701353, tc_HOL_Obool), _1701355), _1701517)))], (45887 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701351)), _1701357) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701353)), _1701359))]]], (42358 ^ _781404) ^ [_1618377, _1618379, _1618381, _1618383, _1618385] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618377), tc_List_Olist(_1618377))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618377), tc_List_Olist(_1618377)), _1618379), _1618381)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1618377), c_List_Olistrel1(_1618377, _1618383)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618377), tc_List_Olist(_1618377))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618377), tc_List_Olist(_1618377)), hAPP(hAPP(c_List_Olist_OCons(_1618377), _1618385), _1618379)), hAPP(hAPP(c_List_Olist_OCons(_1618377), _1618385), _1618381))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1618377), c_List_Olistrel1(_1618377, _1618383)))))], (31946 ^ _781404) ^ [_1356341] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1356341) = _1356341)], (5444 ^ _781404) ^ [_864570, _864572, _864574, _864576, _864578, _864580, _864582, _864584] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_864584, _864580, _864576, _864572) = c_SetInterval_Oord_OgreaterThanLessThan(_864582, _864578, _864574, _864570)), _864584 = _864582, _864580 = _864578, _864576 = _864574, _864572 = _864570], (24124 ^ _781404) ^ [_1214062, _1214064, _1214066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214062), _1214064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214062), _1214066)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214064), _1214066))))], (43665 ^ _781404) ^ [_1651563, _1651565] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651563), tc_List_Olist(_1651563))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651563), tc_List_Olist(_1651563)), c_List_Olist_ONil(_1651563)), c_List_Olist_ONil(_1651563))), c_List_Olistrel(_1651563, _1651565))))], (24232 ^ _781404) ^ [_1215834, _1215836, _1215838, _1215840] : [class_Divides_Osemiring__div(_1215834), -(_1215836 = c_Groups_Ozero__class_Ozero(_1215834)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1215834), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215834), _1215838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215834), _1215840), _1215836))), _1215836) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215834), _1215840), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1215834), _1215838), _1215836)))], (22527 ^ _781404) ^ [_1183322, _1183324, _1183326] : [class_Rings_Olinordered__ring__strict(_1183322), 22530 ^ _781404 : [(22531 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183322), c_Groups_Ozero__class_Ozero(_1183322)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183322), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183322), _1183324), _1183324)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183322), _1183326), _1183326)))), _1183324 = c_Groups_Ozero__class_Ozero(_1183322), _1183326 = c_Groups_Ozero__class_Ozero(_1183322)], (22541 ^ _781404) ^ [] : [22542 ^ _781404 : [(22545 ^ _781404) ^ [] : [-(_1183326 = c_Groups_Ozero__class_Ozero(_1183322))], (22543 ^ _781404) ^ [] : [-(_1183324 = c_Groups_Ozero__class_Ozero(_1183322))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183322), c_Groups_Ozero__class_Ozero(_1183322)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183322), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183322), _1183324), _1183324)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183322), _1183326), _1183326)))))]]], (8239 ^ _781404) ^ [_920025, _920027, _920029] : [class_Complete__Lattice_Ocomplete__lattice(_920025), -(c_Complete__Lattice_OSup__class_OSup(_920025, hAPP(hAPP(c_Set_Oinsert(_920025), _920027), hAPP(hAPP(c_Set_Oinsert(_920025), _920029), c_Orderings_Obot__class_Obot(tc_fun(_920025, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920025), _920027), _920029))], (22619 ^ _781404) ^ [_1185248, _1185250, _1185252, _1185254, _1185256, _1185258] : [class_Rings_Oordered__ring(_1185248), 22622 ^ _781404 : [(22629 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185248), _1185254), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185248), _1185256), _1185250)), _1185252)), _1185258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185248), _1185250), _1185252)), _1185254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185248), _1185256), _1185252)), _1185258))))], (22623 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185248), _1185250), _1185252)), _1185254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185248), _1185256), _1185252)), _1185258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185248), _1185254), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185248), _1185256), _1185250)), _1185252)), _1185258))))]]], (52674 ^ _781404) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (52662 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (49478 ^ _781404) ^ [_1779407, _1779409, _1779411] : [-(c_FunDef_OTHE__default(_1779409, _1779411, _1779407) = c_HOL_OThe(_1779409, _1779407)), 49479 ^ _781404 : [(49480 ^ _781404) ^ [_1779471] : [hBOOL(hAPP(_1779407, _1779471)), 49484 ^ _781404 : [(49487 ^ _781404) ^ [] : [49483 ^ [_1779407, _1779409, _1779411, _1779471] = _1779471], (49485 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1779407, 49483 ^ [_1779407, _1779409, _1779411, _1779471])))]]]]], (43735 ^ _781404) ^ [_1653091, _1653093, _1653095] : [-(hBOOL(hAPP(hAPP(c_member(_1653091), _1653093), hAPP(c_List_Oset(_1653091), _1653095)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653091)), c_List_Oremove1(_1653091, _1653093, _1653095)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653091)), _1653095))], (20351 ^ _781404) ^ [_1142623, _1142625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142623), _1142625)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1142623)), c_Int_OBit0(_1142625))))], (45652 ^ _781404) ^ [_1696175, _1696177] : [hAPP(c_Code__Numeral_Onat__of, _1696175) = hAPP(c_Code__Numeral_Onat__of, _1696177), -(_1696175 = _1696177)], (34199 ^ _781404) ^ [_1411582, _1411584, _1411586, _1411588, _1411590] : [_1411582 = c_Orderings_Obot__class_Obot(tc_fun(_1411584, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411584, tc_fun(_1411586, tc_HOL_Obool)), _1411582), hAPP(hAPP(c_COMBC(_1411584, tc_fun(_1411586, tc_HOL_Obool), tc_fun(_1411586, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411586, tc_HOL_Obool), tc_fun(tc_fun(_1411586, tc_HOL_Obool), tc_fun(_1411586, tc_HOL_Obool)), _1411584), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411586, tc_HOL_Obool))), _1411588)), _1411590)) = c_Orderings_Otop__class_Otop(tc_fun(_1411586, tc_HOL_Obool)))], (5550 ^ _781404) ^ [_866295, _866297] : [_866297 = _866295, -(c_Rings_Odvd__class_Odvd(_866297) = c_Rings_Odvd__class_Odvd(_866295))], (9106 ^ _781404) ^ [_935776, _935778, _935780] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935776, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935776, tc_HOL_Obool)), _935778), _935780)), _935778)))], (42569 ^ _781404) ^ [_1625196] : [-(c_List_Olists(_1625196, c_Orderings_Otop__class_Otop(tc_fun(_1625196, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1625196), tc_HOL_Obool)))], (14402 ^ _781404) ^ [_1033304, _1033306, _1033308, _1033310] : [class_Groups_Ocomm__monoid__add(_1033304), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033306), _1033308)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1033304), _1033310), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1033306), _1033308)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033304), hAPP(_1033310, _1033306)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1033304), _1033310), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1033306)), _1033308))))], (42169 ^ _781404) ^ [_1612194] : [-(c_Nitpick_Onum(_1612194) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1612194, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1612194)))], (42938 ^ _781404) ^ [_1634833, _1634835, _1634837, _1634839] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634833), tc_List_Olist(_1634833))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634833), tc_List_Olist(_1634833)), _1634835), _1634837)), c_List_Olistrel(_1634833, _1634839))), 42941 ^ _781404 : [(42944 ^ _781404) ^ [_1635169] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634833, _1634833)), _1635169), hAPP(c_List_Oset(tc_prod(_1634833, _1634833)), hAPP(hAPP(c_List_Ozip(_1634833, _1634833), _1634835), _1634837)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1634833, _1634833, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1634833, tc_fun(tc_prod(_1634833, _1634833), tc_HOL_Obool), tc_fun(_1634833, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1634833, tc_fun(tc_fun(tc_prod(_1634833, _1634833), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1634833, _1634833), tc_HOL_Obool), tc_fun(_1634833, tc_HOL_Obool)), _1634833), c_COMBC(_1634833, tc_fun(tc_prod(_1634833, _1634833), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1634833, tc_prod(_1634833, _1634833)), tc_fun(_1634833, tc_fun(tc_fun(tc_prod(_1634833, _1634833), tc_HOL_Obool), tc_HOL_Obool)), _1634833), hAPP(c_COMBB(tc_prod(_1634833, _1634833), tc_fun(tc_fun(tc_prod(_1634833, _1634833), tc_HOL_Obool), tc_HOL_Obool), _1634833), c_member(tc_prod(_1634833, _1634833)))), c_Product__Type_OPair(_1634833, _1634833)))), _1634839)), _1635169)))], (42942 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634833)), _1634835) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634833)), _1634837))]]], (49221 ^ _781404) ^ [_1773504, _1773506, _1773508] : [-(hAPP(hAPP(c_List_Oappend(_1773504), c_List_Oreplicate(_1773504, _1773506, _1773508)), hAPP(hAPP(c_List_Olist_OCons(_1773504), _1773508), c_List_Olist_ONil(_1773504))) = hAPP(hAPP(c_List_Olist_OCons(_1773504), _1773508), c_List_Oreplicate(_1773504, _1773506, _1773508)))], (10669 ^ _781404) ^ [_962733, _962735] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962733), _962735))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962733), _962735)), -(_962733 = _962735)], (42760 ^ _781404) ^ [_1630286, _1630288] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1630286), hAPP(c_List_Oset(_1630286), _1630288))))], (43559 ^ _781404) ^ [_1649651, _1649653] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649651)), _1649653) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1649653 = c_List_Olist_ONil(_1649651))], (25049 ^ _781404) ^ [_1229844, _1229846] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1229844))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1229844)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1229846)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17064 ^ _781404) ^ [_1085304, _1085306, _1085308, _1085310, _1085312, _1085314, _1085316, _1085318] : [class_Groups_Ocomm__monoid__add(_1085304), c_Fun_Oinj__on(_1085306, _1085308, _1085310, _1085312), _1085314 = hAPP(c_Set_Oimage(_1085306, _1085308, _1085310), _1085312), 17078 ^ _781404 : [(17081 ^ _781404) ^ [] : [hAPP(_1085316, 17077 ^ [_1085304, _1085306, _1085308, _1085310, _1085312, _1085314, _1085316, _1085318]) = hAPP(_1085318, hAPP(_1085310, 17077 ^ [_1085304, _1085306, _1085308, _1085310, _1085312, _1085314, _1085316, _1085318]))], (17079 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1085306), 17077 ^ [_1085304, _1085306, _1085308, _1085310, _1085312, _1085314, _1085316, _1085318]), _1085312)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085308, _1085304), _1085318), _1085314) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085306, _1085304), _1085316), _1085312))], (44228 ^ _781404) ^ [_1664375, _1664377, _1664379, _1664381, _1664383] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1664375), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664377)), _1664379)))), -(hAPP(hAPP(c_List_Olist__update(_1664377, hAPP(hAPP(c_List_Oappend(_1664377), _1664379), _1664381)), _1664375), _1664383) = hAPP(hAPP(c_List_Oappend(_1664377), _1664379), hAPP(hAPP(c_List_Olist__update(_1664377, _1664381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1664375), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664377)), _1664379))), _1664383)))], (48718 ^ _781404) ^ [_1762808, _1762810, _1762812] : [48720 ^ _781404 : [(48723 ^ _781404) ^ [] : [hBOOL(hAPP(_1762810, 48719 ^ [_1762808, _1762810, _1762812]))], (48721 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1762808), 48719 ^ [_1762808, _1762810, _1762812]), hAPP(c_List_Oset(_1762808), _1762812))))]], -(c_List_Olist__all(_1762808, _1762810, _1762812))], (42376 ^ _781404) ^ [_1619046, _1619048, _1619050, _1619052] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619046), tc_List_Olist(_1619046))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619046), tc_List_Olist(_1619046)), _1619048), _1619050)), c_List_Olistrel1(_1619046, _1619052))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619046)), _1619048) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619046)), _1619050))], (48111 ^ _781404) ^ [_1749466, _1749468] : [-(c_Wellfounded_Owf(_1749466, c_List_Omeasures(_1749466, _1749468)))], (36460 ^ _781404) ^ [_1462713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1462713)), 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), _1462713)) = 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), _1462713))))))], (49551 ^ _781404) ^ [_1780982, _1780984, _1780986] : [c_List_Oall__interval__int(_1780982, _1780984, _1780986), -(c_List_Olist__all(tc_Int_Oint, _1780982, c_List_Oupto(_1780984, _1780986)))], (52192 ^ _781404) ^ [_1836653, _1836655] : [class_Lattices_Odistrib__lattice(_1836653), -(class_Lattices_Odistrib__lattice(tc_fun(_1836655, _1836653)))], (33115 ^ _781404) ^ [_1379018, _1379020, _1379022, _1379024] : [class_Groups_Ocomm__monoid__add(_1379018), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379018), _1379020), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1379022)), hAPP(c_Nat_OSuc, _1379024))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379018), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1379018, tc_Nat_Onat), _1379020), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1379022), _1379024)))], (23335 ^ _781404) ^ [_1199550, _1199552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1199550), 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)))), _1199552)), 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)))), _1199550)) = 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), _1199552), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1199550))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33920 ^ _781404) ^ [_1403433, _1403435, _1403437, _1403439, _1403441] : [33922 ^ _781404 : [(33925 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403433, tc_HOL_Obool)), _1403435), hAPP(_1403441, 33921 ^ [_1403433, _1403435, _1403437, _1403439, _1403441])))], (33923 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403437), 33921 ^ [_1403433, _1403435, _1403437, _1403439, _1403441]), _1403439)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403433, tc_HOL_Obool)), _1403435), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1403437, tc_fun(_1403433, tc_HOL_Obool)), _1403439), _1403441))))], (40136 ^ _781404) ^ [_1562315, _1562317, _1562319, _1562321] : [hBOOL(hAPP(c_Predicate_ODomainP(_1562315, _1562317, hAPP(hAPP(c_COMBC(_1562315, tc_fun(tc_prod(_1562315, _1562317), tc_HOL_Obool), tc_fun(_1562317, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562317, tc_fun(tc_fun(tc_prod(_1562315, _1562317), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1562315, _1562317), tc_HOL_Obool), tc_fun(_1562317, tc_HOL_Obool)), _1562315), c_COMBC(_1562317, tc_fun(tc_prod(_1562315, _1562317), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562317, tc_prod(_1562315, _1562317)), tc_fun(_1562317, tc_fun(tc_fun(tc_prod(_1562315, _1562317), tc_HOL_Obool), tc_HOL_Obool)), _1562315), hAPP(c_COMBB(tc_prod(_1562315, _1562317), tc_fun(tc_fun(tc_prod(_1562315, _1562317), tc_HOL_Obool), tc_HOL_Obool), _1562317), c_member(tc_prod(_1562315, _1562317)))), c_Product__Type_OPair(_1562315, _1562317)))), _1562319)), _1562321)), -(hBOOL(hAPP(hAPP(c_member(_1562315), _1562321), hAPP(c_Relation_ODomain(_1562315, _1562317), _1562319))))], (44094 ^ _781404) ^ [_1661200, _1661202] : [-(hAPP(hAPP(c_List_Oappend(_1661200), _1661202), c_List_Olist_ONil(_1661200)) = _1661202)], (6197 ^ _781404) ^ [_879990, _879992, _879994, _879996, _879998] : [class_Complete__Lattice_Ocomplete__lattice(_879990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879992, tc_HOL_Obool)), _879994), _879996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879990), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_879992, _879990), _879994), _879998)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_879992, _879990), _879996), _879998))))], (10619 ^ _781404) ^ [_961968, _961970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961968), _961970)), -(hAPP(c_Nat_OSuc, _961968) = _961970), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961968)), _961970)))], (14579 ^ _781404) ^ [_1036927, _1036929] : [class_Finite__Set_Ofinite(_1036927), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1036927), _1036929)))], (37902 ^ _781404) ^ [_1497474, _1497476] : [c_Equiv__Relations_Oequiv(_1497474, c_Orderings_Otop__class_Otop(tc_fun(_1497474, tc_HOL_Obool)), _1497476), -(c_Equiv__Relations_Oequivp(_1497474, hAPP(hAPP(c_COMBC(_1497474, tc_fun(tc_prod(_1497474, _1497474), tc_HOL_Obool), tc_fun(_1497474, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497474, tc_fun(tc_fun(tc_prod(_1497474, _1497474), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1497474, _1497474), tc_HOL_Obool), tc_fun(_1497474, tc_HOL_Obool)), _1497474), c_COMBC(_1497474, tc_fun(tc_prod(_1497474, _1497474), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497474, tc_prod(_1497474, _1497474)), tc_fun(_1497474, tc_fun(tc_fun(tc_prod(_1497474, _1497474), tc_HOL_Obool), tc_HOL_Obool)), _1497474), hAPP(c_COMBB(tc_prod(_1497474, _1497474), tc_fun(tc_fun(tc_prod(_1497474, _1497474), tc_HOL_Obool), tc_HOL_Obool), _1497474), c_member(tc_prod(_1497474, _1497474)))), c_Product__Type_OPair(_1497474, _1497474)))), _1497476)))], (12486 ^ _781404) ^ [_996792, _996794, _996796] : [class_Orderings_Oord(_996792), 12489 ^ _781404 : [(12496 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996792), _996796), _996794)), -(hBOOL(hAPP(hAPP(c_member(_996792), _996794), hAPP(c_SetInterval_Oord__class_OatLeast(_996792), _996796))))], (12490 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_996792), _996794), hAPP(c_SetInterval_Oord__class_OatLeast(_996792), _996796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996792), _996796), _996794)))]]], (8058 ^ _781404) ^ [_916262, _916264] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _916262), _916264) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _916262, _916264))], (25931 ^ _781404) ^ [_1244864, _1244866] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244864))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244864)), _1244866) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1244866))], (12408 ^ _781404) ^ [_995359, _995361, _995363, _995365] : [hBOOL(hAPP(hAPP(c_member(_995359), _995361), _995363)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995359, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_995359), _995361), _995365)), _995363) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995359, tc_HOL_Obool)), _995365), _995363))], (46858 ^ _781404) ^ [_1723949] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1723949) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1723949)))], (21973 ^ _781404) ^ [_1172497, _1172499, _1172501, _1172503] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172497), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172497), _1172499), _1172501)), hAPP(c_Int_Onumber__class_Onumber__of(_1172497), _1172503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172497), _1172499), hAPP(c_Int_Onumber__class_Onumber__of(_1172497), _1172503))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172497), _1172501), hAPP(c_Int_Onumber__class_Onumber__of(_1172497), _1172503)))), class_Int_Onumber(_1172497), class_Rings_Osemiring(_1172497)], (14278 ^ _781404) ^ [_1030821, _1030823, _1030825] : [-(hBOOL(hAPP(_1030821, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030823), _1030825)))), 14281 ^ _781404 : [(14284 ^ _781404) ^ [] : [hBOOL(hAPP(_1030821, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14282 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030823), _1030825)))]], 14286 ^ _781404 : [(14289 ^ _781404) ^ [] : [hBOOL(hAPP(_1030821, 14285 ^ [_1030821, _1030823, _1030825]))], (14287 ^ _781404) ^ [] : [-(_1030823 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030825), 14285 ^ [_1030821, _1030823, _1030825]))]]], (18727 ^ _781404) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (48236 ^ _781404) ^ [_1752271, _1752273, _1752275, _1752277, _1752279] : [48237 ^ _781404 : [(48240 ^ _781404) ^ [] : [hBOOL(hAPP(_1752279, hAPP(hAPP(c_List_Ozip(_1752271, _1752275), hAPP(hAPP(c_List_Otake(_1752271), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752271)), _1752273)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752275)), _1752277))), _1752273)), hAPP(hAPP(c_List_Otake(_1752275), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752271)), _1752273)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752275)), _1752277))), _1752277))))], (48238 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752271)), hAPP(hAPP(c_List_Otake(_1752271), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752271)), _1752273)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752275)), _1752277))), _1752273)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752275)), hAPP(hAPP(c_List_Otake(_1752275), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752271)), _1752273)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752275)), _1752277))), _1752277)))]], -(hBOOL(hAPP(_1752279, hAPP(hAPP(c_List_Ozip(_1752271, _1752275), _1752273), _1752277))))], (39544 ^ _781404) ^ [_1546435, _1546437, _1546439, _1546441] : [c_Finite__Set_Ofolding(_1546435, _1546437, _1546439, _1546441), -(hAPP(_1546441, c_Orderings_Obot__class_Obot(tc_fun(_1546435, tc_HOL_Obool))) = c_Fun_Oid(_1546437))], (37506 ^ _781404) ^ [_1487821] : [-(_1487821 = 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), 37503 ^ [_1487821]), 37504 ^ [_1487821])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (21605 ^ _781404) ^ [_1165521, _1165523] : [class_Rings_Olinordered__ring(_1165521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165521), _1165523), _1165523)), c_Groups_Ozero__class_Ozero(_1165521)))], (47485 ^ _781404) ^ [_1736061, _1736063, _1736065, _1736067] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736061)), _1736063) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736065)), _1736067), -(hAPP(hAPP(c_List_Ozip(_1736061, _1736065), hAPP(c_List_Orev(_1736061), _1736063)), hAPP(c_List_Orev(_1736065), _1736067)) = hAPP(c_List_Orev(tc_prod(_1736061, _1736065)), hAPP(hAPP(c_List_Ozip(_1736061, _1736065), _1736063), _1736067)))], (17689 ^ _781404) ^ [_1096747, _1096749, _1096751] : [class_Complete__Lattice_Ocomplete__lattice(_1096747), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096747), _1096749)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096747), _1096751), c_Complete__Lattice_OInf__class_OInf(_1096747, _1096749)) = hAPP(hAPP(c_Finite__Set_Ofold(_1096747, _1096747, c_Lattices_Osemilattice__inf__class_Oinf(_1096747)), _1096751), _1096749))], (26125 ^ _781404) ^ [_1248002, _1248004] : [c_Nat__Transfer_Onat__set(_1248002), c_Nat__Transfer_Onat__set(_1248004), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1248002), _1248004)))], (33448 ^ _781404) ^ [_1389406, _1389408, _1389410, _1389412] : [33450 ^ _781404 : [(33453 ^ _781404) ^ [] : [hAPP(_1389412, 33449 ^ [_1389406, _1389408, _1389410, _1389412]) = c_Orderings_Otop__class_Otop(tc_fun(_1389408, tc_HOL_Obool))], (33451 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389406), 33449 ^ [_1389406, _1389408, _1389410, _1389412]), _1389410)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389406, tc_fun(_1389408, tc_HOL_Obool)), _1389410), _1389412) = c_Orderings_Otop__class_Otop(tc_fun(_1389408, tc_HOL_Obool)))], (48358 ^ _781404) ^ [_1755506, _1755508, _1755510, _1755512, _1755514] : [hAPP(hAPP(c_List_Olist_OCons(_1755506), _1755508), _1755510) = hAPP(c_List_Ofilter(_1755506, _1755512), _1755514), 48363 ^ _781404 : [(48372 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1755512, _1755508)))], (48374 ^ _781404) ^ [] : [-(_1755510 = hAPP(c_List_Ofilter(_1755506, _1755512), 48362 ^ [_1755506, _1755508, _1755510, _1755512, _1755514]))], (48366 ^ _781404) ^ [_1755820] : [hBOOL(hAPP(hAPP(c_member(_1755506), _1755820), hAPP(c_List_Oset(_1755506), 48361 ^ [_1755506, _1755508, _1755510, _1755512, _1755514]))), hBOOL(hAPP(_1755512, _1755820))], (48364 ^ _781404) ^ [] : [-(_1755514 = hAPP(hAPP(c_List_Oappend(_1755506), 48361 ^ [_1755506, _1755508, _1755510, _1755512, _1755514]), hAPP(hAPP(c_List_Olist_OCons(_1755506), _1755508), 48362 ^ [_1755506, _1755508, _1755510, _1755512, _1755514])))]]], (52464 ^ _781404) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (37662 ^ _781404) ^ [] : [-(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))], (39690 ^ _781404) ^ [_1550645, _1550647, _1550649] : [-(hAPP(c_Set_Oimage(tc_prod(_1550645, _1550647), _1550647, c_Product__Type_Osnd(_1550645, _1550647)), _1550649) = hAPP(c_Relation_ORange(_1550645, _1550647), _1550649))], (38520 ^ _781404) ^ [_1512857, _1512859, _1512861, _1512863] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1512857, _1512859)), hAPP(hAPP(c_Product__Type_OSigma(_1512857, _1512859), _1512861), hAPP(c_COMBK(tc_fun(_1512859, tc_HOL_Obool), _1512857), _1512863))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1512857), _1512861)), hAPP(c_Finite__Set_Ocard(_1512859), _1512863)))], (36498 ^ _781404) ^ [_1463479, _1463481, _1463483] : [-(hAPP(c_Product__Type_Ofst(_1463479, _1463481), _1463483) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1463479, _1463481, _1463479), c_COMBK(_1463479, _1463481)), _1463483))], (21277 ^ _781404) ^ [_1159548] : [class_Groups_Oab__semigroup__mult(_1159548), -(c_Finite__Set_Ofun__left__comm(_1159548, _1159548, c_Groups_Otimes__class_Otimes(_1159548)))], (49069 ^ _781404) ^ [_1770787, _1770789, _1770791] : [-(_1770787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1770789, c_List_Oreplicate(_1770789, _1770787, _1770791)) = _1770791)], (20507 ^ _781404) ^ [] : [-(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))))))], (20741 ^ _781404) ^ [_1149207, _1149209] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149207)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149209)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1149207), _1149209)))], (5668 ^ _781404) ^ [_868064, _868066] : [_868066 = _868064, -(c_Orderings_Oord__class_Oless__eq(_868066) = c_Orderings_Oord__class_Oless__eq(_868064))], (32610 ^ _781404) ^ [_1368815, _1368817, _1368819] : [class_Orderings_Olinorder(_1368815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368815), _1368817)), hBOOL(hAPP(hAPP(c_member(_1368815), _1368819), _1368817)), 32621 ^ _781404 : [(32628 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368815, tc_HOL_Obool)), _1368817), hAPP(hAPP(c_Set_Oinsert(_1368815), _1368819), c_Orderings_Obot__class_Obot(tc_fun(_1368815, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1368815, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1368815, c_Orderings_Oord__class_Omax(_1368815), _1368817) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1368815), _1368819), c_Big__Operators_Olattice_OSup__fin(_1368815, c_Orderings_Oord__class_Omax(_1368815), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368815, tc_HOL_Obool)), _1368817), hAPP(hAPP(c_Set_Oinsert(_1368815), _1368819), c_Orderings_Obot__class_Obot(tc_fun(_1368815, tc_HOL_Obool)))))))], (32622 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368815, tc_HOL_Obool)), _1368817), hAPP(hAPP(c_Set_Oinsert(_1368815), _1368819), c_Orderings_Obot__class_Obot(tc_fun(_1368815, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1368815, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1368815, c_Orderings_Oord__class_Omax(_1368815), _1368817) = _1368819)]]], (44812 ^ _781404) ^ [_1677901, _1677903, _1677905] : [class_Orderings_Olinorder(_1677901), -(c_Big__Operators_Olattice_OInf__fin(_1677901, c_Orderings_Oord__class_Omin(_1677901), hAPP(c_List_Oset(_1677901), hAPP(hAPP(c_List_Olist_OCons(_1677901), _1677903), _1677905))) = hAPP(c_List_Ofoldl(_1677901, _1677901, c_Orderings_Oord__class_Omin(_1677901), _1677903), _1677905))], (6885 ^ _781404) ^ [_891814, _891816, _891818] : [class_Lattices_Osemilattice__sup(_891814), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891814), _891816), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891814), _891816), _891818)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891814), _891816), _891818))], (39266 ^ _781404) ^ [_1534788, _1534790] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534788), _1534790)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1534788, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1534788, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1534788, tc_HOL_Obool), tc_fun(_1534788, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1534788, tc_HOL_Obool))), _1534790)))))], (16452 ^ _781404) ^ [_1073704, _1073706, _1073708, _1073710] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1073704, _1073706)), c_Sum__Type_OPlus(_1073704, _1073706, _1073708, _1073710)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073704), _1073708)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073706), _1073710))], (47772 ^ _781404) ^ [_1742084, _1742086] : [-(_1742084 = c_List_Olist_ONil(_1742086)), hBOOL(hAPP(c_List_Odistinct(_1742086), _1742084)), -(c_List_OtakeWhile(_1742086, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1742086), c_fNot), hAPP(hAPP(c_COMBC(_1742086, _1742086, tc_HOL_Obool), c_fequal), c_List_Olast(_1742086, _1742084))), _1742084) = c_List_Obutlast(_1742086, _1742084))], (45545 ^ _781404) ^ [_1693744, _1693746, _1693748] : [-(hAPP(hAPP(c_List_Ozip(_1693744, _1693746), hAPP(hAPP(c_List_Omap(tc_prod(_1693744, _1693746), _1693744), c_Product__Type_Ofst(_1693744, _1693746)), _1693748)), hAPP(hAPP(c_List_Omap(tc_prod(_1693744, _1693746), _1693746), c_Product__Type_Osnd(_1693744, _1693746)), _1693748)) = _1693748)], (13145 ^ _781404) ^ [_1009556, _1009558] : [class_Groups_Ocomm__monoid__add(_1009556), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009556), _1009558), c_Groups_Ozero__class_Ozero(_1009556)) = _1009558)], (48244 ^ _781404) ^ [_1752683, _1752685, _1752687, _1752689] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1752683, _1752685, _1752687, _1752689) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1752683, _1752685), _1752687), _1752689)))], (13139 ^ _781404) ^ [_1009461, _1009463] : [class_Groups_Omonoid__add(_1009461), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009461), _1009463), c_Groups_Ozero__class_Ozero(_1009461)) = _1009463)], (49049 ^ _781404) ^ [_1770398, _1770400, _1770402] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770398)), c_List_Oreplicate(_1770398, _1770400, _1770402)) = _1770400)], (33249 ^ _781404) ^ [_1382419, _1382421, _1382423, _1382425] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382419, tc_fun(_1382421, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1382419, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1382421, tc_HOL_Obool), tc_fun(_1382421, tc_HOL_Obool), _1382419), hAPP(c_COMBC(_1382421, tc_fun(_1382421, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382421))), _1382423)), _1382425)), -(hBOOL(hAPP(hAPP(c_member(_1382421), _1382425), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382419, tc_fun(_1382421, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1382419, tc_HOL_Obool))), _1382423))))], (45531 ^ _781404) ^ [_1693412, _1693414, _1693416, _1693418] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693412)), _1693414) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693416)), _1693418), -(hAPP(hAPP(c_List_Omap(tc_prod(_1693412, _1693416), _1693412), c_Product__Type_Ofst(_1693412, _1693416)), hAPP(hAPP(c_List_Ozip(_1693412, _1693416), _1693414), _1693418)) = _1693414)], (44631 ^ _781404) ^ [_1674129] : [-(c_List_Orotate(_1674129, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1674129)))], (8154 ^ _781404) ^ [_918299] : [-(hAPP(c_Set_OPow(_918299), c_Orderings_Obot__class_Obot(tc_fun(_918299, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_918299, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_918299, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_918299, tc_HOL_Obool), tc_HOL_Obool))))], (44565 ^ _781404) ^ [_1673192, _1673194, _1673196] : [_1673192 = c_List_Olist_ONil(_1673194), -(hAPP(c_List_Ohd(_1673194), hAPP(hAPP(c_List_Oappend(_1673194), _1673192), _1673196)) = hAPP(c_List_Ohd(_1673194), _1673196))], (16875 ^ _781404) ^ [_1081912, _1081914] : [class_Rings_Olinordered__idom(_1081912), 16878 ^ _781404 : [(16885 ^ _781404) ^ [] : [_1081914 = c_Groups_Ozero__class_Ozero(_1081912), -(c_Groups_Osgn__class_Osgn(_1081912, _1081914) = c_Groups_Ozero__class_Ozero(_1081912))], (16879 ^ _781404) ^ [] : [c_Groups_Osgn__class_Osgn(_1081912, _1081914) = c_Groups_Ozero__class_Ozero(_1081912), -(_1081914 = c_Groups_Ozero__class_Ozero(_1081912))]]], (45815 ^ _781404) ^ [_1699865, _1699867, _1699869] : [-(c_List_Olistsp(_1699865, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1699865, tc_HOL_Obool)), _1699867), _1699869)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1699865), tc_HOL_Obool)), c_List_Olistsp(_1699865, _1699867)), c_List_Olistsp(_1699865, _1699869)))], (19484 ^ _781404) ^ [_1127876, _1127878] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1127876), _1127878)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1127876)), _1127878))], (9028 ^ _781404) ^ [_934442, _934444, _934446] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934442, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934442, tc_HOL_Obool)), _934444), _934446)), _934446) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934442, tc_HOL_Obool)), _934444), _934446))], (27799 ^ _781404) ^ [_1278722, _1278724, _1278726, _1278728] : [class_Rings_Odivision__ring(_1278722), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278722), _1278724), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278722), _1278726), _1278728)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278722), _1278724), _1278726)), _1278728))], (6365 ^ _781404) ^ [_882634, _882636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882634), hAPP(c_Nat_OSuc, _882636))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882634), _882636))), -(_882634 = hAPP(c_Nat_OSuc, _882636))], (44513 ^ _781404) ^ [_1671800, _1671802, _1671804, _1671806] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1671800) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1671802), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1671800)), hAPP(hAPP(c_List_Olist_OCons(_1671802), _1671804), _1671806)) = hAPP(hAPP(c_List_Olist_OCons(_1671802), _1671804), _1671806))], (46349 ^ _781404) ^ [_1711448, _1711450, _1711452] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1711448), tc_List_Olist(_1711448), c_List_Oappend(_1711448), _1711450), _1711452) = hAPP(hAPP(c_List_Oappend(_1711448), _1711450), c_List_Oconcat(_1711448, _1711452)))], (19135 ^ _781404) ^ [_1121911, _1121913] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1121911), _1121913)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1121911)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1121913))))], (41891 ^ _781404) ^ [_1604635, _1604637] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604635, _1604635), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604637) = c_Relation_OId(_1604635))], (39313 ^ _781404) ^ [_1536842] : [-(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)))), _1536842)) = 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), _1536842), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (40019 ^ _781404) ^ [_1559447, _1559449, _1559451] : [-(hAPP(c_Set_Oimage(tc_prod(_1559447, _1559449), _1559447, c_Product__Type_Ofst(_1559447, _1559449)), _1559451) = hAPP(c_Relation_ODomain(_1559447, _1559449), _1559451))], (33103 ^ _781404) ^ [_1378637, _1378639] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1378637)), _1378639) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1378637), 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), _1378637)), _1378639))], (44669 ^ _781404) ^ [_1674864, _1674866, _1674868] : [-(hAPP(hAPP(c_List_Odrop(_1674864), hAPP(c_Nat_OSuc, _1674866)), _1674868) = hAPP(hAPP(c_List_Odrop(_1674864), _1674866), hAPP(c_List_Otl(_1674864), _1674868)))], (10407 ^ _781404) ^ [_958498, _958500, _958502] : [class_Groups_Oordered__ab__group__add(_958498), 10410 ^ _781404 : [(10417 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958498), _958502), hAPP(c_Groups_Ouminus__class_Ouminus(_958498), _958500))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958498), _958500), hAPP(c_Groups_Ouminus__class_Ouminus(_958498), _958502))))], (10411 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958498), _958500), hAPP(c_Groups_Ouminus__class_Ouminus(_958498), _958502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958498), _958502), hAPP(c_Groups_Ouminus__class_Ouminus(_958498), _958500))))]]], (17533 ^ _781404) ^ [_1094083, _1094085, _1094087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094083), _1094085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094087), _1094083)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094087), _1094085))))], (38947 ^ _781404) ^ [_1525281, _1525283, _1525285] : [hBOOL(hAPP(_1525281, _1525283)), -(hBOOL(hAPP(hAPP(c_member(_1525285), _1525283), hAPP(c_Set_OCollect(_1525285), _1525281))))], (34457 ^ _781404) ^ [_1419955, _1419957, _1419959, _1419961] : [-(hBOOL(hAPP(hAPP(c_member(_1419955), _1419957), _1419959))), -(hAPP(c_Set_Ovimage(_1419961, _1419955, hAPP(c_COMBK(_1419955, _1419961), _1419957)), _1419959) = c_Orderings_Obot__class_Obot(tc_fun(_1419961, tc_HOL_Obool)))], (5142 ^ _781404) ^ [_859851, _859853, _859855, _859857, _859859, _859861] : [-(c_Set_Oimage(_859861, _859857, _859853) = c_Set_Oimage(_859859, _859855, _859851)), _859861 = _859859, _859857 = _859855, _859853 = _859851], (35642 ^ _781404) ^ [_1446677] : [-(c_Divides_Odivmod__nat(_1446677, 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)), _1446677))], (44052 ^ _781404) ^ [_1660480, _1660482, _1660484] : [hAPP(hAPP(c_List_Oappend(_1660480), _1660482), _1660484) = c_List_Olist_ONil(_1660480), 44055 ^ _781404 : [(44058 ^ _781404) ^ [] : [-(_1660484 = c_List_Olist_ONil(_1660480))], (44056 ^ _781404) ^ [] : [-(_1660482 = c_List_Olist_ONil(_1660480))]]], (43226 ^ _781404) ^ [_1642584, _1642586, _1642588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642584), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642586)), _1642588))), -(hAPP(hAPP(c_List_Otake(_1642586), _1642584), c_List_Obutlast(_1642586, _1642588)) = hAPP(hAPP(c_List_Otake(_1642586), _1642584), _1642588))], (23279 ^ _781404) ^ [_1198421, _1198423, _1198425, _1198427, _1198429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198421), _1198423)), 23282 ^ _781404 : [(23289 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198427), 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), _1198423), _1198421)), _1198425)), _1198429))), -(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), _1198421), _1198425)), _1198427)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198423), _1198425)), _1198429))))], (23283 ^ _781404) ^ [] : [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), _1198421), _1198425)), _1198427)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198423), _1198425)), _1198429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198427), 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), _1198423), _1198421)), _1198425)), _1198429))))]]], (47121 ^ _781404) ^ [_1728612, _1728614, _1728616, _1728618, _1728620] : [class_Orderings_Olinorder(_1728612), c_List_Olinorder__class_Osorted(_1728612, hAPP(hAPP(c_List_Omap(_1728614, _1728612), _1728616), _1728618)), -(c_List_Olinorder__class_Osorted(_1728612, hAPP(hAPP(c_List_Omap(_1728614, _1728612), _1728616), c_List_Oremove1(_1728614, _1728620, _1728618))))], (18349 ^ _781404) ^ [] : [-(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))))], (47976 ^ _781404) ^ [_1746523, _1746525, _1746527, _1746529] : [47978 ^ _781404 : [(47981 ^ _781404) ^ [] : [hBOOL(hAPP(_1746525, hAPP(hAPP(c_List_Onth(_1746527), _1746529), 47977 ^ [_1746523, _1746525, _1746527, _1746529])))], (47979 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47977 ^ [_1746523, _1746525, _1746527, _1746529]), _1746523)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1746523), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746527)), _1746529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1746523), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746527)), c_List_OtakeWhile(_1746527, _1746525, _1746529)))))], (34271 ^ _781404) ^ [_1415149, _1415151, _1415153, _1415155] : [hBOOL(hAPP(hAPP(c_member(_1415149), _1415155), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415149, tc_HOL_Obool)), _1415151), _1415153))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415149, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1415149, tc_fun(_1415149, tc_HOL_Obool), tc_HOL_Obool), c_member(_1415149)), _1415151)), hAPP(hAPP(c_COMBC(_1415149, tc_fun(_1415149, tc_HOL_Obool), tc_HOL_Obool), c_member(_1415149)), _1415153)), _1415155)))], (52654 ^ _781404) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (7549 ^ _781404) ^ [_905001, _905003, _905005, _905007, _905009] : [class_Lattices_Olattice(_905001), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905003, _905001)), _905005), _905007), _905009) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_905001), hAPP(_905005, _905009)), hAPP(_905007, _905009)))], (41345 ^ _781404) ^ [_1591438, _1591440, _1591442, _1591444, _1591446] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591438, _1591438)), hAPP(hAPP(c_Product__Type_OPair(_1591438, _1591438), _1591440), _1591442)), _1591444)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591438, _1591438)), hAPP(hAPP(c_Product__Type_OPair(_1591438, _1591438), _1591442), _1591446)), c_Transitive__Closure_Ortrancl(_1591438, _1591444))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591438, _1591438)), hAPP(hAPP(c_Product__Type_OPair(_1591438, _1591438), _1591440), _1591446)), c_Transitive__Closure_Otrancl(_1591438, _1591444))))], (20481 ^ _781404) ^ [_1144857, _1144859] : [class_Rings_Oring__1__no__zero__divisors(_1144857), 20484 ^ _781404 : [(20491 ^ _781404) ^ [] : [_1144859 = c_Groups_Ozero__class_Ozero(_1144857), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1144857), _1144859), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1144857))], (20485 ^ _781404) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1144857), _1144859), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1144857), -(_1144859 = c_Groups_Ozero__class_Ozero(_1144857))]]], (17881 ^ _781404) ^ [_1100291, _1100293, _1100295, _1100297] : [class_Rings_Olinordered__semidom(_1100291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1100293), _1100295)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100291), c_Groups_Ozero__class_Ozero(_1100291)), _1100297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100291), _1100297), c_Groups_Oone__class_Oone(_1100291))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100291), hAPP(hAPP(c_Power_Opower__class_Opower(_1100291), _1100297), _1100295)), hAPP(hAPP(c_Power_Opower__class_Opower(_1100291), _1100297), _1100293))))], (19498 ^ _781404) ^ [_1128145] : [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)), _1128145))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1128145)))], (45555 ^ _781404) ^ [_1693976, _1693978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1693976), _1693978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1693976)), hAPP(c_Code__Numeral_Oof__nat, _1693978))))], (19823 ^ _781404) ^ [_1133433, _1133435] : [class_Int_Onumber__ring(_1133433), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133433), hAPP(c_Int_Onumber__class_Onumber__of(_1133433), _1133435)), c_Groups_Oone__class_Oone(_1133433)) = hAPP(c_Int_Onumber__class_Onumber__of(_1133433), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1133435), c_Int_OBit1(c_Int_OPls))))], (35412 ^ _781404) ^ [_1441405, _1441407, _1441409, _1441411, _1441413, _1441415, _1441417] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1441405, _1441407)), hAPP(hAPP(c_Product__Type_OPair(_1441405, _1441407), _1441409), _1441411)), _1441413)), -(hBOOL(hAPP(hAPP(c_member(_1441415), hAPP(hAPP(_1441417, _1441409), _1441411)), hAPP(c_Set_Oimage(tc_prod(_1441405, _1441407), _1441415, hAPP(c_Product__Type_Oprod_Oprod__case(_1441405, _1441407, _1441415), _1441417)), _1441413))))], (9413 ^ _781404) ^ [_942783, _942785] : [class_Groups_Oordered__ab__group__add(_942783), -(c_Fun_Oinj__on(_942783, _942783, c_Groups_Ouminus__class_Ouminus(_942783), _942785))], (45569 ^ _781404) ^ [_1694324, _1694326, _1694328, _1694330, _1694332] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694324)), _1694326) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694328)), _1694330), 45572 ^ _781404 : [(45581 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1694324, _1694328), _1694326), _1694330) = _1694332), hAPP(hAPP(c_List_Omap(tc_prod(_1694324, _1694328), _1694324), c_Product__Type_Ofst(_1694324, _1694328)), _1694332) = _1694326, hAPP(hAPP(c_List_Omap(tc_prod(_1694324, _1694328), _1694328), c_Product__Type_Osnd(_1694324, _1694328)), _1694332) = _1694330], (45573 ^ _781404) ^ [] : [hAPP(hAPP(c_List_Ozip(_1694324, _1694328), _1694326), _1694330) = _1694332, 45576 ^ _781404 : [(45579 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1694324, _1694328), _1694328), c_Product__Type_Osnd(_1694324, _1694328)), _1694332) = _1694330)], (45577 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1694324, _1694328), _1694324), c_Product__Type_Ofst(_1694324, _1694328)), _1694332) = _1694326)]]]]], (38197 ^ _781404) ^ [_1505489, _1505491, _1505493, _1505495, _1505497] : [c_Relation_Orefl__on(_1505489, _1505491, _1505493), c_Relation_Orefl__on(_1505489, _1505495, _1505497), -(c_Relation_Orefl__on(_1505489, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1505489, tc_HOL_Obool)), _1505491), _1505495), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1505489, _1505489), tc_HOL_Obool)), _1505493), _1505497)))], (34559 ^ _781404) ^ [_1422344, _1422346, _1422348, _1422350, _1422352, _1422354] : [c_Fun_Oinj__on(_1422344, _1422346, hAPP(c_Fun_Ocomp(_1422348, _1422346, _1422344, _1422350), _1422352), _1422354), -(c_Fun_Oinj__on(_1422348, _1422346, _1422350, hAPP(c_Set_Oimage(_1422344, _1422348, _1422352), _1422354)))], (31878 ^ _781404) ^ [_1355001, _1355003, _1355005] : [class_Orderings_Olinorder(_1355001), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355001), _1355003), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355001), _1355003), _1355005)) = _1355003)], (33179 ^ _781404) ^ [_1380644, _1380646, _1380648] : [class_Groups_Ocomm__monoid__mult(_1380644), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380646, _1380644), hAPP(c_COMBK(_1380644, _1380646), c_Groups_Oone__class_Oone(_1380644))), _1380648) = c_Groups_Oone__class_Oone(_1380644))], (3390 ^ _781404) ^ [_832019, _832021, _832023, _832025] : [-(c_Product__Type_OSigma(_832025, _832021) = c_Product__Type_OSigma(_832023, _832019)), _832025 = _832023, _832021 = _832019], (24676 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (45339 ^ _781404) ^ [_1689415, _1689417, _1689419, _1689421, _1689423] : [hAPP(hAPP(c_List_Omap(_1689415, _1689417), _1689419), _1689421) = hAPP(hAPP(c_List_Omap(_1689415, _1689417), _1689419), _1689423), c_Fun_Oinj__on(_1689415, _1689417, _1689419, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1689415, tc_HOL_Obool)), hAPP(c_List_Oset(_1689415), _1689421)), hAPP(c_List_Oset(_1689415), _1689423))), -(_1689421 = _1689423)], (612 ^ _781404) ^ [_790564, _790566, _790568, _790570, _790572, _790574, _790576, _790578, _790580, _790582] : [-(c_Typedef_Otype__definition(_790580, _790576, _790572, _790568, _790564)), c_Typedef_Otype__definition(_790582, _790578, _790574, _790570, _790566), _790582 = _790580, _790578 = _790576, _790574 = _790572, _790570 = _790568, _790566 = _790564], (21941 ^ _781404) ^ [_1171703, _1171705, _1171707, _1171709, _1171711, _1171713] : [class_Rings_Oring(_1171703), 21944 ^ _781404 : [(21951 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171703), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1171703), _1171705), _1171711)), _1171707)), _1171709) = _1171713, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171703), _1171705), _1171707)), _1171709) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171703), _1171711), _1171707)), _1171713))], (21945 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171703), _1171705), _1171707)), _1171709) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171703), _1171711), _1171707)), _1171713), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171703), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1171703), _1171705), _1171711)), _1171707)), _1171709) = _1171713)]]], (3362 ^ _781404) ^ [_831569, _831571, _831573, _831575] : [-(c_List_Olists(_831575, _831571) = c_List_Olists(_831573, _831569)), _831575 = _831573, _831571 = _831569], (37457 ^ _781404) ^ [] : [-(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))))))], (20321 ^ _781404) ^ [_1142076, _1142078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1142076)), c_Int_OBit1(_1142078))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1142076), _1142078)))], (6576 ^ _781404) ^ [_886355, _886357] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _886355), hAPP(c_Nat_OSuc, _886357)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _886355, _886357))], (48851 ^ _781404) ^ [_1765346, _1765348] : [c_List_Olist__ex1(_1765346, _1765348, c_List_Olist_ONil(_1765346))], (42666 ^ _781404) ^ [_1627755, _1627757, _1627759] : [_1627755 = _1627757, 42669 ^ _781404 : [(42672 ^ _781404) ^ [_1627903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627903), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627759)), _1627755))), -(hAPP(hAPP(c_List_Onth(_1627759), _1627755), _1627903) = hAPP(hAPP(c_List_Onth(_1627759), _1627757), _1627903))], (42670 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627759)), _1627755) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627759)), _1627757))]]], (30776 ^ _781404) ^ [_1334638, _1334640, _1334642] : [class_Orderings_Olinorder(_1334638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334638), _1334640), _1334642)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334638), _1334642), _1334640) = _1334640)], (19510 ^ _781404) ^ [] : [-(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))))], (8497 ^ _781404) ^ [_924720, _924722, _924724] : [class_Complete__Lattice_Ocomplete__lattice(_924720), 8500 ^ _781404 : [(8501 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924720), c_Complete__Lattice_OSup__class_OSup(_924720, _924722)), _924724)), 8504 ^ _781404 : [(8505 ^ _781404) ^ [_924878] : [hBOOL(hAPP(hAPP(c_member(_924720), _924878), _924722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924720), _924878), _924724)))]]], (8511 ^ _781404) ^ [] : [8513 ^ _781404 : [(8516 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924720), 8512 ^ [_924720, _924722, _924724]), _924724))], (8514 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_924720), 8512 ^ [_924720, _924722, _924724]), _924722)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924720), c_Complete__Lattice_OSup__class_OSup(_924720, _924722)), _924724)))]]], (8479 ^ _781404) ^ [_924388] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_924388, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_924388, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_924388, tc_HOL_Obool)))], (21531 ^ _781404) ^ [_1164232, _1164234, _1164236] : [class_Rings_Olinordered__ring__strict(_1164232), 21534 ^ _781404 : [(21549 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164232), _1164234), _1164236)), c_Groups_Ozero__class_Ozero(_1164232)))), 21550 ^ _781404 : [(21557 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164232), _1164234), c_Groups_Ozero__class_Ozero(_1164232))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164232), c_Groups_Ozero__class_Ozero(_1164232)), _1164236))], (21551 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164232), c_Groups_Ozero__class_Ozero(_1164232)), _1164234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164232), _1164236), c_Groups_Ozero__class_Ozero(_1164232)))]]], (21535 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164232), _1164234), _1164236)), c_Groups_Ozero__class_Ozero(_1164232))), 21540 ^ _781404 : [(21543 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164232), _1164236), c_Groups_Ozero__class_Ozero(_1164232))))], (21541 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164232), c_Groups_Ozero__class_Ozero(_1164232)), _1164234)))]], 21544 ^ _781404 : [(21547 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164232), c_Groups_Ozero__class_Ozero(_1164232)), _1164236)))], (21545 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164232), _1164234), c_Groups_Ozero__class_Ozero(_1164232))))]]]]], (51978 ^ _781404) ^ [_1833131, _1833133, _1833135, _1833137] : [class_Divides_Osemiring__div(_1833131), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833131), _1833133), _1833135)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833131), _1833133), _1833137)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1833131), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1833131), _1833135), _1833137)), _1833133) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1833131), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1833131), _1833135), _1833133)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1833131), _1833137), _1833133)))], (6809 ^ _781404) ^ [_890529, _890531, _890533] : [class_Groups_Ogroup__add(_890529), 6812 ^ _781404 : [(6819 ^ _781404) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_890529), _890533) = _890531, -(hAPP(c_Groups_Ouminus__class_Ouminus(_890529), _890531) = _890533)], (6813 ^ _781404) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_890529), _890531) = _890533, -(hAPP(c_Groups_Ouminus__class_Ouminus(_890529), _890533) = _890531)]]], (32182 ^ _781404) ^ [_1360665, _1360667, _1360669, _1360671] : [class_Orderings_Olinorder(_1360665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360665), _1360667), _1360669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360665), _1360667), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360665), _1360669), _1360671))))], (52580 ^ _781404) ^ [_1840587] : [class_Finite__Set_Ofinite(_1840587), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1840587)))], (10739 ^ _781404) ^ [_963796, _963798, _963800, _963802, _963804] : [class_Orderings_Olinorder(_963796), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963796, _963798), _963800) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963796, _963802), _963804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963796), _963798), _963800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963796), _963802), _963804)), -(_963798 = _963802)], (12140 ^ _781404) ^ [_989997, _989999, _990001, _990003] : [-(hBOOL(hAPP(hAPP(c_member(_989997), _989999), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_989997, tc_HOL_Obool)), _990001), _990003)))), hBOOL(hAPP(hAPP(c_member(_989997), _989999), _990001)), -(hBOOL(hAPP(hAPP(c_member(_989997), _989999), _990003)))], (4116 ^ _781404) ^ [_843698, _843700, _843702, _843704, _843706, _843708, _843710, _843712] : [-(c_New__DSequence_Opos__bind(_843712, _843708, _843704, _843700) = c_New__DSequence_Opos__bind(_843710, _843706, _843702, _843698)), _843712 = _843710, _843708 = _843706, _843704 = _843702, _843700 = _843698], (27626 ^ _781404) ^ [_1274824, _1274826, _1274828, _1274830] : [c_Big__Operators_Osemilattice__big(_1274824, _1274826, _1274828), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274824), _1274830)), -(hAPP(_1274828, _1274830) = hAPP(c_Finite__Set_Ofold1(_1274824, _1274826), _1274830))], (34607 ^ _781404) ^ [_1423296, _1423298, _1423300, _1423302, _1423304] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1423296, tc_fun(_1423298, tc_HOL_Obool)), _1423300), hAPP(hAPP(c_COMBS(_1423296, tc_fun(_1423298, tc_HOL_Obool), tc_fun(_1423298, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1423298, tc_HOL_Obool), tc_fun(tc_fun(_1423298, tc_HOL_Obool), tc_fun(_1423298, tc_HOL_Obool)), _1423296), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1423298, tc_HOL_Obool))), _1423302)), _1423304)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1423298, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1423298, tc_HOL_Obool), hAPP(c_Set_Oimage(_1423296, tc_fun(_1423298, tc_HOL_Obool), _1423302), _1423300))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1423298, tc_HOL_Obool), hAPP(c_Set_Oimage(_1423296, tc_fun(_1423298, tc_HOL_Obool), _1423304), _1423300))))], (50991 ^ _781404) ^ [_1812198, _1812200, _1812202, _1812204, _1812206] : [c_Fun_Obij__betw(_1812198, _1812200, _1812202, _1812204, _1812206), -(c_Fun_Obij__betw(_1812200, _1812198, c_Fun_Othe__inv__into(_1812198, _1812200, _1812204, _1812202), _1812206, _1812204))], (7059 ^ _781404) ^ [_895671, _895673, _895675, _895677] : [class_Lattices_Osemilattice__sup(_895671), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895671), _895673), _895675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895671), _895677), _895675)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895671), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895671), _895673), _895677)), _895675)))], (48835 ^ _781404) ^ [_1765008, _1765010, _1765012, _1765014] : [-(c_List_Olist__ex1(_1765008, _1765010, hAPP(hAPP(c_List_Olist_OCons(_1765008), _1765012), _1765014))), 48838 ^ _781404 : [(48841 ^ _781404) ^ [] : [c_List_Olist__all(_1765008, hAPP(hAPP(c_COMBS(_1765008, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765008), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1765008), c_fNot), _1765010))), hAPP(c_fequal, _1765012)), _1765014)], (48839 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1765010, _1765012)))]], 48842 ^ _781404 : [(48845 ^ _781404) ^ [] : [c_List_Olist__ex1(_1765008, _1765010, _1765014)], (48843 ^ _781404) ^ [] : [hBOOL(hAPP(_1765010, _1765012))]]], (34167 ^ _781404) ^ [_1409542, _1409544, _1409546, _1409548, _1409550] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409542, tc_fun(_1409544, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1409542), _1409546), _1409548)), _1409550) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409544, tc_HOL_Obool)), hAPP(_1409550, _1409546)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409542, tc_fun(_1409544, tc_HOL_Obool)), _1409548), _1409550)))], (22957 ^ _781404) ^ [_1191900] : [-(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)))), _1191900) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1191900), _1191900))], (43242 ^ _781404) ^ [_1642990, _1642992, _1642994, _1642996] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642990), tc_List_Olist(_1642990))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642990), tc_List_Olist(_1642990)), _1642992), _1642994)), c_List_Olistrel1(_1642990, _1642996))), 43247 ^ _781404 : [(43252 ^ _781404) ^ [] : [-(_1642994 = hAPP(hAPP(c_List_Olist__update(_1642990, _1642992), 43246 ^ [_1642990, _1642992, _1642994, _1642996]), 43245 ^ [_1642990, _1642992, _1642994, _1642996]))], (43250 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43246 ^ [_1642990, _1642992, _1642994, _1642996]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642990)), _1642992))))], (43248 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1642990, _1642990)), hAPP(hAPP(c_Product__Type_OPair(_1642990, _1642990), hAPP(hAPP(c_List_Onth(_1642990), _1642992), 43246 ^ [_1642990, _1642992, _1642994, _1642996])), 43245 ^ [_1642990, _1642992, _1642994, _1642996])), _1642996)))]]], (42897 ^ _781404) ^ [_1633417, _1633419, _1633421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1633417), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633419)), _1633421))), -(hBOOL(hAPP(hAPP(c_member(_1633419), hAPP(hAPP(c_List_Onth(_1633419), _1633421), _1633417)), hAPP(c_List_Oset(_1633419), _1633421))))], (47471 ^ _781404) ^ [_1735708, _1735710, _1735712] : [_1735712 = hAPP(hAPP(c_List_Olist_OCons(_1735708), _1735710), c_List_Olist_ONil(_1735708)), -(hAPP(hAPP(c_List_Olist_OCons(_1735708), _1735710), c_List_Olist_ONil(_1735708)) = hAPP(c_List_Orev(_1735708), _1735712))], (27019 ^ _781404) ^ [_1263683, _1263685] : [class_Groups_Oordered__ab__group__add__abs(_1263683), 27022 ^ _781404 : [(27029 ^ _781404) ^ [] : [_1263685 = c_Groups_Ozero__class_Ozero(_1263683), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263683), hAPP(c_Groups_Oabs__class_Oabs(_1263683), _1263685)), c_Groups_Ozero__class_Ozero(_1263683))))], (27023 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263683), hAPP(c_Groups_Oabs__class_Oabs(_1263683), _1263685)), c_Groups_Ozero__class_Ozero(_1263683))), -(_1263685 = c_Groups_Ozero__class_Ozero(_1263683))]]], (52650 ^ _781404) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (45200 ^ _781404) ^ [_1685896, _1685898, _1685900, _1685902] : [_1685902 = c_List_Olist_ONil(_1685898), -(c_List_Olist_ONil(_1685896) = hAPP(hAPP(c_List_Omap(_1685898, _1685896), _1685900), _1685902))], (23425 ^ _781404) ^ [_1201687, _1201689] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201687), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1201689), _1201687)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1201689), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1201689, _1201687)))], (8840 ^ _781404) ^ [_930603] : [class_Lattices_Oboolean__algebra(_930603), -(hAPP(c_Groups_Ouminus__class_Ouminus(_930603), c_Orderings_Otop__class_Otop(_930603)) = c_Orderings_Obot__class_Obot(_930603))], (34811 ^ _781404) ^ [_1428396, _1428398] : [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(_1428396))), 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)), _1428398))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428396) = hAPP(c_Nat_OSuc, _1428398))], (10985 ^ _781404) ^ [_967957, _967959] : [class_Groups_Oordered__ab__group__add(_967957), 10988 ^ _781404 : [(10995 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967957), c_Groups_Ozero__class_Ozero(_967957)), _967959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967957), hAPP(c_Groups_Ouminus__class_Ouminus(_967957), _967959)), c_Groups_Ozero__class_Ozero(_967957))))], (10989 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967957), hAPP(c_Groups_Ouminus__class_Ouminus(_967957), _967959)), c_Groups_Ozero__class_Ozero(_967957))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967957), c_Groups_Ozero__class_Ozero(_967957)), _967959)))]]], (46562 ^ _781404) ^ [_1716900, _1716902, _1716904, _1716906] : [hBOOL(hAPP(_1716900, _1716902)), -(hAPP(c_List_Ofilter(_1716904, _1716900), hAPP(hAPP(c_List_Olist_OCons(_1716904), _1716902), _1716906)) = hAPP(hAPP(c_List_Olist_OCons(_1716904), _1716902), hAPP(c_List_Ofilter(_1716904, _1716900), _1716906)))], (18001 ^ _781404) ^ [_1102418, _1102420, _1102422] : [class_Power_Opower(_1102418), class_Rings_Omult__zero(_1102418), class_Rings_Ono__zero__divisors(_1102418), class_Rings_Ozero__neq__one(_1102418), 18016 ^ _781404 : [(18025 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1102418), _1102420), _1102422) = c_Groups_Ozero__class_Ozero(_1102418)), _1102420 = c_Groups_Ozero__class_Ozero(_1102418), -(_1102422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18017 ^ _781404) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1102418), _1102420), _1102422) = c_Groups_Ozero__class_Ozero(_1102418), 18020 ^ _781404 : [(18023 ^ _781404) ^ [] : [_1102422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18021 ^ _781404) ^ [] : [-(_1102420 = c_Groups_Ozero__class_Ozero(_1102418))]]]]], (9130 ^ _781404) ^ [_936350, _936352, _936354] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_936350, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936350, tc_HOL_Obool)), _936352), _936354)), _936354) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_936350, tc_HOL_Obool)), _936352), _936354))], (24991 ^ _781404) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37465 ^ _781404) ^ [_1486749] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1486749) = 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, _1486749)), 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))))))))], (39844 ^ _781404) ^ [_1556020, _1556022] : [c_Wellfounded_Owf(_1556020, _1556022), -(c_Wellfounded_Owf(_1556020, hAPP(hAPP(c_Relation_Orel__comp(_1556020, _1556020, _1556020), _1556022), _1556022)))], (47399 ^ _781404) ^ [_1734178, _1734180, _1734182, _1734184] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1734178), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1734178))), _1734180))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734182), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1734178))), c_List_Otranspose(_1734178, _1734180)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734184), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1734178))), hAPP(c_List_Ofilter(tc_List_Olist(_1734178), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1734178)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734182)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734178)))), _1734180)))), -(hAPP(hAPP(c_List_Onth(_1734178), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1734178)), c_List_Otranspose(_1734178, _1734180)), _1734182)), _1734184) = hAPP(hAPP(c_List_Onth(_1734178), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1734178)), _1734180), _1734184)), _1734182))], (23003 ^ _781404) ^ [_1192987, _1192989, _1192991, _1192993, _1192995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1192987), _1192989)), 23006 ^ _781404 : [(23013 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1192993), 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), _1192989), _1192987)), _1192991)), _1192995))), -(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), _1192987), _1192991)), _1192993)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1192989), _1192991)), _1192995))))], (23007 ^ _781404) ^ [] : [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), _1192987), _1192991)), _1192993)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1192989), _1192991)), _1192995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1192993), 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), _1192989), _1192987)), _1192991)), _1192995))))]]], (36528 ^ _781404) ^ [_1464065, _1464067, _1464069, _1464071, _1464073, _1464075] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1464065, _1464067), _1464067, _1464069), hAPP(hAPP(c_COMBB(_1464071, tc_fun(_1464067, _1464069), tc_prod(_1464065, _1464067)), _1464073), hAPP(hAPP(c_COMBB(_1464065, _1464071, tc_prod(_1464065, _1464067)), _1464075), c_Product__Type_Ofst(_1464065, _1464067)))), c_Product__Type_Osnd(_1464065, _1464067)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1464065, _1464067, _1464069), hAPP(hAPP(c_COMBB(_1464071, tc_fun(_1464067, _1464069), _1464065), _1464073), _1464075)))], (49343 ^ _781404) ^ [_1776020, _1776022, _1776024] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1776020, _1776022), _1776024) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1776020, tc_Lazy__Sequence_Olazy__sequence(_1776020)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1776020, tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1776020, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_Nat_Onat)), _1776020), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1776020), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1776020)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1776020, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1776020), tc_Nat_Onat)), _1776020), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1776020))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1776020), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1776022))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1776020, _1776022))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1776020), _1776024)))], (27953 ^ _781404) ^ [_1281283, _1281285, _1281287] : [class_Rings_Odivision__ring(_1281283), -(_1281285 = c_Groups_Ozero__class_Ozero(_1281283)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1281283), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281283), _1281287), _1281285)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281283), _1281287), hAPP(c_Groups_Ouminus__class_Ouminus(_1281283), _1281285)))], (41744 ^ _781404) ^ [_1600811, _1600813, _1600815] : [c_Relation_Osingle__valued(_1600811, _1600813, _1600815), 41747 ^ _781404 : [(41748 ^ _781404) ^ [_1600932, _1600934] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600811, _1600813)), hAPP(hAPP(c_Product__Type_OPair(_1600811, _1600813), _1600934), _1600932)), _1600815)), 41751 ^ _781404 : [(41752 ^ _781404) ^ [_1601058] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600811, _1600813)), hAPP(hAPP(c_Product__Type_OPair(_1600811, _1600813), _1600934), _1601058)), _1600815)), -(_1600932 = _1601058)]]]]], (16929 ^ _781404) ^ [_1082761, _1082763, _1082765, _1082767, _1082769] : [c_Finite__Set_Ofolding__one__idem(_1082761, _1082763, _1082765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082761), _1082767)), hBOOL(hAPP(hAPP(c_member(_1082761), _1082769), _1082767)), -(hAPP(hAPP(_1082763, _1082769), hAPP(_1082765, _1082767)) = hAPP(_1082765, _1082767))], (7721 ^ _781404) ^ [_908420, _908422, _908424] : [class_Lattices_Osemilattice__inf(_908420), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908420), _908422), _908424)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_908420), _908422), _908424) = _908422)], (4840 ^ _781404) ^ [_855084, _855086] : [_855086 = _855084, -(c_List_Oset(_855086) = c_List_Oset(_855084))], (46736 ^ _781404) ^ [_1721796, _1721798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1721796), _1721798)), -(c_List_Oupt(_1721796, hAPP(c_Nat_OSuc, _1721798)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1721796, _1721798)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1721798), c_List_Olist_ONil(tc_Nat_Onat))))], (17359 ^ _781404) ^ [_1091063, _1091065] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091063)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091065)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1091063), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1091065))))], (20711 ^ _781404) ^ [_1148519, _1148521, _1148523] : [class_Rings_Olinordered__idom(_1148519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148519), c_Groups_Ozero__class_Ozero(_1148519)), hAPP(hAPP(c_Power_Opower__class_Opower(_1148519), _1148521), 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)))), _1148523))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148519), c_Groups_Ozero__class_Ozero(_1148519)), _1148521)))], (44860 ^ _781404) ^ [_1679062, _1679064, _1679066] : [44861 ^ _781404 : [(44862 ^ _781404) ^ [_1679151, _1679153] : [_1679064 = hAPP(hAPP(c_List_Olist_OCons(_1679062), _1679153), _1679151)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679062), tc_List_Olist(_1679062))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679062), tc_List_Olist(_1679062)), c_List_Olist_ONil(_1679062)), _1679064)), c_List_Olexord(_1679062, _1679066))))], (7990 ^ _781404) ^ [_914656, _914658, _914660] : [class_Lattices_Oboolean__algebra(_914656), -(hAPP(c_Groups_Ouminus__class_Ouminus(_914656), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914656), _914658), _914660)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_914656), hAPP(c_Groups_Ouminus__class_Ouminus(_914656), _914658)), hAPP(c_Groups_Ouminus__class_Ouminus(_914656), _914660)))], (45495 ^ _781404) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (22329 ^ _781404) ^ [_1179522, _1179524, _1179526, _1179528] : [class_Rings_Olinordered__semiring(_1179522), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179522), _1179524), _1179526)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179522), _1179524), _1179528))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179522), c_Groups_Ozero__class_Ozero(_1179522)), _1179524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179522), _1179526), _1179528)))], (50600 ^ _781404) ^ [_1803821, _1803823, _1803825, _1803827] : [c_Fun_Oinj__on(_1803821, _1803823, _1803825, c_Orderings_Otop__class_Otop(tc_fun(_1803821, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1803823, _1803821, c_Hilbert__Choice_Oinv__into(_1803821, _1803823, c_Orderings_Otop__class_Otop(tc_fun(_1803821, tc_HOL_Obool)), _1803825)), hAPP(c_Set_Oimage(_1803821, _1803823, _1803825), _1803827)) = _1803827)], (37150 ^ _781404) ^ [_1478454, _1478456, _1478458, _1478460] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1478454), _1478456)), 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)), _1478454), _1478458)), 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)), _1478456), _1478460)), 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)), _1478456), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1478458), _1478460))), c_FunDef_Omin__strict)))], (47421 ^ _781404) ^ [_1734748, _1734750] : [hBOOL(hAPP(c_List_Odistinct(_1734748), _1734750)), -(hBOOL(hAPP(c_List_Odistinct(_1734748), hAPP(c_List_Orev(_1734748), _1734750))))], (25127 ^ _781404) ^ [_1231183] : [hAPP(c_Int_Onat, _1231183) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231183), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (1726 ^ _781404) ^ [_806019, _806021] : [-(class_Rings_Oordered__semiring(_806019)), _806021 = _806019, class_Rings_Oordered__semiring(_806021)], (44571 ^ _781404) ^ [_1673305, _1673307, _1673309] : [-(_1673305 = c_List_Olist_ONil(_1673307)), -(hAPP(c_List_Ohd(_1673307), hAPP(hAPP(c_List_Oappend(_1673307), _1673305), _1673309)) = hAPP(c_List_Ohd(_1673307), _1673305))], (36707 ^ _781404) ^ [_1468026, _1468028, _1468030, _1468032, _1468034] : [-(hAPP(c_Fun_Othe__inv__into(_1468026, _1468028, _1468030, _1468032), _1468034) = c_HOL_OThe(_1468026, hAPP(hAPP(c_COMBS(_1468026, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1468026), c_fconj), hAPP(hAPP(c_COMBC(_1468026, tc_fun(_1468026, tc_HOL_Obool), tc_HOL_Obool), c_member(_1468026)), _1468030))), hAPP(hAPP(c_COMBC(_1468026, _1468028, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1468028, tc_fun(_1468028, tc_HOL_Obool), _1468026), c_fequal), _1468032)), _1468034))))], (52694 ^ _781404) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (51436 ^ _781404) ^ [_1823222] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823222), _1823222)))], (5104 ^ _781404) ^ [_859244, _859246, _859248, _859250, _859252, _859254, _859256, _859258] : [-(c_Hilbert__Choice_Oinv__into(_859258, _859254, _859250, _859246) = c_Hilbert__Choice_Oinv__into(_859256, _859252, _859248, _859244)), _859258 = _859256, _859254 = _859252, _859250 = _859248, _859246 = _859244], (12246 ^ _781404) ^ [_991941, _991943, _991945] : [hBOOL(hAPP(hAPP(c_member(_991941), _991943), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_991941, tc_HOL_Obool)), _991945))), hBOOL(hAPP(hAPP(c_member(_991941), _991943), _991945))], (47551 ^ _781404) ^ [_1737398, _1737400, _1737402, _1737404, _1737406] : [-(c_List_Ofoldr(_1737398, _1737400, _1737402, _1737404, _1737406) = hAPP(c_List_Ofoldl(_1737400, _1737398, hAPP(c_COMBC(_1737398, _1737400, _1737400), _1737402), _1737406), hAPP(c_List_Orev(_1737398), _1737404)))], (6437 ^ _781404) ^ [_883680, _883682, _883684, _883686] : [class_Orderings_Oorder(_883680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883680), hAPP(_883682, 6442 ^ [_883680, _883682, _883684, _883686])), hAPP(_883682, hAPP(c_Nat_OSuc, 6442 ^ [_883680, _883682, _883684, _883686])))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883684), _883686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883680), hAPP(_883682, _883684)), hAPP(_883682, _883686))))], (49267 ^ _781404) ^ [_1774555, _1774557, _1774559, _1774561] : [-(c_Lazy__Sequence_Oappend(_1774555, c_Lazy__Sequence_Olazy__sequence_OInsert(_1774555, _1774557, _1774559), _1774561) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1774555, _1774557, c_Lazy__Sequence_Oappend(_1774555, _1774559, _1774561)))], (6025 ^ _781404) ^ [_876868, _876870, _876872] : [class_Orderings_Olinorder(_876868), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876868), _876870), _876872))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876868), _876872), _876870)))], (50129 ^ _781404) ^ [_1794485, _1794487, _1794489, _1794491, _1794493, _1794495] : [-(c_Partial__Function_Ofun__lub(_1794485, _1794487, _1794489, _1794491, _1794493, _1794495) = hAPP(_1794491, hAPP(c_Set_OCollect(_1794485), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1794489, _1794485), tc_HOL_Obool), tc_HOL_Obool, _1794485), c_HOL_OEx(tc_fun(_1794489, _1794485))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1794489, _1794485), tc_HOL_Obool), tc_fun(tc_fun(_1794489, _1794485), tc_HOL_Obool), _1794485), hAPP(c_COMBS(tc_fun(_1794489, _1794485), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1794489, _1794485)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1794489, _1794485), tc_fun(tc_fun(_1794489, _1794485), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1794489, _1794485))), _1794493)))), hAPP(hAPP(c_COMBC(_1794485, tc_fun(tc_fun(_1794489, _1794485), _1794485), tc_fun(tc_fun(_1794489, _1794485), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1794485, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1794489, _1794485), _1794485), tc_fun(tc_fun(_1794489, _1794485), tc_HOL_Obool)), _1794485), c_COMBB(_1794485, tc_HOL_Obool, tc_fun(_1794489, _1794485))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1794489, _1794485), _1794489, _1794485), c_COMBI(tc_fun(_1794489, _1794485))), _1794495)))))))], (4484 ^ _781404) ^ [_849468, _849470, _849472, _849474, _849476, _849478, _849480, _849482, _849484, _849486] : [-(c_Option_Ooption_Ooption__case(_849486, _849482, _849478, _849474, _849470) = c_Option_Ooption_Ooption__case(_849484, _849480, _849476, _849472, _849468)), _849486 = _849484, _849482 = _849480, _849478 = _849476, _849474 = _849472, _849470 = _849468], (47687 ^ _781404) ^ [_1740364, _1740366, _1740368] : [c_List_OtakeWhile(_1740364, _1740366, _1740368) = _1740368, 47690 ^ _781404 : [(47691 ^ _781404) ^ [_1740451] : [hBOOL(hAPP(hAPP(c_member(_1740364), _1740451), hAPP(c_List_Oset(_1740364), _1740368))), -(hBOOL(hAPP(_1740366, _1740451)))]]], (43763 ^ _781404) ^ [_1653475] : [-(c_List_Olistset(_1653475, c_List_Olist_ONil(tc_fun(_1653475, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1653475)), c_List_Olist_ONil(_1653475)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1653475), tc_HOL_Obool))))], (20095 ^ _781404) ^ [_1138305] : [c_Int_OPls = _1138305, -(c_Int_OPls = c_Int_OBit0(_1138305))], (37932 ^ _781404) ^ [_1498458, _1498460] : [-(c_Equiv__Relations_Oequivp(_1498458, _1498460)), 37937 ^ _781404 : [(37940 ^ _781404) ^ [] : [hAPP(_1498460, 37933 ^ [_1498458, _1498460]) = hAPP(_1498460, 37934 ^ [_1498458, _1498460])], (37938 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1498460, 37933 ^ [_1498458, _1498460]), 37934 ^ [_1498458, _1498460])))]], 37941 ^ _781404 : [(37944 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1498460, 37933 ^ [_1498458, _1498460]), 37934 ^ [_1498458, _1498460]))], (37942 ^ _781404) ^ [] : [-(hAPP(_1498460, 37933 ^ [_1498458, _1498460]) = hAPP(_1498460, 37934 ^ [_1498458, _1498460]))]]], (20315 ^ _781404) ^ [_1141916, _1141918] : [class_Int_Onumber__ring(_1141916), -(hAPP(c_Int_Onumber__class_Onumber__of(_1141916), c_Int_OBit0(_1141918)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141916), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141916), c_Groups_Ozero__class_Ozero(_1141916)), hAPP(c_Int_Onumber__class_Onumber__of(_1141916), _1141918))), hAPP(c_Int_Onumber__class_Onumber__of(_1141916), _1141918)))], (7473 ^ _781404) ^ [_903441, _903443, _903445] : [class_Lattices_Osemilattice__inf(_903441), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903441), _903443), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903441), _903443), _903445)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903441), _903443), _903445))], (46012 ^ _781404) ^ [_1704362, _1704364, _1704366, _1704368] : [c_List_Olist__all2(_1704362, _1704364, _1704366, _1704368, c_List_Olist_ONil(_1704364)), -(_1704368 = c_List_Olist_ONil(_1704362))], (14350 ^ _781404) ^ [_1032322, _1032324, _1032326] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1032322), _1032324)), 14353 ^ _781404 : [(14373 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1032322, tc_Nat_Onat), _1032326), _1032324) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 14374 ^ _781404 : [(14375 ^ _781404) ^ [_1032803] : [hBOOL(hAPP(hAPP(c_member(_1032322), _1032803), _1032324)), hAPP(_1032326, _1032803) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14383 ^ _781404 : [(14388 ^ _781404) ^ [] : [hAPP(_1032326, 14382 ^ [_1032322, _1032324, _1032326, _1032803]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14386 ^ _781404) ^ [] : [_1032803 = 14382 ^ [_1032322, _1032324, _1032326, _1032803]], (14384 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1032322), 14382 ^ [_1032322, _1032324, _1032326, _1032803]), _1032324)))]]]]], (14354 ^ _781404) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1032322, tc_Nat_Onat), _1032326), _1032324) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14358 ^ _781404 : [(14363 ^ _781404) ^ [_1032642] : [hBOOL(hAPP(hAPP(c_member(_1032322), _1032642), _1032324)), -(14357 ^ [_1032322, _1032324, _1032326] = _1032642), -(hAPP(_1032326, _1032642) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14361 ^ _781404) ^ [] : [-(hAPP(_1032326, 14357 ^ [_1032322, _1032324, _1032326]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14359 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1032322), 14357 ^ [_1032322, _1032324, _1032326]), _1032324)))]]]]], (562 ^ _781404) ^ [_789817, _789819, _789821, _789823, _789825, _789827, _789829, _789831] : [-(c_List_Olistrelp(_789829, _789825, _789821, _789817)), c_List_Olistrelp(_789831, _789827, _789823, _789819), _789831 = _789829, _789827 = _789825, _789823 = _789821, _789819 = _789817], (22943 ^ _781404) ^ [_1191651, _1191653] : [class_Rings_Ocomm__semiring__1(_1191651), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191651), _1191653), _1191653) = hAPP(hAPP(c_Power_Opower__class_Opower(_1191651), _1191653), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (18859 ^ _781404) ^ [_1117410, _1117412] : [class_Int_Onumber__ring(_1117410), class_Rings_Olinordered__idom(_1117410), 18866 ^ _781404 : [(18873 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117412), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117410), hAPP(c_Int_Onumber__class_Onumber__of(_1117410), _1117412)), c_Groups_Ozero__class_Ozero(_1117410))))], (18867 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117410), hAPP(c_Int_Onumber__class_Onumber__of(_1117410), _1117412)), c_Groups_Ozero__class_Ozero(_1117410))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117412), c_Int_OPls)))]]], (52362 ^ _781404) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (34297 ^ _781404) ^ [_1415951, _1415953, _1415955, _1415957, _1415959] : [-(_1415951 = c_Orderings_Obot__class_Obot(tc_fun(_1415953, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415953, tc_fun(_1415955, tc_HOL_Obool)), _1415951), hAPP(hAPP(c_COMBC(_1415953, tc_fun(_1415955, tc_HOL_Obool), tc_fun(_1415955, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1415955, tc_HOL_Obool), tc_fun(tc_fun(_1415955, tc_HOL_Obool), tc_fun(_1415955, tc_HOL_Obool)), _1415953), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415955, tc_HOL_Obool))), _1415957)), _1415959)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415955, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415953, tc_fun(_1415955, tc_HOL_Obool)), _1415951), _1415957)), _1415959))], (45543 ^ _781404) ^ [] : [-(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))], (33490 ^ _781404) ^ [_1390385, _1390387, _1390389] : [class_Groups_Ocomm__monoid__add(_1390385), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1390387, _1390385), hAPP(c_COMBK(_1390385, _1390387), c_Groups_Ozero__class_Ozero(_1390385))), _1390389) = c_Groups_Ozero__class_Ozero(_1390385))], (52578 ^ _781404) ^ [_1840560, _1840562] : [-(class_Nat_Osize(tc_sum(_1840560, _1840562)))], (34955 ^ _781404) ^ [_1431757, _1431759, _1431761, _1431763, _1431765] : [-(c_Nat_Onat_Onat__case(_1431757, _1431759, _1431761, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431763)), _1431765)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1431757), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1431763))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1431757, _1431757), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1431757, tc_fun(_1431757, _1431757)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1431757, tc_fun(_1431757, _1431757)), tc_Int_Oint), c_If(_1431757)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1431757, _1431759, _1431761, _1431765))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1431757, tc_Int_Oint), _1431761), 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)), _1431765)))))], (36384 ^ _781404) ^ [_1461051, _1461053, _1461055, _1461057, _1461059, _1461061] : [c_Finite__Set_Ofolding(_1461051, _1461053, _1461055, _1461057), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461051), _1461059)), -(hBOOL(hAPP(hAPP(c_member(_1461051), _1461061), _1461059))), -(hAPP(_1461057, hAPP(hAPP(c_Set_Oinsert(_1461051), _1461061), _1461059)) = hAPP(c_Fun_Ocomp(_1461053, _1461053, _1461053, hAPP(_1461057, _1461059)), hAPP(_1461055, _1461061)))], (18621 ^ _781404) ^ [_1113606, _1113608, _1113610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1113606)), 18624 ^ _781404 : [(18625 ^ _781404) ^ [_1113740] : [18627 ^ _781404 : [(18633 ^ _781404) ^ [] : [-(_1113740 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 18629 ^ [_1113606, _1113608, _1113610, _1113740]), 18626 ^ [_1113606, _1113608, _1113610, _1113740]))], (18631 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18629 ^ [_1113606, _1113608, _1113610, _1113740]), _1113608)))], (18628 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18626 ^ [_1113606, _1113608, _1113610, _1113740]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1113606))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113610), _1113740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113610), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1113740), _1113606))))]]], (45473 ^ _781404) ^ [_1692420, _1692422, _1692424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692420), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692422)), _1692424))), -(hAPP(c_Random_Opick(_1692422, hAPP(hAPP(c_List_Omap(_1692422, tc_prod(tc_Code__Numeral_Ocode__numeral, _1692422)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1692422), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1692424)), hAPP(c_Code__Numeral_Oof__nat, _1692420)) = hAPP(hAPP(c_List_Onth(_1692422), _1692424), _1692420))], (41648 ^ _781404) ^ [_1598902, _1598904, _1598906] : [hAPP(hAPP(c_Relation_Orel__comp(_1598902, _1598902, _1598902), hAPP(c_Relation_Oconverse(_1598902, _1598902), _1598904)), _1598904) = _1598904, hAPP(c_Relation_ODomain(_1598902, _1598902), _1598904) = _1598906, -(c_Equiv__Relations_Oequiv(_1598902, _1598906, _1598904))], (12082 ^ _781404) ^ [_988701, _988703, _988705, _988707] : [12083 ^ _781404 : [(12086 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_988701), _988703), _988707))], (12084 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_988701), _988703), _988705))]], -(hBOOL(hAPP(hAPP(c_member(_988701), _988703), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_988701, tc_HOL_Obool)), _988705), _988707))))], (41846 ^ _781404) ^ [_1603496, _1603498, _1603500] : [c_Relation_Osingle__valued(_1603496, _1603496, _1603498), -(c_Relation_Osingle__valued(_1603496, _1603496, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603496, _1603496), tc_HOL_Obool), _1603500), _1603498)))], (37451 ^ _781404) ^ [_1486316, _1486318, _1486320, _1486322] : [-(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), _1486316), _1486318)), 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), _1486320), _1486322)), 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), _1486316), _1486320)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1486318), _1486322))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1486316), _1486322)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1486318), _1486320)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (45650 ^ _781404) ^ [_1696114, _1696116] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1696114), _1696116) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1696114)), hAPP(c_Code__Numeral_Onat__of, _1696116))))], (29107 ^ _781404) ^ [_1302416, _1302418, _1302420, _1302422] : [class_Fields_Ofield__inverse__zero(_1302416), 29110 ^ _781404 : [(29111 ^ _781404) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302416), _1302418), _1302420) = _1302422, 29114 ^ _781404 : [(29121 ^ _781404) ^ [] : [_1302420 = c_Groups_Ozero__class_Ozero(_1302416), -(_1302422 = c_Groups_Ozero__class_Ozero(_1302416))], (29115 ^ _781404) ^ [] : [-(_1302420 = c_Groups_Ozero__class_Ozero(_1302416)), -(_1302418 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302416), _1302422), _1302420))]]], (29127 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302416), _1302418), _1302420) = _1302422), 29130 ^ _781404 : [(29133 ^ _781404) ^ [] : [_1302418 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302416), _1302422), _1302420)], (29131 ^ _781404) ^ [] : [_1302420 = c_Groups_Ozero__class_Ozero(_1302416)]], 29134 ^ _781404 : [(29137 ^ _781404) ^ [] : [_1302422 = c_Groups_Ozero__class_Ozero(_1302416)], (29135 ^ _781404) ^ [] : [-(_1302420 = c_Groups_Ozero__class_Ozero(_1302416))]]]]], (31300 ^ _781404) ^ [_1344513, _1344515, _1344517] : [class_Orderings_Olinorder(_1344513), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344513), _1344515)), -(_1344515 = c_Orderings_Obot__class_Obot(tc_fun(_1344513, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1344513, c_Orderings_Oord__class_Omin(_1344513), hAPP(hAPP(c_Set_Oinsert(_1344513), _1344517), _1344515)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1344513), _1344517), c_Big__Operators_Olattice_OInf__fin(_1344513, c_Orderings_Oord__class_Omin(_1344513), _1344515)))], (19719 ^ _781404) ^ [_1131788] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1131788))) = 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)))), _1131788))], (7920 ^ _781404) ^ [_912693, _912695, _912697, _912699, _912701] : [c_Orderings_Oorder__class_Omono(tc_fun(_912693, tc_HOL_Obool), tc_fun(_912695, tc_HOL_Obool), _912697), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912695, tc_HOL_Obool)), hAPP(_912697, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912693, tc_HOL_Obool)), _912699), _912701))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912695, tc_HOL_Obool)), hAPP(_912697, _912699)), hAPP(_912697, _912701)))))], (38758 ^ _781404) ^ [_1519802, _1519804, _1519806, _1519808] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519804, _1519802), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1519802, tc_prod(_1519804, _1519802), 38754 ^ [_1519802, _1519804, _1519806, _1519808]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519804, tc_fun(_1519802, tc_HOL_Obool)), _1519806), _1519808))), hAPP(hAPP(c_Product__Type_OSigma(_1519804, _1519802), _1519806), _1519808))))], (33645 ^ _781404) ^ [_1394907, _1394909, _1394911, _1394913] : [class_Complete__Lattice_Ocomplete__lattice(_1394907), -(_1394909 = c_Orderings_Obot__class_Obot(tc_fun(_1394911, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394911, _1394907), _1394909), hAPP(c_COMBK(_1394907, _1394911), _1394913)) = _1394913)], (17375 ^ _781404) ^ [_1091378, _1091380] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1091378), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1091380) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1091378, _1091380))], (52532 ^ _781404) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (5684 ^ _781404) ^ [_868298, _868300, _868302, _868304] : [-(hAPP(_868304, _868300) = hAPP(_868302, _868298)), _868304 = _868302, _868300 = _868298], (7029 ^ _781404) ^ [_895092, _895094, _895096] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895092, tc_HOL_Obool)), _895094), _895096) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895092, tc_HOL_Obool)), _895096), _895094))], (2486 ^ _781404) ^ [_817859, _817861, _817863, _817865] : [-(c_Divides_OposDivAlg(_817865, _817861) = c_Divides_OposDivAlg(_817863, _817859)), _817865 = _817863, _817861 = _817859], (37382 ^ _781404) ^ [_1484413, _1484415, _1484417, _1484419, _1484421, _1484423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1484413, _1484415), tc_HOL_Obool)), _1484417), _1484419)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484413, tc_HOL_Obool)), _1484421), _1484423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484415, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1484413, _1484415, _1484417), _1484421)), hAPP(c_Relation_OImage(_1484413, _1484415, _1484419), _1484423))))], (41522 ^ _781404) ^ [_1595501, _1595503, _1595505] : [-(hAPP(c_Relation_Oconverse(_1595501, _1595503), hAPP(c_Relation_Oconverse(_1595503, _1595501), _1595505)) = _1595505)], (24905 ^ _781404) ^ [_1227653, _1227655, _1227657] : [-(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), _1227653), _1227655)), _1227657), _1227655) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1227657, _1227655))], (38850 ^ _781404) ^ [_1522370, _1522372, _1522374, _1522376, _1522378] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522370, _1522372)), _1522374), hAPP(hAPP(c_Product__Type_OSigma(_1522370, _1522372), _1522376), _1522378))), 38854 ^ _781404 : [(38860 ^ _781404) ^ [] : [-(_1522374 = hAPP(hAPP(c_Product__Type_OPair(_1522370, _1522372), 38853 ^ [_1522370, _1522372, _1522374, _1522376, _1522378]), 38856 ^ [_1522370, _1522372, _1522374, _1522376, _1522378]))], (38858 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1522372), 38856 ^ [_1522370, _1522372, _1522374, _1522376, _1522378]), hAPP(_1522378, 38853 ^ [_1522370, _1522372, _1522374, _1522376, _1522378]))))], (38855 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1522370), 38853 ^ [_1522370, _1522372, _1522374, _1522376, _1522378]), _1522376)))]]], (22343 ^ _781404) ^ [_1179791, _1179793, _1179795, _1179797] : [class_Rings_Olinordered__semiring__strict(_1179791), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179791), _1179793), _1179795)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179791), _1179797), _1179795))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179791), c_Groups_Ozero__class_Ozero(_1179791)), _1179795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179791), _1179793), _1179797)))], (7852 ^ _781404) ^ [_911177, _911179, _911181] : [class_Lattices_Olattice(_911177), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_911177), _911179), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911177), _911179), _911181)) = _911179)], (34689 ^ _781404) ^ [_1425409, _1425411, _1425413, _1425415] : [class_Complete__Lattice_Ocomplete__lattice(_1425409), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425411), _1425413)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1425411, _1425409), _1425413), _1425415) = hAPP(hAPP(c_Finite__Set_Ofold(_1425411, _1425409, hAPP(hAPP(c_COMBB(_1425409, tc_fun(_1425409, _1425409), _1425411), c_Lattices_Osemilattice__inf__class_Oinf(_1425409)), _1425415)), c_Orderings_Otop__class_Otop(_1425409)), _1425413))], (21171 ^ _781404) ^ [_1157509, _1157511, _1157513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1157509), _1157511)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157509), _1157513)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157511), _1157513))))], (36277 ^ _781404) ^ [_1458570, _1458572, _1458574, _1458576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1458576, _1458572)), hAPP(_1458576, _1458574))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1458570, _1458570)), hAPP(hAPP(c_Product__Type_OPair(_1458570, _1458570), _1458572), _1458574)), hAPP(c_Wellfounded_Omeasure(_1458570), _1458576))))], (23605 ^ _781404) ^ [_1205355, _1205357] : [-(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, _1205355, _1205357)), _1205357) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205355), _1205357))], (45441 ^ _781404) ^ [_1691624, _1691626, _1691628, _1691630] : [class_Rings_Osemiring__1(_1691624), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1691624), hAPP(hAPP(c_List_Omap(_1691626, _1691624), hAPP(c_COMBK(_1691624, _1691626), _1691628)), _1691630)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1691624), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1691624), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691626)), _1691630))), _1691628))], (4356 ^ _781404) ^ [_847370, _847372] : [_847372 = _847370, -(c_If(_847372) = c_If(_847370))], (29759 ^ _781404) ^ [_1314489, _1314491, _1314493, _1314495] : [class_Fields_Olinordered__field(_1314489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314489), c_Groups_Ozero__class_Ozero(_1314489)), _1314491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1314489), _1314493), _1314491)), _1314495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314489), _1314493), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314489), _1314495), _1314491))))], (36848 ^ _781404) ^ [_1470973, _1470975] : [hBOOL(hAPP(_1470973, _1470975)), -(hBOOL(hAPP(_1470973, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1470973) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat), _1470973), c_Nat_OSuc))))], (33337 ^ _781404) ^ [_1384772, _1384774, _1384776, _1384778, _1384780, _1384782] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384772, tc_fun(_1384774, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1384776, _1384772, _1384778), _1384780)), _1384782) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384776, tc_fun(_1384774, tc_HOL_Obool)), _1384780), hAPP(hAPP(c_COMBB(_1384772, tc_fun(_1384774, tc_HOL_Obool), _1384776), _1384782), _1384778)))], (30270 ^ _781404) ^ [_1325050, _1325052, _1325054, _1325056, _1325058, _1325060] : [c_Finite__Set_Ofun__left__comm__idem(_1325050, _1325052, _1325054), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325050), _1325056)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1325050, _1325052, _1325054), _1325058), hAPP(hAPP(c_Set_Oinsert(_1325050), _1325060), _1325056)) = hAPP(hAPP(c_Finite__Set_Ofold(_1325050, _1325052, _1325054), hAPP(hAPP(_1325054, _1325060), _1325058)), _1325056))], (38664 ^ _781404) ^ [_1517041, _1517043, _1517045, _1517047] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1517041, _1517043)), hAPP(hAPP(c_Product__Type_OSigma(_1517041, _1517043), _1517045), hAPP(c_COMBK(tc_fun(_1517043, tc_HOL_Obool), _1517041), _1517047)))), -(_1517045 = c_Orderings_Obot__class_Obot(tc_fun(_1517041, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1517043), _1517047)))], (3058 ^ _781404) ^ [_826783, _826785, _826787, _826789, _826791, _826793, _826795, _826797, _826799, _826801, _826803, _826805] : [-(c_Product__Type_Omap__pair(_826805, _826801, _826797, _826793, _826789, _826785) = c_Product__Type_Omap__pair(_826803, _826799, _826795, _826791, _826787, _826783)), _826805 = _826803, _826801 = _826799, _826797 = _826795, _826793 = _826791, _826789 = _826787, _826785 = _826783], (1406 ^ _781404) ^ [_802019, _802021] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_802019)), _802021 = _802019, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_802021)], (20621 ^ _781404) ^ [_1147136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147136), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1147136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1147136 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49321 ^ _781404) ^ [_1775472, _1775474, _1775476] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1775472), _1775474))), -(hBOOL(hAPP(hAPP(_1775476, _1775472), _1775474))), 49328 ^ _781404 : [(49331 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 49326 ^ [_1775472, _1775474, _1775476]), 49327 ^ [_1775472, _1775474, _1775476]))), -(hBOOL(hAPP(hAPP(_1775476, 49326 ^ [_1775472, _1775474, _1775476]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 49327 ^ [_1775472, _1775474, _1775476]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (49337 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1775476, 49326 ^ [_1775472, _1775474, _1775476]), 49327 ^ [_1775472, _1775474, _1775476]))], (49329 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 49326 ^ [_1775472, _1775474, _1775476]), 49327 ^ [_1775472, _1775474, _1775476]))))]]], (25943 ^ _781404) ^ [_1245033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245033)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245033) = 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, _1245033))))], (10543 ^ _781404) ^ [_960796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960796), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13101 ^ _781404) ^ [_1008835, _1008837, _1008839, _1008841] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1008835), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008835), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008835), _1008837), _1008839)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008835), _1008837), _1008841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008835), _1008839), _1008841)))], (4892 ^ _781404) ^ [_855952, _855954, _855956, _855958, _855960, _855962] : [-(c_Relation_Orel__comp(_855962, _855958, _855954) = c_Relation_Orel__comp(_855960, _855956, _855952)), _855962 = _855960, _855958 = _855956, _855954 = _855952], (50873 ^ _781404) ^ [_1809859, _1809861, _1809863, _1809865] : [c_Fun_Obij__betw(_1809859, _1809861, _1809863, c_Orderings_Otop__class_Otop(tc_fun(_1809859, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1809861, tc_HOL_Obool))), 50876 ^ _781404 : [(50883 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1809861), _1809865)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1809859), hAPP(c_Set_Ovimage(_1809859, _1809861, _1809863), _1809865))))], (50877 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1809859), hAPP(c_Set_Ovimage(_1809859, _1809861, _1809863), _1809865))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1809861), _1809865)))]]], (21873 ^ _781404) ^ [_1170466, _1170468, _1170470, _1170472] : [class_Rings_Olinordered__ring__strict(_1170466), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170466), _1170468), _1170470)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170466), _1170472), c_Groups_Ozero__class_Ozero(_1170466))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170466), _1170472), _1170470)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170466), _1170472), _1170468))))], (41624 ^ _781404) ^ [_1598158, _1598160, _1598162, _1598164] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1598158, _1598158)), hAPP(hAPP(c_Product__Type_OPair(_1598158, _1598158), _1598160), _1598162)), c_Transitive__Closure_Otrancl(_1598158, hAPP(c_Relation_Oconverse(_1598158, _1598158), _1598164)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598158, _1598158)), hAPP(hAPP(c_Product__Type_OPair(_1598158, _1598158), _1598160), _1598162)), hAPP(c_Relation_Oconverse(_1598158, _1598158), c_Transitive__Closure_Otrancl(_1598158, _1598164)))))], (46722 ^ _781404) ^ [_1721578, _1721580] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1721578), _1721580) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1721578, _1721580)))], (8762 ^ _781404) ^ [_929123, _929125] : [_929125 = c_Orderings_Obot__class_Obot(tc_fun(_929123, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929123, tc_HOL_Obool)), _929125), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_929123, tc_HOL_Obool)), _929125))))], (50757 ^ _781404) ^ [_1807463, _1807465, _1807467, _1807469, _1807471, _1807473] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1807463, _1807465, _1807467, _1807469, c_Lazy__Sequence_Olazy__sequence_OInsert(_1807465, _1807471, _1807473)) = hAPP(hAPP(hAPP(_1807469, _1807471), _1807473), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1807463, _1807465, _1807467, _1807469, _1807473)))], (42810 ^ _781404) ^ [_1631405, _1631407, _1631409, _1631411] : [-(hBOOL(hAPP(hAPP(c_member(_1631405), _1631407), hAPP(c_List_Oset(_1631405), _1631409)))), hBOOL(hAPP(hAPP(c_member(_1631405), _1631407), hAPP(c_List_Oset(_1631405), c_List_Osublist(_1631405, _1631409, _1631411))))], (34253 ^ _781404) ^ [_1413609, _1413611, _1413613, _1413615, _1413617, _1413619] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413609, tc_fun(_1413611, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1413609, tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_fun(_1413611, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1413611, tc_fun(tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_fun(_1413611, tc_HOL_Obool)), _1413609), c_COMBC(_1413611, tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1413611, tc_prod(_1413609, _1413611)), tc_fun(_1413611, tc_fun(tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_HOL_Obool)), _1413609), hAPP(c_COMBB(tc_prod(_1413609, _1413611), tc_fun(tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_HOL_Obool), _1413611), c_member(tc_prod(_1413609, _1413611)))), c_Product__Type_OPair(_1413609, _1413611)))), _1413613)), hAPP(hAPP(c_COMBC(_1413609, tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_fun(_1413611, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1413611, tc_fun(tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_fun(_1413611, tc_HOL_Obool)), _1413609), c_COMBC(_1413611, tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1413611, tc_prod(_1413609, _1413611)), tc_fun(_1413611, tc_fun(tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_HOL_Obool)), _1413609), hAPP(c_COMBB(tc_prod(_1413609, _1413611), tc_fun(tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool), tc_HOL_Obool), _1413611), c_member(tc_prod(_1413609, _1413611)))), c_Product__Type_OPair(_1413609, _1413611)))), _1413615)), _1413617), _1413619)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1413609, _1413611)), hAPP(hAPP(c_Product__Type_OPair(_1413609, _1413611), _1413617), _1413619)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1413609, _1413611), tc_HOL_Obool)), _1413613), _1413615))))], (41387 ^ _781404) ^ [_1592370, _1592372, _1592374, _1592376] : [-(hBOOL(hAPP(hAPP(c_member(_1592370), _1592372), hAPP(c_Relation_ODomain(_1592370, _1592370), _1592374)))), 41390 ^ _781404 : [(41397 ^ _781404) ^ [] : [_1592372 = _1592376, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592370, _1592370)), hAPP(hAPP(c_Product__Type_OPair(_1592370, _1592370), _1592372), _1592376)), c_Transitive__Closure_Ortrancl(_1592370, _1592374))))], (41391 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592370, _1592370)), hAPP(hAPP(c_Product__Type_OPair(_1592370, _1592370), _1592372), _1592376)), c_Transitive__Closure_Ortrancl(_1592370, _1592374))), -(_1592372 = _1592376)]]], (52492 ^ _781404) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (8906 ^ _781404) ^ [_932046, _932048, _932050] : [class_Orderings_Oorder(_932046), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932046, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_932046, _932048, _932050)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_932046), _932050)) = c_Orderings_Obot__class_Obot(tc_fun(_932046, tc_HOL_Obool)))], (11383 ^ _781404) ^ [_975356, _975358, _975360, _975362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_975356, tc_HOL_Obool)), _975358), hAPP(hAPP(c_Set_Oinsert(_975356), _975360), _975362))), 11386 ^ _781404 : [(11393 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_975356), _975360), _975362))), 11396 ^ _781404 : [(11403 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_975356), _975360), _975358))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_975356, tc_HOL_Obool)), _975358), _975362)))], (11397 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_975356), _975360), _975358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_975356, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975356, tc_HOL_Obool)), _975358), hAPP(hAPP(c_Set_Oinsert(_975356), _975360), c_Orderings_Obot__class_Obot(tc_fun(_975356, tc_HOL_Obool))))), _975362)))]]], (11387 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_975356), _975360), _975362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_975356, tc_HOL_Obool)), _975358), _975362)))]]], (30490 ^ _781404) ^ [_1329204, _1329206, _1329208, _1329210] : [class_Rings_Olinordered__semidom(_1329204), 30496 ^ _781404 : [(30499 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329204), c_Groups_Ozero__class_Ozero(_1329204)), hAPP(_1329210, 30495 ^ [_1329204, _1329206, _1329208, _1329210])))], (30497 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329206), 30495 ^ [_1329204, _1329206, _1329208, _1329210]), _1329208)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329204), c_Groups_Ozero__class_Ozero(_1329204)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329206, _1329204), _1329210), _1329208))))], (35549 ^ _781404) ^ [_1444947, _1444949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1444947)), 35552 ^ _781404 : [(35559 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1444949))), 35562 ^ _781404 : [(35569 ^ _781404) ^ [] : [-(_1444947 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1444947, _1444949) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1444947), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1444949))))], (35563 ^ _781404) ^ [] : [_1444947 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1444947, _1444949) = 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)))]]], (35553 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1444949)), -(c_Divides_Odivmod__int(_1444947, _1444949) = c_Divides_OposDivAlg(_1444947, _1444949))]]], (48857 ^ _781404) ^ [_1765428, _1765430, _1765432] : [c_List_Olist__ex1(_1765428, _1765430, _1765432), 48861 ^ _781404 : [(48866 ^ _781404) ^ [_1765674] : [-(_1765674 = 48860 ^ [_1765428, _1765430, _1765432]), hBOOL(hAPP(hAPP(c_member(_1765428), _1765674), hAPP(c_List_Oset(_1765428), _1765432))), hBOOL(hAPP(_1765430, _1765674))], (48864 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1765430, 48860 ^ [_1765428, _1765430, _1765432])))], (48862 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765428), 48860 ^ [_1765428, _1765430, _1765432]), hAPP(c_List_Oset(_1765428), _1765432))))]]], (36522 ^ _781404) ^ [_1463921, _1463923, _1463925] : [-(hAPP(hAPP(c_Product__Type_OPair(_1463921, _1463923), hAPP(c_Product__Type_Ofst(_1463921, _1463923), _1463925)), hAPP(c_Product__Type_Osnd(_1463921, _1463923), _1463925)) = _1463925)], (4800 ^ _781404) ^ [_854464, _854466, _854468, _854470, _854472, _854474, _854476, _854478] : [-(c_Wellfounded_Olex__prod(_854478, _854474, _854470, _854466) = c_Wellfounded_Olex__prod(_854476, _854472, _854468, _854464)), _854478 = _854476, _854474 = _854472, _854470 = _854468, _854466 = _854464], (37017 ^ _781404) ^ [_1475394, _1475396, _1475398, _1475400, _1475402, _1475404] : [c_Finite__Set_Ofolding__idem(_1475394, _1475396, _1475398, _1475400), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475394), _1475402)), -(hAPP(_1475400, hAPP(hAPP(c_Set_Oinsert(_1475394), _1475404), _1475402)) = hAPP(c_Fun_Ocomp(_1475396, _1475396, _1475396, hAPP(_1475400, _1475402)), hAPP(_1475398, _1475404)))], (22905 ^ _781404) ^ [_1190888, _1190890, _1190892, _1190894, _1190896, _1190898] : [class_Rings_Olinordered__semiring__1__strict(_1190888), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190888), _1190890), _1190892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190888), _1190894), _1190892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190888), c_Groups_Ozero__class_Ozero(_1190888)), _1190896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190888), c_Groups_Ozero__class_Ozero(_1190888)), _1190898)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190888), _1190896), _1190898) = c_Groups_Oone__class_Oone(_1190888), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190888), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190888), _1190896), _1190890)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190888), _1190898), _1190894))), _1190892)))], (45593 ^ _781404) ^ [_1694834] : [-(_1694834 = 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)), _1694834)))], (6564 ^ _781404) ^ [_886135, _886137, _886139] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886135, tc_HOL_Obool)), _886137) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886135, tc_HOL_Obool)), _886139), -(_886137 = _886139)], (31902 ^ _781404) ^ [_1355537, _1355539, _1355541, _1355543] : [class_Orderings_Olinorder(_1355537), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355537), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355537), _1355539), _1355541)), _1355543) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355537), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355537), _1355539), _1355543)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355537), _1355541), _1355543)))], (19969 ^ _781404) ^ [_1136158, _1136160] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1136158) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1136160), -(_1136158 = _1136160)], (42382 ^ _781404) ^ [_1619236, _1619238, _1619240, _1619242] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619236), tc_List_Olist(_1619236))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619236), tc_List_Olist(_1619236)), _1619238), _1619240)), c_List_Olistrel1(_1619236, hAPP(c_Relation_Oconverse(_1619236, _1619236), _1619242)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619236), tc_List_Olist(_1619236))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619236), tc_List_Olist(_1619236)), _1619238), _1619240)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1619236), tc_List_Olist(_1619236)), c_List_Olistrel1(_1619236, _1619242)))))], (45220 ^ _781404) ^ [_1686278, _1686280, _1686282, _1686284, _1686286, _1686288] : [-(hAPP(hAPP(c_List_Omap(_1686278, _1686280), _1686282), hAPP(hAPP(c_List_Olist__update(_1686278, _1686284), _1686286), _1686288)) = hAPP(hAPP(c_List_Olist__update(_1686280, hAPP(hAPP(c_List_Omap(_1686278, _1686280), _1686282), _1686284)), _1686286), hAPP(_1686282, _1686288)))], (45742 ^ _781404) ^ [_1697734, _1697736, _1697738, _1697740, _1697742] : [c_List_Opartition(_1697734, _1697736, _1697738) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1697734), tc_List_Olist(_1697734)), _1697740), _1697742), 45745 ^ _781404 : [(45752 ^ _781404) ^ [_1697996] : [hBOOL(hAPP(hAPP(c_member(_1697734), _1697996), hAPP(c_List_Oset(_1697734), _1697742))), hBOOL(hAPP(_1697736, _1697996))], (45746 ^ _781404) ^ [_1697887] : [hBOOL(hAPP(hAPP(c_member(_1697734), _1697887), hAPP(c_List_Oset(_1697734), _1697740))), -(hBOOL(hAPP(_1697736, _1697887)))]]], (4442 ^ _781404) ^ [_848851, _848853] : [_848853 = _848851, -(c_Lazy__Sequence_Oempty(_848853) = c_Lazy__Sequence_Oempty(_848851))], (45644 ^ _781404) ^ [_1696027] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1696027)) = _1696027)], (33406 ^ _781404) ^ [_1388048, _1388050, _1388052, _1388054] : [hBOOL(hAPP(hAPP(c_member(_1388050), _1388054), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388048, tc_fun(_1388050, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1388048, tc_HOL_Obool))), _1388052))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388048, tc_fun(_1388050, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1388048, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1388050, tc_HOL_Obool), tc_fun(_1388050, tc_HOL_Obool), _1388048), hAPP(c_COMBC(_1388050, tc_fun(_1388050, tc_HOL_Obool), tc_HOL_Obool), c_member(_1388050))), _1388052)), _1388054)))], (44397 ^ _781404) ^ [_1668884, _1668886, _1668888, _1668890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1668884), _1668886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1668888, tc_HOL_Obool)), hAPP(c_List_Oset(_1668888), hAPP(hAPP(c_List_Odrop(_1668888), _1668886), _1668890))), hAPP(c_List_Oset(_1668888), hAPP(hAPP(c_List_Odrop(_1668888), _1668884), _1668890)))))], (5128 ^ _781404) ^ [_859630, _859632, _859634, _859636, _859638, _859640] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_859640, _859636, _859632) = c_SetInterval_Oord__class_OatLeastAtMost(_859638, _859634, _859630)), _859640 = _859638, _859636 = _859634, _859632 = _859630], (43874 ^ _781404) ^ [_1656512, _1656514, _1656516, _1656518, _1656520] : [hAPP(hAPP(c_List_Oappend(_1656512), _1656514), _1656516) = hAPP(hAPP(c_List_Olist_OCons(_1656512), _1656518), _1656520), 43879 ^ _781404 : [(43882 ^ _781404) ^ [] : [-(_1656516 = hAPP(hAPP(c_List_Olist_OCons(_1656512), _1656518), _1656520))], (43880 ^ _781404) ^ [] : [-(_1656514 = c_List_Olist_ONil(_1656512))]], 43884 ^ _781404 : [(43887 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1656512), 43883 ^ [_1656512, _1656514, _1656516, _1656518, _1656520]), _1656516) = _1656520)], (43885 ^ _781404) ^ [] : [-(_1656514 = hAPP(hAPP(c_List_Olist_OCons(_1656512), _1656518), 43883 ^ [_1656512, _1656514, _1656516, _1656518, _1656520]))]]], (28949 ^ _781404) ^ [_1299722, _1299724, _1299726] : [class_Fields_Olinordered__field(_1299722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299722), _1299724), c_Groups_Ozero__class_Ozero(_1299722))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299722), _1299726), c_Groups_Ozero__class_Ozero(_1299722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299722), c_Groups_Ozero__class_Ozero(_1299722)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299722), _1299724), _1299726))))], (33129 ^ _781404) ^ [_1379438, _1379440] : [-(hAPP(c_Finite__Set_Ocard(_1379438), _1379440) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1379438, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1379438), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1379440))], (21599 ^ _781404) ^ [_1165412, _1165414] : [class_Rings_Olinordered__ring(_1165412), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165412), c_Groups_Ozero__class_Ozero(_1165412)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165412), _1165414), _1165414))))], (37766 ^ _781404) ^ [_1494259, _1494261, _1494263, _1494265, _1494267] : [c_Equiv__Relations_Oequiv(_1494259, _1494261, _1494263), hBOOL(hAPP(hAPP(c_member(_1494259), _1494265), _1494261)), hBOOL(hAPP(hAPP(c_member(_1494259), _1494267), _1494261)), 37777 ^ _781404 : [(37784 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494259, _1494259)), hAPP(hAPP(c_Product__Type_OPair(_1494259, _1494259), _1494265), _1494267)), _1494263)), -(hAPP(c_Relation_OImage(_1494259, _1494259, _1494263), hAPP(hAPP(c_Set_Oinsert(_1494259), _1494265), c_Orderings_Obot__class_Obot(tc_fun(_1494259, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1494259, _1494259, _1494263), hAPP(hAPP(c_Set_Oinsert(_1494259), _1494267), c_Orderings_Obot__class_Obot(tc_fun(_1494259, tc_HOL_Obool)))))], (37778 ^ _781404) ^ [] : [hAPP(c_Relation_OImage(_1494259, _1494259, _1494263), hAPP(hAPP(c_Set_Oinsert(_1494259), _1494265), c_Orderings_Obot__class_Obot(tc_fun(_1494259, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1494259, _1494259, _1494263), hAPP(hAPP(c_Set_Oinsert(_1494259), _1494267), c_Orderings_Obot__class_Obot(tc_fun(_1494259, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494259, _1494259)), hAPP(hAPP(c_Product__Type_OPair(_1494259, _1494259), _1494265), _1494267)), _1494263)))]]], (39632 ^ _781404) ^ [_1549088, _1549090, _1549092, _1549094] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1549088, _1549090, _1549092), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549088, _1549090), tc_HOL_Obool))), _1549094) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549088, _1549092), tc_HOL_Obool)))], (8034 ^ _781404) ^ [_915747, _915749, _915751] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_915747, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915747, tc_HOL_Obool)), _915749), _915751)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915747, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_915747, tc_HOL_Obool)), _915749)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_915747, tc_HOL_Obool)), _915751)))], (33992 ^ _781404) ^ [_1405220, _1405222, _1405224, _1405226, _1405228] : [33994 ^ _781404 : [(33997 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1405220, tc_HOL_Obool)), hAPP(_1405226, 33993 ^ [_1405220, _1405222, _1405224, _1405226, _1405228])), _1405228))], (33995 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405222), 33993 ^ [_1405220, _1405222, _1405224, _1405226, _1405228]), _1405224)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1405220, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405222, tc_fun(_1405220, tc_HOL_Obool)), _1405224), _1405226)), _1405228)))], (24252 ^ _781404) ^ [_1216190, _1216192, _1216194] : [class_Divides_Osemiring__div(_1216190), -(_1216192 = c_Groups_Ozero__class_Ozero(_1216190)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216190), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216190), _1216192), _1216194)), _1216192) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216190), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216190), _1216194), _1216192)), c_Groups_Oone__class_Oone(_1216190)))], (41465 ^ _781404) ^ [_1594224, _1594226] : [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), _1594224), _1594226)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1594224), _1594226)))], (48949 ^ _781404) ^ [_1767727, _1767729] : [-(c_List_Osplice(_1767727, _1767729, c_List_Olist_ONil(_1767727)) = _1767729)], (2014 ^ _781404) ^ [_810473, _810475] : [_810475 = _810473, -(c_Set_OBall(_810475) = c_Set_OBall(_810473))], (36173 ^ _781404) ^ [_1456559, _1456561] : [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), _1456559), _1456561))), 36176 ^ _781404 : [(36183 ^ _781404) ^ [] : [-(_1456561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1456559, _1456561) = c_Nitpick_Onat__gcd(_1456561, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1456559, _1456561)))], (36177 ^ _781404) ^ [] : [_1456561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1456559, _1456561) = _1456559)]]], (43280 ^ _781404) ^ [_1644019, _1644021, _1644023] : [hBOOL(hAPP(c_List_Odistinct(_1644019), _1644021)), -(hBOOL(hAPP(c_List_Odistinct(_1644019), hAPP(hAPP(c_List_Otake(_1644019), _1644023), _1644021))))], (46127 ^ _781404) ^ [_1706883] : [-(c_Enum_Osublists(_1706883, c_List_Olist_ONil(_1706883)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1706883)), c_List_Olist_ONil(_1706883)), c_List_Olist_ONil(tc_List_Olist(_1706883))))], (18205 ^ _781404) ^ [_1105729, _1105731, _1105733, _1105735] : [class_Rings_Olinordered__semidom(_1105729), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105729), c_Groups_Oone__class_Oone(_1105729)), _1105731)), 18212 ^ _781404 : [(18219 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1105733), _1105735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105729), hAPP(hAPP(c_Power_Opower__class_Opower(_1105729), _1105731), _1105733)), hAPP(hAPP(c_Power_Opower__class_Opower(_1105729), _1105731), _1105735))))], (18213 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105729), hAPP(hAPP(c_Power_Opower__class_Opower(_1105729), _1105731), _1105733)), hAPP(hAPP(c_Power_Opower__class_Opower(_1105729), _1105731), _1105735))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1105733), _1105735)))]]], (5789 ^ _781404) ^ [_873126, _873128, _873130, _873132, _873134] : [class_Orderings_Oord(_873126), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873128, _873126)), _873130), _873132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873126), hAPP(_873130, _873134)), hAPP(_873132, _873134))))], (50071 ^ _781404) ^ [_1793256, _1793258] : [c_Relation_Oantisym(_1793256, _1793258), 50074 ^ _781404 : [(50075 ^ _781404) ^ [_1793368, _1793370] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1793256, _1793256)), hAPP(hAPP(c_Product__Type_OPair(_1793256, _1793256), _1793370), _1793368)), _1793258)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1793256, _1793256)), hAPP(hAPP(c_Product__Type_OPair(_1793256, _1793256), _1793368), _1793370)), _1793258)), -(_1793370 = _1793368)]]], (24518 ^ _781404) ^ [_1221244, _1221246, _1221248, _1221250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1221246), _1221248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1221248), 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), _1221246), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1221250, _1221244))), _1221248)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40182 ^ _781404) ^ [_1563652, _1563654] : [c_Wellfounded_Owf(_1563652, _1563654), -(c_Wellfounded_Owf(tc_List_Olist(_1563652), c_List_Olex(_1563652, _1563654)))], (37549 ^ _781404) ^ [_1489073, _1489075, _1489077] : [_1489075 = c_Orderings_Obot__class_Obot(tc_fun(_1489073, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1489073, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1489073), _1489075), _1489077))], (22959 ^ _781404) ^ [_1191932, _1191934, _1191936] : [class_Groups_Omonoid__mult(_1191932), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191932), _1191934), 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)))), _1191936)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1191932), hAPP(hAPP(c_Power_Opower__class_Opower(_1191932), _1191934), _1191936)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (48434 ^ _781404) ^ [_1757193, _1757195] : [class_Enum_Oenum(_1757193), 48437 ^ _781404 : [(48445 ^ _781404) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1757193), _1757195)), 48448 ^ _781404 : [(48449 ^ _781404) ^ [_1757411] : [-(hBOOL(hAPP(_1757195, _1757411)))]]], (48438 ^ _781404) ^ [] : [hBOOL(hAPP(_1757195, 48439 ^ [_1757193, _1757195])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1757193), _1757195)))]]], (43140 ^ _781404) ^ [_1640675, _1640677, _1640679, _1640681] : [_1640675 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640677)), _1640679)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1640677, hAPP(hAPP(c_List_Olist__update(_1640677, _1640679), _1640675), _1640681)) = c_List_Obutlast(_1640677, _1640679))], (1456 ^ _781404) ^ [_802644, _802646] : [-(class_Lattices_Osemilattice__sup(_802644)), _802646 = _802644, class_Lattices_Osemilattice__sup(_802646)], (20375 ^ _781404) ^ [] : [-(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))], (18641 ^ _781404) ^ [_1114014, _1114016, _1114018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114014)), 18644 ^ _781404 : [(18645 ^ _781404) ^ [_1114148] : [18647 ^ _781404 : [(18653 ^ _781404) ^ [] : [-(_1114148 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 18649 ^ [_1114014, _1114016, _1114018, _1114148]), 18646 ^ [_1114014, _1114016, _1114018, _1114148]))], (18651 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18649 ^ [_1114014, _1114016, _1114018, _1114148]), _1114016)))], (18648 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18646 ^ [_1114014, _1114016, _1114018, _1114148]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1114014))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114148), _1114018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1114148), _1114014)), _1114018)))]]], (35599 ^ _781404) ^ [_1445723, _1445725] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1445723, _1445723)), hAPP(hAPP(c_Product__Type_OPair(_1445723, _1445723), 35600 ^ [_1445723, _1445725]), 35600 ^ [_1445723, _1445725])), _1445725)), -(c_Nitpick_Orefl_H(_1445723, _1445725))], (50771 ^ _781404) ^ [_1807663, _1807665, _1807667, _1807669] : [c_Fun_Obij__betw(_1807663, _1807665, _1807667, c_Orderings_Otop__class_Otop(tc_fun(_1807663, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1807665, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1807663, _1807665, _1807667), hAPP(c_Set_OCollect(_1807663), _1807669)) = hAPP(c_Set_OCollect(_1807665), hAPP(hAPP(c_COMBB(_1807663, tc_HOL_Obool, _1807665), _1807669), c_Hilbert__Choice_Oinv__into(_1807663, _1807665, c_Orderings_Otop__class_Otop(tc_fun(_1807663, tc_HOL_Obool)), _1807667))))], (44509 ^ _781404) ^ [_1671688, _1671690, _1671692, _1671694] : [-(hAPP(c_List_Orotate1(_1671688), c_List_Olist_ONil(_1671688)) = c_List_Olist_ONil(_1671688))], (45206 ^ _781404) ^ [_1686005, _1686007, _1686009] : [-(hAPP(hAPP(c_List_Omap(_1686005, _1686007), _1686009), c_List_Olist_ONil(_1686005)) = c_List_Olist_ONil(_1686007))], (43952 ^ _781404) ^ [_1658277, _1658279, _1658281, _1658283, _1658285] : [-(hAPP(hAPP(c_List_Oappend(_1658277), _1658279), _1658281) = hAPP(hAPP(c_List_Oappend(_1658277), _1658283), _1658285)), 43953 ^ _781404 : [(43960 ^ _781404) ^ [_1658501] : [hAPP(hAPP(c_List_Oappend(_1658277), _1658279), _1658501) = _1658283, _1658281 = hAPP(hAPP(c_List_Oappend(_1658277), _1658501), _1658285)], (43954 ^ _781404) ^ [_1658389] : [_1658279 = hAPP(hAPP(c_List_Oappend(_1658277), _1658283), _1658389), hAPP(hAPP(c_List_Oappend(_1658277), _1658389), _1658281) = _1658285]]], (6849 ^ _781404) ^ [_891146, _891148] : [class_Lattices_Osemilattice__sup(_891146), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891146), _891148), _891148) = _891148)], (45978 ^ _781404) ^ [_1703704, _1703706, _1703708, _1703710, _1703712, _1703714, _1703716] : [-(c_List_Olist__all2(_1703704, _1703706, _1703708, hAPP(hAPP(c_List_Olist_OCons(_1703704), _1703710), _1703712), hAPP(hAPP(c_List_Olist_OCons(_1703706), _1703714), _1703716))), hBOOL(hAPP(hAPP(_1703708, _1703710), _1703714)), c_List_Olist__all2(_1703704, _1703706, _1703708, _1703712, _1703716)], (47131 ^ _781404) ^ [_1728795, _1728797, _1728799, _1728801, _1728803] : [class_Orderings_Olinorder(_1728795), 47134 ^ _781404 : [(47141 ^ _781404) ^ [] : [c_List_Olinorder__class_Osorted(_1728795, hAPP(hAPP(c_List_Omap(_1728797, _1728795), _1728799), _1728803)), -(c_List_Olinorder__class_Osorted(_1728795, hAPP(hAPP(c_List_Omap(_1728797, _1728795), _1728799), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1728797, _1728795, _1728799), _1728801), _1728803))))], (47135 ^ _781404) ^ [] : [c_List_Olinorder__class_Osorted(_1728795, hAPP(hAPP(c_List_Omap(_1728797, _1728795), _1728799), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1728797, _1728795, _1728799), _1728801), _1728803))), -(c_List_Olinorder__class_Osorted(_1728795, hAPP(hAPP(c_List_Omap(_1728797, _1728795), _1728799), _1728803)))]]], (9399 ^ _781404) ^ [_942553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942553), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8876 ^ _781404) ^ [_931403, _931405, _931407] : [class_Orderings_Oorder(_931403), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931403, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_931403), _931405)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_931403, _931405), _931407)) = c_Orderings_Obot__class_Obot(tc_fun(_931403, tc_HOL_Obool)))], (24955 ^ _781404) ^ [_1228477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1228477)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228477), c_Int_OMin)))], (14695 ^ _781404) ^ [_1039078, _1039080, _1039082] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039078), _1039080)), 14698 ^ _781404 : [(14705 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039078), _1039082)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039078), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1039078, tc_HOL_Obool)), _1039082), _1039080))))], (14699 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039078), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1039078, tc_HOL_Obool)), _1039082), _1039080))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039078), _1039082)))]]], (36792 ^ _781404) ^ [_1470020] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1470020)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1470020)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43254 ^ _781404) ^ [_1643338, _1643340, _1643342, _1643344] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643338), tc_List_Olist(_1643338))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643338), tc_List_Olist(_1643338)), _1643340), _1643342)), c_List_Olistrel1(_1643338, _1643344)))), 43255 ^ _781404 : [(43256 ^ _781404) ^ [_1643471, _1643473] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643338, _1643338)), hAPP(hAPP(c_Product__Type_OPair(_1643338, _1643338), hAPP(hAPP(c_List_Onth(_1643338), _1643340), _1643471)), _1643473)), _1643344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1643471), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643338)), _1643340))), _1643342 = hAPP(hAPP(c_List_Olist__update(_1643338, _1643340), _1643471), _1643473)]]], (8532 ^ _781404) ^ [_925340, _925342] : [class_Lattices_Obounded__lattice__bot(_925340), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925340), c_Orderings_Obot__class_Obot(_925340)), _925342) = _925342)], (43461 ^ _781404) ^ [_1648041, _1648043] : [-(_1648041 = c_List_Olist_ONil(_1648043)), hBOOL(hAPP(c_List_Odistinct(_1648043), _1648041)), -(hBOOL(hAPP(c_List_Odistinct(_1648043), c_List_Obutlast(_1648043, _1648041))))], (13415 ^ _781404) ^ [_1014687, _1014689, _1014691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014687), _1014689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014687), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014691), _1014689))))], (39079 ^ _781404) ^ [_1528300, _1528302, _1528304] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1528300, tc_HOL_Obool)), _1528302), _1528304) = hAPP(c_Set_OCollect(_1528300), hAPP(hAPP(c_COMBS(_1528300, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1528300), c_fconj), hAPP(hAPP(c_COMBC(_1528300, tc_fun(_1528300, tc_HOL_Obool), tc_HOL_Obool), c_member(_1528300)), _1528302))), hAPP(hAPP(c_COMBC(_1528300, tc_fun(_1528300, tc_HOL_Obool), tc_HOL_Obool), c_member(_1528300)), _1528304))))], (46538 ^ _781404) ^ [_1716386, _1716388, _1716390, _1716392] : [-(hAPP(c_List_Ofilter(_1716386, _1716388), c_List_Oremove1(_1716386, _1716390, _1716392)) = c_List_Oremove1(_1716386, _1716390, hAPP(c_List_Ofilter(_1716386, _1716388), _1716392)))], (47477 ^ _781404) ^ [_1735839, _1735841, _1735843] : [-(hAPP(c_List_Orev(_1735839), hAPP(hAPP(c_List_Oappend(_1735839), _1735841), _1735843)) = hAPP(hAPP(c_List_Oappend(_1735839), hAPP(c_List_Orev(_1735839), _1735843)), hAPP(c_List_Orev(_1735839), _1735841)))], (8966 ^ _781404) ^ [_933221, _933223] : [-(c_Set_Othe__elem(_933221, hAPP(hAPP(c_Set_Oinsert(_933221), _933223), c_Orderings_Obot__class_Obot(tc_fun(_933221, tc_HOL_Obool)))) = _933223)], (33601 ^ _781404) ^ [_1393457, _1393459, _1393461, _1393463, _1393465, _1393467] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393457, tc_fun(_1393459, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393461, tc_fun(_1393457, tc_HOL_Obool)), _1393463), _1393465)), _1393467) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393461, tc_fun(_1393459, tc_HOL_Obool)), _1393463), hAPP(hAPP(c_COMBC(_1393461, tc_fun(_1393457, tc_fun(_1393459, tc_HOL_Obool)), tc_fun(_1393459, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393457, tc_HOL_Obool), tc_fun(tc_fun(_1393457, tc_fun(_1393459, tc_HOL_Obool)), tc_fun(_1393459, tc_HOL_Obool)), _1393461), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393457, tc_fun(_1393459, tc_HOL_Obool))), _1393465)), _1393467)))], (42370 ^ _781404) ^ [_1618867, _1618869, _1618871, _1618873] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618867), tc_List_Olist(_1618867))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618867), tc_List_Olist(_1618867)), _1618869), _1618871)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1618867), c_List_Olistrel1(_1618867, _1618873)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618867)), _1618869) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618867)), _1618871))], (50667 ^ _781404) ^ [_1805456, _1805458, _1805460, _1805462, _1805464, _1805466] : [class_Groups_Ocomm__monoid__mult(_1805456), hBOOL(hAPP(c_Finite__Set_Ofinite(_1805458), _1805460)), 50677 ^ _781404 : [(50680 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805462), hAPP(_1805464, 50676 ^ [_1805456, _1805458, _1805460, _1805462, _1805464, _1805466])))], (50678 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805458), 50676 ^ [_1805456, _1805458, _1805460, _1805462, _1805464, _1805466]), _1805460)))]], 50684 ^ _781404 : [(50688 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805458), 50686 ^ [_1805456, _1805458, _1805460, _1805462, _1805464, _1805466]), _1805460)))], (50690 ^ _781404) ^ [] : [50683 ^ [_1805456, _1805458, _1805460, _1805462, _1805464, _1805466] = 50686 ^ [_1805456, _1805458, _1805460, _1805462, _1805464, _1805466]], (50692 ^ _781404) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1805462, tc_HOL_Obool)), hAPP(_1805464, 50683 ^ [_1805456, _1805458, _1805460, _1805462, _1805464, _1805466])), hAPP(_1805464, 50686 ^ [_1805456, _1805458, _1805460, _1805462, _1805464, _1805466])) = c_Orderings_Obot__class_Obot(tc_fun(_1805462, tc_HOL_Obool))], (50685 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805458), 50683 ^ [_1805456, _1805458, _1805460, _1805462, _1805464, _1805466]), _1805460)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1805456, _1805462, c_Groups_Otimes__class_Otimes(_1805456)), _1805466), c_Groups_Oone__class_Oone(_1805456)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1805458, tc_fun(_1805462, tc_HOL_Obool)), _1805460), _1805464)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1805456, _1805458, c_Groups_Otimes__class_Otimes(_1805456)), hAPP(hAPP(c_COMBB(tc_fun(_1805462, tc_HOL_Obool), _1805456, _1805458), hAPP(hAPP(c_Finite__Set_Ofold__image(_1805456, _1805462, c_Groups_Otimes__class_Otimes(_1805456)), _1805466), c_Groups_Oone__class_Oone(_1805456))), _1805464)), c_Groups_Oone__class_Oone(_1805456)), _1805460))], (34531 ^ _781404) ^ [_1421658, _1421660, _1421662, _1421664, _1421666] : [hAPP(c_Set_Oimage(_1421658, _1421660, _1421662), c_Orderings_Otop__class_Otop(tc_fun(_1421658, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1421660, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1421660, _1421664, _1421666), c_Orderings_Otop__class_Otop(tc_fun(_1421660, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1421664, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1421658, _1421664, hAPP(c_Fun_Ocomp(_1421660, _1421664, _1421658, _1421666), _1421662)), c_Orderings_Otop__class_Otop(tc_fun(_1421658, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1421664, tc_HOL_Obool)))], (11899 ^ _781404) ^ [_985165, _985167, _985169, _985171, _985173] : [hAPP(_985171, _985167) = _985173, -(hBOOL(hAPP(hAPP(c_member(_985165), _985167), hAPP(c_Set_Ovimage(_985165, _985169, _985171), hAPP(hAPP(c_Set_Oinsert(_985169), _985173), c_Orderings_Obot__class_Obot(tc_fun(_985169, tc_HOL_Obool)))))))], (2336 ^ _781404) ^ [_815474, _815476, _815478, _815480] : [-(c_Divides_Opdivmod(_815480, _815476) = c_Divides_Opdivmod(_815478, _815474)), _815480 = _815478, _815476 = _815474], (25795 ^ _781404) ^ [_1242380, _1242382, _1242384] : [-(hBOOL(hAPP(_1242380, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242382), _1242384)))), 25796 ^ _781404 : [(25803 ^ _781404) ^ [_1242548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242384), _1242548)), _1242382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1242382), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242384), hAPP(c_Nat_OSuc, _1242548)))), hBOOL(hAPP(_1242380, _1242548))], (25797 ^ _781404) ^ [] : [_1242384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1242380, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (5973 ^ _781404) ^ [_876096, _876098, _876100] : [class_Orderings_Oorder(_876096), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876096), _876098), _876100)), 5980 ^ _781404 : [(5987 ^ _781404) ^ [] : [_876100 = _876098, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876096), _876100), _876098)))], (5981 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876096), _876100), _876098)), -(_876100 = _876098)]]], (14522 ^ _781404) ^ [_1035823, _1035825, _1035827] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035823), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035825), _1035827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035825), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035823), _1035827)))], (36520 ^ _781404) ^ [_1463873, _1463875, _1463877] : [-(_1463873 = hAPP(hAPP(c_Product__Type_OPair(_1463875, _1463877), hAPP(c_Product__Type_Ofst(_1463875, _1463877), _1463873)), hAPP(c_Product__Type_Osnd(_1463875, _1463877), _1463873)))], (37276 ^ _781404) ^ [_1481413, _1481415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1481413), _1481415)), -(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), _1481413), _1481415)), c_Wellfounded_Oless__than)))], (47027 ^ _781404) ^ [_1727086] : [class_Orderings_Olinorder(_1727086), -(c_List_Olinorder__class_Osorted(_1727086, c_List_Olist_ONil(_1727086)))], (39461 ^ _781404) ^ [_1543300, _1543302, _1543304, _1543306] : [-(c_Nitpick_Oprod(_1543300, _1543302, _1543304, _1543306) = hAPP(c_Set_OCollect(tc_prod(_1543300, _1543302)), hAPP(c_Product__Type_Oprod_Oprod__case(_1543300, _1543302, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1543300, tc_fun(_1543302, tc_HOL_Obool), tc_fun(_1543302, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1543302, tc_HOL_Obool), tc_fun(_1543302, tc_HOL_Obool)), _1543300), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1543302)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543300), c_fconj), hAPP(hAPP(c_COMBC(_1543300, tc_fun(_1543300, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543300)), _1543304)))), hAPP(hAPP(c_COMBC(_1543302, tc_fun(_1543302, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543302)), _1543306)))))], (21197 ^ _781404) ^ [_1158029, _1158031, _1158033] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1158031), _1158033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158029), _1158031)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158029), _1158033)))], (35324 ^ _781404) ^ [_1439744, _1439746, _1439748, _1439750, _1439752, _1439754] : [hBOOL(hAPP(hAPP(_1439744, _1439746), _1439748)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439750, tc_fun(_1439752, tc_HOL_Obool))), _1439754), _1439744), _1439746), _1439748)))], (16272 ^ _781404) ^ [_1070696, _1070698, _1070700, _1070702] : [16273 ^ _781404 : [(16276 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1070700), _1070702)))], (16274 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1070696), _1070698)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1070696, _1070700)), c_Sum__Type_OPlus(_1070696, _1070700, _1070698, _1070702)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46754 ^ _781404) ^ [_1722188, _1722190] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722188), _1722190))), -(c_List_Oupt(_1722188, _1722190) = c_List_Olist_ONil(tc_Nat_Onat))], (35866 ^ _781404) ^ [_1451068, _1451070, _1451072] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451068, _1451068), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1451070), _1451072))), -(_1451068 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1451072 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (2668 ^ _781404) ^ [_820766, _820768] : [_820768 = _820766, -(c_HOL_OAll(_820768) = c_HOL_OAll(_820766))], (35754 ^ _781404) ^ [_1448741, _1448743] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1448741, _1448743), c_Divides_Odivmod__nat(_1448741, _1448743))))], (34547 ^ _781404) ^ [_1422070, _1422072, _1422074, _1422076, _1422078, _1422080] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1422070, tc_fun(_1422072, tc_HOL_Obool)), _1422074), hAPP(c_Fun_Ocomp(_1422076, tc_fun(_1422072, tc_HOL_Obool), _1422070, _1422078), _1422080)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1422076, tc_fun(_1422072, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1422070, _1422076, _1422080), _1422074)), _1422078))], (1346 ^ _781404) ^ [_801269, _801271] : [-(class_Int_Onumber__ring(_801269)), _801271 = _801269, class_Int_Onumber__ring(_801271)], (9242 ^ _781404) ^ [_939232, _939234, _939236] : [class_Groups_Oordered__ab__group__add(_939232), -(hAPP(c_Set_Oimage(_939232, _939232, c_Groups_Ouminus__class_Ouminus(_939232)), c_SetInterval_Oord__class_OgreaterThanLessThan(_939232, _939234, _939236)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_939232, hAPP(c_Groups_Ouminus__class_Ouminus(_939232), _939236), hAPP(c_Groups_Ouminus__class_Ouminus(_939232), _939234)))], (26121 ^ _781404) ^ [_1247959] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1247959)], (8756 ^ _781404) ^ [_929004, _929006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929004, tc_HOL_Obool)), _929006), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_929004, tc_HOL_Obool)), _929006))), -(_929006 = c_Orderings_Obot__class_Obot(tc_fun(_929004, tc_HOL_Obool)))], (39552 ^ _781404) ^ [_1546583, _1546585, _1546587, _1546589] : [-(c_Product__Type_Oapsnd(_1546583, _1546585, _1546587, _1546589) = c_Product__Type_Omap__pair(_1546587, _1546587, _1546583, _1546585, c_Fun_Oid(_1546587), _1546589))], (24967 ^ _781404) ^ [_1228685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1228685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1228685)))], (40616 ^ _781404) ^ [_1573286, _1573288] : [class_Complete__Lattice_Ocomplete__lattice(_1573286), c_Orderings_Oorder__class_Omono(_1573286, _1573286, _1573288), -(c_Inductive_Ocomplete__lattice__class_Ogfp(_1573286, _1573288) = hAPP(_1573288, c_Inductive_Ocomplete__lattice__class_Ogfp(_1573286, _1573288)))], (12594 ^ _781404) ^ [_999054, _999056, _999058, _999060] : [c_Fun_Oinj__on(_999054, _999056, _999058, c_Orderings_Otop__class_Otop(tc_fun(_999054, tc_HOL_Obool))), 12597 ^ _781404 : [(12611 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_999056), _999060), hAPP(c_Set_Oimage(_999054, _999056, _999058), c_Orderings_Otop__class_Otop(tc_fun(_999054, tc_HOL_Obool)))))), 12612 ^ _781404 : [(12613 ^ _781404) ^ [_999457] : [_999060 = hAPP(_999058, _999457), 12617 ^ _781404 : [(12620 ^ _781404) ^ [] : [12616 ^ [_999054, _999056, _999058, _999060, _999457] = _999457], (12618 ^ _781404) ^ [] : [-(_999060 = hAPP(_999058, 12616 ^ [_999054, _999056, _999058, _999060, _999457]))]]]]], (12598 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_999056), _999060), hAPP(c_Set_Oimage(_999054, _999056, _999058), c_Orderings_Otop__class_Otop(tc_fun(_999054, tc_HOL_Obool))))), 12602 ^ _781404 : [(12605 ^ _781404) ^ [_999319] : [_999060 = hAPP(_999058, _999319), -(_999319 = 12601 ^ [_999054, _999056, _999058, _999060])], (12603 ^ _781404) ^ [] : [-(_999060 = hAPP(_999058, 12601 ^ [_999054, _999056, _999058, _999060]))]]]]], (9136 ^ _781404) ^ [_936578, _936580, _936582, _936584] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936578, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936578, tc_HOL_Obool)), _936580), _936582)), _936584) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936578, tc_HOL_Obool)), _936580), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936578, tc_HOL_Obool)), _936582), _936584)))], (40028 ^ _781404) ^ [_1559711, _1559713] : [40030 ^ _781404 : [(40031 ^ _781404) ^ [_1559736] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559711, _1559711)), hAPP(hAPP(c_Product__Type_OPair(_1559711, _1559711), hAPP(40029 ^ [_1559711, _1559713], hAPP(c_Nat_OSuc, _1559736))), hAPP(40029 ^ [_1559711, _1559713], _1559736))), _1559713)))]], -(c_Wellfounded_Owf(_1559711, _1559713))], (3182 ^ _781404) ^ [_828769, _828771, _828773, _828775] : [-(c_Finite__Set_Ofold1(_828775, _828771) = c_Finite__Set_Ofold1(_828773, _828769)), _828775 = _828773, _828771 = _828769], (1050 ^ _781404) ^ [_797165, _797167, _797169, _797171] : [-(c_Wellfounded_Owf(_797169, _797165)), c_Wellfounded_Owf(_797171, _797167), _797171 = _797169, _797167 = _797165], (8190 ^ _781404) ^ [_918902, _918904, _918906] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_918902, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_918902, tc_HOL_Obool), _918904)), _918906) = c_Orderings_Obot__class_Obot(tc_fun(_918902, tc_HOL_Obool)), 8193 ^ _781404 : [(8194 ^ _781404) ^ [_919037] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_918902, tc_HOL_Obool)), _919037), _918904)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_918902, tc_HOL_Obool)), _919037), _918906) = c_Orderings_Obot__class_Obot(tc_fun(_918902, tc_HOL_Obool)))]]], (47429 ^ _781404) ^ [_1734900, _1734902] : [c_List_Olist_ONil(_1734900) = hAPP(c_List_Orev(_1734900), _1734902), -(_1734902 = c_List_Olist_ONil(_1734900))], (12696 ^ _781404) ^ [_1001014, _1001016, _1001018, _1001020] : [hBOOL(hAPP(hAPP(c_member(_1001014), _1001016), c_SetInterval_Oord_OgreaterThan(_1001014, _1001018, _1001020))), -(hBOOL(hAPP(hAPP(_1001018, _1001020), _1001016)))], (52440 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (984 ^ _781404) ^ [_796098, _796100, _796102, _796104, _796106, _796108, _796110, _796112] : [-(c_Fun_Oinj__on(_796110, _796106, _796102, _796098)), c_Fun_Oinj__on(_796112, _796108, _796104, _796100), _796112 = _796110, _796108 = _796106, _796104 = _796102, _796100 = _796098], (19717 ^ _781404) ^ [] : [-(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))))))], (43693 ^ _781404) ^ [_1652242, _1652244, _1652246] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1652242))), -(c_List_Osublist(_1652244, hAPP(hAPP(c_List_Olist_OCons(_1652244), _1652246), c_List_Olist_ONil(_1652244)), _1652242) = c_List_Olist_ONil(_1652244))], (33898 ^ _781404) ^ [_1401943, _1401945, _1401947, _1401949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401943, tc_fun(_1401945, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1401943, tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_fun(_1401945, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401945, tc_fun(tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_fun(_1401945, tc_HOL_Obool)), _1401943), c_COMBC(_1401945, tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401945, tc_prod(_1401943, _1401945)), tc_fun(_1401945, tc_fun(tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_HOL_Obool)), _1401943), hAPP(c_COMBB(tc_prod(_1401943, _1401945), tc_fun(tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_HOL_Obool), _1401945), c_member(tc_prod(_1401943, _1401945)))), c_Product__Type_OPair(_1401943, _1401945)))), _1401947)), hAPP(hAPP(c_COMBC(_1401943, tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_fun(_1401945, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401945, tc_fun(tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_fun(_1401945, tc_HOL_Obool)), _1401943), c_COMBC(_1401945, tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401945, tc_prod(_1401943, _1401945)), tc_fun(_1401945, tc_fun(tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_HOL_Obool)), _1401943), hAPP(c_COMBB(tc_prod(_1401943, _1401945), tc_fun(tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool), tc_HOL_Obool), _1401945), c_member(tc_prod(_1401943, _1401945)))), c_Product__Type_OPair(_1401943, _1401945)))), _1401949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1401943, _1401945), tc_HOL_Obool)), _1401947), _1401949)))], (10757 ^ _781404) ^ [_964103, _964105, _964107, _964109, _964111] : [class_Orderings_Olinorder(_964103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964103), _964105), _964107)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964103), _964109), _964111)), 10768 ^ _781404 : [(10777 ^ _781404) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_964103, _964105), _964107) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_964103, _964109), _964111)), _964105 = _964109, _964107 = _964111], (10769 ^ _781404) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_964103, _964105), _964107) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_964103, _964109), _964111), 10772 ^ _781404 : [(10775 ^ _781404) ^ [] : [-(_964107 = _964111)], (10773 ^ _781404) ^ [] : [-(_964105 = _964109)]]]]], (38725 ^ _781404) ^ [_1518542, _1518544, _1518546, _1518548] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518542), _1518544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518542, _1518542), tc_HOL_Obool)), _1518546), hAPP(hAPP(c_Product__Type_OSigma(_1518542, _1518542), _1518544), hAPP(c_COMBK(tc_fun(_1518542, tc_HOL_Obool), _1518542), _1518544)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1518542, tc_HOL_Obool)), _1518548), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1518542), _1518544), _1518546))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1518542), _1518548)))], (8156 ^ _781404) ^ [_918356] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_918356, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_918356, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_918356, tc_HOL_Obool)))], (26323 ^ _781404) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24834 ^ _781404) ^ [_1226645, _1226647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226645)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226647)), 24841 ^ _781404 : [(24848 ^ _781404) ^ [] : [_1226645 = _1226647, -(hAPP(c_Int_Onat, _1226645) = hAPP(c_Int_Onat, _1226647))], (24842 ^ _781404) ^ [] : [hAPP(c_Int_Onat, _1226645) = hAPP(c_Int_Onat, _1226647), -(_1226645 = _1226647)]]], (24656 ^ _781404) ^ [_1223756, _1223758] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223756), _1223758)), _1223756)))], (11457 ^ _781404) ^ [_977030, _977032, _977034, _977036] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977030, tc_HOL_Obool)), _977032), hAPP(hAPP(c_Set_Oinsert(_977030), _977034), _977036)))), 11460 ^ _781404 : [(11463 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977030, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977030, tc_HOL_Obool)), _977032), hAPP(hAPP(c_Set_Oinsert(_977030), _977034), c_Orderings_Obot__class_Obot(tc_fun(_977030, tc_HOL_Obool))))), _977036))], (11461 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_977030), _977034), _977032)))]], 11464 ^ _781404 : [(11467 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977030, tc_HOL_Obool)), _977032), _977036))], (11465 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_977030), _977034), _977032))]]], (46720 ^ _781404) ^ [_1721541, _1721543] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1721541, _1721543)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1721541), _1721543))], (32108 ^ _781404) ^ [_1359351, _1359353, _1359355] : [class_Orderings_Olinorder(_1359351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359351), _1359353), _1359355)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359351), _1359353), _1359355) = _1359355)], (51197 ^ _781404) ^ [_1816372, _1816374, _1816376] : [c_Equiv__Relations_Oequivp(_1816372, _1816374), 51200 ^ _781404 : [(51201 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1816376, 51208 ^ [_1816372, _1816374, _1816376]))), 51202 ^ _781404 : [(51203 ^ _781404) ^ [_1816494] : [hBOOL(hAPP(hAPP(c_member(_1816372), _1816494), c_Quotient_ORespects(_1816372, _1816374))), hBOOL(hAPP(_1816376, _1816494))]]], (51212 ^ _781404) ^ [] : [51213 ^ _781404 : [(51214 ^ _781404) ^ [_1816661] : [hBOOL(hAPP(_1816376, _1816661))]], 51216 ^ _781404 : [(51219 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1816376, 51215 ^ [_1816372, _1816374, _1816376])))], (51217 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1816372), 51215 ^ [_1816372, _1816374, _1816376]), c_Quotient_ORespects(_1816372, _1816374))))]]]]], (18967 ^ _781404) ^ [_1119209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119209), 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), _1119209)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17509 ^ _781404) ^ [_1093608, _1093610] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093608), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1093610)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1093608), _1093610))], (16252 ^ _781404) ^ [_1070247, _1070249, _1070251] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1070247), _1070249)), hBOOL(hAPP(hAPP(c_member(_1070247), _1070251), _1070249)), -(hAPP(c_Finite__Set_Ocard(_1070247), _1070249) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1070247), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1070247, tc_HOL_Obool)), _1070249), hAPP(hAPP(c_Set_Oinsert(_1070247), _1070251), c_Orderings_Obot__class_Obot(tc_fun(_1070247, tc_HOL_Obool)))))))], (32372 ^ _781404) ^ [_1364625, _1364627] : [class_Orderings_Olinorder(_1364625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364625), _1364627)), -(c_Big__Operators_Olinorder__class_OMax(_1364625, _1364627) = hAPP(c_Finite__Set_Ofold1(_1364625, c_Orderings_Oord__class_Omax(_1364625)), _1364627))], (46249 ^ _781404) ^ [_1709608, _1709610] : [-(c_List_Oremdups(_1709608, c_List_Oremdups(_1709608, _1709610)) = c_List_Oremdups(_1709608, _1709610))], (7319 ^ _781404) ^ [_900629, _900631, _900633] : [class_Groups_Ogroup__add(_900629), 7322 ^ _781404 : [(7329 ^ _781404) ^ [] : [_900633 = hAPP(c_Groups_Ouminus__class_Ouminus(_900629), _900631), -(_900631 = hAPP(c_Groups_Ouminus__class_Ouminus(_900629), _900633))], (7323 ^ _781404) ^ [] : [_900631 = hAPP(c_Groups_Ouminus__class_Ouminus(_900629), _900633), -(_900633 = hAPP(c_Groups_Ouminus__class_Ouminus(_900629), _900631))]]], (45895 ^ _781404) ^ [_1701676, _1701678, _1701680, _1701682, _1701684] : [-(c_List_Olist__all2(_1701676, _1701678, _1701680, _1701682, _1701684)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701676)), _1701682) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701678)), _1701684), 45901 ^ _781404 : [(45904 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1701676, _1701678, tc_HOL_Obool), _1701680), 45900 ^ [_1701676, _1701678, _1701680, _1701682, _1701684]))], (45902 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1701676, _1701678)), 45900 ^ [_1701676, _1701678, _1701680, _1701682, _1701684]), hAPP(c_List_Oset(tc_prod(_1701676, _1701678)), hAPP(hAPP(c_List_Ozip(_1701676, _1701678), _1701682), _1701684)))))]]], (18129 ^ _781404) ^ [_1104389, _1104391, _1104393, _1104395] : [class_Rings_Olinordered__semidom(_1104389), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104389), hAPP(hAPP(c_Power_Opower__class_Opower(_1104389), _1104391), _1104393)), hAPP(hAPP(c_Power_Opower__class_Opower(_1104389), _1104395), _1104393))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104389), c_Groups_Ozero__class_Ozero(_1104389)), _1104395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104389), _1104391), _1104395)))], (45760 ^ _781404) ^ [_1698164, _1698166, _1698168, _1698170] : [-(c_List_Opartition(_1698164, _1698166, hAPP(hAPP(c_List_Olist_OCons(_1698164), _1698168), _1698170)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1698164), tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1698164), tc_fun(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164))), tc_fun(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1698164), tc_fun(tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)))), tc_fun(tc_fun(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164))), tc_fun(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)))), tc_List_Olist(_1698164)), c_COMBS(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164))), tc_fun(tc_List_Olist(_1698164), tc_fun(tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)))), tc_List_Olist(_1698164)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)), tc_fun(tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164))), tc_List_Olist(_1698164)), hAPP(c_If(tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164))), hAPP(_1698166, _1698168)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1698164), tc_fun(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164))), tc_List_Olist(_1698164)), c_Product__Type_OPair(tc_List_Olist(_1698164), tc_List_Olist(_1698164))), hAPP(c_List_Olist_OCons(_1698164), _1698168))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698164), tc_fun(tc_List_Olist(_1698164), tc_List_Olist(_1698164)), tc_fun(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164))), tc_fun(tc_fun(tc_List_Olist(_1698164), tc_List_Olist(_1698164)), tc_fun(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)))), tc_List_Olist(_1698164)), c_COMBB(tc_List_Olist(_1698164), tc_prod(tc_List_Olist(_1698164), tc_List_Olist(_1698164)), tc_List_Olist(_1698164))), c_Product__Type_OPair(tc_List_Olist(_1698164), tc_List_Olist(_1698164)))), hAPP(c_List_Olist_OCons(_1698164), _1698168)))), c_List_Opartition(_1698164, _1698166, _1698170)))], (26845 ^ _781404) ^ [_1260459, _1260461, _1260463, _1260465, _1260467] : [class_Groups_Oab__semigroup__mult(_1260459), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1260459, _1260459, c_Groups_Otimes__class_Otimes(_1260459), _1260461, _1260463), _1260465)), hBOOL(hAPP(hAPP(c_member(_1260459), _1260467), _1260463)), -(hBOOL(hAPP(hAPP(c_member(_1260459), _1260461), _1260463))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1260459, _1260459, c_Groups_Otimes__class_Otimes(_1260459), _1260467, hAPP(hAPP(c_Set_Oinsert(_1260459), _1260461), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260459, tc_HOL_Obool)), _1260463), hAPP(hAPP(c_Set_Oinsert(_1260459), _1260467), c_Orderings_Obot__class_Obot(tc_fun(_1260459, tc_HOL_Obool)))))), _1260465)))], (17288 ^ _781404) ^ [_1089756, _1089758] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1089756), _1089758)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1089756, tc_HOL_Obool)), hAPP(c_Set_OPow(_1089756), _1089758)) = 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(_1089756), _1089758)))], (37491 ^ _781404) ^ [_1487628, _1487630] : [c_Relation_Oirrefl(_1487628, _1487630), 37494 ^ _781404 : [(37495 ^ _781404) ^ [_1487710] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1487628, _1487628)), hAPP(hAPP(c_Product__Type_OPair(_1487628, _1487628), _1487710), _1487710)), _1487630))]]], (33621 ^ _781404) ^ [_1394429, _1394431, _1394433, _1394435, _1394437] : [c_Finite__Set_Ofun__left__comm(_1394429, _1394431, _1394433), -(c_Finite__Set_Ofun__left__comm(_1394435, _1394431, hAPP(hAPP(c_COMBB(_1394429, tc_fun(_1394431, _1394431), _1394435), _1394433), _1394437)))], (46097 ^ _781404) ^ [_1706231, _1706233, _1706235, _1706237, _1706239, _1706241, _1706243, _1706245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706231), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706233)), _1706235))), c_List_Olist__all2(_1706233, _1706237, _1706239, _1706235, _1706241), hBOOL(hAPP(hAPP(_1706239, _1706243), _1706245)), -(c_List_Olist__all2(_1706233, _1706237, _1706239, hAPP(hAPP(c_List_Olist__update(_1706233, _1706235), _1706231), _1706243), hAPP(hAPP(c_List_Olist__update(_1706237, _1706241), _1706231), _1706245)))], (25027 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (40925 ^ _781404) ^ [_1580199, _1580201, _1580203, _1580205, _1580207, _1580209] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580199, _1580201)), hAPP(hAPP(c_Product__Type_OPair(_1580199, _1580201), _1580203), _1580205)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1580199, _1580201), tc_HOL_Obool), _1580207))), c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(_1580199, _1580201), tc_HOL_Obool), tc_fun(tc_prod(_1580199, _1580201), tc_HOL_Obool), _1580207), 40936 ^ _781404 : [(40939 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1580209, 40934 ^ [_1580199, _1580201, _1580203, _1580205, _1580207, _1580209]), 40935 ^ [_1580199, _1580201, _1580203, _1580205, _1580207, _1580209]))], (40937 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580199, _1580201)), hAPP(hAPP(c_Product__Type_OPair(_1580199, _1580201), 40934 ^ [_1580199, _1580201, _1580203, _1580205, _1580207, _1580209]), 40935 ^ [_1580199, _1580201, _1580203, _1580205, _1580207, _1580209])), hAPP(_1580207, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1580199, _1580201), tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1580199, _1580201), tc_HOL_Obool), _1580207)), hAPP(c_Set_OCollect(tc_prod(_1580199, _1580201)), hAPP(c_Product__Type_Oprod_Oprod__case(_1580199, _1580201, tc_HOL_Obool), _1580209)))))))]], -(hBOOL(hAPP(hAPP(_1580209, _1580203), _1580205)))], (11135 ^ _781404) ^ [_970471, _970473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970471), _970473)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _970471)), _970473)))], (21065 ^ _781404) ^ [_1155499, _1155501] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155499), _1155501) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1155499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1155501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52050 ^ _781404) ^ [_1834373, _1834375, _1834377] : [class_Rings_Olinordered__idom(_1834373), hAPP(c_Groups_Oabs__class_Oabs(_1834373), _1834375) = hAPP(c_Groups_Oabs__class_Oabs(_1834373), _1834377), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834373), _1834375), _1834377)))], (8526 ^ _781404) ^ [_925247] : [class_Complete__Lattice_Ocomplete__lattice(_925247), -(c_Complete__Lattice_OSup__class_OSup(_925247, c_Orderings_Otop__class_Otop(tc_fun(_925247, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_925247))], (40584 ^ _781404) ^ [_1572728, _1572730, _1572732, _1572734, _1572736] : [_1572728 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1572730, tc_HOL_Obool), _1572732), c_Orderings_Oorder__class_Omono(tc_fun(_1572730, tc_HOL_Obool), tc_fun(_1572730, tc_HOL_Obool), _1572732), hBOOL(hAPP(hAPP(c_member(_1572730), _1572734), _1572736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1572730, tc_HOL_Obool)), _1572736), hAPP(_1572732, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572730, tc_HOL_Obool)), _1572736), _1572728)))), -(hBOOL(hAPP(hAPP(c_member(_1572730), _1572734), _1572728)))], (21029 ^ _781404) ^ [_1154956, _1154958, _1154960] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1154956), _1154958) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1154960), _1154958), -(_1154956 = _1154960), -(_1154958 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36205 ^ _781404) ^ [_1457178, _1457180, _1457182, _1457184, _1457186, _1457188] : [hAPP(_1457184, hAPP(c_Product__Type_Osnd(_1457182, _1457178), _1457186)) = hAPP(_1457188, hAPP(c_Product__Type_Osnd(_1457182, _1457178), _1457186)), -(hAPP(c_Product__Type_Oapsnd(_1457178, _1457180, _1457182, _1457184), _1457186) = hAPP(c_Product__Type_Oapsnd(_1457178, _1457180, _1457182, _1457188), _1457186))], (9807 ^ _781404) ^ [_948964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _948964)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948964), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _948964)], (43164 ^ _781404) ^ [_1641204, _1641206, _1641208, _1641210, _1641212] : [-(hAPP(hAPP(c_List_Olist__update(_1641204, hAPP(hAPP(c_List_Olist_OCons(_1641204), _1641206), _1641208)), _1641210), _1641212) = c_Nat_Onat_Onat__case(tc_List_Olist(_1641204), hAPP(hAPP(c_List_Olist_OCons(_1641204), _1641212), _1641208), hAPP(hAPP(c_COMBB(tc_List_Olist(_1641204), tc_List_Olist(_1641204), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1641204), _1641206)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1641204, tc_List_Olist(_1641204)), c_List_Olist__update(_1641204, _1641208)), _1641212)), _1641210))], (46607 ^ _781404) ^ [_1717721, _1717723] : [-(c_List_Otranspose(_1717721, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1717721)), c_List_Olist_ONil(_1717721)), _1717723)) = c_List_Otranspose(_1717721, _1717723))], (27221 ^ _781404) ^ [_1267407, _1267409, _1267411, _1267413, _1267415, _1267417, _1267419] : [-(hBOOL(hAPP(hAPP(c_member(_1267407), _1267409), _1267411))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1267407, _1267413, _1267415, _1267417, _1267411), _1267419)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1267407, _1267413, _1267415, _1267417, hAPP(hAPP(c_Set_Oinsert(_1267407), _1267409), _1267411)), hAPP(hAPP(_1267415, _1267409), _1267419))))], (14524 ^ _781404) ^ [_1035874, _1035876, _1035878] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035874), _1035876)), _1035878) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035876), _1035878)))], (16350 ^ _781404) ^ [_1071843] : [class_Rings_Olinordered__semidom(_1071843), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071843), c_Groups_Ozero__class_Ozero(_1071843)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071843), c_Groups_Oone__class_Oone(_1071843)), c_Groups_Oone__class_Oone(_1071843)))))], (50161 ^ _781404) ^ [_1795376, _1795378] : [50164 ^ _781404 : [(50167 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1795376, _1795376)), hAPP(hAPP(c_Product__Type_OPair(_1795376, _1795376), 50163 ^ [_1795376, _1795378]), 50162 ^ [_1795376, _1795378])), _1795378))], (50165 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1795376, _1795376)), hAPP(hAPP(c_Product__Type_OPair(_1795376, _1795376), 50162 ^ [_1795376, _1795378]), 50163 ^ [_1795376, _1795378])), _1795378)))]], -(c_Relation_Osym(_1795376, _1795378))], (25169 ^ _781404) ^ [_1231863, _1231865] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1231863)), hAPP(c_Int_Onat, _1231865)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231863), _1231865))], (40148 ^ _781404) ^ [_1563023, _1563025] : [c_Wellfounded_Owf(_1563023, _1563025), -(c_Wellfounded_Owf(tc_List_Olist(_1563023), c_List_Olenlex(_1563023, _1563025)))], (39818 ^ _781404) ^ [_1555545] : [-(c_Wellfounded_Owf(_1555545, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1555545, _1555545), tc_HOL_Obool))))], (26067 ^ _781404) ^ [_1247127, _1247129] : [c_Nat__Transfer_Onat__set(_1247127), c_Nat__Transfer_Onat__set(_1247129), 26074 ^ _781404 : [(26081 ^ _781404) ^ [] : [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), _1247127)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1247129))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1247127), _1247129)))], (26075 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1247127), _1247129)), -(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), _1247127)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1247129))))]]], (17194 ^ _781404) ^ [_1087758, _1087760, _1087762] : [class_Int_Onumber__ring(_1087758), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087758), hAPP(c_Int_Onumber__class_Onumber__of(_1087758), _1087760)), hAPP(c_Int_Onumber__class_Onumber__of(_1087758), _1087762)) = hAPP(c_Int_Onumber__class_Onumber__of(_1087758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1087760), _1087762)))], (29461 ^ _781404) ^ [_1308910, _1308912, _1308914, _1308916] : [class_Fields_Olinordered__field__inverse__zero(_1308910), 29464 ^ _781404 : [(29465 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308910), _1308912), _1308914)), _1308916)), 29468 ^ _781404 : [(29475 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), c_Groups_Ozero__class_Ozero(_1308910)), _1308914))), 29478 ^ _781404 : [(29485 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), _1308914), c_Groups_Ozero__class_Ozero(_1308910)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), c_Groups_Ozero__class_Ozero(_1308910)), _1308916)))], (29479 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), _1308914), c_Groups_Ozero__class_Ozero(_1308910))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308910), _1308916), _1308914)), _1308912)))]]], (29469 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), c_Groups_Ozero__class_Ozero(_1308910)), _1308914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), _1308912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308910), _1308916), _1308914))))]]], (29491 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308910), _1308912), _1308914)), _1308916))), 29494 ^ _781404 : [(29497 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), _1308912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308910), _1308916), _1308914)))], (29495 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), c_Groups_Ozero__class_Ozero(_1308910)), _1308914)))]], 29498 ^ _781404 : [(29501 ^ _781404) ^ [] : [29502 ^ _781404 : [(29505 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308910), _1308916), _1308914)), _1308912))], (29503 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), _1308914), c_Groups_Ozero__class_Ozero(_1308910))))]], 29506 ^ _781404 : [(29509 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), c_Groups_Ozero__class_Ozero(_1308910)), _1308916))], (29507 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), _1308914), c_Groups_Ozero__class_Ozero(_1308910)))]]], (29499 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308910), c_Groups_Ozero__class_Ozero(_1308910)), _1308914))]]]]], (44367 ^ _781404) ^ [_1668229, _1668231, _1668233, _1668235, _1668237] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1668229, _1668231)), _1668233), hAPP(hAPP(c_List_Ozip(_1668229, _1668231), _1668235), _1668237)) = hAPP(hAPP(c_List_Ozip(_1668229, _1668231), hAPP(hAPP(c_List_Odrop(_1668229), _1668233), _1668235)), hAPP(hAPP(c_List_Odrop(_1668231), _1668233), _1668237)))], (21221 ^ _781404) ^ [_1158594] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1158594) = _1158594)], (34315 ^ _781404) ^ [_1416355, _1416357, _1416359, _1416361, _1416363] : [_1416355 = c_Orderings_Obot__class_Obot(tc_fun(_1416357, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1416359, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416357, tc_fun(_1416359, tc_HOL_Obool)), _1416355), _1416361)), _1416363) = _1416363)], (40485 ^ _781404) ^ [_1570129, _1570131, _1570133] : [hBOOL(hAPP(_1570129, _1570131)), -(hBOOL(hAPP(_1570129, c_Hilbert__Choice_OEps(_1570133, _1570129))))], (34933 ^ _781404) ^ [_1431193, _1431195] : [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(_1431195))), 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), _1431193)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1431193)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431195))))], (34155 ^ _781404) ^ [_1409003, _1409005, _1409007, _1409009, _1409011] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409003, tc_HOL_Obool)), _1409005), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409007, tc_fun(_1409003, tc_HOL_Obool)), _1409009), _1409011)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409007, tc_fun(_1409003, tc_HOL_Obool)), _1409009), hAPP(hAPP(c_COMBB(tc_fun(_1409003, tc_HOL_Obool), tc_fun(_1409003, tc_HOL_Obool), _1409007), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409003, tc_HOL_Obool)), _1409005)), _1409011)))], (18119 ^ _781404) ^ [_1104208, _1104210, _1104212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1104208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1104208), _1104210)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1104208), _1104212))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1104210), _1104212)))], (49265 ^ _781404) ^ [_1774504, _1774506, _1774508] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1774504)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1774504, _1774506, _1774508)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1774504)), _1774508)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4982 ^ _781404) ^ [_857309, _857311, _857313, _857315] : [-(c_Orderings_Oord__class_OLeast(_857315, _857311) = c_Orderings_Oord__class_OLeast(_857313, _857309)), _857315 = _857313, _857311 = _857309], (9206 ^ _781404) ^ [_938368, _938370, _938372, _938374] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938368, tc_HOL_Obool)), _938370), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938368, tc_HOL_Obool)), _938372), _938374)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938368, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938368, tc_HOL_Obool)), _938370), _938372)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938368, tc_HOL_Obool)), _938370), _938374)))], (41143 ^ _781404) ^ [_1585958, _1585960, _1585962, _1585964] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1585958, tc_fun(_1585958, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1585958, tc_fun(tc_prod(_1585958, _1585958), tc_HOL_Obool), tc_fun(_1585958, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585958, tc_fun(tc_fun(tc_prod(_1585958, _1585958), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585958, _1585958), tc_HOL_Obool), tc_fun(_1585958, tc_HOL_Obool)), _1585958), c_COMBC(_1585958, tc_fun(tc_prod(_1585958, _1585958), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585958, tc_prod(_1585958, _1585958)), tc_fun(_1585958, tc_fun(tc_fun(tc_prod(_1585958, _1585958), tc_HOL_Obool), tc_HOL_Obool)), _1585958), hAPP(c_COMBB(tc_prod(_1585958, _1585958), tc_fun(tc_fun(tc_prod(_1585958, _1585958), tc_HOL_Obool), tc_HOL_Obool), _1585958), c_member(tc_prod(_1585958, _1585958)))), c_Product__Type_OPair(_1585958, _1585958)))), _1585960)), c_fequal), _1585962), _1585964)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585958, _1585958)), hAPP(hAPP(c_Product__Type_OPair(_1585958, _1585958), _1585962), _1585964)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585958, _1585958), tc_HOL_Obool)), _1585960), c_Relation_OId(_1585958)))))], (23601 ^ _781404) ^ [_1205253, _1205255, _1205257] : [-(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, _1205253, _1205255)), _1205257), _1205255) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1205253), _1205257), _1205255))], (23631 ^ _781404) ^ [_1205826, _1205828, _1205830] : [class_Divides_Osemiring__div(_1205826), -(c_Divides_Odiv__class_Omod(_1205826, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205826), _1205828), _1205830), _1205828) = c_Groups_Ozero__class_Ozero(_1205826))], (8461 ^ _781404) ^ [_924121] : [hAPP(c_Nat_OSuc, _924121) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2744 ^ _781404) ^ [_821988, _821990, _821992, _821994, _821996, _821998] : [-(c_Wellfounded_Omlex__prod(_821998, _821994, _821990) = c_Wellfounded_Omlex__prod(_821996, _821992, _821988)), _821998 = _821996, _821994 = _821992, _821990 = _821988], (27663 ^ _781404) ^ [_1275529, _1275531] : [class_Groups_Oab__semigroup__mult(_1275529), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275529), _1275531)), -(_1275531 = c_Orderings_Obot__class_Obot(tc_fun(_1275529, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1275529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1275529), 27676 ^ [_1275529, _1275531]), 27677 ^ [_1275529, _1275531])), hAPP(hAPP(c_Set_Oinsert(_1275529), 27676 ^ [_1275529, _1275531]), hAPP(hAPP(c_Set_Oinsert(_1275529), 27677 ^ [_1275529, _1275531]), c_Orderings_Obot__class_Obot(tc_fun(_1275529, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1275529), hAPP(c_Finite__Set_Ofold1(_1275529, c_Groups_Otimes__class_Otimes(_1275529)), _1275531)), _1275531)))], (20051 ^ _781404) ^ [_1137546, _1137548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1137546)), c_Int_OBit0(_1137548))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137546), _1137548)))], (21433 ^ _781404) ^ [_1162419, _1162421, _1162423, _1162425] : [class_Rings_Oordered__semiring(_1162419), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162419), _1162421), _1162423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162419), c_Groups_Ozero__class_Ozero(_1162419)), _1162425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162419), _1162425), _1162421)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162419), _1162425), _1162423))))], (22187 ^ _781404) ^ [_1176746, _1176748, _1176750] : [class_Rings_Ocomm__semiring__1(_1176746), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176746), hAPP(hAPP(c_Power_Opower__class_Opower(_1176746), _1176748), _1176750)), _1176748) = hAPP(hAPP(c_Power_Opower__class_Opower(_1176746), _1176748), hAPP(c_Nat_OSuc, _1176750)))], (8245 ^ _781404) ^ [_920166, _920168, _920170] : [hAPP(hAPP(c_Set_Oinsert(_920166), _920168), c_Orderings_Obot__class_Obot(tc_fun(_920166, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_920166), _920170), c_Orderings_Obot__class_Obot(tc_fun(_920166, tc_HOL_Obool))), -(_920168 = _920170)], (37098 ^ _781404) ^ [_1477123, _1477125, _1477127, _1477129, _1477131, _1477133, _1477135] : [-(hAPP(c_Product__Type_Oapsnd(_1477123, _1477125, _1477127, _1477129), hAPP(c_Product__Type_Oapfst(_1477131, _1477127, _1477123, _1477133), _1477135)) = hAPP(hAPP(c_Product__Type_OPair(_1477127, _1477125), hAPP(_1477133, hAPP(c_Product__Type_Ofst(_1477131, _1477123), _1477135))), hAPP(_1477129, hAPP(c_Product__Type_Osnd(_1477131, _1477123), _1477135))))], (18307 ^ _781404) ^ [] : [-(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))))], (32252 ^ _781404) ^ [_1361911, _1361913, _1361915] : [class_Int_Onumber(_1361911), class_Orderings_Oord(_1361911), 32259 ^ _781404 : [(32266 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361911), hAPP(c_Int_Onumber__class_Onumber__of(_1361911), _1361913)), hAPP(c_Int_Onumber__class_Onumber__of(_1361911), _1361915)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361911), hAPP(c_Int_Onumber__class_Onumber__of(_1361911), _1361913)), hAPP(c_Int_Onumber__class_Onumber__of(_1361911), _1361915)) = hAPP(c_Int_Onumber__class_Onumber__of(_1361911), _1361913))], (32260 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361911), hAPP(c_Int_Onumber__class_Onumber__of(_1361911), _1361913)), hAPP(c_Int_Onumber__class_Onumber__of(_1361911), _1361915))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361911), hAPP(c_Int_Onumber__class_Onumber__of(_1361911), _1361913)), hAPP(c_Int_Onumber__class_Onumber__of(_1361911), _1361915)) = hAPP(c_Int_Onumber__class_Onumber__of(_1361911), _1361915))]]], (13706 ^ _781404) ^ [_1020262, _1020264, _1020266, _1020268, _1020270] : [class_Groups_Oab__group__add(_1020262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020264), _1020266)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020264), _1020268)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1020264, _1020262), _1020270), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1020264, tc_HOL_Obool)), _1020266), _1020268)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1020262), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020262), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1020264, _1020262), _1020270), _1020266)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1020264, _1020262), _1020270), _1020268))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1020264, _1020262), _1020270), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1020264, tc_HOL_Obool)), _1020266), _1020268))))], (8477 ^ _781404) ^ [_924352, _924354] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_924352, tc_HOL_Obool), hAPP(c_Set_OPow(_924352), _924354)) = _924354)], (22949 ^ _781404) ^ [_1191758, _1191760] : [class_Groups_Omonoid__mult(_1191758), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191758), _1191760), 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(_1191758), _1191760), _1191760))], (19205 ^ _781404) ^ [_1122950] : [-(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), _1122950))))], (35644 ^ _781404) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (8106 ^ _781404) ^ [_917255, _917257] : [class_Orderings_Olinorder(_917255), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917255, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_917255), _917257), c_Orderings_Obot__class_Obot(tc_fun(_917255, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_917255), _917257)) = hAPP(c_SetInterval_Oord__class_OatLeast(_917255), _917257))], (41131 ^ _781404) ^ [_1585419, _1585421, _1585423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585419, _1585419), tc_HOL_Obool)), _1585421), _1585423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585419, _1585419), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1585419, _1585419, _1585419), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1585419, _1585419), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1585419, _1585421)), _1585423)), _1585421)), _1585423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585419, _1585419), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1585419, _1585421)), _1585423)))], (44842 ^ _781404) ^ [_1678622, _1678624, _1678626] : [class_Orderings_Olinorder(_1678622), hBOOL(hAPP(c_Finite__Set_Ofinite(_1678622), _1678624)), -(c_List_Olinorder__class_Osorted__list__of__set(_1678622, hAPP(hAPP(c_Set_Oinsert(_1678622), _1678626), _1678624)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1678622, _1678622, c_COMBI(_1678622)), _1678626), c_List_Olinorder__class_Osorted__list__of__set(_1678622, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1678622, tc_HOL_Obool)), _1678624), hAPP(hAPP(c_Set_Oinsert(_1678622), _1678626), c_Orderings_Obot__class_Obot(tc_fun(_1678622, tc_HOL_Obool)))))))], (18485 ^ _781404) ^ [_1111084, _1111086, _1111088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1111084)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1111086), _1111088)), 18492 ^ _781404 : [(18493 ^ _781404) ^ [_1111274] : [18495 ^ _781404 : [(18501 ^ _781404) ^ [] : [-(_1111274 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 18497 ^ [_1111084, _1111086, _1111088, _1111274]), 18494 ^ [_1111084, _1111086, _1111088, _1111274]))], (18499 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18497 ^ [_1111084, _1111086, _1111088, _1111274]), _1111088)))], (18496 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18494 ^ [_1111084, _1111086, _1111088, _1111274]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1111084))))]], -(_1111274 = _1111086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1111274), _1111084) = _1111086]]], (41259 ^ _781404) ^ [_1589305, _1589307, _1589309, _1589311] : [41260 ^ _781404 : [(41263 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589305, _1589305)), _1589307), c_Transitive__Closure_Ortrancl(_1589305, _1589311)))], (41261 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589305, _1589305)), _1589307), c_Transitive__Closure_Ortrancl(_1589305, _1589309)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589305, _1589305)), _1589307), c_Transitive__Closure_Ortrancl(_1589305, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1589305, _1589305), tc_HOL_Obool)), _1589309), _1589311)))))], (20119 ^ _781404) ^ [_1138667, _1138669] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1138667)), c_Int_OBit0(_1138669)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1138667), _1138669)))], (26875 ^ _781404) ^ [_1261097, _1261099, _1261101] : [class_Groups_Oab__semigroup__mult(_1261097), hBOOL(hAPP(c_Finite__Set_Ofinite(_1261097), _1261099)), -(hBOOL(hAPP(hAPP(c_member(_1261097), _1261101), _1261099))), -(hAPP(c_Finite__Set_Ofold1(_1261097, c_Groups_Otimes__class_Otimes(_1261097)), hAPP(hAPP(c_Set_Oinsert(_1261097), _1261101), _1261099)) = hAPP(hAPP(c_Finite__Set_Ofold(_1261097, _1261097, c_Groups_Otimes__class_Otimes(_1261097)), _1261101), _1261099))], (16242 ^ _781404) ^ [_1070012, _1070014, _1070016] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1070012), _1070014)), hBOOL(hAPP(hAPP(c_member(_1070012), _1070016), _1070014)), -(hAPP(c_Finite__Set_Ocard(_1070012), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1070012, tc_HOL_Obool)), _1070014), hAPP(hAPP(c_Set_Oinsert(_1070012), _1070016), c_Orderings_Obot__class_Obot(tc_fun(_1070012, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1070012), _1070014)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44737 ^ _781404) ^ [_1676398, _1676400, _1676402, _1676404, _1676406, _1676408] : [-(hAPP(c_List_Ofoldl(_1676398, _1676400, _1676402, _1676404), hAPP(hAPP(c_List_Oappend(_1676400), _1676406), _1676408)) = hAPP(c_List_Ofoldl(_1676398, _1676400, _1676402, hAPP(c_List_Ofoldl(_1676398, _1676400, _1676402, _1676404), _1676406)), _1676408))], (36512 ^ _781404) ^ [_1463716, _1463718, _1463720, _1463722] : [-(hAPP(c_Product__Type_Ofst(_1463716, _1463718), hAPP(hAPP(c_Product__Type_OPair(_1463716, _1463718), _1463720), _1463722)) = _1463720)], (41281 ^ _781404) ^ [_1589900, _1589902] : [-(c_Transitive__Closure_Ortrancl(_1589900, _1589902) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1589900, _1589900), tc_HOL_Obool)), c_Relation_OId(_1589900)), hAPP(hAPP(c_Relation_Orel__comp(_1589900, _1589900, _1589900), c_Transitive__Closure_Ortrancl(_1589900, _1589902)), _1589902)))], (49969 ^ _781404) ^ [_1791424, _1791426, _1791428, _1791430] : [c_Predicate_Osymp(_1791424, _1791426), hBOOL(hAPP(hAPP(_1791426, _1791428), _1791430)), -(hBOOL(hAPP(hAPP(_1791426, _1791430), _1791428)))], (12957 ^ _781404) ^ [_1006191, _1006193, _1006195, _1006197] : [class_Groups_Oab__semigroup__add(_1006191), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006191), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006191), _1006193), _1006195)), _1006197) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006191), _1006193), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006191), _1006195), _1006197)))], (49569 ^ _781404) ^ [_1781247, _1781249, _1781251] : [c_List_Oall__interval__int(_1781247, _1781249, _1781251), 49572 ^ _781404 : [(49573 ^ _781404) ^ [_1781325] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1781325), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1781249, _1781251))), -(hBOOL(hAPP(_1781247, _1781325)))]]], (36398 ^ _781404) ^ [_1461287, _1461289, _1461291, _1461293, _1461295, _1461297] : [c_Finite__Set_Ofolding(_1461287, _1461289, _1461291, _1461293), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461287), _1461295)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461287), _1461297)), -(hAPP(c_Fun_Ocomp(_1461289, _1461289, _1461289, hAPP(_1461293, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461287, tc_HOL_Obool)), _1461295), _1461297))), hAPP(_1461293, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461287, tc_HOL_Obool)), _1461295), _1461297))) = hAPP(c_Fun_Ocomp(_1461289, _1461289, _1461289, hAPP(_1461293, _1461295)), hAPP(_1461293, _1461297)))], (31814 ^ _781404) ^ [_1353710, _1353712] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1353710), _1353712) = 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), _1353710)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1353712)))))], (40218 ^ _781404) ^ [_1564538, _1564540] : [c_Wellfounded_OwfP(_1564538, _1564540), -(c_Wellfounded_Owf(_1564538, hAPP(c_Set_OCollect(tc_prod(_1564538, _1564538)), hAPP(c_Product__Type_Oprod_Oprod__case(_1564538, _1564538, tc_HOL_Obool), _1564540))))], (41524 ^ _781404) ^ [_1595540, _1595542, _1595544, _1595546] : [-(hAPP(c_Relation_Oconverse(_1595540, _1595542), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1595540, _1595542), tc_HOL_Obool)), _1595544), _1595546)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1595542, _1595540), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1595540, _1595542), _1595544)), hAPP(c_Relation_Oconverse(_1595540, _1595542), _1595546)))], (36086 ^ _781404) ^ [_1454759, _1454761, _1454763] : [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), _1454759), _1454761))), -(hBOOL(hAPP(hAPP(_1454763, _1454759), _1454761))), 36093 ^ _781404 : [(36096 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1454763, 36091 ^ [_1454759, _1454761, _1454763]), 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)))), 36092 ^ [_1454759, _1454761, _1454763])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 36091 ^ [_1454759, _1454761, _1454763]), 36092 ^ [_1454759, _1454761, _1454763]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 36092 ^ [_1454759, _1454761, _1454763]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36106 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1454763, 36091 ^ [_1454759, _1454761, _1454763]), 36092 ^ [_1454759, _1454761, _1454763]))], (36094 ^ _781404) ^ [] : [-(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), 36091 ^ [_1454759, _1454761, _1454763]), 36092 ^ [_1454759, _1454761, _1454763]))))]]], (26959 ^ _781404) ^ [_1262642] : [class_Groups_Oordered__ab__group__add__abs(_1262642), -(hAPP(c_Groups_Oabs__class_Oabs(_1262642), c_Groups_Ozero__class_Ozero(_1262642)) = c_Groups_Ozero__class_Ozero(_1262642))], (44601 ^ _781404) ^ [_1673580, _1673582, _1673584] : [-(_1673580 = c_List_Olist_ONil(_1673582)), -(hAPP(c_List_Ohd(_1673582), hAPP(c_List_Orotate(_1673582, _1673584), _1673580)) = hAPP(hAPP(c_List_Onth(_1673582), _1673580), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1673584, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673582)), _1673580))))], (35964 ^ _781404) ^ [_1452423, _1452425, _1452427, _1452429] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1452423, _1452425), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1452427), _1452429))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1452423), _1452425), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1452429), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1452427)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1452427)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1452429), 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), _1452425), _1452429))))))], (43507 ^ _781404) ^ [_1648780, _1648782, _1648784] : [c_List_Olist_ONil(_1648780) = hAPP(hAPP(c_List_Olist_OCons(_1648780), _1648782), _1648784)], (12436 ^ _781404) ^ [_995915, _995917, _995919] : [class_Complete__Lattice_Ocomplete__lattice(_995915), hBOOL(hAPP(hAPP(c_member(_995915), _995917), _995919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995915), c_Complete__Lattice_OInf__class_OInf(_995915, _995919)), _995917)))], (12126 ^ _781404) ^ [_989670, _989672, _989674, _989676] : [hBOOL(hAPP(hAPP(c_member(_989670), _989672), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989670, tc_HOL_Obool)), _989674), _989676))), -(hBOOL(hAPP(hAPP(c_member(_989670), _989672), _989676)))], (49253 ^ _781404) ^ [_1774295, _1774297, _1774299] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1774295, _1774297), _1774299) = c_Lazy__Sequence_Oproduct(_1774295, _1774297, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1774295, _1774299), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1774297, _1774299))), class_Lazy__Sequence_Osmall__lazy(_1774295), class_Lazy__Sequence_Osmall__lazy(_1774297)], (7936 ^ _781404) ^ [_913258, _913260, _913262, _913264] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913258, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913258, tc_HOL_Obool)), _913260), _913262)), _913264) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913258, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913258, tc_HOL_Obool)), _913260), _913264)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913258, tc_HOL_Obool)), _913262), _913264)))], (42996 ^ _781404) ^ [_1637420, _1637422, _1637424, _1637426] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637420, _1637420)), hAPP(hAPP(c_Product__Type_OPair(_1637420, _1637420), _1637422), _1637424)), hAPP(c_List_Oset(tc_prod(_1637420, _1637420)), hAPP(hAPP(c_List_Ozip(_1637420, _1637420), _1637426), _1637426)))), 42999 ^ _781404 : [(43002 ^ _781404) ^ [] : [-(_1637422 = _1637424)], (43000 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1637420), _1637422), hAPP(c_List_Oset(_1637420), _1637426))))]]], (52478 ^ _781404) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (24752 ^ _781404) ^ [_1225335, _1225337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1225335), _1225337)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1225335), _1225337) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52424 ^ _781404) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (2802 ^ _781404) ^ [_822901, _822903, _822905, _822907, _822909, _822911] : [-(c_Predicate_ODomainP(_822911, _822907, _822903) = c_Predicate_ODomainP(_822909, _822905, _822901)), _822911 = _822909, _822907 = _822905, _822903 = _822901], (34369 ^ _781404) ^ [_1417677, _1417679, _1417681, _1417683, _1417685] : [class_Groups_Ocomm__monoid__add(_1417677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417679), _1417681)), 34376 ^ _781404 : [(34383 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417679), _1417683), _1417681))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417679, _1417677), hAPP(hAPP(c_COMBC(_1417679, _1417677, _1417677), hAPP(hAPP(c_COMBS(_1417679, _1417677, tc_fun(_1417677, _1417677)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417677, tc_fun(_1417677, _1417677)), _1417679), c_If(_1417677)), hAPP(hAPP(c_COMBC(_1417679, _1417679, tc_HOL_Obool), c_fequal), _1417683))), _1417685)), c_Groups_Ozero__class_Ozero(_1417677))), _1417681) = c_Groups_Ozero__class_Ozero(_1417677))], (34377 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1417679), _1417683), _1417681)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417679, _1417677), hAPP(hAPP(c_COMBC(_1417679, _1417677, _1417677), hAPP(hAPP(c_COMBS(_1417679, _1417677, tc_fun(_1417677, _1417677)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417677, tc_fun(_1417677, _1417677)), _1417679), c_If(_1417677)), hAPP(hAPP(c_COMBC(_1417679, _1417679, tc_HOL_Obool), c_fequal), _1417683))), _1417685)), c_Groups_Ozero__class_Ozero(_1417677))), _1417681) = hAPP(_1417685, _1417683))]]], (37435 ^ _781404) ^ [_1485931, _1485933, _1485935, _1485937, _1485939] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1485935, _1485931)), hAPP(hAPP(c_Product__Type_OPair(_1485935, _1485931), _1485939), _1485933)), _1485937)), -(hBOOL(hAPP(hAPP(c_member(_1485931), _1485933), hAPP(c_Relation_OImage(_1485935, _1485931, _1485937), hAPP(hAPP(c_Set_Oinsert(_1485935), _1485939), c_Orderings_Obot__class_Obot(tc_fun(_1485935, tc_HOL_Obool)))))))], (48702 ^ _781404) ^ [_1762525, _1762527] : [-(c_FunDef_Ois__measure(_1762525, _1762527))], (19097 ^ _781404) ^ [_1121263, _1121265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1121263)), c_Int_OBit1(_1121265))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121263), _1121265)))], (44503 ^ _781404) ^ [_1671517, _1671519, _1671521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1671517), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671519)), _1671521))), -(hAPP(hAPP(c_List_Olist_OCons(_1671519), hAPP(hAPP(c_List_Onth(_1671519), _1671521), _1671517)), hAPP(hAPP(c_List_Odrop(_1671519), hAPP(c_Nat_OSuc, _1671517)), _1671521)) = hAPP(hAPP(c_List_Odrop(_1671519), _1671517), _1671521))], (36582 ^ _781404) ^ [_1465180, _1465182, _1465184, _1465186, _1465188] : [-(c_Product__Type_Oprod_Oprod__size(_1465180, _1465182, _1465184, _1465186, _1465188) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1465184, hAPP(c_Product__Type_Ofst(_1465180, _1465182), _1465188))), hAPP(_1465186, hAPP(c_Product__Type_Osnd(_1465180, _1465182), _1465188)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11503 ^ _781404) ^ [_978042, _978044, _978046, _978048] : [_978042 = _978044, 11508 ^ _781404 : [(11511 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_978046), _978048), _978044)))], (11509 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_978046), _978048), _978042)))]], 11512 ^ _781404 : [(11515 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_978046), _978048), _978044))], (11513 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_978046), _978048), _978042))]]], (45076 ^ _781404) ^ [_1683033, _1683035, _1683037] : [-(_1683033 = c_List_Olist_ONil(_1683035)), -(c_List_Olast(_1683035, hAPP(hAPP(c_List_Oappend(_1683035), _1683037), _1683033)) = c_List_Olast(_1683035, _1683033))], (3642 ^ _781404) ^ [_835953, _835955, _835957, _835959, _835961, _835963] : [-(c_List_Oremove1(_835963, _835959, _835955) = c_List_Oremove1(_835961, _835957, _835953)), _835963 = _835961, _835959 = _835957, _835955 = _835953], (3784 ^ _781404) ^ [_838170, _838172, _838174, _838176] : [-(c_List_Olex(_838176, _838172) = c_List_Olex(_838174, _838170)), _838176 = _838174, _838172 = _838170], (35330 ^ _781404) ^ [_1439877, _1439879, _1439881, _1439883, _1439885, _1439887] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439877, tc_fun(_1439879, tc_HOL_Obool))), _1439881), _1439883), _1439885), _1439887)), -(hBOOL(hAPP(hAPP(_1439883, _1439885), _1439887)))], (6411 ^ _781404) ^ [_883281, _883283] : [_883281 = _883283, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883281), _883283)))], (11349 ^ _781404) ^ [_974572, _974574] : [class_Rings_Olinordered__idom(_974572), 11352 ^ _781404 : [(11359 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974572), _974574), c_Groups_Ozero__class_Ozero(_974572))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974572), _974574), hAPP(c_Groups_Ouminus__class_Ouminus(_974572), _974574))))], (11353 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974572), _974574), hAPP(c_Groups_Ouminus__class_Ouminus(_974572), _974574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974572), _974574), c_Groups_Ozero__class_Ozero(_974572))))]]], (36959 ^ _781404) ^ [_1474146, _1474148, _1474150] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1474146, tc_HOL_Obool), tc_fun(_1474146, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1474146, tc_HOL_Obool), tc_fun(_1474146, tc_HOL_Obool)), _1474148), _1474150)), c_Wellfounded_Ofinite__psubset(_1474146))), 36962 ^ _781404 : [(36965 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1474146), _1474150)))], (36963 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1474146, tc_HOL_Obool)), _1474148), _1474150)))]]], (13285 ^ _781404) ^ [_1012231, _1012233] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012231), _1012233) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1012231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1012233 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18687 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (22141 ^ _781404) ^ [_1175755, _1175757, _1175759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1175755), _1175757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175759), _1175755)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175759), _1175757))))], (38540 ^ _781404) ^ [_1513414, _1513416, _1513418, _1513420] : [38541 ^ _781404 : [(38544 ^ _781404) ^ [] : [_1513420 = c_Orderings_Obot__class_Obot(tc_fun(_1513416, tc_HOL_Obool))], (38542 ^ _781404) ^ [] : [_1513418 = c_Orderings_Obot__class_Obot(tc_fun(_1513414, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1513414, _1513416), _1513418), hAPP(c_COMBK(tc_fun(_1513416, tc_HOL_Obool), _1513414), _1513420)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513414, _1513416), tc_HOL_Obool)))], (10529 ^ _781404) ^ [_960639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960639), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37188 ^ _781404) ^ [_1479122] : [-(_1479122 = 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)), _1479122), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (45726 ^ _781404) ^ [_1697438, _1697440] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1697438, _1697440) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1697438), hAPP(c_Code__Numeral_Onat__of, _1697440))))], (35418 ^ _781404) ^ [_1441590, _1441592] : [class_Rings_Oring__1(_1441590), 35421 ^ _781404 : [(35428 ^ _781404) ^ [] : [-(_1441592 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35431 ^ _781404 : [(35438 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441592), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1441590), _1441592) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1441590), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1441590, _1441590)), tc_fun(tc_Int_Oint, _1441590)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1441590, _1441590), _1441590), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1441590, _1441590)), tc_fun(tc_Int_Oint, _1441590)), tc_Int_Oint), c_COMBB(tc_fun(_1441590, _1441590), _1441590, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1441590, tc_fun(tc_fun(_1441590, _1441590), _1441590), tc_Int_Oint), c_HOL_OLet(_1441590, _1441590)), c_Int_Oring__1__class_Oof__int(_1441590)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1441590, _1441590), tc_fun(_1441590, _1441590)), hAPP(hAPP(c_COMBB(tc_fun(_1441590, tc_fun(_1441590, _1441590)), tc_fun(tc_fun(_1441590, _1441590), tc_fun(_1441590, _1441590)), tc_Int_Oint), c_COMBS(_1441590, _1441590, _1441590)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1441590, _1441590), tc_fun(_1441590, tc_fun(_1441590, _1441590))), hAPP(hAPP(c_COMBB(tc_fun(_1441590, tc_fun(_1441590, _1441590)), tc_fun(tc_fun(_1441590, _1441590), tc_fun(_1441590, tc_fun(_1441590, _1441590))), tc_Int_Oint), c_COMBB(_1441590, tc_fun(_1441590, _1441590), _1441590)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1441590, tc_fun(_1441590, _1441590)), tc_Int_Oint), c_If(_1441590)), 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(_1441590, _1441590, _1441590), c_Groups_Oplus__class_Oplus(_1441590)), c_COMBI(_1441590))))), hAPP(hAPP(c_COMBC(_1441590, _1441590, _1441590), hAPP(hAPP(c_COMBB(_1441590, tc_fun(_1441590, _1441590), _1441590), c_Groups_Oplus__class_Oplus(_1441590)), hAPP(hAPP(c_COMBS(_1441590, _1441590, _1441590), c_Groups_Oplus__class_Oplus(_1441590)), c_COMBI(_1441590)))), c_Groups_Oone__class_Oone(_1441590))))), c_Divides_Odivmod__int(_1441592, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (35432 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441592), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1441590), _1441592) = hAPP(c_Groups_Ouminus__class_Ouminus(_1441590), hAPP(c_Int_Oring__1__class_Oof__int(_1441590), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1441592))))]]], (35422 ^ _781404) ^ [] : [_1441592 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1441590), _1441592) = c_Groups_Ozero__class_Ozero(_1441590))]]], (46327 ^ _781404) ^ [_1710946, _1710948, _1710950, _1710952, _1710954] : [c_Fun_Oinj__on(_1710946, _1710948, _1710950, c_Orderings_Otop__class_Otop(tc_fun(_1710946, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1710946, _1710948), _1710950), hAPP(c_List_OremoveAll(_1710946, _1710952), _1710954)) = hAPP(c_List_OremoveAll(_1710948, hAPP(_1710950, _1710952)), hAPP(hAPP(c_List_Omap(_1710946, _1710948), _1710950), _1710954)))], (45762 ^ _781404) ^ [_1698583, _1698585, _1698587] : [-(c_List_Olistsp(_1698583, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1698583, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1698583, tc_fun(_1698583, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698583)), _1698585)), hAPP(hAPP(c_COMBC(_1698583, tc_fun(_1698583, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698583)), _1698587))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1698583), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698583), tc_fun(tc_List_Olist(_1698583), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1698583))), c_List_Olists(_1698583, _1698585))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698583), tc_fun(tc_List_Olist(_1698583), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1698583))), c_List_Olists(_1698583, _1698587))))], (45329 ^ _781404) ^ [_1689081, _1689083, _1689085, _1689087, _1689089, _1689091] : [-(hAPP(hAPP(c_List_Omap(_1689081, _1689083), _1689085), hAPP(hAPP(c_List_Omap(_1689087, _1689081), _1689089), _1689091)) = hAPP(hAPP(c_List_Omap(_1689087, _1689083), hAPP(c_Fun_Ocomp(_1689081, _1689083, _1689087, _1689085), _1689089)), _1689091))], (3022 ^ _781404) ^ [_826243, _826245] : [_826245 = _826243, -(c_Nitpick_ORep__Frac(_826245) = c_Nitpick_ORep__Frac(_826243))], (12542 ^ _781404) ^ [_997862, _997864, _997866, _997868, _997870] : [class_Groups_Oab__group__add(_997862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997864), _997866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997866), _997868)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_997862), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _997862), _997870), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _997864), _997868))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _997862), _997870), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _997864), _997866))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _997862), _997870), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _997866), _997868)))], (25710 ^ _781404) ^ [_1240825, _1240827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240825)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240825), _1240827)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1240825)), hAPP(c_Int_Onat, _1240827)))], (40035 ^ _781404) ^ [_1559812, _1559814, _1559816] : [c_Wellfounded_Owf(_1559812, _1559814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1559812, tc_HOL_Obool)), _1559816), hAPP(c_Relation_OImage(_1559812, _1559812, _1559814), _1559816))), -(_1559816 = c_Orderings_Obot__class_Obot(tc_fun(_1559812, tc_HOL_Obool)))], (31972 ^ _781404) ^ [_1356801, _1356803, _1356805] : [class_Orderings_Olinorder(_1356801), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356801), _1356803), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356801), _1356803), _1356805)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356801), _1356803), _1356805))], (1996 ^ _781404) ^ [_809390, _809392, _809394, _809396, _809398, _809400] : [-(c_Hoare__Mirabelle_Otriple__valid(_809398, _809394, _809390)), c_Hoare__Mirabelle_Otriple__valid(_809400, _809396, _809392), _809400 = _809398, _809396 = _809394, _809392 = _809390], (17939 ^ _781404) ^ [_1101356] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1101356) = _1101356)], (34597 ^ _781404) ^ [_1423105, _1423107, _1423109] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1423105), _1423107), _1423109) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1423105), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1423105, tc_Int_Oint), _1423107), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1423109))), class_Groups_Ocomm__monoid__add(_1423105), class_Groups_Ocomm__monoid__mult(_1423105)], (25039 ^ _781404) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (34243 ^ _781404) ^ [_1413235, _1413237, _1413239, _1413241, _1413243] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413235, tc_fun(_1413237, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413235, tc_HOL_Obool)), _1413239), _1413241)), _1413243) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413237, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413235, tc_fun(_1413237, tc_HOL_Obool)), _1413239), _1413243)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413235, tc_fun(_1413237, tc_HOL_Obool)), _1413241), _1413243)))], (1426 ^ _781404) ^ [_802269, _802271] : [-(class_Complete__Lattice_Ocomplete__lattice(_802269)), _802271 = _802269, class_Complete__Lattice_Ocomplete__lattice(_802271)], (52508 ^ _781404) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (40835 ^ _781404) ^ [_1577801, _1577803] : [class_Complete__Lattice_Ocomplete__lattice(_1577801), c_Orderings_Oorder__class_Omono(_1577801, _1577801, _1577803), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577801), c_Inductive_Ocomplete__lattice__class_Olfp(_1577801, _1577803)), hAPP(_1577803, c_Inductive_Ocomplete__lattice__class_Olfp(_1577801, _1577803)))))], (9567 ^ _781404) ^ [_945241, _945243, _945245, _945247] : [class_Orderings_Oord(_945241), _945243 = _945245, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945241), _945245), _945247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945241), _945243), _945247)))], (46353 ^ _781404) ^ [_1711544, _1711546, _1711548, _1711550] : [class_Orderings_Olinorder(_1711544), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711546)), c_List_Olinorder__class_Osort__key(_1711546, _1711544, _1711548, _1711550)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711546)), _1711550))], (44519 ^ _781404) ^ [_1671935, _1671937, _1671939, _1671941] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1671935) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1671937), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1671935)), hAPP(hAPP(c_List_Olist_OCons(_1671937), _1671939), _1671941)) = hAPP(hAPP(c_List_Odrop(_1671937), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1671935)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1671941))], (52814 ^ _781404) ^ [_1843275, _1843277] : [hBOOL(_1843275), -(hBOOL(hAPP(hAPP(c_fimplies, _1843277), _1843275)))], (15903 ^ _781404) ^ [_1063054, _1063056, _1063058] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1063054), _1063056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1063054), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1063054, tc_HOL_Obool)), _1063056), hAPP(hAPP(c_Set_Oinsert(_1063054), _1063058), c_Orderings_Obot__class_Obot(tc_fun(_1063054, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1063054), _1063056))))], (46359 ^ _781404) ^ [_1711661, _1711663, _1711665, _1711667] : [class_Orderings_Olinorder(_1711661), -(hAPP(c_List_Oset(_1711663), c_List_Olinorder__class_Osort__key(_1711663, _1711661, _1711665, _1711667)) = hAPP(c_List_Oset(_1711663), _1711667))], (18225 ^ _781404) ^ [_1106104, _1106106, _1106108, _1106110] : [class_Rings_Olinordered__semidom(_1106104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106104), c_Groups_Oone__class_Oone(_1106104)), _1106106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106104), hAPP(hAPP(c_Power_Opower__class_Opower(_1106104), _1106106), _1106108)), hAPP(hAPP(c_Power_Opower__class_Opower(_1106104), _1106106), _1106110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1106108), _1106110)))], (24776 ^ _781404) ^ [_1225691, _1225693] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1225691, _1225693)) = _1225693, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1225691), _1225693) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29846 ^ _781404) ^ [_1316367, _1316369, _1316371] : [29848 ^ _781404 : [(29851 ^ _781404) ^ [] : [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(_1316369, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 29847 ^ [_1316367, _1316369, _1316371]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1316369, 29847 ^ [_1316367, _1316369, _1316371])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29849 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29847 ^ [_1316367, _1316369, _1316371]), _1316367)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1316369, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1316371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1316371), hAPP(_1316369, _1316367))), 29861 ^ _781404 : [(29864 ^ _781404) ^ [] : [-(hAPP(_1316369, 29860 ^ [_1316367, _1316369, _1316371]) = _1316371)], (29862 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29860 ^ [_1316367, _1316369, _1316371]), _1316367)))]]], (34757 ^ _781404) ^ [_1427107, _1427109, _1427111] : [class_Groups_Ocomm__monoid__add(_1427107), class_Groups_Ocomm__monoid__mult(_1427107), c_Nat__Transfer_Onat__set(_1427109), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1427107), _1427111), _1427109) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1427107), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1427107, tc_Nat_Onat), _1427111), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1427109)))], (11549 ^ _781404) ^ [_978881, _978883, _978885, _978887, _978889, _978891] : [_978881 = hAPP(_978883, _978885), hBOOL(hAPP(hAPP(c_member(_978887), _978885), _978889)), -(hBOOL(hAPP(hAPP(c_member(_978891), _978881), hAPP(c_Set_Oimage(_978887, _978891, _978883), _978889))))], (20069 ^ _781404) ^ [_1137870, _1137872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137870), _1137872)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1137870)), c_Int_OBit0(_1137872))))], (34903 ^ _781404) ^ [_1430462, _1430464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1430462)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430464))), -(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(_1430464))), 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), _1430462)), c_Int_Onat))))))], (33333 ^ _781404) ^ [_1384674, _1384676] : [-(hAPP(c_Set_Oimage(_1384674, _1384674, c_COMBI(_1384674)), _1384676) = _1384676)], (24953 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (51116 ^ _781404) ^ [_1814654, _1814656, _1814658, _1814660] : [c_Fun_Obij__betw(_1814654, _1814656, _1814658, c_Orderings_Otop__class_Otop(tc_fun(_1814654, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1814656, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1814654, _1814656, _1814658), _1814660) = hAPP(c_Set_Oimage(_1814656, _1814654, c_Hilbert__Choice_Oinv__into(_1814654, _1814656, c_Orderings_Otop__class_Otop(tc_fun(_1814654, tc_HOL_Obool)), _1814658)), _1814660))], (44665 ^ _781404) ^ [_1674758, _1674760, _1674762] : [-(hAPP(hAPP(c_List_Otake(_1674758), _1674760), hAPP(c_List_Otl(_1674758), _1674762)) = hAPP(c_List_Otl(_1674758), hAPP(hAPP(c_List_Otake(_1674758), hAPP(c_Nat_OSuc, _1674760)), _1674762)))], (25207 ^ _781404) ^ [_1232462, _1232464, _1232466] : [-(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), _1232462), _1232464)), _1232466)), _1232464) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1232466), _1232464))], (5889 ^ _781404) ^ [_874774, _874776, _874778, _874780] : [class_Orderings_Opreorder(_874774), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874774), _874776), _874778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874774), _874778), _874780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874774), _874776), _874780)))], (45331 ^ _781404) ^ [_1689149, _1689151, _1689153, _1689155, _1689157, _1689159] : [-(hAPP(hAPP(c_List_Omap(_1689149, _1689151), _1689153), hAPP(hAPP(c_List_Omap(_1689155, _1689149), _1689157), _1689159)) = hAPP(hAPP(c_List_Omap(_1689155, _1689151), hAPP(c_Fun_Ocomp(_1689149, _1689151, _1689155, _1689153), _1689157)), _1689159))], (13379 ^ _781404) ^ [_1014000, _1014002, _1014004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014000), _1014002)), _1014004)), 13382 ^ _781404 : [(13385 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014002), _1014004)))], (13383 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014000), _1014004)))]]], (41618 ^ _781404) ^ [_1597965, _1597967, _1597969, _1597971] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597965, _1597965)), hAPP(hAPP(c_Product__Type_OPair(_1597965, _1597965), _1597967), _1597969)), hAPP(c_Relation_Oconverse(_1597965, _1597965), c_Transitive__Closure_Otrancl(_1597965, _1597971)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597965, _1597965)), hAPP(hAPP(c_Product__Type_OPair(_1597965, _1597965), _1597967), _1597969)), c_Transitive__Closure_Otrancl(_1597965, hAPP(c_Relation_Oconverse(_1597965, _1597965), _1597971)))))], (33520 ^ _781404) ^ [_1391341, _1391343, _1391345, _1391347, _1391349, _1391351] : [-(hAPP(hAPP(c_Fun_Ocomp(_1391341, _1391343, _1391345, _1391347), _1391349), _1391351) = hAPP(_1391347, hAPP(_1391349, _1391351)))], (11042 ^ _781404) ^ [_968934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968934), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_968934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51155 ^ _781404) ^ [_1815416, _1815418] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1815416), _1815418)), -(c_Fun_Obij__betw(_1815416, tc_Nat_Onat, 51158 ^ [_1815416, _1815418], _1815418, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1815416), _1815418))))], (16648 ^ _781404) ^ [_1077675, _1077677, _1077679] : [class_Rings_Oring__1(_1077675), hBOOL(hAPP(hAPP(c_member(_1077675), _1077677), c_Int_Oring__1__class_OInts(_1077675))), hBOOL(hAPP(hAPP(c_member(_1077675), _1077679), c_Int_Oring__1__class_OInts(_1077675))), -(hBOOL(hAPP(hAPP(c_member(_1077675), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077675), _1077677), _1077679)), c_Int_Oring__1__class_OInts(_1077675))))], (32192 ^ _781404) ^ [_1360844, _1360846, _1360848, _1360850] : [class_Orderings_Olinorder(_1360844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360844), _1360846), _1360848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360844), _1360846), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360844), _1360850), _1360848))))], (48068 ^ _781404) ^ [_1748284, _1748286, _1748288, _1748290] : [-(c_List_Oconcat(_1748284, hAPP(hAPP(c_List_Omap(_1748286, tc_List_Olist(_1748284)), _1748288), _1748290)) = c_List_Omaps(_1748286, _1748284, _1748288, _1748290))], (51768 ^ _781404) ^ [_1829583, _1829585, _1829587] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829583), _1829585)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829583), _1829587))), -(_1829583 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829585), _1829587)))], (7633 ^ _781404) ^ [_906808, _906810, _906812] : [-(hAPP(c_Set_OPow(_906808), hAPP(hAPP(c_Set_Oinsert(_906808), _906810), _906812)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_906808, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_906808), _906812)), hAPP(c_Set_Oimage(tc_fun(_906808, tc_HOL_Obool), tc_fun(_906808, tc_HOL_Obool), hAPP(c_Set_Oinsert(_906808), _906810)), hAPP(c_Set_OPow(_906808), _906812))))], (48933 ^ _781404) ^ [_1767221, _1767223, _1767225, _1767227] : [-(c_New__Random__Sequence_Oneg__map(_1767221, _1767223, _1767225, _1767227) = c_New__Random__Sequence_Oneg__bind(_1767221, _1767223, _1767227, hAPP(c_Fun_Ocomp(_1767223, 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(_1767223)))))), _1767221, c_New__Random__Sequence_Oneg__single(_1767223)), _1767225)))], (18557 ^ _781404) ^ [_1112456, _1112458, _1112460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1112456)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1112458), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1112460)), 18567 ^ _781404 : [(18573 ^ _781404) ^ [] : [-(_1112458 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 18569 ^ [_1112456, _1112458, _1112460]), 18566 ^ [_1112456, _1112458, _1112460]))], (18571 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18569 ^ [_1112456, _1112458, _1112460]), _1112460)))], (18568 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18566 ^ [_1112456, _1112458, _1112460]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1112456))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1112458), _1112456) = _1112458)], (45182 ^ _781404) ^ [_1684967, _1684969] : [-(hAPP(hAPP(c_List_Ozip(_1684967, _1684967), _1684969), _1684969) = hAPP(hAPP(c_List_Omap(_1684967, tc_prod(_1684967, _1684967)), hAPP(hAPP(c_COMBS(_1684967, _1684967, tc_prod(_1684967, _1684967)), c_Product__Type_OPair(_1684967, _1684967)), c_COMBI(_1684967))), _1684969))], (31542 ^ _781404) ^ [_1348809, _1348811, _1348813] : [class_Orderings_Olinorder(_1348809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348809), _1348811)), -(hBOOL(hAPP(hAPP(c_member(_1348809), _1348813), _1348811))), -(_1348811 = c_Orderings_Obot__class_Obot(tc_fun(_1348809, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1348809, hAPP(hAPP(c_Set_Oinsert(_1348809), _1348813), _1348811)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1348809), _1348813), c_Big__Operators_Olinorder__class_OMin(_1348809, _1348811)))], (26619 ^ _781404) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (21087 ^ _781404) ^ [_1155781, _1155783, _1155785] : [class_Rings_Oring(_1155781), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1155781), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155781), _1155783), _1155785)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155781), _1155783), hAPP(c_Groups_Ouminus__class_Ouminus(_1155781), _1155785)))], (43707 ^ _781404) ^ [_1652476, _1652478, _1652480, _1652482] : [-(_1652476 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1652478), _1652476), hAPP(hAPP(c_List_Olist_OCons(_1652478), _1652480), _1652482)) = hAPP(hAPP(c_List_Olist_OCons(_1652478), _1652480), hAPP(hAPP(c_List_Otake(_1652478), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1652476), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1652482)))], (33506 ^ _781404) ^ [_1390928, _1390930, _1390932, _1390934, _1390936, _1390938, _1390940, _1390942, _1390944, _1390946, _1390948] : [hAPP(_1390928, hAPP(_1390930, _1390932)) = hAPP(_1390934, hAPP(_1390936, _1390938)), -(hAPP(hAPP(c_Fun_Ocomp(_1390940, _1390942, _1390944, _1390928), _1390930), _1390932) = hAPP(hAPP(c_Fun_Ocomp(_1390946, _1390942, _1390948, _1390934), _1390936), _1390938))], (48977 ^ _781404) ^ [_1768404, _1768406, _1768408] : [-(_1768406 = _1768408), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1768404, _1768404, hAPP(hAPP(c_COMBB(tc_fun(_1768404, tc_HOL_Obool), tc_fun(_1768404, tc_HOL_Obool), _1768404), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1768404), c_fNot)), c_fequal)), _1768406), _1768408)))], (41875 ^ _781404) ^ [_1604175, _1604177, _1604179] : [41876 ^ _781404 : [(41877 ^ _781404) ^ [_1604251] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604175, _1604175)), _1604177), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604175, _1604175), tc_HOL_Obool), _1604251), _1604179)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604175, _1604175)), _1604177), c_Transitive__Closure_Ortrancl(_1604175, _1604179))))], (46808 ^ _781404) ^ [_1723038, _1723040] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1723038, _1723040))))], (48601 ^ _781404) ^ [_1760472, _1760474, _1760476, _1760478] : [48602 ^ _781404 : [(48605 ^ _781404) ^ [] : [c_List_Olist__ex(_1760472, _1760474, _1760478)], (48603 ^ _781404) ^ [] : [hBOOL(hAPP(_1760474, _1760476))]], -(c_List_Olist__ex(_1760472, _1760474, hAPP(hAPP(c_List_Olist_OCons(_1760472), _1760476), _1760478)))], (9208 ^ _781404) ^ [_938452, _938454, _938456, _938458] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938452, tc_HOL_Obool)), _938454), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938452, tc_HOL_Obool)), _938456), _938458)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938452, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938452, tc_HOL_Obool)), _938454), _938456)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938452, tc_HOL_Obool)), _938454), _938458)))], (41289 ^ _781404) ^ [_1590071, _1590073] : [-(hAPP(c_Relation_OImage(_1590071, _1590071, c_Relation_OId(_1590071)), _1590073) = _1590073)], (23047 ^ _781404) ^ [_1193836, _1193838, _1193840, _1193842, _1193844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1193836), _1193838)), 23050 ^ _781404 : [(23057 ^ _781404) ^ [] : [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), _1193838), _1193836)), _1193840)), _1193842)), _1193844)), -(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), _1193838), _1193840)), _1193842)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1193836), _1193840)), _1193844))))], (23051 ^ _781404) ^ [] : [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), _1193838), _1193840)), _1193842)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1193836), _1193840)), _1193844))), -(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), _1193838), _1193836)), _1193840)), _1193842)), _1193844)))]]], (48947 ^ _781404) ^ [_1767656, _1767658, _1767660, _1767662, _1767664] : [-(c_List_Osplice(_1767656, hAPP(hAPP(c_List_Olist_OCons(_1767656), _1767658), _1767660), hAPP(hAPP(c_List_Olist_OCons(_1767656), _1767662), _1767664)) = hAPP(hAPP(c_List_Olist_OCons(_1767656), _1767658), hAPP(hAPP(c_List_Olist_OCons(_1767656), _1767662), c_List_Osplice(_1767656, _1767660, _1767664))))], (38606 ^ _781404) ^ [_1515585, _1515587, _1515589, _1515591, _1515593, _1515595] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515585, _1515587)), hAPP(hAPP(c_Product__Type_OPair(_1515585, _1515587), _1515589), _1515591)), hAPP(hAPP(c_Product__Type_OSigma(_1515585, _1515587), _1515593), _1515595))), -(hBOOL(hAPP(hAPP(c_member(_1515585), _1515589), _1515593)))], (33149 ^ _781404) ^ [_1379933, _1379935, _1379937, _1379939, _1379941] : [class_Groups_Ocomm__monoid__add(_1379933), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379933), _1379935), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1379937), _1379939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1379941), _1379939))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379933), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1379933, tc_Nat_Onat), _1379935), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1379939))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1379937, _1379941)))], (20695 ^ _781404) ^ [_1148193, _1148195] : [class_Rings_Oring__1(_1148193), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1148193), hAPP(c_Groups_Ouminus__class_Ouminus(_1148193), c_Groups_Oone__class_Oone(_1148193))), 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)))), _1148195))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1148193), c_Groups_Oone__class_Oone(_1148193)))], (33762 ^ _781404) ^ [_1398454, _1398456, _1398458] : [hAPP(hAPP(c_COMBC(_1398454, tc_fun(_1398454, tc_HOL_Obool), tc_HOL_Obool), c_member(_1398454)), _1398456) = hAPP(hAPP(c_COMBC(_1398454, tc_fun(_1398454, tc_HOL_Obool), tc_HOL_Obool), c_member(_1398454)), _1398458), -(_1398456 = _1398458)], (4742 ^ _781404) ^ [_853559, _853561, _853563, _853565, _853567, _853569, _853571, _853573] : [-(c_Random__Sequence_Obind(_853573, _853569, _853565, _853561) = c_Random__Sequence_Obind(_853571, _853567, _853563, _853559)), _853573 = _853571, _853569 = _853567, _853565 = _853563, _853561 = _853559], (34235 ^ _781404) ^ [_1412856, _1412858, _1412860, _1412862, _1412864] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412856, tc_HOL_Obool)), _1412858), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412860, tc_fun(_1412856, tc_HOL_Obool)), _1412862), _1412864)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412860, tc_fun(_1412856, tc_HOL_Obool)), _1412862), hAPP(hAPP(c_COMBB(tc_fun(_1412856, tc_HOL_Obool), tc_fun(_1412856, tc_HOL_Obool), _1412860), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412856, tc_HOL_Obool)), _1412858)), _1412864)))], (36676 ^ _781404) ^ [_1467090, _1467092, _1467094, _1467096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467090, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1467090, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36677 ^ [_1467090, _1467092, _1467094, _1467096])), _1467092)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1467090, 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), 36677 ^ [_1467090, _1467092, _1467094, _1467096]), _1467094))), _1467096))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467090, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1467090, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1467092)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1467090, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1467096))))], (27514 ^ _781404) ^ [_1272685, _1272687, _1272689] : [class_Lattices_Oab__semigroup__idem__mult(_1272685), -(_1272687 = c_Orderings_Obot__class_Obot(tc_fun(_1272685, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272685), _1272687)), -(hAPP(c_Finite__Set_Ofold1(_1272685, c_Groups_Otimes__class_Otimes(_1272685)), hAPP(hAPP(c_Set_Oinsert(_1272685), _1272689), _1272687)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272685), _1272689), hAPP(c_Finite__Set_Ofold1(_1272685, c_Groups_Otimes__class_Otimes(_1272685)), _1272687)))], (25843 ^ _781404) ^ [_1243315] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1243315))), 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), _1243315), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (40974 ^ _781404) ^ [_1581614, _1581616] : [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), _1581614), _1581616)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581614), _1581616)))], (30397 ^ _781404) ^ [_1327552, _1327554, _1327556, _1327558] : [class_Lattices_Osemilattice__sup(_1327552), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327552), _1327554)), 30407 ^ _781404 : [(30410 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327552), 30406 ^ [_1327552, _1327554, _1327556, _1327558]), _1327556))], (30408 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327552), 30406 ^ [_1327552, _1327554, _1327556, _1327558]), _1327554)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327552), hAPP(hAPP(c_Finite__Set_Ofold(_1327552, _1327552, c_Lattices_Osemilattice__sup__class_Osup(_1327552)), _1327558), _1327554)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1327552), _1327556), _1327558))))], (13151 ^ _781404) ^ [_1009651, _1009653, _1009655, _1009657] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1009651), 13154 ^ _781404 : [(13161 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009651), _1009653), _1009657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009651), _1009653), _1009655)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009651), _1009657), _1009655))))], (13155 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009651), _1009653), _1009655)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009651), _1009657), _1009655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009651), _1009653), _1009657)))]]], (24154 ^ _781404) ^ [_1214589, _1214591, _1214593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214589)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1214593), _1214589)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214591), _1214593)), _1214589))], (38739 ^ _781404) ^ [_1518849, _1518851, _1518853, _1518855, _1518857, _1518859] : [-(hAPP(c_Set_Ovimage(_1518849, tc_prod(_1518851, _1518853), _1518855), hAPP(hAPP(c_Product__Type_OSigma(_1518851, _1518853), _1518857), hAPP(c_COMBK(tc_fun(_1518853, tc_HOL_Obool), _1518851), _1518859))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518849, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1518849, _1518851, hAPP(c_Fun_Ocomp(tc_prod(_1518851, _1518853), _1518851, _1518849, c_Product__Type_Ofst(_1518851, _1518853)), _1518855)), _1518857)), hAPP(c_Set_Ovimage(_1518849, _1518853, hAPP(c_Fun_Ocomp(tc_prod(_1518851, _1518853), _1518853, _1518849, c_Product__Type_Osnd(_1518851, _1518853)), _1518855)), _1518859)))], (13560 ^ _781404) ^ [_1017545, _1017547, _1017549, _1017551, _1017553] : [class_Groups_Ocomm__monoid__add(_1017545), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017547), _1017549)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1017547, _1017545), _1017551), hAPP(hAPP(c_Set_Oinsert(_1017547), _1017553), _1017549)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017545), hAPP(_1017551, _1017553)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1017547, _1017545), _1017551), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017547, tc_HOL_Obool)), _1017549), hAPP(hAPP(c_Set_Oinsert(_1017547), _1017553), c_Orderings_Obot__class_Obot(tc_fun(_1017547, tc_HOL_Obool)))))))], (10969 ^ _781404) ^ [_967689, _967691] : [class_Groups_Olinordered__ab__group__add(_967689), 10972 ^ _781404 : [(10979 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967689), c_Groups_Ozero__class_Ozero(_967689)), _967691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967689), hAPP(c_Groups_Ouminus__class_Ouminus(_967689), _967691)), _967691)))], (10973 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967689), hAPP(c_Groups_Ouminus__class_Ouminus(_967689), _967691)), _967691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967689), c_Groups_Ozero__class_Ozero(_967689)), _967691)))]]], (21193 ^ _781404) ^ [_1157946] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1157946) = c_Int_OPls)], (6133 ^ _781404) ^ [_878822, _878824, _878826] : [class_Orderings_Olinorder(_878822), 6136 ^ _781404 : [(6143 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878822), _878826), _878824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878822, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_878822), _878824)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_878822), _878826))))], (6137 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878822, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_878822), _878824)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_878822), _878826))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878822), _878826), _878824)))]]], (44369 ^ _781404) ^ [_1668305, _1668307, _1668309] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668305)), hAPP(hAPP(c_List_Odrop(_1668305), _1668307), _1668309)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668305)), _1668309)), _1668307))], (51538 ^ _781404) ^ [_1825391, _1825393, _1825395, _1825397, _1825399] : [class_Divides_Osemiring__div(_1825391), -(_1825393 = c_Groups_Ozero__class_Ozero(_1825391)), -(_1825395 = c_Groups_Ozero__class_Ozero(_1825391)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825391), _1825393), _1825397)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825391), _1825395), _1825399)), 51557 ^ _781404 : [(51564 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825391), _1825397), _1825395) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825391), _1825393), _1825399), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825391), _1825397), _1825393) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825391), _1825399), _1825395))], (51558 ^ _781404) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825391), _1825397), _1825393) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825391), _1825399), _1825395), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825391), _1825397), _1825395) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825391), _1825393), _1825399))]]], (12426 ^ _781404) ^ [_995750, _995752, _995754] : [class_Complete__Lattice_Ocomplete__lattice(_995750), hBOOL(hAPP(hAPP(c_member(_995750), _995752), _995754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995750), _995752), c_Complete__Lattice_OSup__class_OSup(_995750, _995754))))], (39748 ^ _781404) ^ [_1553565, _1553567, _1553569, _1553571, _1553573, _1553575, _1553577] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553565, _1553569)), hAPP(hAPP(c_Product__Type_OPair(_1553565, _1553569), _1553575), _1553577)), hAPP(hAPP(c_Relation_Orel__comp(_1553565, _1553567, _1553569), _1553571), _1553573))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1553565, _1553567, _1553569, hAPP(hAPP(c_COMBC(_1553565, tc_fun(tc_prod(_1553565, _1553567), tc_HOL_Obool), tc_fun(_1553567, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553567, tc_fun(tc_fun(tc_prod(_1553565, _1553567), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1553565, _1553567), tc_HOL_Obool), tc_fun(_1553567, tc_HOL_Obool)), _1553565), c_COMBC(_1553567, tc_fun(tc_prod(_1553565, _1553567), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553567, tc_prod(_1553565, _1553567)), tc_fun(_1553567, tc_fun(tc_fun(tc_prod(_1553565, _1553567), tc_HOL_Obool), tc_HOL_Obool)), _1553565), hAPP(c_COMBB(tc_prod(_1553565, _1553567), tc_fun(tc_fun(tc_prod(_1553565, _1553567), tc_HOL_Obool), tc_HOL_Obool), _1553567), c_member(tc_prod(_1553565, _1553567)))), c_Product__Type_OPair(_1553565, _1553567)))), _1553571), hAPP(hAPP(c_COMBC(_1553567, tc_fun(tc_prod(_1553567, _1553569), tc_HOL_Obool), tc_fun(_1553569, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553569, tc_fun(tc_fun(tc_prod(_1553567, _1553569), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1553567, _1553569), tc_HOL_Obool), tc_fun(_1553569, tc_HOL_Obool)), _1553567), c_COMBC(_1553569, tc_fun(tc_prod(_1553567, _1553569), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553569, tc_prod(_1553567, _1553569)), tc_fun(_1553569, tc_fun(tc_fun(tc_prod(_1553567, _1553569), tc_HOL_Obool), tc_HOL_Obool)), _1553567), hAPP(c_COMBB(tc_prod(_1553567, _1553569), tc_fun(tc_fun(tc_prod(_1553567, _1553569), tc_HOL_Obool), tc_HOL_Obool), _1553569), c_member(tc_prod(_1553567, _1553569)))), c_Product__Type_OPair(_1553567, _1553569)))), _1553573)), _1553575), _1553577)))], (39628 ^ _781404) ^ [_1548906, _1548908, _1548910, _1548912, _1548914, _1548916] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1548906, _1548908, _1548910), _1548912), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1548908, _1548910), tc_HOL_Obool)), _1548914), _1548916)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1548906, _1548910), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1548906, _1548908, _1548910), _1548912), _1548914)), hAPP(hAPP(c_Relation_Orel__comp(_1548906, _1548908, _1548910), _1548912), _1548916)))], (8172 ^ _781404) ^ [_918606, _918608] : [class_Groups_Ozero(_918606), 8175 ^ _781404 : [(8182 ^ _781404) ^ [] : [_918608 = c_Groups_Ozero__class_Ozero(_918606), -(c_Groups_Ozero__class_Ozero(_918606) = _918608)], (8176 ^ _781404) ^ [] : [c_Groups_Ozero__class_Ozero(_918606) = _918608, -(_918608 = c_Groups_Ozero__class_Ozero(_918606))]]], (5799 ^ _781404) ^ [_873311, _873313] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873311, tc_HOL_Obool)), _873313), _873313)))], (7149 ^ _781404) ^ [_897229, _897231, _897233] : [class_Lattices_Osemilattice__sup(_897229), 7152 ^ _781404 : [(7159 ^ _781404) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897229), _897231), _897233) = _897233, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897229), _897231), _897233)))], (7153 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897229), _897231), _897233)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897229), _897231), _897233) = _897233)]]], (24650 ^ _781404) ^ [_1223633, _1223635, _1223637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223633), _1223635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223633), _1223637)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1223635), _1223637))))], (17737 ^ _781404) ^ [_1097659, _1097661] : [class_Complete__Lattice_Ocomplete__lattice(_1097659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097659), _1097661)), -(c_Complete__Lattice_OSup__class_OSup(_1097659, _1097661) = hAPP(hAPP(c_Finite__Set_Ofold(_1097659, _1097659, c_Lattices_Osemilattice__sup__class_Osup(_1097659)), c_Orderings_Obot__class_Obot(_1097659)), _1097661))], (32596 ^ _781404) ^ [_1368617, _1368619] : [class_Orderings_Olinorder(_1368617), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368617), _1368619)), -(_1368619 = c_Orderings_Obot__class_Obot(tc_fun(_1368617, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368617), c_Big__Operators_Olattice_OInf__fin(_1368617, c_Orderings_Oord__class_Omin(_1368617), _1368619)), c_Big__Operators_Olattice_OSup__fin(_1368617, c_Orderings_Oord__class_Omax(_1368617), _1368619))))], (14095 ^ _781404) ^ [_1027369, _1027371, _1027373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027369), _1027371)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027371), _1027373)), _1027369) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027371), _1027369)), _1027373))], (46293 ^ _781404) ^ [_1710360, _1710362, _1710364, _1710366] : [-(c_List_Oremdups(_1710360, hAPP(hAPP(c_List_Omap(_1710362, _1710360), _1710364), c_List_Oremdups(_1710362, _1710366))) = c_List_Oremdups(_1710360, hAPP(hAPP(c_List_Omap(_1710362, _1710360), _1710364), _1710366)))], (49201 ^ _781404) ^ [_1773115, _1773117, _1773119, _1773121, _1773123] : [-(hAPP(hAPP(c_List_Omap(_1773115, _1773117), _1773119), c_List_Oreplicate(_1773115, _1773121, _1773123)) = c_List_Oreplicate(_1773117, _1773121, hAPP(_1773119, _1773123)))], (3698 ^ _781404) ^ [_836861, _836863] : [_836863 = _836861, -(c_Orderings_Oord__class_Omax(_836863) = c_Orderings_Oord__class_Omax(_836861))], (20833 ^ _781404) ^ [_1151441, _1151443] : [class_Lattices_Oab__semigroup__idem__mult(_1151441), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151441), _1151443), _1151443) = _1151443)], (41141 ^ _781404) ^ [_1585690, _1585692, _1585694, _1585696] : [-(c_Transitive__Closure_Otrancl(_1585690, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1585690, _1585690)), hAPP(hAPP(c_Product__Type_OPair(_1585690, _1585690), _1585692), _1585694)), _1585696)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585690, _1585690), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1585690, _1585696)), hAPP(c_Set_OCollect(tc_prod(_1585690, _1585690)), hAPP(c_Product__Type_Oprod_Oprod__case(_1585690, _1585690, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1585690, tc_fun(_1585690, tc_HOL_Obool), tc_fun(_1585690, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1585690, tc_HOL_Obool), tc_fun(_1585690, tc_HOL_Obool)), _1585690), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1585690)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1585690), c_fconj), hAPP(hAPP(c_COMBC(_1585690, tc_fun(tc_prod(_1585690, _1585690), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1585690, _1585690), tc_fun(tc_fun(tc_prod(_1585690, _1585690), tc_HOL_Obool), tc_HOL_Obool), _1585690), c_member(tc_prod(_1585690, _1585690))), hAPP(hAPP(c_COMBC(_1585690, _1585690, tc_prod(_1585690, _1585690)), c_Product__Type_OPair(_1585690, _1585690)), _1585692))), c_Transitive__Closure_Ortrancl(_1585690, _1585696))))), hAPP(hAPP(c_COMBC(_1585690, tc_fun(tc_prod(_1585690, _1585690), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1585690, _1585690), tc_fun(tc_fun(tc_prod(_1585690, _1585690), tc_HOL_Obool), tc_HOL_Obool), _1585690), c_member(tc_prod(_1585690, _1585690))), hAPP(c_Product__Type_OPair(_1585690, _1585690), _1585694))), c_Transitive__Closure_Ortrancl(_1585690, _1585696)))))))], (456 ^ _781404) ^ [_788298, _788300, _788302, _788304] : [-(c_Relation_Oirrefl(_788302, _788298)), c_Relation_Oirrefl(_788304, _788300), _788304 = _788302, _788300 = _788298], (50141 ^ _781404) ^ [_1794885, _1794887, _1794889, _1794891] : [c_Relation_Osym(_1794885, _1794887), hBOOL(hAPP(hAPP(c_member(tc_prod(_1794885, _1794885)), hAPP(hAPP(c_Product__Type_OPair(_1794885, _1794885), _1794889), _1794891)), _1794887)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1794885, _1794885)), hAPP(hAPP(c_Product__Type_OPair(_1794885, _1794885), _1794891), _1794889)), _1794887)))], (17637 ^ _781404) ^ [_1095699, _1095701] : [class_Rings_Ocomm__semiring__1(_1095699), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095699), _1095701), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1095699))], (29073 ^ _781404) ^ [_1301922, _1301924, _1301926, _1301928] : [class_Fields_Ofield__inverse__zero(_1301922), 29076 ^ _781404 : [(29077 ^ _781404) ^ [] : [_1301924 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301922), _1301926), _1301928), 29080 ^ _781404 : [(29087 ^ _781404) ^ [] : [_1301928 = c_Groups_Ozero__class_Ozero(_1301922), -(_1301924 = c_Groups_Ozero__class_Ozero(_1301922))], (29081 ^ _781404) ^ [] : [-(_1301928 = c_Groups_Ozero__class_Ozero(_1301922)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301922), _1301924), _1301928) = _1301926)]]], (29093 ^ _781404) ^ [] : [-(_1301924 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301922), _1301926), _1301928)), 29096 ^ _781404 : [(29099 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301922), _1301924), _1301928) = _1301926], (29097 ^ _781404) ^ [] : [_1301928 = c_Groups_Ozero__class_Ozero(_1301922)]], 29100 ^ _781404 : [(29103 ^ _781404) ^ [] : [_1301924 = c_Groups_Ozero__class_Ozero(_1301922)], (29101 ^ _781404) ^ [] : [-(_1301928 = c_Groups_Ozero__class_Ozero(_1301922))]]]]], (39770 ^ _781404) ^ [_1554536, _1554538, _1554540, _1554542, _1554544, _1554546, _1554548] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1554536, _1554538, _1554540, _1554542, _1554544), _1554546), _1554548)), 39774 ^ _781404 : [(39777 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1554544, 39773 ^ [_1554536, _1554538, _1554540, _1554542, _1554544, _1554546, _1554548]), _1554548)))], (39775 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1554542, _1554546), 39773 ^ [_1554536, _1554538, _1554540, _1554542, _1554544, _1554546, _1554548])))]]], (38500 ^ _781404) ^ [_1512279, _1512281, _1512283, _1512285, _1512287] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1512279, _1512281), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1512279, tc_HOL_Obool)), _1512283), _1512285)), hAPP(c_COMBK(tc_fun(_1512281, tc_HOL_Obool), _1512279), _1512287)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1512279, _1512281), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1512279, _1512281), _1512283), hAPP(c_COMBK(tc_fun(_1512281, tc_HOL_Obool), _1512279), _1512287))), hAPP(hAPP(c_Product__Type_OSigma(_1512279, _1512281), _1512285), hAPP(c_COMBK(tc_fun(_1512281, tc_HOL_Obool), _1512279), _1512287))))], (41694 ^ _781404) ^ [_1599910, _1599912, _1599914, _1599916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1599910, _1599912), tc_HOL_Obool)), _1599914), _1599916)), c_Relation_Osingle__valued(_1599910, _1599912, _1599916), -(c_Relation_Osingle__valued(_1599910, _1599912, _1599914))], (39055 ^ _781404) ^ [_1527646, _1527648, _1527650] : [-(hAPP(hAPP(c_Set_Oinsert(_1527646), _1527648), _1527650) = hAPP(c_Set_OCollect(_1527646), hAPP(hAPP(c_COMBS(_1527646, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527646), c_fdisj), hAPP(hAPP(c_COMBC(_1527646, _1527646, tc_HOL_Obool), c_fequal), _1527648))), hAPP(hAPP(c_COMBC(_1527646, tc_fun(_1527646, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527646)), _1527650))))], (7443 ^ _781404) ^ [_902932, _902934] : [class_Lattices_Osemilattice__inf(_902932), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_902932), _902934), _902934) = _902934)], (23369 ^ _781404) ^ [_1200425, _1200427, _1200429] : [class_Divides_Osemiring__div(_1200425), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200425), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1200425), _1200427), _1200429)), _1200429)), c_Divides_Odiv__class_Omod(_1200425, _1200427, _1200429)) = _1200427)], (21099 ^ _781404) ^ [_1156039, _1156041, _1156043] : [class_Rings_Oring(_1156039), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156039), hAPP(c_Groups_Ouminus__class_Ouminus(_1156039), _1156041)), _1156043) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156039), _1156041), hAPP(c_Groups_Ouminus__class_Ouminus(_1156039), _1156043)))], (26719 ^ _781404) ^ [_1257903, _1257905, _1257907, _1257909, _1257911] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1257903, _1257905, _1257907), _1257909), _1257911), c_Orderings_Obot__class_Obot(tc_fun(_1257905, tc_HOL_Obool))) = _1257911)], (42070 ^ _781404) ^ [_1609824, _1609826] : [-(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)))), _1609824)) = 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)))), _1609826))), 42072 ^ _781404 : [(42075 ^ _781404) ^ [] : [42076 ^ _781404 : [(42079 ^ _781404) ^ [] : [hBOOL(hAPP(_1609826, 42071 ^ [_1609824, _1609826]))], (42077 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1609824, 42071 ^ [_1609824, _1609826])))]], 42080 ^ _781404 : [(42083 ^ _781404) ^ [] : [hBOOL(hAPP(_1609824, 42071 ^ [_1609824, _1609826]))], (42081 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1609826, 42071 ^ [_1609824, _1609826])))]]], (42073 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 42071 ^ [_1609824, _1609826])))]]], (49243 ^ _781404) ^ [_1773845, _1773847, _1773849] : [-(hAPP(c_List_Oset(_1773845), c_List_Oreplicate(_1773845, hAPP(c_Nat_OSuc, _1773847), _1773849)) = hAPP(hAPP(c_Set_Oinsert(_1773845), _1773849), c_Orderings_Obot__class_Obot(tc_fun(_1773845, tc_HOL_Obool))))], (43917 ^ _781404) ^ [_1657443, _1657445, _1657447, _1657449] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657443)), hAPP(hAPP(c_List_Oappend(_1657443), _1657445), _1657447)), c_List_Olists(_1657443, _1657449))), 43920 ^ _781404 : [(43923 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657443)), _1657447), c_List_Olists(_1657443, _1657449))))], (43921 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657443)), _1657445), c_List_Olists(_1657443, _1657449))))]]], (25847 ^ _781404) ^ [_1243406] : [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, _1243406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1243406)))], (23389 ^ _781404) ^ [_1200897, _1200899] : [-(_1200897 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200899), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1200897), _1200899))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1200897, _1200899)))], (12046 ^ _781404) ^ [_987984, _987986, _987988, _987990, _987992] : [-(hBOOL(hAPP(hAPP(c_member(_987984), _987986), hAPP(c_Set_Oimage(_987988, _987984, _987990), _987992)))), 12047 ^ _781404 : [(12048 ^ _781404) ^ [_988054] : [hBOOL(hAPP(hAPP(c_member(_987988), _988054), _987992)), _987986 = hAPP(_987990, _988054)]]], (12328 ^ _781404) ^ [_993631, _993633, _993635, _993637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993631, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_993631), _993633), _993635)), _993637)), 12331 ^ _781404 : [(12334 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_993631, tc_HOL_Obool)), _993635), _993637)))], (12332 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_993631), _993633), _993637)))]]], (40299 ^ _781404) ^ [_1566554] : [-(_1566554 = hAPP(c_Int_OAbs__Integ, 40297 ^ [_1566554]))], (8112 ^ _781404) ^ [_917407, _917409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _917407), _917409)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _917407), hAPP(c_Nat_OSuc, _917409)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _917409), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _917407), _917409)))], (43729 ^ _781404) ^ [_1652946, _1652948, _1652950] : [hBOOL(hAPP(hAPP(c_member(_1652946), _1652948), hAPP(c_List_Oset(_1652946), _1652950))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652946)), c_List_Oremove1(_1652946, _1652948, _1652950)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652946)), _1652950)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (23593 ^ _781404) ^ [_1205065, _1205067] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205065)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205067)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205065), _1205067))], (4584 ^ _781404) ^ [_851022, _851024] : [_851024 = _851022, -(c_Nat_Osize__class_Osize(_851024) = c_Nat_Osize__class_Osize(_851022))], (21217 ^ _781404) ^ [_1158508, _1158510, _1158512] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158508), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158510), _1158512)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158508), _1158510)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158508), _1158512)))], (37140 ^ _781404) ^ [_1478251, _1478253, _1478255, _1478257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1478251), _1478253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1478255), _1478257)), -(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), _1478251), _1478255)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1478253), _1478257))), c_FunDef_Opair__leq)))], (24933 ^ _781404) ^ [_1228138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228138), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1228138)), c_Int_OMin)))], (20087 ^ _781404) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (13498 ^ _781404) ^ [_1016318] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1016318)), 13502 ^ _781404 : [(13503 ^ _781404) ^ [_1016398] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1016398), _1016318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016398), 13501 ^ [_1016318])))]]], (21645 ^ _781404) ^ [_1166237, _1166239, _1166241, _1166243] : [class_Rings_Olinordered__ring__strict(_1166237), 21648 ^ _781404 : [(21663 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166237), _1166239), _1166241)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166237), _1166239), _1166243)))), 21664 ^ _781404 : [(21671 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166237), _1166239), c_Groups_Ozero__class_Ozero(_1166237))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166237), _1166243), _1166241))], (21665 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166237), c_Groups_Ozero__class_Ozero(_1166237)), _1166239)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166237), _1166241), _1166243))]]], (21649 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166237), _1166239), _1166241)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166237), _1166239), _1166243))), 21654 ^ _781404 : [(21657 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166237), _1166241), _1166243)))], (21655 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166237), c_Groups_Ozero__class_Ozero(_1166237)), _1166239)))]], 21658 ^ _781404 : [(21661 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166237), _1166243), _1166241)))], (21659 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166237), _1166239), c_Groups_Ozero__class_Ozero(_1166237))))]]]]], (12678 ^ _781404) ^ [_1000633, _1000635, _1000637, _1000639] : [hBOOL(hAPP(hAPP(_1000637, _1000639), _1000635)), -(hBOOL(hAPP(hAPP(c_member(_1000633), _1000635), c_SetInterval_Oord_OatLeast(_1000633, _1000637, _1000639))))], (8489 ^ _781404) ^ [_924566, _924568] : [hAPP(c_Set_OPow(_924566), _924568) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_924566, tc_HOL_Obool), tc_HOL_Obool))], (31802 ^ _781404) ^ [_1353585, _1353587] : [_1353585 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1353587, _1353585) = _1353587)], (44409 ^ _781404) ^ [_1669188, _1669190, _1669192] : [hAPP(hAPP(c_List_Odrop(_1669188), _1669190), _1669192) = c_List_Olist_ONil(_1669188), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669188)), _1669192)), _1669190)))], (15050 ^ _781404) ^ [_1046753, _1046755, _1046757, _1046759] : [c_Finite__Set_Ofolding__one(_1046753, _1046755, _1046757), -(hAPP(_1046757, hAPP(hAPP(c_Set_Oinsert(_1046753), _1046759), c_Orderings_Obot__class_Obot(tc_fun(_1046753, tc_HOL_Obool)))) = _1046759)], (42950 ^ _781404) ^ [_1635562, _1635564, _1635566, _1635568] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635562), tc_List_Olist(_1635562))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635562), tc_List_Olist(_1635562)), _1635564), _1635566)), c_List_Olistrel(_1635562, _1635568)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635562)), _1635564) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635562)), _1635566), 42956 ^ _781404 : [(42959 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1635562, _1635562, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1635562, tc_fun(tc_prod(_1635562, _1635562), tc_HOL_Obool), tc_fun(_1635562, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1635562, tc_fun(tc_fun(tc_prod(_1635562, _1635562), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1635562, _1635562), tc_HOL_Obool), tc_fun(_1635562, tc_HOL_Obool)), _1635562), c_COMBC(_1635562, tc_fun(tc_prod(_1635562, _1635562), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1635562, tc_prod(_1635562, _1635562)), tc_fun(_1635562, tc_fun(tc_fun(tc_prod(_1635562, _1635562), tc_HOL_Obool), tc_HOL_Obool)), _1635562), hAPP(c_COMBB(tc_prod(_1635562, _1635562), tc_fun(tc_fun(tc_prod(_1635562, _1635562), tc_HOL_Obool), tc_HOL_Obool), _1635562), c_member(tc_prod(_1635562, _1635562)))), c_Product__Type_OPair(_1635562, _1635562)))), _1635568)), 42955 ^ [_1635562, _1635564, _1635566, _1635568]))], (42957 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635562, _1635562)), 42955 ^ [_1635562, _1635564, _1635566, _1635568]), hAPP(c_List_Oset(tc_prod(_1635562, _1635562)), hAPP(hAPP(c_List_Ozip(_1635562, _1635562), _1635564), _1635566)))))]]], (33155 ^ _781404) ^ [_1380116, _1380118, _1380120, _1380122, _1380124] : [c_Finite__Set_Ofun__left__comm__idem(_1380116, _1380118, _1380120), -(c_Finite__Set_Ofun__left__comm__idem(_1380122, _1380118, hAPP(hAPP(c_COMBB(_1380116, tc_fun(_1380118, _1380118), _1380122), _1380120), _1380124)))], (23423 ^ _781404) ^ [_1201640, _1201642] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1201640, _1201642) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1201640), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1201640), _1201642)), _1201642)))], (36486 ^ _781404) ^ [_1463243, _1463245, _1463247, _1463249] : [hAPP(c_Product__Type_Ofst(_1463243, _1463245), _1463247) = hAPP(c_Product__Type_Ofst(_1463243, _1463245), _1463249), hAPP(c_Product__Type_Osnd(_1463243, _1463245), _1463247) = hAPP(c_Product__Type_Osnd(_1463243, _1463245), _1463249), -(_1463247 = _1463249)], (43687 ^ _781404) ^ [_1652117, _1652119, _1652121] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1652117)), -(c_List_Osublist(_1652119, hAPP(hAPP(c_List_Olist_OCons(_1652119), _1652121), c_List_Olist_ONil(_1652119)), _1652117) = hAPP(hAPP(c_List_Olist_OCons(_1652119), _1652121), c_List_Olist_ONil(_1652119)))], (36215 ^ _781404) ^ [_1457431, _1457433, _1457435, _1457437, _1457439] : [hAPP(c_Product__Type_Osnd(_1457431, _1457433), hAPP(hAPP(c_Product__Type_OPair(_1457431, _1457433), _1457435), _1457437)) = _1457439, -(_1457437 = _1457439)], (35686 ^ _781404) ^ [_1447285, _1447287] : [_1447285 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1447285, _1447287) = 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)))], (44794 ^ _781404) ^ [_1677514, _1677516, _1677518] : [class_Lattices_Olattice(_1677514), -(c_Big__Operators_Olattice__class_OInf__fin(_1677514, hAPP(c_List_Oset(_1677514), hAPP(hAPP(c_List_Olist_OCons(_1677514), _1677516), _1677518))) = hAPP(c_List_Ofoldl(_1677514, _1677514, c_Lattices_Osemilattice__inf__class_Oinf(_1677514), _1677516), _1677518))], (52314 ^ _781404) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (17747 ^ _781404) ^ [_1097828, _1097830] : [class_Complete__Lattice_Ocomplete__lattice(_1097828), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097828), _1097830)), -(c_Complete__Lattice_OInf__class_OInf(_1097828, _1097830) = hAPP(hAPP(c_Finite__Set_Ofold(_1097828, _1097828, c_Lattices_Osemilattice__inf__class_Oinf(_1097828)), c_Orderings_Otop__class_Otop(_1097828)), _1097830))], (42697 ^ _781404) ^ [_1628526, _1628528, _1628530, _1628532] : [_1628526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1628528), hAPP(hAPP(c_List_Olist_OCons(_1628528), _1628530), _1628532)), _1628526) = _1628530)], (28801 ^ _781404) ^ [_1296892, _1296894, _1296896, _1296898, _1296900] : [class_Fields_Ofield__inverse__zero(_1296892), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296892), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296892), _1296894), _1296896)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296892), _1296898), _1296900)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296892), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296892), _1296894), _1296898)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296892), _1296896), _1296900)))], (40887 ^ _781404) ^ [_1579375, _1579377, _1579379, _1579381, _1579383] : [_1579375 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1579377, tc_HOL_Obool), _1579379), c_Orderings_Oorder__class_Omono(tc_fun(_1579377, tc_HOL_Obool), tc_fun(_1579377, tc_HOL_Obool), _1579379), hBOOL(hAPP(hAPP(c_member(_1579377), _1579381), _1579375)), 40901 ^ _781404 : [(40904 ^ _781404) ^ [] : [hBOOL(hAPP(_1579383, 40900 ^ [_1579375, _1579377, _1579379, _1579381, _1579383]))], (40902 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1579377), 40900 ^ [_1579375, _1579377, _1579379, _1579381, _1579383]), hAPP(_1579379, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1579377, tc_HOL_Obool)), _1579375), hAPP(c_Set_OCollect(_1579377), _1579383))))))]], -(hBOOL(hAPP(_1579383, _1579381)))], (17961 ^ _781404) ^ [_1101692, _1101694] : [class_Groups_Omonoid__mult(_1101692), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1101692), _1101694), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1101694)], (23427 ^ _781404) ^ [_1201734, _1201736, _1201738, _1201740] : [class_Divides_Osemiring__div(_1201734), -(c_Divides_Odiv__class_Omod(_1201734, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201734), _1201736), _1201738), _1201740) = c_Divides_Odiv__class_Omod(_1201734, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201734), _1201736), c_Divides_Odiv__class_Omod(_1201734, _1201738, _1201740)), _1201740))], (33639 ^ _781404) ^ [_1394756, _1394758, _1394760, _1394762, _1394764, _1394766] : [class_Complete__Lattice_Ocomplete__lattice(_1394756), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394758, tc_fun(_1394760, _1394756)), _1394762), _1394764), _1394766) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394758, _1394756), _1394762), hAPP(hAPP(c_COMBC(_1394758, _1394760, _1394756), _1394764), _1394766)))], (40473 ^ _781404) ^ [_1569921, _1569923] : [40474 ^ _781404 : [(40475 ^ _781404) ^ [_1569967] : [hBOOL(hAPP(_1569921, _1569967))]], -(hBOOL(hAPP(_1569921, c_Hilbert__Choice_OEps(_1569923, _1569921))))], (42400 ^ _781404) ^ [_1619940, _1619942, _1619944, _1619946, _1619948, _1619950] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619940), tc_List_Olist(_1619940))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619940), tc_List_Olist(_1619940)), hAPP(hAPP(c_List_Olist_OCons(_1619940), _1619942), _1619944)), hAPP(hAPP(c_List_Olist_OCons(_1619940), _1619946), _1619948))), c_List_Olistrel1(_1619940, _1619950))), 42405 ^ _781404 : [(42408 ^ _781404) ^ [] : [-(_1619944 = _1619948)], (42406 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619940, _1619940)), hAPP(hAPP(c_Product__Type_OPair(_1619940, _1619940), _1619942), _1619946)), _1619950)))]], 42409 ^ _781404 : [(42412 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619940), tc_List_Olist(_1619940))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619940), tc_List_Olist(_1619940)), _1619944), _1619948)), c_List_Olistrel1(_1619940, _1619950))))], (42410 ^ _781404) ^ [] : [-(_1619942 = _1619946)]]], (43328 ^ _781404) ^ [_1644973, _1644975] : [hBOOL(hAPP(c_List_Odistinct(_1644973), _1644975)), -(hAPP(c_Finite__Set_Ocard(_1644973), hAPP(c_List_Oset(_1644973), _1644975)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644973)), _1644975))], (41049 ^ _781404) ^ [_1583390, _1583392, _1583394] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583390, _1583390)), _1583392), _1583394)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583390, _1583390)), _1583392), c_Transitive__Closure_Otrancl(_1583390, _1583394))))], (23433 ^ _781404) ^ [_1201869, _1201871, _1201873, _1201875] : [class_Divides_Osemiring__div(_1201869), -(c_Divides_Odiv__class_Omod(_1201869, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201869), _1201871), _1201873), _1201875) = c_Divides_Odiv__class_Omod(_1201869, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201869), c_Divides_Odiv__class_Omod(_1201869, _1201871, _1201875)), _1201873), _1201875))], (44852 ^ _781404) ^ [_1678879, _1678881, _1678883] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1678879), tc_List_Olist(_1678879))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678879), tc_List_Olist(_1678879)), c_List_Olist_ONil(_1678879)), _1678881)), c_List_Olexord(_1678879, _1678883))), -(_1678881 = hAPP(hAPP(c_List_Olist_OCons(_1678879), 44855 ^ [_1678879, _1678881, _1678883]), 44856 ^ [_1678879, _1678881, _1678883]))], (50477 ^ _781404) ^ [_1801012, _1801014, _1801016, _1801018, _1801020] : [c_Fun_Oinj__on(_1801012, _1801014, _1801016, c_Orderings_Otop__class_Otop(tc_fun(_1801012, tc_HOL_Obool))), hAPP(_1801016, _1801018) = _1801020, -(hAPP(c_Hilbert__Choice_Oinv__into(_1801012, _1801014, c_Orderings_Otop__class_Otop(tc_fun(_1801012, tc_HOL_Obool)), _1801016), _1801020) = _1801018)], (9158 ^ _781404) ^ [_937102, _937104] : [class_Groups_Ogroup__add(_937102), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937102), c_Groups_Ozero__class_Ozero(_937102)), _937104) = hAPP(c_Groups_Ouminus__class_Ouminus(_937102), _937104))], (38349 ^ _781404) ^ [_1508987, _1508989, _1508991, _1508993, _1508995, _1508997, _1508999] : [c_Typedef_Otype__definition(_1508987, _1508989, _1508991, _1508993, _1508995), 38352 ^ _781404 : [(38359 ^ _781404) ^ [] : [_1508997 = _1508999, -(hAPP(_1508991, _1508997) = hAPP(_1508991, _1508999))], (38353 ^ _781404) ^ [] : [hAPP(_1508991, _1508997) = hAPP(_1508991, _1508999), -(_1508997 = _1508999)]]], (39155 ^ _781404) ^ [_1530691, _1530693, _1530695, _1530697] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1530691, tc_fun(_1530693, tc_HOL_Obool)), _1530695), _1530697) = hAPP(c_Set_OCollect(_1530693), hAPP(hAPP(c_COMBB(tc_fun(_1530691, tc_HOL_Obool), tc_HOL_Obool, _1530693), c_HOL_OAll(_1530691)), hAPP(hAPP(c_COMBB(tc_fun(_1530691, tc_HOL_Obool), tc_fun(_1530691, tc_HOL_Obool), _1530693), hAPP(c_COMBS(_1530691, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1530691), c_fimplies), hAPP(hAPP(c_COMBC(_1530691, tc_fun(_1530691, tc_HOL_Obool), tc_HOL_Obool), c_member(_1530691)), _1530695)))), hAPP(hAPP(c_COMBC(_1530693, tc_fun(_1530691, tc_fun(_1530693, tc_HOL_Obool)), tc_fun(_1530691, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1530693, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1530691, tc_fun(_1530693, tc_HOL_Obool)), tc_fun(_1530691, tc_HOL_Obool)), _1530693), c_COMBB(tc_fun(_1530693, tc_HOL_Obool), tc_HOL_Obool, _1530691)), c_member(_1530693))), _1530697)))))], (21755 ^ _781404) ^ [_1168244, _1168246, _1168248] : [class_Rings_Olinordered__semiring__strict(_1168244), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168244), c_Groups_Ozero__class_Ozero(_1168244)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168244), _1168246), _1168248))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168244), c_Groups_Ozero__class_Ozero(_1168244)), _1168248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168244), c_Groups_Ozero__class_Ozero(_1168244)), _1168246)))], (19073 ^ _781404) ^ [_1120817, _1120819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1120817)), c_Int_OBit1(_1120819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120817), _1120819)))], (38550 ^ _781404) ^ [_1513699, _1513701, _1513703] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1513699, _1513701), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1513699, _1513701), c_Orderings_Otop__class_Otop(tc_fun(_1513699, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1513701, tc_HOL_Obool), _1513699), _1513703))) = hAPP(hAPP(c_Product__Type_OSigma(_1513699, _1513701), c_Orderings_Otop__class_Otop(tc_fun(_1513699, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1513701, tc_HOL_Obool), _1513699), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1513701, tc_HOL_Obool)), _1513703))))], (52682 ^ _781404) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (34945 ^ _781404) ^ [_1431486, _1431488] : [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(_1431486))), 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)), _1431488)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431486)), hAPP(c_Nat_OSuc, _1431488))))], (8140 ^ _781404) ^ [_917964, _917966, _917968] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917964, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_917964, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_917964, tc_HOL_Obool), tc_HOL_Obool)), _917966), _917968))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_917964, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_917964, tc_HOL_Obool), _917966)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_917964, tc_HOL_Obool), _917968)))))], (33488 ^ _781404) ^ [_1390336, _1390338, _1390340] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390336, tc_fun(_1390338, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1390336, tc_HOL_Obool))), _1390340) = c_Orderings_Otop__class_Otop(tc_fun(_1390338, tc_HOL_Obool)))], (38882 ^ _781404) ^ [_1523307, _1523309, _1523311] : [-(hAPP(c_Product__Type_Omap__pair(_1523307, _1523307, _1523309, _1523309, c_COMBI(_1523307), c_COMBI(_1523309)), _1523311) = _1523311)], (40801 ^ _781404) ^ [_1577294, _1577296] : [class_Complete__Lattice_Ocomplete__lattice(_1577294), c_Orderings_Oorder__class_Omono(_1577294, _1577294, _1577296), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1577294, _1577296) = hAPP(_1577296, c_Inductive_Ocomplete__lattice__class_Olfp(_1577294, _1577296)))], (44070 ^ _781404) ^ [_1660790, _1660792, _1660794] : [_1660790 = hAPP(hAPP(c_List_Oappend(_1660792), _1660794), _1660790), -(_1660794 = c_List_Olist_ONil(_1660792))], (25885 ^ _781404) ^ [_1244040, _1244042] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244040, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1244042)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244040, 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)))), _1244042)))], (19857 ^ _781404) ^ [_1134111, _1134113, _1134115] : [-(hBOOL(hAPP(_1134111, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1134113), _1134115))))), 19860 ^ _781404 : [(19863 ^ _781404) ^ [] : [hBOOL(hAPP(_1134111, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134113)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1134115))))], (19861 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1134115), _1134113)))]], 19864 ^ _781404 : [(19867 ^ _781404) ^ [] : [hBOOL(hAPP(_1134111, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (19865 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1134113), _1134115)))]]], (44653 ^ _781404) ^ [_1674572] : [-(hAPP(c_List_Otl(_1674572), c_List_Olist_ONil(_1674572)) = c_List_Olist_ONil(_1674572))], (44210 ^ _781404) ^ [_1663950, _1663952, _1663954, _1663956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663952)), _1663954))), -(hAPP(hAPP(c_List_Onth(_1663952), hAPP(hAPP(c_List_Oappend(_1663952), _1663954), _1663956)), _1663950) = hAPP(hAPP(c_List_Onth(_1663952), _1663954), _1663950))], (45170 ^ _781404) ^ [_1684687, _1684689, _1684691, _1684693] : [-(_1684687 = c_List_Olist_ONil(_1684689)), -(c_List_Olast(_1684691, hAPP(hAPP(c_List_Omap(_1684689, _1684691), _1684693), _1684687)) = hAPP(_1684693, c_List_Olast(_1684689, _1684687)))], (17943 ^ _781404) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (15044 ^ _781404) ^ [_1046644, _1046646, _1046648] : [class_Rings_Ocomm__semiring__1(_1046644), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046644), _1046646), _1046648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046644), _1046648), _1046646))], (5392 ^ _781404) ^ [_863780, _863782] : [_863782 = _863780, -(c_Groups_Ominus__class_Ominus(_863782) = c_Groups_Ominus__class_Ominus(_863780))], (32008 ^ _781404) ^ [_1357589, _1357591, _1357593, _1357595] : [class_Groups_Oordered__ab__group__add(_1357589), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357589), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357589), _1357591), _1357593)), _1357595) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357589), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357589), _1357591), _1357595)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357589), _1357593), _1357595)))], (44449 ^ _781404) ^ [_1670143, _1670145, _1670147, _1670149] : [-(_1670143 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1670145), _1670143), hAPP(hAPP(c_List_Olist_OCons(_1670145), _1670147), _1670149)) = hAPP(hAPP(c_List_Odrop(_1670145), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1670143), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1670149))], (33741 ^ _781404) ^ [_1397063, _1397065, _1397067, _1397069, _1397071] : [33743 ^ _781404 : [(33746 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1397063), _1397065), hAPP(_1397071, 33742 ^ [_1397063, _1397065, _1397067, _1397069, _1397071])))], (33744 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1397067), 33742 ^ [_1397063, _1397065, _1397067, _1397069, _1397071]), _1397069)))]], -(hBOOL(hAPP(hAPP(c_member(_1397063), _1397065), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397067, tc_fun(_1397063, tc_HOL_Obool)), _1397069), _1397071))))], (38723 ^ _781404) ^ [_1518389, _1518391, _1518393, _1518395, _1518397, _1518399] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518389, _1518391), hAPP(hAPP(c_Set_Oinsert(_1518389), _1518393), _1518395)), hAPP(c_COMBK(tc_fun(_1518391, tc_HOL_Obool), _1518389), hAPP(hAPP(c_Set_Oinsert(_1518391), _1518397), _1518399))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1518389, _1518391)), hAPP(hAPP(c_Product__Type_OPair(_1518389, _1518391), _1518393), _1518397)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518389, _1518391), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518389, _1518391), _1518395), hAPP(c_COMBK(tc_fun(_1518391, tc_HOL_Obool), _1518389), hAPP(hAPP(c_Set_Oinsert(_1518391), _1518397), _1518399)))), hAPP(hAPP(c_Product__Type_OSigma(_1518389, _1518391), hAPP(hAPP(c_Set_Oinsert(_1518389), _1518393), _1518395)), hAPP(c_COMBK(tc_fun(_1518391, tc_HOL_Obool), _1518389), _1518399)))))], (11587 ^ _781404) ^ [_979620, _979622, _979624, _979626] : [hBOOL(hAPP(hAPP(c_member(_979620), _979622), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979620, tc_HOL_Obool)), _979624), _979626))), 11590 ^ _781404 : [(11593 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_979620), _979622), _979626)))], (11591 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_979620), _979622), _979624)))]]], (7601 ^ _781404) ^ [_906139, _906141, _906143, _906145] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_906139, tc_HOL_Obool)), _906141), _906143), _906145)), -(hBOOL(hAPP(_906141, _906145)))], (19305 ^ _781404) ^ [_1124758, _1124760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124758), _1124760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124758)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124760))))], (8026 ^ _781404) ^ [_915483, _915485, _915487, _915489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915483, tc_HOL_Obool)), _915489), _915485)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915483, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915483, tc_HOL_Obool)), _915485), _915487)), _915489) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915483, tc_HOL_Obool)), _915485), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915483, tc_HOL_Obool)), _915487), _915489)))], (1130 ^ _781404) ^ [_798449, _798451, _798453, _798455, _798457, _798459, _798461, _798463, _798465, _798467] : [-(c_Finite__Set_Ofolding__image(_798465, _798461, _798457, _798453, _798449)), c_Finite__Set_Ofolding__image(_798467, _798463, _798459, _798455, _798451), _798467 = _798465, _798463 = _798461, _798459 = _798457, _798455 = _798453, _798451 = _798449], (30049 ^ _781404) ^ [_1320224, _1320226, _1320228, _1320230] : [class_Groups_Ocomm__monoid__mult(_1320224), 30052 ^ _781404 : [(30059 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1320226), _1320228))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1320226, _1320224), _1320230), _1320228) = c_Groups_Oone__class_Oone(_1320224))], (30053 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1320226), _1320228)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1320226, _1320224), _1320230), _1320228) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1320224, _1320226, c_Groups_Otimes__class_Otimes(_1320224)), _1320230), c_Groups_Oone__class_Oone(_1320224)), _1320228))]]], (39912 ^ _781404) ^ [_1557265, _1557267, _1557269] : [c_Wellfounded_Owf(_1557265, _1557267), -(c_Wellfounded_Owf(_1557265, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1557265, _1557265), tc_HOL_Obool)), _1557269), _1557267)))], (40285 ^ _781404) ^ [_1566091, _1566093, _1566095, _1566097] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1566091), _1566093))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566095), hAPP(c_Set_Oimage(_1566091, _1566095, _1566097), _1566093))), 40293 ^ _781404 : [(40296 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1566091), hAPP(c_Set_OCollect(_1566091), hAPP(hAPP(c_COMBS(_1566091, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566091), c_fconj), hAPP(hAPP(c_COMBC(_1566091, tc_fun(_1566091, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566091)), _1566093))), hAPP(hAPP(c_COMBC(_1566091, _1566095, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1566095, tc_fun(_1566095, tc_HOL_Obool), _1566091), c_fequal), _1566097)), hAPP(_1566097, 40292 ^ [_1566091, _1566093, _1566095, _1566097]))))))], (40294 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566091), 40292 ^ [_1566091, _1566093, _1566095, _1566097]), _1566093)))]]], (21391 ^ _781404) ^ [_1161612, _1161614, _1161616, _1161618] : [class_Rings_Oordered__ring(_1161612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161612), _1161614), _1161616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161612), _1161618), c_Groups_Ozero__class_Ozero(_1161612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161612), _1161618), _1161616)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161612), _1161618), _1161614))))], (22357 ^ _781404) ^ [_1180060, _1180062, _1180064, _1180066] : [class_Rings_Olinordered__semiring(_1180060), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180060), _1180062), _1180064)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180060), _1180066), _1180064))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180060), c_Groups_Ozero__class_Ozero(_1180060)), _1180064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180060), _1180062), _1180066)))], (44002 ^ _781404) ^ [_1659364, _1659366, _1659368] : [class_Groups_Omonoid__add(_1659364), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1659364), hAPP(hAPP(c_List_Oappend(_1659364), _1659366), _1659368)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1659364), hAPP(c_List_Omonoid__add__class_Olistsum(_1659364), _1659366)), hAPP(c_List_Omonoid__add__class_Olistsum(_1659364), _1659368)))], (19737 ^ _781404) ^ [_1132076, _1132078] : [class_Int_Onumber__ring(_1132076), class_Rings_Olinordered__idom(_1132076), 19744 ^ _781404 : [(19751 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1132078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132076), c_Groups_Oone__class_Oone(_1132076)), hAPP(c_Int_Onumber__class_Onumber__of(_1132076), _1132078))))], (19745 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132076), c_Groups_Oone__class_Oone(_1132076)), hAPP(c_Int_Onumber__class_Onumber__of(_1132076), _1132078))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1132078)))]]], (39538 ^ _781404) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (10277 ^ _781404) ^ [_956141, _956143, _956145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956141), _956143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956145), _956143)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956145), _956141))))], (39692 ^ _781404) ^ [_1550712, _1550714, _1550716, _1550718] : [hBOOL(hAPP(hAPP(c_member(_1550712), _1550714), hAPP(c_Relation_ORange(_1550716, _1550712), _1550718))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1550716, _1550712)), hAPP(hAPP(c_Product__Type_OPair(_1550716, _1550712), 39695 ^ [_1550712, _1550714, _1550716, _1550718]), _1550714)), _1550718)))], (46714 ^ _781404) ^ [_1721172, _1721174] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1721172))), c_List_Otranspose(_1721172, _1721174)) = c_List_Ofoldr(tc_List_Olist(_1721172), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1721172)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1721172))), _1721174, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44010 ^ _781404) ^ [_1659565, _1659567, _1659569, _1659571, _1659573, _1659575] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659565)), _1659567) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659569)), _1659571), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659565)), _1659573) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659569)), _1659575), -(hAPP(hAPP(c_List_Ozip(_1659565, _1659569), hAPP(hAPP(c_List_Oappend(_1659565), _1659567), _1659573)), hAPP(hAPP(c_List_Oappend(_1659569), _1659571), _1659575)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1659565, _1659569)), hAPP(hAPP(c_List_Ozip(_1659565, _1659569), _1659567), _1659571)), hAPP(hAPP(c_List_Ozip(_1659565, _1659569), _1659573), _1659575)))], (18333 ^ _781404) ^ [_1108032, _1108034, _1108036, _1108038, _1108040, _1108042] : [c_Finite__Set_Ofun__left__comm(_1108032, _1108034, _1108036), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108032), _1108038)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1108032, _1108034, _1108036), _1108040), hAPP(hAPP(c_Set_Oinsert(_1108032), _1108042), _1108038)) = hAPP(hAPP(_1108036, _1108042), hAPP(hAPP(c_Finite__Set_Ofold(_1108032, _1108034, _1108036), _1108040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108032, tc_HOL_Obool)), _1108038), hAPP(hAPP(c_Set_Oinsert(_1108032), _1108042), c_Orderings_Obot__class_Obot(tc_fun(_1108032, tc_HOL_Obool)))))))], (11279 ^ _781404) ^ [_972904, _972906, _972908, _972910, _972912, _972914] : [c_Fun_Oinj__on(_972904, _972906, _972908, _972910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972904, tc_HOL_Obool)), _972912), _972910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972904, tc_HOL_Obool)), _972914), _972910)), -(hAPP(c_Set_Oimage(_972904, _972906, _972908), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972904, tc_HOL_Obool)), _972912), _972914)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972906, tc_HOL_Obool)), hAPP(c_Set_Oimage(_972904, _972906, _972908), _972912)), hAPP(c_Set_Oimage(_972904, _972906, _972908), _972914)))], (19715 ^ _781404) ^ [_1131733] : [-(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, _1131733)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32938 ^ _781404) ^ [_1375053, _1375055, _1375057] : [class_Fields_Olinordered__field(_1375053), 32944 ^ _781404 : [(32947 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375053), _1375055), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1375053), _1375057), 32943 ^ [_1375053, _1375055, _1375057])))], (32945 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1375053), c_Groups_Ozero__class_Ozero(_1375053)), 32943 ^ [_1375053, _1375055, _1375057])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375053), _1375055), _1375057)))], (13067 ^ _781404) ^ [_1008174, _1008176, _1008178, _1008180] : [class_Groups_Oordered__ab__semigroup__add(_1008174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008174), _1008176), _1008178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008174), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008174), _1008180), _1008176)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008174), _1008180), _1008178))))], (14262 ^ _781404) ^ [_1030529, _1030531, _1030533] : [hBOOL(hAPP(_1030529, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030531), _1030533))), 14265 ^ _781404 : [(14272 ^ _781404) ^ [_1030720] : [_1030531 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030533), _1030720), -(hBOOL(hAPP(_1030529, _1030720)))], (14266 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030531), _1030533)), -(hBOOL(hAPP(_1030529, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (39789 ^ _781404) ^ [_1554967, _1554969, _1554971, _1554973] : [hBOOL(hAPP(c_Predicate_ORangeP(_1554967, _1554969, _1554971), _1554973)), -(hBOOL(hAPP(hAPP(_1554971, 39792 ^ [_1554967, _1554969, _1554971, _1554973]), _1554973)))], (36163 ^ _781404) ^ [_1456392, _1456394, _1456396, _1456398] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1456392, _1456394), _1456396)), hBOOL(hAPP(hAPP(_1456394, _1456398), _1456396)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1456392, _1456394), _1456398)))], (34321 ^ _781404) ^ [_1416488, _1416490, _1416492, _1416494, _1416496] : [-(_1416488 = c_Orderings_Obot__class_Obot(tc_fun(_1416490, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1416492, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416490, tc_fun(_1416492, tc_HOL_Obool)), _1416488), _1416494)), _1416496) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416490, tc_fun(_1416492, tc_HOL_Obool)), _1416488), hAPP(hAPP(c_COMBC(_1416490, tc_fun(_1416492, tc_HOL_Obool), tc_fun(_1416492, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1416492, tc_HOL_Obool), tc_fun(tc_fun(_1416492, tc_HOL_Obool), tc_fun(_1416492, tc_HOL_Obool)), _1416490), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1416492, tc_HOL_Obool))), _1416494)), _1416496)))], (14887 ^ _781404) ^ [_1042861, _1042863, _1042865, _1042867, _1042869] : [class_Groups_Oordered__comm__monoid__add(_1042861), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042863), _1042865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1042863, tc_HOL_Obool)), _1042867), _1042865)), 14901 ^ _781404 : [(14904 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042861), c_Groups_Ozero__class_Ozero(_1042861)), hAPP(_1042869, 14900 ^ [_1042861, _1042863, _1042865, _1042867, _1042869])))], (14902 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1042863), 14900 ^ [_1042861, _1042863, _1042865, _1042867, _1042869]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042863, tc_HOL_Obool)), _1042865), _1042867))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042861), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042863, _1042861), _1042869), _1042867)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1042863, _1042861), _1042869), _1042865))))], (3546 ^ _781404) ^ [_834417, _834419] : [_834419 = _834417, -(c_Int_Onumber__class_Onumber__of(_834419) = c_Int_Onumber__class_Onumber__of(_834417))], (48759 ^ _781404) ^ [_1763574, _1763576, _1763578, _1763580] : [-(c_List_Olist__all(_1763574, _1763576, hAPP(hAPP(c_List_Olist_OCons(_1763574), _1763578), _1763580))), hBOOL(hAPP(_1763576, _1763578)), c_List_Olist__all(_1763574, _1763576, _1763580)], (15038 ^ _781404) ^ [_1046501, _1046503, _1046505, _1046507] : [class_Rings_Ocomm__semiring__1(_1046501), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046501), _1046503), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046501), _1046505), _1046507)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046501), _1046505), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046501), _1046503), _1046507)))], (210 ^ _781404) ^ [_784737, _784739, _784741, _784743, _784745, _784747] : [-(c_Big__Operators_Osemilattice__big(_784745, _784741, _784737)), c_Big__Operators_Osemilattice__big(_784747, _784743, _784739), _784747 = _784745, _784743 = _784741, _784739 = _784737], (39764 ^ _781404) ^ [_1554401, _1554403, _1554405, _1554407, _1554409] : [hBOOL(hAPP(hAPP(_1554401, _1554403), _1554405)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1554407, _1554409, _1554401), _1554405)))], (35502 ^ _781404) ^ [_1443833, _1443835, _1443837, _1443839, _1443841, _1443843] : [-(hAPP(hAPP(c_Product__Type_OPair(_1443833, _1443835), _1443837), _1443839) = hAPP(hAPP(c_Product__Type_OPair(_1443833, _1443835), _1443841), _1443843)), _1443837 = _1443841, _1443839 = _1443843], (24720 ^ _781404) ^ [_1224785, _1224787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224785)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224787)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1224785)), hAPP(c_Int_Onat, _1224787)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1224785), _1224787)))], (49856 ^ _781404) ^ [_1788183, _1788185, _1788187, _1788189] : [class_Complete__Lattice_Ocomplete__lattice(_1788183), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1788185, _1788183), _1788187), _1788189) = c_Complete__Lattice_OSup__class_OSup(_1788183, hAPP(c_Set_OCollect(_1788183), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1788185, _1788183), tc_HOL_Obool), tc_HOL_Obool, _1788183), c_HOL_OEx(tc_fun(_1788185, _1788183))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1788185, _1788183), tc_HOL_Obool), tc_fun(tc_fun(_1788185, _1788183), tc_HOL_Obool), _1788183), hAPP(c_COMBS(tc_fun(_1788185, _1788183), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1788185, _1788183)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1788185, _1788183), tc_fun(tc_fun(_1788185, _1788183), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1788185, _1788183))), _1788187)))), hAPP(hAPP(c_COMBC(_1788183, tc_fun(tc_fun(_1788185, _1788183), _1788183), tc_fun(tc_fun(_1788185, _1788183), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788183, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1788185, _1788183), _1788183), tc_fun(tc_fun(_1788185, _1788183), tc_HOL_Obool)), _1788183), c_COMBB(_1788183, tc_HOL_Obool, tc_fun(_1788185, _1788183))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1788185, _1788183), _1788185, _1788183), c_COMBI(tc_fun(_1788185, _1788183))), _1788189)))))))], (11519 ^ _781404) ^ [_978354, _978356, _978358, _978360] : [hBOOL(hAPP(hAPP(c_member(_978354), _978356), hAPP(hAPP(c_Set_Oinsert(_978354), _978358), _978360))), -(_978356 = _978358), -(hBOOL(hAPP(hAPP(c_member(_978354), _978356), _978360)))], (24951 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (6767 ^ _781404) ^ [_889852, _889854, _889856] : [class_Orderings_Olinorder(_889852), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889852), _889854), _889856)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889852, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_889852), _889854)), c_SetInterval_Oord__class_OatLeastAtMost(_889852, _889854, _889856)) = hAPP(c_SetInterval_Oord__class_OatMost(_889852), _889856))], (23719 ^ _781404) ^ [_1207400, _1207402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1207400), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23722 ^ _781404 : [(23729 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1207402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1207402), _1207400)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23723 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1207402), _1207400)), 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)), _1207402)))]]], (50059 ^ _781404) ^ [_1793057] : [-(c_Relation_Oantisym(_1793057, c_Relation_OId(_1793057)))], (37888 ^ _781404) ^ [_1497158, _1497160, _1497162, _1497164, _1497166, _1497168] : [c_Equiv__Relations_Oequiv(_1497158, _1497160, _1497162), c_Equiv__Relations_Ocongruent(_1497158, tc_fun(_1497164, tc_HOL_Obool), _1497162, _1497166), hBOOL(hAPP(hAPP(c_member(_1497158), _1497168), _1497160)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1497158, tc_fun(_1497164, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1497158, _1497158, _1497162), hAPP(hAPP(c_Set_Oinsert(_1497158), _1497168), c_Orderings_Obot__class_Obot(tc_fun(_1497158, tc_HOL_Obool))))), _1497166) = hAPP(_1497166, _1497168))], (44583 ^ _781404) ^ [_1673415, _1673417] : [-(_1673415 = c_List_Olist_ONil(_1673417)), -(hBOOL(hAPP(hAPP(c_member(_1673417), hAPP(c_List_Ohd(_1673417), _1673415)), hAPP(c_List_Oset(_1673417), _1673415))))], (9230 ^ _781404) ^ [_939031, _939033, _939035] : [class_Orderings_Oorder(_939031), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939031), _939033), _939035)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_939031, _939035, _939033) = c_Orderings_Obot__class_Obot(tc_fun(_939031, tc_HOL_Obool)))], (30954 ^ _781404) ^ [_1337915, _1337917, _1337919, _1337921] : [class_Orderings_Olinorder(_1337915), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337915, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1337915, _1337917, _1337919)), hAPP(c_SetInterval_Oord__class_OatMost(_1337915), _1337921)) = c_SetInterval_Oord__class_OatLeastAtMost(_1337915, _1337917, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1337915), _1337919), _1337921)))], (25067 ^ _781404) ^ [_1230130, _1230132] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1230130)))), 25070 ^ _781404 : [(25077 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1230132)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1230130), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1230132)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1230130), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1230132))))], (25071 ^ _781404) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1230132))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1230130), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1230132)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1230130))]]], (7886 ^ _781404) ^ [_911939, _911941, _911943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911939, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911939, tc_HOL_Obool)), _911941), _911943)), _911943)))], (44866 ^ _781404) ^ [_1679246, _1679248, _1679250, _1679252] : [class_Orderings_Olinorder(_1679246), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679248, _1679246, _1679250), _1679252), c_List_Olist_ONil(_1679248)) = hAPP(hAPP(c_List_Olist_OCons(_1679248), _1679252), c_List_Olist_ONil(_1679248)))], (32744 ^ _781404) ^ [_1371225, _1371227, _1371229] : [class_Orderings_Olinorder(_1371225), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371225), _1371227)), -(hBOOL(hAPP(hAPP(c_member(_1371225), _1371229), _1371227))), -(_1371227 = c_Orderings_Obot__class_Obot(tc_fun(_1371225, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1371225, c_Orderings_Oord__class_Omax(_1371225), hAPP(hAPP(c_Set_Oinsert(_1371225), _1371229), _1371227)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371225), _1371229), c_Big__Operators_Olattice_OSup__fin(_1371225, c_Orderings_Oord__class_Omax(_1371225), _1371227)))], (41020 ^ _781404) ^ [_1582840, _1582842] : [c_Wellfounded_Owf(_1582840, _1582842), -(c_Wellfounded_Owf(_1582840, c_Transitive__Closure_Otrancl(_1582840, _1582842)))], (12564 ^ _781404) ^ [_998392, _998394, _998396, _998398, _998400] : [hAPP(c_Set_Oimage(_998392, _998394, _998396), c_Orderings_Otop__class_Otop(tc_fun(_998392, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_998394, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998392, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_998392, _998394, _998396), _998398)), _998400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998394, tc_HOL_Obool)), _998398), hAPP(c_Set_Oimage(_998392, _998394, _998396), _998400))))], (6506 ^ _781404) ^ [_885070, _885072, _885074, _885076, _885078] : [class_Orderings_Olinorder(_885070), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885070, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_885070, _885072), _885074)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_885070, _885076), _885078))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885070), _885074), _885072))), 6517 ^ _781404 : [(6520 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885070), _885074), _885078)))], (6518 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885070), _885076), _885072)))]]], (16752 ^ _781404) ^ [_1079585, _1079587, _1079589, _1079591] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1079585), _1079587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1079585, tc_HOL_Obool)), _1079587), _1079589)), hBOOL(hAPP(_1079591, c_Orderings_Obot__class_Obot(tc_fun(_1079585, tc_HOL_Obool)))), 16767 ^ _781404 : [(16768 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1079585), 16766 ^ [_1079585, _1079587, _1079589, _1079591])))], (16772 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1079585), 16765 ^ [_1079585, _1079587, _1079589, _1079591]), 16766 ^ [_1079585, _1079587, _1079589, _1079591]))], (16776 ^ _781404) ^ [] : [hBOOL(hAPP(_1079591, hAPP(hAPP(c_Set_Oinsert(_1079585), 16765 ^ [_1079585, _1079587, _1079589, _1079591]), 16766 ^ [_1079585, _1079587, _1079589, _1079591])))], (16774 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1079591, 16766 ^ [_1079585, _1079587, _1079589, _1079591])))], (16770 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1079585), 16765 ^ [_1079585, _1079587, _1079589, _1079591]), _1079589)))]], -(hBOOL(hAPP(_1079591, _1079587)))], (488 ^ _781404) ^ [_788760, _788762, _788764, _788766, _788768, _788770] : [-(c_Relation_Osingle__valued(_788768, _788764, _788760)), c_Relation_Osingle__valued(_788770, _788766, _788762), _788770 = _788768, _788766 = _788764, _788762 = _788760], (50730 ^ _781404) ^ [_1806970, _1806972, _1806974, _1806976] : [hBOOL(hAPP(_1806970, _1806972)), hBOOL(hAPP(_1806974, _1806976)), -(hBOOL(hAPP(_1806970, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1806970) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1806974))), 50746 ^ _781404 : [(50749 ^ _781404) ^ [] : [hBOOL(hAPP(_1806974, 50743 ^ [_1806970, _1806972, _1806974, _1806976]))], (50747 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1806970, hAPP(c_Nat_OSuc, 50743 ^ [_1806970, _1806972, _1806974, _1806976]))))]], 50750 ^ _781404 : [(50753 ^ _781404) ^ [] : [hBOOL(hAPP(_1806970, hAPP(c_Nat_OSuc, 50743 ^ [_1806970, _1806972, _1806974, _1806976])))], (50751 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1806974, 50743 ^ [_1806970, _1806972, _1806974, _1806976])))]]], (27045 ^ _781404) ^ [_1264091, _1264093] : [class_Groups_Oordered__ab__group__add__abs(_1264091), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264091), hAPP(c_Groups_Oabs__class_Oabs(_1264091), _1264093)), c_Groups_Ozero__class_Ozero(_1264091)))], (46038 ^ _781404) ^ [_1704798, _1704800, _1704802, _1704804, _1704806, _1704808] : [c_List_Olist__all2(_1704798, _1704800, _1704802, _1704804, _1704806), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704808), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704800)), _1704806))), -(hBOOL(hAPP(hAPP(_1704802, hAPP(hAPP(c_List_Onth(_1704798), _1704804), _1704808)), hAPP(hAPP(c_List_Onth(_1704800), _1704806), _1704808))))], (32570 ^ _781404) ^ [_1368086] : [class_Orderings_Oord(_1368086), -(c_Orderings_Oord__class_Omax(_1368086) = c_Orderings_Oord_Omax(_1368086, c_Orderings_Oord__class_Oless__eq(_1368086)))], (4912 ^ _781404) ^ [_856258, _856260, _856262, _856264] : [-(c_Relation_OId__on(_856264, _856260) = c_Relation_OId__on(_856262, _856258)), _856264 = _856262, _856260 = _856258], (14248 ^ _781404) ^ [_1030256, _1030258, _1030260] : [class_Groups_Oordered__comm__monoid__add(_1030256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030256), c_Groups_Ozero__class_Ozero(_1030256)), _1030258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030256), c_Groups_Ozero__class_Ozero(_1030256)), _1030260)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030256), c_Groups_Ozero__class_Ozero(_1030256)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030256), _1030258), _1030260))))], (40303 ^ _781404) ^ [_1566617, _1566619] : [c_Wellfounded_Owf(_1566617, _1566619), -(c_Wellfounded_Oacyclic(_1566617, _1566619))], (49047 ^ _781404) ^ [_1770342, _1770344, _1770346] : [-(c_List_Oreplicate(_1770342, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770342)), hAPP(c_List_Ofilter(_1770342, hAPP(c_fequal, _1770344)), _1770346)), _1770344) = hAPP(c_List_Ofilter(_1770342, hAPP(c_fequal, _1770344)), _1770346))], (26771 ^ _781404) ^ [_1258894, _1258896, _1258898, _1258900, _1258902] : [class_Groups_Ocomm__monoid__mult(_1258894), hBOOL(hAPP(c_Finite__Set_Ofinite(_1258896), _1258898)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1258896), _1258900)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1258894), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1258894, _1258896, c_Groups_Otimes__class_Otimes(_1258894)), _1258902), c_Groups_Oone__class_Oone(_1258894)), _1258898)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1258894, _1258896, c_Groups_Otimes__class_Otimes(_1258894)), _1258902), c_Groups_Oone__class_Oone(_1258894)), _1258900)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1258894), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1258894, _1258896, c_Groups_Otimes__class_Otimes(_1258894)), _1258902), c_Groups_Oone__class_Oone(_1258894)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258896, tc_HOL_Obool)), _1258898), _1258900))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1258894, _1258896, c_Groups_Otimes__class_Otimes(_1258894)), _1258902), c_Groups_Oone__class_Oone(_1258894)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1258896, tc_HOL_Obool)), _1258898), _1258900))))], (18081 ^ _781404) ^ [_1103697, _1103699] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1103697), _1103699) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1103699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1103697 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50963 ^ _781404) ^ [_1811710, _1811712, _1811714, _1811716, _1811718] : [-(c_Fun_Obij__betw(_1811710, _1811712, _1811714, _1811716, _1811718)), c_Fun_Oinj__on(_1811710, _1811712, _1811714, _1811716), hAPP(c_Set_Oimage(_1811710, _1811712, _1811714), _1811716) = _1811718], (38886 ^ _781404) ^ [_1523408, _1523410, _1523412, _1523414, _1523416, _1523418, _1523420, _1523422, _1523424, _1523426] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1523408, _1523410), tc_prod(_1523412, _1523414), tc_prod(_1523416, _1523418), c_Product__Type_Omap__pair(_1523408, _1523412, _1523410, _1523414, _1523420, _1523422)), c_Product__Type_Omap__pair(_1523416, _1523408, _1523418, _1523410, _1523424, _1523426)) = c_Product__Type_Omap__pair(_1523416, _1523412, _1523418, _1523414, hAPP(c_Fun_Ocomp(_1523408, _1523412, _1523416, _1523420), _1523424), hAPP(c_Fun_Ocomp(_1523410, _1523414, _1523418, _1523422), _1523426)))], (15471 ^ _781404) ^ [_1055145, _1055147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1055145), _1055147))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1055145), _1055147)))], (8465 ^ _781404) ^ [_924184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _924184), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_924184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24272 ^ _781404) ^ [_1216518, _1216520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216518), _1216520)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1216518, _1216520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216518), _1216520))], (38953 ^ _781404) ^ [_1525388, _1525390, _1525392] : [38954 ^ _781404 : [(38957 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1525388), hAPP(c_Set_OCollect(_1525388), _1525392)))], (38955 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1525388), hAPP(c_Set_OCollect(_1525388), _1525390)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1525388), hAPP(c_Set_OCollect(_1525388), hAPP(hAPP(c_COMBS(_1525388, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525388), c_fconj), _1525390)), _1525392)))))], (41181 ^ _781404) ^ [_1587405, _1587407] : [-(c_Transitive__Closure_Ortrancl(_1587405, c_Transitive__Closure_Otrancl(_1587405, _1587407)) = c_Transitive__Closure_Ortrancl(_1587405, _1587407))], (18465 ^ _781404) ^ [_1110676, _1110678, _1110680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110676)), 18468 ^ _781404 : [(18469 ^ _781404) ^ [_1110810] : [18471 ^ _781404 : [(18477 ^ _781404) ^ [] : [-(_1110810 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 18473 ^ [_1110676, _1110678, _1110680, _1110810]), 18470 ^ [_1110676, _1110678, _1110680, _1110810]))], (18475 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18473 ^ [_1110676, _1110678, _1110680, _1110810]), _1110678)))], (18472 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18470 ^ [_1110676, _1110678, _1110680, _1110810]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1110676))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110810), _1110680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1110810), _1110676)), _1110680)))]]], (12588 ^ _781404) ^ [_998977, _998979, _998981] : [-(hBOOL(hAPP(hAPP(c_member(_998977), _998979), _998981))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998977, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_998977), _998979), _998981)), hAPP(hAPP(c_Set_Oinsert(_998977), _998979), c_Orderings_Obot__class_Obot(tc_fun(_998977, tc_HOL_Obool)))) = _998981)], (16780 ^ _781404) ^ [_1080250, _1080252, _1080254, _1080256, _1080258] : [c_Finite__Set_Ofolding__one__idem(_1080250, _1080252, _1080254), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080250), _1080256)), -(_1080258 = c_Orderings_Obot__class_Obot(tc_fun(_1080250, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1080250, tc_HOL_Obool)), _1080258), _1080256)), -(hAPP(hAPP(_1080252, hAPP(_1080254, _1080258)), hAPP(_1080254, _1080256)) = hAPP(_1080254, _1080256))], (15789 ^ _781404) ^ [_1061044, _1061046, _1061048] : [class_Lattices_Olattice(_1061044), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061044), _1061046)), -(_1061046 = c_Orderings_Obot__class_Obot(tc_fun(_1061044, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1061044, hAPP(hAPP(c_Set_Oinsert(_1061044), _1061048), _1061046)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1061044), _1061048), c_Big__Operators_Olattice__class_OInf__fin(_1061044, _1061046)))], (29629 ^ _781404) ^ [_1311953, _1311955, _1311957, _1311959] : [class_Fields_Ofield(_1311953), -(_1311955 = c_Groups_Ozero__class_Ozero(_1311953)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1311953), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311953), _1311957), _1311955)), _1311959) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311953), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1311953), _1311957), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311953), _1311955), _1311959))), _1311955))], (9443 ^ _781404) ^ [_943283, _943285, _943287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _943283), _943285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _943283), _943287)), 9450 ^ _781404 : [(9457 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943285), _943287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _943285), _943283)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _943287), _943283))))], (9451 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _943285), _943283)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _943287), _943283))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943285), _943287)))]]], (1846 ^ _781404) ^ [_807519, _807521] : [-(class_Groups_Omonoid__add(_807519)), _807521 = _807519, class_Groups_Omonoid__add(_807521)], (18723 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8044 ^ _781404) ^ [_915997, _915999, _916001, _916003] : [class_Orderings_Olinorder(_915997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915997), _915999), _916001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915997), _916001), _916003)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915997, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_915997, _915999, _916001)), c_SetInterval_Oord__class_OgreaterThanAtMost(_915997, _916001, _916003)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_915997, _915999, _916003))], (52540 ^ _781404) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (48674 ^ _781404) ^ [] : [-(c_FunDef_Ois__measure(tc_Int_Oint, hAPP(c_Fun_Ocomp(tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, c_Int_Onat), c_Groups_Oabs__class_Oabs(tc_Int_Oint))))], (20129 ^ _781404) ^ [_1138846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1138846)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138846), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52630 ^ _781404) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (41113 ^ _781404) ^ [_1584940, _1584942, _1584944, _1584946] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584940, _1584940)), _1584942), c_Transitive__Closure_Otrancl(_1584940, _1584944))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584940, _1584940), tc_HOL_Obool)), _1584944), _1584946)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584940, _1584940)), _1584942), c_Transitive__Closure_Otrancl(_1584940, _1584946))))], (37408 ^ _781404) ^ [_1485163, _1485165, _1485167, _1485169, _1485171] : [hBOOL(hAPP(hAPP(c_member(_1485163), _1485165), hAPP(c_Relation_OImage(_1485167, _1485163, _1485169), _1485171))), 37412 ^ _781404 : [(37415 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1485167, _1485163)), hAPP(hAPP(c_Product__Type_OPair(_1485167, _1485163), 37411 ^ [_1485163, _1485165, _1485167, _1485169, _1485171]), _1485165)), _1485169)))], (37413 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1485167), 37411 ^ [_1485163, _1485165, _1485167, _1485169, _1485171]), _1485171)))]]], (27271 ^ _781404) ^ [_1268591, _1268593] : [class_Groups_Oordered__ab__group__add__abs(_1268591), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268591), hAPP(c_Groups_Ouminus__class_Ouminus(_1268591), hAPP(c_Groups_Oabs__class_Oabs(_1268591), _1268593))), c_Groups_Ozero__class_Ozero(_1268591))))], (17250 ^ _781404) ^ [_1088887, _1088889, _1088891, _1088893] : [class_Int_Onumber__ring(_1088887), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088887), hAPP(c_Int_Onumber__class_Onumber__of(_1088887), _1088889)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088887), _1088891), hAPP(c_Int_Onumber__class_Onumber__of(_1088887), _1088893))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088887), hAPP(c_Int_Onumber__class_Onumber__of(_1088887), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088889), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1088893)))), _1088891))], (14929 ^ _781404) ^ [_1043842, _1043844, _1043846, _1043848, _1043850] : [class_Groups_Ocomm__monoid__add(_1043842), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043844), _1043846)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043844), _1043848)), 14943 ^ _781404 : [(14946 ^ _781404) ^ [] : [hAPP(_1043850, 14942 ^ [_1043842, _1043844, _1043846, _1043848, _1043850]) = c_Groups_Ozero__class_Ozero(_1043842)], (14944 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1043844), 14942 ^ [_1043842, _1043844, _1043846, _1043848, _1043850]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1043844, tc_HOL_Obool)), _1043846), _1043848))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043844, _1043842), _1043850), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1043844, tc_HOL_Obool)), _1043846), _1043848)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043842), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043844, _1043842), _1043850), _1043846)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043844, _1043842), _1043850), _1043848)))], (21419 ^ _781404) ^ [_1162150, _1162152, _1162154, _1162156] : [class_Rings_Oordered__comm__semiring(_1162150), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162150), _1162152), _1162154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162150), c_Groups_Ozero__class_Ozero(_1162150)), _1162156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162150), _1162156), _1162152)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162150), _1162156), _1162154))))], (25700 ^ _781404) ^ [_1240646, _1240648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240648)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1240646)), hAPP(c_Int_Onat, _1240648)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240646), _1240648)))], (22743 ^ _781404) ^ [_1187951, _1187953] : [-(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), _1187951), _1187953)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1187951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1187953))], (21247 ^ _781404) ^ [_1159046] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159046), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1159046)], (33341 ^ _781404) ^ [_1384926, _1384928, _1384930, _1384932, _1384934, _1384936] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384926, tc_fun(_1384928, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1384930, _1384926, _1384932), _1384934)), _1384936) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384930, tc_fun(_1384928, tc_HOL_Obool)), _1384934), hAPP(hAPP(c_COMBB(_1384926, tc_fun(_1384928, tc_HOL_Obool), _1384930), _1384936), _1384932)))], (21199 ^ _781404) ^ [_1158086, _1158088, _1158090, _1158092] : [class_Groups_Omonoid__mult(_1158086), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1158086), _1158088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158090), _1158092)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1158086), hAPP(hAPP(c_Power_Opower__class_Opower(_1158086), _1158088), _1158090)), _1158092))], (24917 ^ _781404) ^ [_1227907] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1227907)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1227907))], (17303 ^ _781404) ^ [_1090075, _1090077, _1090079, _1090081, _1090083, _1090085, _1090087, _1090089] : [c_Finite__Set_Ofolding__image__simple__idem(_1090075, _1090077, _1090079, _1090081, _1090083, _1090085), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090077), _1090087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1090077, tc_HOL_Obool)), _1090089), _1090087)), -(hAPP(hAPP(_1090079, hAPP(_1090085, _1090089)), hAPP(_1090085, _1090087)) = hAPP(_1090085, _1090087))], (25405 ^ _781404) ^ [_1235524, _1235526] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1235524), _1235526)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1235526), _1235524)))], (42186 ^ _781404) ^ [_1612518, _1612520] : [-(c_List_Olenlex(_1612518, _1612520) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1612518)), tc_List_Olist(_1612518)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1612518), c_Wellfounded_Oless__than, c_List_Olex(_1612518, _1612520))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1612518), tc_List_Olist(_1612518), tc_prod(tc_Nat_Onat, tc_List_Olist(_1612518))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1612518), tc_prod(tc_Nat_Onat, tc_List_Olist(_1612518))), tc_List_Olist(_1612518)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1612518))), c_Nat_Osize__class_Osize(tc_List_Olist(_1612518)))), c_COMBI(tc_List_Olist(_1612518)))))], (5604 ^ _781404) ^ [_867082, _867084] : [_867084 = _867082, -(tc_Lazy__Sequence_Olazy__sequence(_867084) = tc_Lazy__Sequence_Olazy__sequence(_867082))], (5700 ^ _781404) ^ [_868528, _868530] : [_868530 = _868528, -(tc_Hoare__Mirabelle_Otriple(_868530) = tc_Hoare__Mirabelle_Otriple(_868528))], (20763 ^ _781404) ^ [_1149738, _1149740, _1149742] : [class_Int_Onumber__ring(_1149738), -(hAPP(c_Int_Onumber__class_Onumber__of(_1149738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1149740), _1149742)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149738), hAPP(c_Int_Onumber__class_Onumber__of(_1149738), _1149740)), hAPP(c_Int_Onumber__class_Onumber__of(_1149738), _1149742)))], (34611 ^ _781404) ^ [_1423475, _1423477, _1423479] : [class_Groups_Ocomm__monoid__add(_1423475), class_Groups_Ocomm__monoid__mult(_1423475), c_Nat__Transfer_Onat__set(_1423477), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1423475), _1423479), _1423477) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1423475), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1423475, tc_Nat_Onat), _1423479), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1423477)))], (4454 ^ _781404) ^ [_849021, _849023, _849025, _849027] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_849027, _849023) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_849025, _849021)), _849027 = _849025, _849023 = _849021], (20369 ^ _781404) ^ [] : [-(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))))], (41670 ^ _781404) ^ [_1599412, _1599414, _1599416, _1599418, _1599420, _1599422] : [c_Relation_Osingle__valued(_1599412, _1599414, hAPP(c_Relation_Oconverse(_1599414, _1599412), _1599416)), -(_1599418 = c_Orderings_Obot__class_Obot(tc_fun(_1599420, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1599414, _1599412, _1599416), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599420, tc_fun(_1599414, tc_HOL_Obool)), _1599418), _1599422)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599420, tc_fun(_1599412, tc_HOL_Obool)), _1599418), hAPP(hAPP(c_COMBB(tc_fun(_1599414, tc_HOL_Obool), tc_fun(_1599412, tc_HOL_Obool), _1599420), c_Relation_OImage(_1599414, _1599412, _1599416)), _1599422)))], (50295 ^ _781404) ^ [_1797523, _1797525] : [c_Predicate_Osymp(_1797523, _1797525), -(c_Relation_Osym(_1797523, hAPP(c_Set_OCollect(tc_prod(_1797523, _1797523)), hAPP(c_Product__Type_Oprod_Oprod__case(_1797523, _1797523, tc_HOL_Obool), _1797525))))], (34675 ^ _781404) ^ [_1425136, _1425138] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1425136), _1425138))), -(hAPP(c_Finite__Set_Ocard(_1425136), _1425138) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14807 ^ _781404) ^ [_1041222, _1041224] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041222), c_Orderings_Otop__class_Otop(tc_fun(_1041222, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1041222, _1041222, _1041224), c_Orderings_Otop__class_Otop(tc_fun(_1041222, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041222, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1041222, _1041222, _1041224, c_Orderings_Otop__class_Otop(tc_fun(_1041222, tc_HOL_Obool))))], (34507 ^ _781404) ^ [_1421054, _1421056, _1421058, _1421060, _1421062] : [class_Complete__Lattice_Ocomplete__lattice(_1421054), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421056), _1421058)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1421054), _1421060), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1421056, _1421054), _1421058), _1421062)) = hAPP(hAPP(c_Finite__Set_Ofold(_1421056, _1421054, hAPP(hAPP(c_COMBB(_1421054, tc_fun(_1421054, _1421054), _1421056), c_Lattices_Osemilattice__sup__class_Osup(_1421054)), _1421062)), _1421060), _1421058))], (31186 ^ _781404) ^ [_1342542, _1342544, _1342546] : [class_Orderings_Olinorder(_1342542), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342542), _1342544)), hBOOL(hAPP(hAPP(c_member(_1342542), _1342546), _1342544)), 31197 ^ _781404 : [(31204 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1342542, tc_HOL_Obool)), _1342544), hAPP(hAPP(c_Set_Oinsert(_1342542), _1342546), c_Orderings_Obot__class_Obot(tc_fun(_1342542, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1342542, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1342542, c_Orderings_Oord__class_Omin(_1342542), _1342544) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342542), _1342546), c_Big__Operators_Olattice_OInf__fin(_1342542, c_Orderings_Oord__class_Omin(_1342542), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1342542, tc_HOL_Obool)), _1342544), hAPP(hAPP(c_Set_Oinsert(_1342542), _1342546), c_Orderings_Obot__class_Obot(tc_fun(_1342542, tc_HOL_Obool)))))))], (31198 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1342542, tc_HOL_Obool)), _1342544), hAPP(hAPP(c_Set_Oinsert(_1342542), _1342546), c_Orderings_Obot__class_Obot(tc_fun(_1342542, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1342542, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1342542, c_Orderings_Oord__class_Omin(_1342542), _1342544) = _1342546)]]], (41067 ^ _781404) ^ [_1583759, _1583761] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583759, _1583759)), _1583761)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583759, _1583759)), c_Transitive__Closure_Otrancl(_1583759, _1583761))))], (15950 ^ _781404) ^ [_1064021, _1064023, _1064025] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1064021), _1064023)), hBOOL(hAPP(hAPP(c_member(_1064021), _1064025), _1064023)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1064021), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064021, tc_HOL_Obool)), _1064023), hAPP(hAPP(c_Set_Oinsert(_1064021), _1064025), c_Orderings_Obot__class_Obot(tc_fun(_1064021, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1064021), _1064023))], (2878 ^ _781404) ^ [_824091, _824093] : [_824093 = _824091, -(c_Relation_OField(_824093) = c_Relation_OField(_824091))], (30219 ^ _781404) ^ [_1324012, _1324014, _1324016, _1324018, _1324020] : [class_Groups_Ocomm__monoid__mult(_1324012), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324014), _1324016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1324014, tc_HOL_Obool)), _1324018), _1324016)), 30233 ^ _781404 : [(30236 ^ _781404) ^ [] : [hAPP(_1324020, 30232 ^ [_1324012, _1324014, _1324016, _1324018, _1324020]) = c_Groups_Oone__class_Oone(_1324012)], (30234 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1324014), 30232 ^ [_1324012, _1324014, _1324016, _1324018, _1324020]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324014, tc_HOL_Obool)), _1324016), _1324018))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1324014, _1324012), _1324020), _1324016) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1324014, _1324012), _1324020), _1324018))], (20743 ^ _781404) ^ [_1149253, _1149255] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1149253), _1149255)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149253)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149255)))], (38988 ^ _781404) ^ [_1526250, _1526252] : [c_Orderings_Obot__class_Obot(tc_fun(_1526250, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1526250), _1526252), 38991 ^ _781404 : [(38992 ^ _781404) ^ [_1526335] : [hBOOL(hAPP(_1526252, _1526335))]]], (12096 ^ _781404) ^ [_989017, _989019, _989021, _989023] : [hBOOL(hAPP(hAPP(c_member(_989017), _989019), _989021)), -(hBOOL(hAPP(hAPP(c_member(_989017), _989019), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_989017, tc_HOL_Obool)), _989023), _989021))))], (19993 ^ _781404) ^ [_1136560, _1136562] : [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)), _1136560)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1136562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1136560), _1136562)))], (11921 ^ _781404) ^ [_985780, _985782] : [-(hBOOL(hAPP(hAPP(c_member(_985780), 11922 ^ [_985780, _985782]), _985782))), -(_985782 = c_Orderings_Obot__class_Obot(tc_fun(_985780, tc_HOL_Obool)))], (11067 ^ _781404) ^ [_969305, _969307, _969309] : [class_Orderings_Oorder(_969305), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969305), _969307), _969309)), -(c_SetInterval_Oord__class_OatLeastAtMost(_969305, _969309, _969307) = c_Orderings_Obot__class_Obot(tc_fun(_969305, tc_HOL_Obool)))], (5234 ^ _781404) ^ [_861275, _861277, _861279, _861281, _861283, _861285, _861287, _861289] : [-(c_Quotient_OBabs(_861289, _861285, _861281, _861277) = c_Quotient_OBabs(_861287, _861283, _861279, _861275)), _861289 = _861287, _861285 = _861283, _861281 = _861279, _861277 = _861275], (29605 ^ _781404) ^ [_1311528, _1311530, _1311532, _1311534, _1311536] : [class_Fields_Ofield(_1311528), -(_1311530 = c_Groups_Ozero__class_Ozero(_1311528)), -(_1311532 = c_Groups_Ozero__class_Ozero(_1311528)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1311528), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311528), _1311534), _1311530)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311528), _1311536), _1311532)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1311528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311528), _1311534), _1311532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311528), _1311536), _1311530))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311528), _1311530), _1311532)))], (45028 ^ _781404) ^ [_1682371, _1682373] : [-(_1682371 = c_List_Olist_ONil(_1682373)), -(c_List_Olast(_1682373, _1682371) = hAPP(hAPP(c_List_Onth(_1682373), _1682371), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682373)), _1682371)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (27109 ^ _781404) ^ [_1265335, _1265337, _1265339] : [class_Groups_Oordered__ab__group__add__abs(_1265335), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265335), hAPP(c_Groups_Oabs__class_Oabs(_1265335), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265335), hAPP(c_Groups_Oabs__class_Oabs(_1265335), _1265337)), hAPP(c_Groups_Oabs__class_Oabs(_1265335), _1265339)))), hAPP(c_Groups_Oabs__class_Oabs(_1265335), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265335), _1265337), _1265339)))))], (41285 ^ _781404) ^ [_1589993, _1589995, _1589997] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589993, _1589995, _1589995), _1589997), c_Relation_OId(_1589995)) = _1589997)], (38087 ^ _781404) ^ [_1502218, _1502220, _1502222, _1502224, _1502226, _1502228, _1502230, _1502232, _1502234, _1502236, _1502238] : [c_Equiv__Relations_Oequiv(_1502218, _1502220, _1502222), c_Equiv__Relations_Oequiv(_1502224, _1502226, _1502228), c_Equiv__Relations_Ocongruent2(_1502218, _1502224, tc_fun(_1502230, tc_HOL_Obool), _1502222, _1502228, _1502232), hBOOL(hAPP(hAPP(c_member(tc_fun(_1502218, tc_HOL_Obool)), _1502234), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1502218), _1502220), _1502222))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1502224, tc_HOL_Obool)), _1502236), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1502224), _1502226), _1502228))), 38109 ^ _781404 : [(38115 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1502230, tc_HOL_Obool)), hAPP(hAPP(_1502232, 38108 ^ [_1502218, _1502220, _1502222, _1502224, _1502226, _1502228, _1502230, _1502232, _1502234, _1502236, _1502238]), 38111 ^ [_1502218, _1502220, _1502222, _1502224, _1502226, _1502228, _1502230, _1502232, _1502234, _1502236, _1502238])), _1502238))], (38113 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502224), 38111 ^ [_1502218, _1502220, _1502222, _1502224, _1502226, _1502228, _1502230, _1502232, _1502234, _1502236, _1502238]), _1502226)))], (38110 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502218), 38108 ^ [_1502218, _1502220, _1502222, _1502224, _1502226, _1502228, _1502230, _1502232, _1502234, _1502236, _1502238]), _1502220)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1502230, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1502218, tc_fun(_1502230, tc_HOL_Obool)), _1502234), hAPP(hAPP(c_COMBB(tc_fun(_1502224, tc_fun(_1502230, tc_HOL_Obool)), tc_fun(_1502230, tc_HOL_Obool), _1502218), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1502224, tc_fun(_1502230, tc_HOL_Obool)), _1502236)), _1502232))), _1502238)))], (35241 ^ _781404) ^ [_1437672, _1437674, _1437676, _1437678, _1437680, _1437682] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437672, tc_fun(_1437674, tc_HOL_Obool))), _1437676), _1437678), _1437680), _1437682)), 35244 ^ _781404 : [(35247 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1437678, _1437680), _1437682)))], (35245 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1437676, _1437680), _1437682)))]]], (7227 ^ _781404) ^ [_898816, _898818, _898820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898816, tc_HOL_Obool)), _898818), _898820)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898816, tc_HOL_Obool)), _898818), _898820) = _898820)], (5594 ^ _781404) ^ [_866933, _866935, _866937, _866939] : [-(tc_prod(_866939, _866935) = tc_prod(_866937, _866933)), _866939 = _866937, _866935 = _866933], (44383 ^ _781404) ^ [_1668659, _1668661] : [hAPP(c_List_Orotate1(_1668659), _1668661) = c_List_Olist_ONil(_1668659), -(_1668661 = c_List_Olist_ONil(_1668659))], (26609 ^ _781404) ^ [_1255548, _1255550] : [class_Rings_Oring__1(_1255548), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255550)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1255548), hAPP(c_Int_Onat, _1255550)) = hAPP(c_Int_Oring__1__class_Oof__int(_1255548), _1255550))], (51836 ^ _781404) ^ [_1830788, _1830790, _1830792] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830788, _1830790) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1830792), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 51839 ^ _781404 : [(51842 ^ _781404) ^ [] : [-(_1830790 = _1830792)], (51840 ^ _781404) ^ [] : [-(_1830788 = _1830790)]]], (10603 ^ _781404) ^ [_961717, _961719] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961717), _961719))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961717), hAPP(c_Nat_OSuc, _961719))), -(_961719 = _961717)], (34469 ^ _781404) ^ [_1420167, _1420169, _1420171] : [class_Int_Onumber__ring(_1420167), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1420167), _1420169), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1420171))) = hAPP(hAPP(c_HOL_OLet(_1420167, _1420167), hAPP(hAPP(c_Power_Opower__class_Opower(_1420167), _1420169), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420171))), hAPP(hAPP(c_COMBS(_1420167, _1420167, _1420167), c_Groups_Otimes__class_Otimes(_1420167)), c_COMBI(_1420167))))], (42179 ^ _781404) ^ [_1612358, _1612360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 42180 ^ [_1612358, _1612360]), hAPP(_1612358, 42180 ^ [_1612358, _1612360]))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), _1612358)), _1612360)))))], (49189 ^ _781404) ^ [_1772935, _1772937, _1772939] : [c_List_Oreplicate(_1772935, _1772937, _1772939) = c_List_Olist_ONil(_1772935), -(_1772937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35468 ^ _781404) ^ [_1443061, _1443063, _1443065, _1443067, _1443069, _1443071, _1443073] : [hBOOL(hAPP(hAPP(c_member(_1443061), _1443063), hAPP(hAPP(_1443065, _1443067), _1443069))), -(hBOOL(hAPP(hAPP(c_member(_1443061), _1443063), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1443071, _1443073, tc_fun(_1443061, tc_HOL_Obool)), _1443065), hAPP(hAPP(c_Product__Type_OPair(_1443071, _1443073), _1443067), _1443069)))))], (51401 ^ _781404) ^ [_1822457, _1822459, _1822461, _1822463] : [-(hAPP(c_Lazy__Sequence_Obind(_1822457, _1822459, _1822461), _1822463) = c_Lazy__Sequence_Oflat(_1822459, c_Lazy__Sequence_Omap(_1822457, tc_Lazy__Sequence_Olazy__sequence(_1822459), _1822463, _1822461)))], (51660 ^ _781404) ^ [_1827569, _1827571, _1827573, _1827575] : [class_Rings_Ocomm__semiring__1(_1827569), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827569), _1827571), _1827573)), _1827575)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827569), _1827573), _1827575)))], (35153 ^ _781404) ^ [_1436305, _1436307] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436305), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1436307)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1436305)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436307), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1436305)))), 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)))], (31896 ^ _781404) ^ [_1355378, _1355380, _1355382, _1355384] : [class_Orderings_Olinorder(_1355378), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355378), _1355380), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355378), _1355382), _1355384)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355378), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355378), _1355380), _1355382)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355378), _1355380), _1355384)))], (48769 ^ _781404) ^ [_1763755, _1763757, _1763759] : [48771 ^ _781404 : [(48774 ^ _781404) ^ [] : [hBOOL(hAPP(_1763759, 48770 ^ [_1763755, _1763757, _1763759]))], (48772 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763755), 48770 ^ [_1763755, _1763757, _1763759]), hAPP(c_List_Oset(_1763755), _1763757))))]], -(c_List_Olist__all(_1763755, _1763759, _1763757))], (14309 ^ _781404) ^ [_1031416, _1031418, _1031420] : [-(hBOOL(hAPP(_1031416, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031418), _1031420)))), 14312 ^ _781404 : [(14315 ^ _781404) ^ [] : [hBOOL(hAPP(_1031416, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14313 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1031418), _1031420)))]], 14317 ^ _781404 : [(14320 ^ _781404) ^ [] : [hBOOL(hAPP(_1031416, 14316 ^ [_1031416, _1031418, _1031420]))], (14318 ^ _781404) ^ [] : [-(_1031418 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031420), 14316 ^ [_1031416, _1031418, _1031420]))]]], (44689 ^ _781404) ^ [_1675326, _1675328, _1675330] : [-(hAPP(c_List_Otl(_1675326), hAPP(hAPP(c_List_Otake(_1675326), _1675328), _1675330)) = hAPP(hAPP(c_List_Otake(_1675326), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1675328), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1675326), _1675330)))], (25311 ^ _781404) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (10567 ^ _781404) ^ [_961111, _961113] : [10568 ^ _781404 : [(10571 ^ _781404) ^ [] : [_961111 = _961113], (10569 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961111), _961113))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961111), hAPP(c_Nat_OSuc, _961113))))], (43765 ^ _781404) ^ [_1653525, _1653527, _1653529, _1653531, _1653533] : [-(hAPP(hAPP(c_List_Ozip(_1653525, _1653527), hAPP(hAPP(c_List_Olist_OCons(_1653525), _1653529), _1653531)), _1653533) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1653525, _1653527)), _1653527, c_List_Olist_ONil(tc_prod(_1653525, _1653527)), hAPP(hAPP(c_COMBC(_1653527, tc_fun(tc_List_Olist(_1653527), tc_List_Olist(tc_prod(_1653525, _1653527))), tc_fun(tc_List_Olist(_1653527), tc_List_Olist(tc_prod(_1653525, _1653527)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1653525, _1653527)), tc_List_Olist(tc_prod(_1653525, _1653527))), tc_fun(tc_fun(tc_List_Olist(_1653527), tc_List_Olist(tc_prod(_1653525, _1653527))), tc_fun(tc_List_Olist(_1653527), tc_List_Olist(tc_prod(_1653525, _1653527)))), _1653527), c_COMBB(tc_List_Olist(tc_prod(_1653525, _1653527)), tc_List_Olist(tc_prod(_1653525, _1653527)), tc_List_Olist(_1653527))), hAPP(hAPP(c_COMBB(tc_prod(_1653525, _1653527), tc_fun(tc_List_Olist(tc_prod(_1653525, _1653527)), tc_List_Olist(tc_prod(_1653525, _1653527))), _1653527), c_List_Olist_OCons(tc_prod(_1653525, _1653527))), hAPP(c_Product__Type_OPair(_1653525, _1653527), _1653529)))), hAPP(c_List_Ozip(_1653525, _1653527), _1653531))), _1653533))], (19530 ^ _781404) ^ [_1128672] : [class_Int_Onumber__ring(_1128672), -(hAPP(c_Int_Onumber__class_Onumber__of(_1128672), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1128672))], (27411 ^ _781404) ^ [_1270866, _1270868] : [class_Int_Onumber__ring(_1270866), class_Rings_Olinordered__idom(_1270866), 27418 ^ _781404 : [(27425 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270866), hAPP(c_Int_Onumber__class_Onumber__of(_1270866), _1270868)), c_Groups_Ozero__class_Ozero(_1270866)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1270866), hAPP(c_Int_Onumber__class_Onumber__of(_1270866), _1270868)) = hAPP(c_Int_Onumber__class_Onumber__of(_1270866), _1270868))], (27419 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270866), hAPP(c_Int_Onumber__class_Onumber__of(_1270866), _1270868)), c_Groups_Ozero__class_Ozero(_1270866))), -(hAPP(c_Groups_Oabs__class_Oabs(_1270866), hAPP(c_Int_Onumber__class_Onumber__of(_1270866), _1270868)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1270866), hAPP(c_Int_Onumber__class_Onumber__of(_1270866), _1270868)))]]], (16322 ^ _781404) ^ [_1071386] : [class_Rings_Olinordered__semidom(_1071386), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071386), c_Groups_Ozero__class_Ozero(_1071386)), c_Groups_Oone__class_Oone(_1071386))))], (45190 ^ _781404) ^ [_1685449, _1685451, _1685453, _1685455, _1685457, _1685459, _1685461, _1685463] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1685449, _1685451), _1685453), _1685455), hAPP(hAPP(c_List_Ozip(_1685449, _1685451), _1685457), hAPP(hAPP(c_List_Omap(_1685459, _1685451), _1685461), _1685463))) = hAPP(hAPP(c_List_Omap(tc_prod(_1685449, _1685459), _1685453), hAPP(c_Product__Type_Oprod_Oprod__case(_1685449, _1685459, _1685453), hAPP(hAPP(c_COMBB(tc_fun(_1685459, tc_prod(_1685449, _1685451)), tc_fun(_1685459, _1685453), _1685449), hAPP(c_COMBB(tc_prod(_1685449, _1685451), _1685453, _1685459), _1685455)), hAPP(hAPP(c_COMBC(_1685449, tc_fun(_1685459, _1685451), tc_fun(_1685459, tc_prod(_1685449, _1685451))), hAPP(hAPP(c_COMBB(tc_fun(_1685451, tc_prod(_1685449, _1685451)), tc_fun(tc_fun(_1685459, _1685451), tc_fun(_1685459, tc_prod(_1685449, _1685451))), _1685449), c_COMBB(_1685451, tc_prod(_1685449, _1685451), _1685459)), c_Product__Type_OPair(_1685449, _1685451))), _1685461)))), hAPP(hAPP(c_List_Ozip(_1685449, _1685459), _1685457), _1685463)))], (42709 ^ _781404) ^ [_1628720, _1628722, _1628724, _1628726] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628720) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1628722), hAPP(hAPP(c_List_Olist_OCons(_1628722), _1628724), _1628726)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628720)) = _1628724)], (37128 ^ _781404) ^ [_1477931, _1477933, _1477935, _1477937, _1477939] : [-(hAPP(c_Product__Type_Ofst(_1477931, _1477933), hAPP(c_Product__Type_Oapfst(_1477935, _1477931, _1477933, _1477937), _1477939)) = hAPP(_1477937, hAPP(c_Product__Type_Ofst(_1477935, _1477933), _1477939)))], (17477 ^ _781404) ^ [_1093174, _1093176, _1093178, _1093180, _1093182, _1093184, _1093186] : [c_Finite__Set_Ofolding__image__simple__idem(_1093174, _1093176, _1093178, _1093180, _1093182, _1093184), -(hAPP(hAPP(_1093178, _1093186), _1093186) = _1093186)], (39723 ^ _781404) ^ [_1552027, _1552029, _1552031, _1552033] : [hBOOL(hAPP(c_Predicate_ORangeP(_1552027, _1552029, hAPP(hAPP(c_COMBC(_1552027, tc_fun(tc_prod(_1552027, _1552029), tc_HOL_Obool), tc_fun(_1552029, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552029, tc_fun(tc_fun(tc_prod(_1552027, _1552029), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1552027, _1552029), tc_HOL_Obool), tc_fun(_1552029, tc_HOL_Obool)), _1552027), c_COMBC(_1552029, tc_fun(tc_prod(_1552027, _1552029), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552029, tc_prod(_1552027, _1552029)), tc_fun(_1552029, tc_fun(tc_fun(tc_prod(_1552027, _1552029), tc_HOL_Obool), tc_HOL_Obool)), _1552027), hAPP(c_COMBB(tc_prod(_1552027, _1552029), tc_fun(tc_fun(tc_prod(_1552027, _1552029), tc_HOL_Obool), tc_HOL_Obool), _1552029), c_member(tc_prod(_1552027, _1552029)))), c_Product__Type_OPair(_1552027, _1552029)))), _1552031)), _1552033)), -(hBOOL(hAPP(hAPP(c_member(_1552029), _1552033), hAPP(c_Relation_ORange(_1552027, _1552029), _1552031))))], (38294 ^ _781404) ^ [_1507893, _1507895, _1507897] : [38296 ^ _781404 : [(38299 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1507893), 38295 ^ [_1507893, _1507895, _1507897]), c_Wellfounded_Oacc(_1507893, _1507897)))], (38297 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1507893, _1507893)), hAPP(hAPP(c_Product__Type_OPair(_1507893, _1507893), 38295 ^ [_1507893, _1507895, _1507897]), _1507895)), _1507897)))]], -(hBOOL(hAPP(hAPP(c_member(_1507893), _1507895), c_Wellfounded_Oacc(_1507893, _1507897))))], (47581 ^ _781404) ^ [_1737994, _1737996] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1737994), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1737994))), c_List_Otranspose(_1737994, _1737996)))))], (48686 ^ _781404) ^ [_1762287, _1762289, _1762291, _1762293] : [-(c_List_Olist__all(_1762287, _1762289, hAPP(hAPP(c_List_Oappend(_1762287), _1762291), _1762293))), c_List_Olist__all(_1762287, _1762289, _1762291), c_List_Olist__all(_1762287, _1762289, _1762293)], (29353 ^ _781404) ^ [_1306848, _1306850, _1306852, _1306854] : [class_Fields_Olinordered__field(_1306848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306848), _1306850), c_Groups_Ozero__class_Ozero(_1306848))), 29360 ^ _781404 : [(29367 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306848), _1306854), _1306850)), _1306852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306848), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306848), _1306852), _1306850)), _1306854)))], (29361 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306848), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306848), _1306852), _1306850)), _1306854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306848), _1306854), _1306850)), _1306852)))]]], (14639 ^ _781404) ^ [_1038017, _1038019] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1038017, _1038019)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1038017, _1038019), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038017), c_Orderings_Otop__class_Otop(tc_fun(_1038017, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038019), c_Orderings_Otop__class_Otop(tc_fun(_1038019, tc_HOL_Obool))))], (9601 ^ _781404) ^ [_945780, _945782, _945784] : [class_Orderings_Oorder(_945780), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945780), _945782), _945784)), _945784 = _945782], (48708 ^ _781404) ^ [_1762618, _1762620, _1762622] : [c_List_Olist__all(_1762618, _1762620, _1762622), 48711 ^ _781404 : [(48712 ^ _781404) ^ [_1762699] : [hBOOL(hAPP(hAPP(c_member(_1762618), _1762699), hAPP(c_List_Oset(_1762618), _1762622))), -(hBOOL(hAPP(_1762620, _1762699)))]]], (17981 ^ _781404) ^ [_1102052, _1102054, _1102056] : [class_Rings_Olinordered__semidom(_1102052), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102052), c_Groups_Ozero__class_Ozero(_1102052)), _1102054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102052), c_Groups_Ozero__class_Ozero(_1102052)), hAPP(hAPP(c_Power_Opower__class_Opower(_1102052), _1102054), _1102056))))], (13015 ^ _781404) ^ [_1007198, _1007200, _1007202, _1007204] : [class_Groups_Ocancel__semigroup__add(_1007198), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007198), _1007200), _1007202) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007198), _1007204), _1007202), -(_1007200 = _1007204)], (41692 ^ _781404) ^ [_1599884] : [-(c_Relation_Osingle__valued(_1599884, _1599884, c_Relation_OId(_1599884)))], (48925 ^ _781404) ^ [_1766969, _1766971] : [-(hAPP(c_New__DSequence_Opos__empty(_1766969), _1766971) = c_Lazy__Sequence_Oempty(_1766969))], (17379 ^ _781404) ^ [_1091458, _1091460] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1091458), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1091460), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1091458, _1091460))], (13748 ^ _781404) ^ [_1021165, _1021167, _1021169, _1021171] : [class_Rings_Olinordered__semidom(_1021165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021165), c_Groups_Ozero__class_Ozero(_1021165)), _1021167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021165), _1021169), _1021171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021165), _1021169), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021165), _1021167), _1021171))))], (26210 ^ _781404) ^ [_1249231] : [c_Nat__Transfer_Onat__set(_1249231), 26213 ^ _781404 : [(26220 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1249231))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1249231)))], (26214 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1249231)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1249231))))]]], (40517 ^ _781404) ^ [_1571023, _1571025, _1571027] : [40519 ^ _781404 : [(40522 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1571023), 40518 ^ [_1571023, _1571025, _1571027]), c_Wellfounded_Oacc(_1571023, _1571027)))], (40520 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571023, _1571023)), hAPP(hAPP(c_Product__Type_OPair(_1571023, _1571023), 40518 ^ [_1571023, _1571025, _1571027]), _1571025)), _1571027)))]], -(hBOOL(hAPP(hAPP(c_member(_1571023), _1571025), c_Wellfounded_Oacc(_1571023, _1571027))))], (30654 ^ _781404) ^ [_1332491, _1332493] : [class_Orderings_Olinorder(_1332491), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332491), _1332493), _1332493) = _1332493)], (36937 ^ _781404) ^ [_1473448, _1473450, _1473452, _1473454, _1473456, _1473458, _1473460, _1473462] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1473448, _1473450), tc_prod(_1473448, _1473450))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1473448, _1473450), tc_prod(_1473448, _1473450)), hAPP(hAPP(c_Product__Type_OPair(_1473448, _1473450), _1473452), _1473454)), hAPP(hAPP(c_Product__Type_OPair(_1473448, _1473450), _1473456), _1473458))), c_Wellfounded_Olex__prod(_1473448, _1473450, _1473460, _1473462)))), 36938 ^ _781404 : [(36941 ^ _781404) ^ [] : [_1473452 = _1473456, hBOOL(hAPP(hAPP(c_member(tc_prod(_1473450, _1473450)), hAPP(hAPP(c_Product__Type_OPair(_1473450, _1473450), _1473454), _1473458)), _1473462))], (36939 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1473448, _1473448)), hAPP(hAPP(c_Product__Type_OPair(_1473448, _1473448), _1473452), _1473456)), _1473460))]]], (40309 ^ _781404) ^ [_1566694, _1566696, _1566698] : [c_Wellfounded_Oacyclic(_1566694, _1566696), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566694, _1566694), tc_HOL_Obool)), _1566698), _1566696)), -(c_Wellfounded_Oacyclic(_1566694, _1566698))], (30327 ^ _781404) ^ [_1326080, _1326082, _1326084, _1326086] : [class_Groups_Ocomm__monoid__mult(_1326080), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326082), _1326084)), 30337 ^ _781404 : [(30340 ^ _781404) ^ [] : [hAPP(_1326086, 30336 ^ [_1326080, _1326082, _1326084, _1326086]) = c_Groups_Oone__class_Oone(_1326080)], (30338 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1326082), 30336 ^ [_1326080, _1326082, _1326084, _1326086]), _1326084)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1326080, _1326082, c_Groups_Otimes__class_Otimes(_1326080)), _1326086), c_Groups_Oone__class_Oone(_1326080)), _1326084) = c_Groups_Oone__class_Oone(_1326080))], (3586 ^ _781404) ^ [_835029, _835031] : [_835031 = _835029, -(c_SetInterval_Oord__class_OatMost(_835031) = c_SetInterval_Oord__class_OatMost(_835029))], (26297 ^ _781404) ^ [_1250693, _1250695, _1250697] : [class_Int_Oring__char__0(_1250693), 26300 ^ _781404 : [(26307 ^ _781404) ^ [] : [_1250695 = _1250697, -(hAPP(c_Int_Oring__1__class_Oof__int(_1250693), _1250695) = hAPP(c_Int_Oring__1__class_Oof__int(_1250693), _1250697))], (26301 ^ _781404) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1250693), _1250695) = hAPP(c_Int_Oring__1__class_Oof__int(_1250693), _1250697), -(_1250695 = _1250697)]]], (17469 ^ _781404) ^ [_1093022, _1093024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1093022), _1093024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093022), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093024), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (19841 ^ _781404) ^ [_1133822, _1133824, _1133826] : [hBOOL(hAPP(_1133822, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1133824), _1133826)))), 19844 ^ _781404 : [(19851 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1133824), _1133826)), -(hBOOL(hAPP(_1133822, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19845 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1133826), _1133824)), -(hBOOL(hAPP(_1133822, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133824)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1133826)))))]]], (24570 ^ _781404) ^ [_1222166, _1222168] : [-(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), _1222166)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1222168))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1222166))) = 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), _1222168)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222166)))], (14601 ^ _781404) ^ [_1037304, _1037306, _1037308] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037304), _1037306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1037304, tc_HOL_Obool)), _1037308), _1037306)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1037304), _1037308)))], (36836 ^ _781404) ^ [_1470694, _1470696, _1470698, _1470700, _1470702, _1470704, _1470706, _1470708] : [c_Finite__Set_Ofolding__image(_1470694, _1470696, _1470698, _1470700, _1470702), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470696), _1470704)), -(hAPP(hAPP(_1470702, hAPP(hAPP(c_COMBS(_1470696, _1470694, _1470694), hAPP(hAPP(c_COMBB(_1470694, tc_fun(_1470694, _1470694), _1470696), _1470698), _1470706)), _1470708)), _1470704) = hAPP(hAPP(_1470698, hAPP(hAPP(_1470702, _1470706), _1470704)), hAPP(hAPP(_1470702, _1470708), _1470704)))], (45690 ^ _781404) ^ [_1696791] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1696791)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (52342 ^ _781404) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (30572 ^ _781404) ^ [_1330927] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1330927) = c_Orderings_Oord__class_Omin(_1330927)), class_Lattices_Osemilattice__inf(_1330927), class_Orderings_Olinorder(_1330927)], (13439 ^ _781404) ^ [_1015186, _1015188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015186), _1015188)), -(_1015188 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015186), 13442 ^ [_1015186, _1015188]))], (37541 ^ _781404) ^ [_1488892, _1488894] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1488892), c_Orderings_Obot__class_Obot(tc_fun(_1488892, tc_HOL_Obool))), _1488894) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1488892, tc_HOL_Obool), tc_HOL_Obool)))], (49039 ^ _781404) ^ [_1770168, _1770170, _1770172, _1770174] : [-(c_Lazy__Sequence_Oproduct(_1770168, _1770170, _1770172, _1770174) = hAPP(c_Lazy__Sequence_Obind(_1770168, tc_prod(_1770168, _1770170), _1770172), hAPP(hAPP(c_COMBB(tc_fun(_1770170, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1770168, _1770170))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1770168, _1770170)), _1770168), c_Lazy__Sequence_Obind(_1770170, tc_prod(_1770168, _1770170), _1770174)), hAPP(hAPP(c_COMBB(tc_fun(_1770170, tc_prod(_1770168, _1770170)), tc_fun(_1770170, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1770168, _1770170))), _1770168), hAPP(c_COMBB(tc_prod(_1770168, _1770170), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1770168, _1770170)), _1770170), c_Lazy__Sequence_Osingle(tc_prod(_1770168, _1770170)))), c_Product__Type_OPair(_1770168, _1770170)))))], (46676 ^ _781404) ^ [_1720129, _1720131] : [-(c_Random_Opick(_1720129, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1720129), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1720129, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1720129, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1720129)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1720131)) = c_Random_Opick(_1720129, _1720131))], (43565 ^ _781404) ^ [_1649742, _1649744] : [_1649744 = c_List_Olist_ONil(_1649742), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649742)), _1649744) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25313 ^ _781404) ^ [_1234182, _1234184] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234182), _1234184) = c_Groups_Oone__class_Oone(tc_Int_Oint), 25318 ^ _781404 : [(25321 ^ _781404) ^ [] : [-(_1234184 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25319 ^ _781404) ^ [] : [-(_1234182 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 25322 ^ _781404 : [(25325 ^ _781404) ^ [] : [-(_1234184 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (25323 ^ _781404) ^ [] : [-(_1234182 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (39918 ^ _781404) ^ [_1557372, _1557374, _1557376] : [c_Wellfounded_Owf(_1557372, _1557374), -(c_Wellfounded_Owf(_1557372, c_Wellfounded_Omlex__prod(_1557372, _1557376, _1557374)))], (45261 ^ _781404) ^ [_1687540, _1687542, _1687544, _1687546, _1687548] : [class_Rings_Osemiring__0(_1687540), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687540), hAPP(hAPP(c_List_Omap(_1687542, _1687540), hAPP(hAPP(c_COMBC(_1687542, _1687540, _1687540), hAPP(hAPP(c_COMBB(_1687540, tc_fun(_1687540, _1687540), _1687542), c_Groups_Otimes__class_Otimes(_1687540)), _1687544)), _1687546)), _1687548)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1687540), hAPP(c_List_Omonoid__add__class_Olistsum(_1687540), hAPP(hAPP(c_List_Omap(_1687542, _1687540), _1687544), _1687548))), _1687546))], (52244 ^ _781404) ^ [_1837335, _1837337] : [class_Orderings_Obot(_1837335), -(class_Orderings_Obot(tc_fun(_1837337, _1837335)))], (36440 ^ _781404) ^ [_1462240, _1462242, _1462244] : [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), _1462240), _1462242))), -(hBOOL(hAPP(hAPP(_1462244, _1462240), _1462242))), 36447 ^ _781404 : [(36450 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 36446 ^ [_1462240, _1462242, _1462244]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1462244, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 36445 ^ [_1462240, _1462242, _1462244])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 36446 ^ [_1462240, _1462242, _1462244]))))], (36456 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1462244, 36445 ^ [_1462240, _1462242, _1462244]), 36446 ^ [_1462240, _1462242, _1462244]))], (36448 ^ _781404) ^ [] : [-(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), 36445 ^ [_1462240, _1462242, _1462244]), 36446 ^ [_1462240, _1462242, _1462244]))))]]], (37569 ^ _781404) ^ [_1489548] : [-(c_Relation_OId__on(_1489548, c_Orderings_Obot__class_Obot(tc_fun(_1489548, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489548, _1489548), tc_HOL_Obool)))], (20339 ^ _781404) ^ [_1142400, _1142402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1142400), _1142402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1142400)), c_Int_OBit1(_1142402))))], (37122 ^ _781404) ^ [_1477776, _1477778, _1477780, _1477782, _1477784, _1477786] : [hAPP(_1477782, hAPP(c_Product__Type_Ofst(_1477776, _1477780), _1477784)) = hAPP(_1477786, hAPP(c_Product__Type_Ofst(_1477776, _1477780), _1477784)), -(hAPP(c_Product__Type_Oapfst(_1477776, _1477778, _1477780, _1477782), _1477784) = hAPP(c_Product__Type_Oapfst(_1477776, _1477778, _1477780, _1477786), _1477784))], (37244 ^ _781404) ^ [_1480067, _1480069, _1480071, _1480073, _1480075, _1480077] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480067, tc_HOL_Obool), tc_fun(_1480067, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480067, tc_HOL_Obool), tc_fun(_1480067, tc_HOL_Obool)), _1480069), _1480071)), c_Wellfounded_Omax__ext(_1480067, _1480073))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480067, tc_HOL_Obool), tc_fun(_1480067, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480067, tc_HOL_Obool), tc_fun(_1480067, tc_HOL_Obool)), _1480075), _1480077)), c_Wellfounded_Omax__ext(_1480067, _1480073))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480067, tc_HOL_Obool), tc_fun(_1480067, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480067, tc_HOL_Obool), tc_fun(_1480067, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480067, tc_HOL_Obool)), _1480069), _1480075)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480067, tc_HOL_Obool)), _1480071), _1480077))), c_Wellfounded_Omax__ext(_1480067, _1480073))))], (32666 ^ _781404) ^ [_1369880, _1369882, _1369884] : [class_Orderings_Olinorder(_1369880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369880), _1369882)), -(_1369882 = c_Orderings_Obot__class_Obot(tc_fun(_1369880, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1369880, c_Orderings_Oord__class_Omax(_1369880), hAPP(hAPP(c_Set_Oinsert(_1369880), _1369884), _1369882)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1369880), _1369884), c_Big__Operators_Olattice_OSup__fin(_1369880, c_Orderings_Oord__class_Omax(_1369880), _1369882)))], (27361 ^ _781404) ^ [_1270086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1270086), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1270086) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1270086))], (24214 ^ _781404) ^ [_1215614, _1215616] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215614, _1215616) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215614, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1215616)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215614, _1215616)), _1215616))], (16060 ^ _781404) ^ [_1066252, _1066254, _1066256] : [class_Lattices_Olattice(_1066252), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066252), _1066254)), -(_1066254 = c_Orderings_Obot__class_Obot(tc_fun(_1066252, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066252), _1066256)), -(_1066256 = c_Orderings_Obot__class_Obot(tc_fun(_1066252, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1066252, tc_HOL_Obool)), _1066254), _1066256) = c_Orderings_Obot__class_Obot(tc_fun(_1066252, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1066252, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1066252, tc_HOL_Obool)), _1066254), _1066256)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066252), c_Big__Operators_Olattice__class_OSup__fin(_1066252, _1066254)), c_Big__Operators_Olattice__class_OSup__fin(_1066252, _1066256)))], (35692 ^ _781404) ^ [_1447363, _1447365] : [-(_1447363 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35695 ^ _781404 : [(35702 ^ _781404) ^ [] : [-(_1447365 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1447363, _1447365) = 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, _1447365))), 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, _1447363)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1447365))), c_Divides_Opdivmod(_1447363, _1447365)), 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), _1447365))))), c_Divides_Opdivmod(_1447363, _1447365)))))], (35696 ^ _781404) ^ [] : [_1447365 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1447363, _1447365) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1447363))]]], (15435 ^ _781404) ^ [_1054507, _1054509] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1054507), _1054509)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1054509), _1054507))], (25029 ^ _781404) ^ [_1229563, _1229565] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1229563), _1229565) = 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)), _1229563)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1229565))))], (3866 ^ _781404) ^ [_839461, _839463] : [_839463 = _839461, -(c_List_Odistinct(_839463) = c_List_Odistinct(_839461))], (33859 ^ _781404) ^ [_1401013, _1401015, _1401017, _1401019] : [-(hAPP(c_Finite__Set_Ofold__image(_1401013, _1401015, _1401017), _1401019) = c_Finite__Set_Ofold(_1401015, _1401013, hAPP(hAPP(c_COMBB(_1401013, tc_fun(_1401013, _1401013), _1401015), _1401017), _1401019)))], (30904 ^ _781404) ^ [_1336878, _1336880, _1336882, _1336884] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1336878), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1336878), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1336878), _1336880), _1336882)), _1336884) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1336878), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1336878), _1336880), _1336884)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1336878), _1336882), _1336884)))], (46790 ^ _781404) ^ [_1722694] : [-(c_List_Oupt(_1722694, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (36997 ^ _781404) ^ [_1475008, _1475010, _1475012, _1475014, _1475016] : [c_Finite__Set_Ofolding__idem(_1475008, _1475010, _1475012, _1475014), -(hAPP(c_Fun_Ocomp(_1475010, _1475010, _1475010, hAPP(_1475012, _1475016)), hAPP(_1475012, _1475016)) = hAPP(_1475012, _1475016))], (19238 ^ _781404) ^ [_1123520] : [19239 ^ _781404 : [(19240 ^ _781404) ^ [_1123577] : [hBOOL(hAPP(_1123520, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123577)))]], 19242 ^ _781404 : [(19245 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1123520, 19241 ^ [_1123520])))], (19243 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19241 ^ [_1123520])))]]], (38710 ^ _781404) ^ [_1518040, _1518042, _1518044] : [-(c_Relation_Orefl__on(_1518040, _1518042, _1518044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518040, _1518040), tc_HOL_Obool)), _1518044), hAPP(hAPP(c_Product__Type_OSigma(_1518040, _1518040), _1518042), hAPP(c_COMBK(tc_fun(_1518040, tc_HOL_Obool), _1518040), _1518042)))), 38716 ^ _781404 : [(38719 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1518040, _1518040)), hAPP(hAPP(c_Product__Type_OPair(_1518040, _1518040), 38715 ^ [_1518040, _1518042, _1518044]), 38715 ^ [_1518040, _1518042, _1518044])), _1518044))], (38717 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1518040), 38715 ^ [_1518040, _1518042, _1518044]), _1518042)))]]], (41379 ^ _781404) ^ [_1592250] : [-(hAPP(c_Relation_ODomain(_1592250, _1592250), c_Relation_OId(_1592250)) = c_Orderings_Otop__class_Otop(tc_fun(_1592250, tc_HOL_Obool)))], (49642 ^ _781404) ^ [_1783309, _1783311, _1783313, _1783315] : [c_Relation_Otrans(_1783309, _1783311), c_Relation_Otrans(_1783313, _1783315), -(c_Relation_Otrans(tc_prod(_1783309, _1783313), c_Wellfounded_Olex__prod(_1783309, _1783313, _1783311, _1783315)))], (19929 ^ _781404) ^ [_1135375, _1135377, _1135379] : [class_Rings_Olinordered__idom(_1135375), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135375), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135375), hAPP(hAPP(c_Power_Opower__class_Opower(_1135375), _1135377), 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(_1135375), _1135379), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1135375)))], (44122 ^ _781404) ^ [_1661697, _1661699, _1661701] : [-(_1661697 = c_List_Olist_ONil(_1661699)), -(c_List_Obutlast(_1661699, hAPP(hAPP(c_List_Oappend(_1661699), _1661701), _1661697)) = hAPP(hAPP(c_List_Oappend(_1661699), _1661701), c_List_Obutlast(_1661699, _1661697)))], (46834 ^ _781404) ^ [_1723519, _1723521, _1723523, _1723525] : [-(c_List_Oupt(_1723519, _1723521) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1723523), _1723525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723519), _1723521)), _1723519 = _1723523, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1723519), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1723521) = _1723525], (41508 ^ _781404) ^ [_1595284, _1595286] : [c_Wellfounded_Oacyclic(_1595284, hAPP(c_Relation_Oconverse(_1595284, _1595284), _1595286)), -(c_Wellfounded_Oacyclic(_1595284, _1595286))], (15713 ^ _781404) ^ [_1059493, _1059495, _1059497, _1059499, _1059501, _1059503] : [c_Fun_Oinj__on(_1059493, _1059495, _1059497, _1059499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059495, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1059493, _1059495, _1059497), _1059499)), _1059501)), c_Fun_Oinj__on(_1059495, _1059493, _1059503, _1059501), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059493, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1059495, _1059493, _1059503), _1059501)), _1059499)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059493), _1059499)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059495), _1059501)), -(hAPP(c_Finite__Set_Ocard(_1059493), _1059499) = hAPP(c_Finite__Set_Ocard(_1059495), _1059501))], (46907 ^ _781404) ^ [_1725234, _1725236, _1725238, _1725240, _1725242] : [class_Orderings_Olinorder(_1725234), hBOOL(hAPP(hAPP(c_member(_1725236), _1725238), hAPP(c_List_Oset(_1725236), _1725240))), c_List_Olinorder__class_Osorted(_1725234, hAPP(hAPP(c_List_Omap(_1725236, _1725234), _1725242), _1725240)), hAPP(c_List_Ohd(_1725236), hAPP(c_List_Ofilter(_1725236, hAPP(hAPP(c_COMBB(_1725234, tc_HOL_Obool, _1725236), hAPP(c_fequal, hAPP(_1725242, _1725238))), _1725242)), _1725240)) = _1725238, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1725236, _1725234, _1725242), _1725238), c_List_Oremove1(_1725236, _1725238, _1725240)) = _1725240)], (1756 ^ _781404) ^ [_806394, _806396] : [-(class_Rings_Ocomm__semiring__1(_806394)), _806396 = _806394, class_Rings_Ocomm__semiring__1(_806396)], (33619 ^ _781404) ^ [_1394345, _1394347, _1394349, _1394351, _1394353] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394345, tc_fun(_1394347, tc_HOL_Obool)), _1394349), hAPP(hAPP(c_COMBB(tc_fun(_1394347, tc_HOL_Obool), tc_fun(_1394347, tc_HOL_Obool), _1394345), hAPP(c_Set_Oinsert(_1394347), _1394351)), _1394353)) = hAPP(hAPP(c_Set_Oinsert(_1394347), _1394351), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394345, tc_fun(_1394347, tc_HOL_Obool)), _1394349), _1394353)))], (26337 ^ _781404) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (42455 ^ _781404) ^ [_1621468, _1621470, _1621472, _1621474, _1621476] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621468), tc_List_Olist(_1621468))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621468), tc_List_Olist(_1621468)), _1621470), _1621472)), c_List_Olistrel(_1621468, c_Transitive__Closure_Ortrancl(_1621468, _1621474)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621468), tc_List_Olist(_1621468))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621468), tc_List_Olist(_1621468)), _1621472), _1621476)), c_List_Olistrel(_1621468, c_Transitive__Closure_Ortrancl(_1621468, _1621474)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621468), tc_List_Olist(_1621468))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621468), tc_List_Olist(_1621468)), _1621470), _1621476)), c_List_Olistrel(_1621468, c_Transitive__Closure_Ortrancl(_1621468, _1621474)))))], (16104 ^ _781404) ^ [_1067077, _1067079, _1067081] : [class_Lattices_Olattice(_1067077), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067077), _1067079)), -(_1067079 = c_Orderings_Obot__class_Obot(tc_fun(_1067077, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067077), _1067081)), -(_1067081 = c_Orderings_Obot__class_Obot(tc_fun(_1067077, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1067077, tc_HOL_Obool)), _1067079), _1067081) = c_Orderings_Obot__class_Obot(tc_fun(_1067077, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1067077, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1067077, tc_HOL_Obool)), _1067079), _1067081)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067077), c_Big__Operators_Olattice__class_OInf__fin(_1067077, _1067079)), c_Big__Operators_Olattice__class_OInf__fin(_1067077, _1067081)))], (29921 ^ _781404) ^ [_1317789, _1317791, _1317793] : [class_Groups_Ocomm__monoid__mult(_1317789), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317791, _1317789), _1317793), c_Orderings_Obot__class_Obot(tc_fun(_1317791, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1317789))], (31528 ^ _781404) ^ [_1348589, _1348591, _1348593] : [class_Orderings_Olinorder(_1348589), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348589), _1348591)), -(hBOOL(hAPP(hAPP(c_member(_1348589), _1348593), _1348591))), -(c_Big__Operators_Olattice_OInf__fin(_1348589, c_Orderings_Oord__class_Omin(_1348589), hAPP(hAPP(c_Set_Oinsert(_1348589), _1348593), _1348591)) = hAPP(hAPP(c_Finite__Set_Ofold(_1348589, _1348589, c_Orderings_Oord__class_Omin(_1348589)), _1348593), _1348591))], (49812 ^ _781404) ^ [_1786951, _1786953] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1786951, tc_HOL_Obool), _1786953) = hAPP(c_Set_OCollect(_1786951), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1786951, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1786951), c_HOL_OEx(tc_fun(_1786951, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1786951, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1786951, tc_HOL_Obool), tc_HOL_Obool), _1786951), hAPP(c_COMBS(tc_fun(_1786951, 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(_1786951, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1786951, tc_HOL_Obool), tc_fun(tc_fun(_1786951, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1786951, tc_HOL_Obool))), _1786953)))), c_member(_1786951)))))], (47198 ^ _781404) ^ [_1730092, _1730094, _1730096] : [class_Orderings_Olinorder(_1730092), 47201 ^ _781404 : [(47220 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1730092, hAPP(hAPP(c_List_Oappend(_1730092), _1730094), _1730096))), c_List_Olinorder__class_Osorted(_1730092, _1730094), c_List_Olinorder__class_Osorted(_1730092, _1730096), 47230 ^ _781404 : [(47236 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1730092), 47229 ^ [_1730092, _1730094, _1730096]), 47232 ^ [_1730092, _1730094, _1730096]))], (47234 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730092), 47232 ^ [_1730092, _1730094, _1730096]), hAPP(c_List_Oset(_1730092), _1730096))))], (47231 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730092), 47229 ^ [_1730092, _1730094, _1730096]), hAPP(c_List_Oset(_1730092), _1730094))))]]], (47202 ^ _781404) ^ [] : [c_List_Olinorder__class_Osorted(_1730092, hAPP(hAPP(c_List_Oappend(_1730092), _1730094), _1730096)), 47205 ^ _781404 : [(47210 ^ _781404) ^ [_1730328] : [hBOOL(hAPP(hAPP(c_member(_1730092), _1730328), hAPP(c_List_Oset(_1730092), _1730094))), 47213 ^ _781404 : [(47214 ^ _781404) ^ [_1730438] : [hBOOL(hAPP(hAPP(c_member(_1730092), _1730438), hAPP(c_List_Oset(_1730092), _1730096))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1730092), _1730328), _1730438)))]]], (47208 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1730092, _1730096))], (47206 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1730092, _1730094))]]]]], (40134 ^ _781404) ^ [_1562263, _1562265] : [-(c_HOL_OThe(_1562263, hAPP(c_fequal, _1562265)) = _1562265)], (534 ^ _781404) ^ [_789423, _789425, _789427, _789429, _789431, _789433] : [-(c_Nitpick_Oless__eq__frac(_789431, _789427, _789423)), c_Nitpick_Oless__eq__frac(_789433, _789429, _789425), _789433 = _789431, _789429 = _789427, _789425 = _789423], (14178 ^ _781404) ^ [_1028985, _1028987, _1028989] : [class_Groups_Oordered__comm__monoid__add(_1028985), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028985), _1028987), c_Groups_Ozero__class_Ozero(_1028985))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028985), _1028989), c_Groups_Ozero__class_Ozero(_1028985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028985), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028985), _1028987), _1028989)), c_Groups_Ozero__class_Ozero(_1028985))))], (48615 ^ _781404) ^ [_1760725, _1760727, _1760729] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1760725), _1760727, _1760729)), -(c_List_Olist__ex(tc_Nat_Onat, _1760725, c_List_Oupt(_1760727, _1760729)))], (42691 ^ _781404) ^ [_1628357, _1628359, _1628361] : [-(hAPP(hAPP(c_List_Onth(_1628357), hAPP(hAPP(c_List_Olist_OCons(_1628357), _1628359), _1628361)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1628359)], (44060 ^ _781404) ^ [_1660609, _1660611, _1660613] : [-(hAPP(hAPP(c_List_Oappend(_1660609), _1660611), _1660613) = c_List_Olist_ONil(_1660609)), _1660611 = c_List_Olist_ONil(_1660609), _1660613 = c_List_Olist_ONil(_1660609)], (39252 ^ _781404) ^ [_1534290, _1534292, _1534294] : [class_Orderings_Olinorder(_1534290), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534290), _1534292)), -(_1534292 = c_Orderings_Obot__class_Obot(tc_fun(_1534290, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1534290), _1534294), c_Big__Operators_Olattice_OSup__fin(_1534290, c_Orderings_Oord__class_Omax(_1534290), _1534292)) = c_Big__Operators_Olattice_OSup__fin(_1534290, c_Orderings_Oord__class_Omax(_1534290), hAPP(c_Set_OCollect(_1534290), hAPP(hAPP(c_COMBB(tc_fun(_1534290, tc_HOL_Obool), tc_HOL_Obool, _1534290), c_HOL_OEx(_1534290)), hAPP(hAPP(c_COMBC(_1534290, tc_fun(_1534290, tc_HOL_Obool), tc_fun(_1534290, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534290, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1534290, tc_HOL_Obool), tc_fun(_1534290, tc_HOL_Obool)), _1534290), c_COMBS(_1534290, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534290, tc_HOL_Obool), tc_fun(_1534290, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1534290), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534290), c_fconj)), hAPP(hAPP(c_COMBC(_1534290, tc_fun(_1534290, _1534290), tc_fun(_1534290, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534290, tc_HOL_Obool), tc_fun(tc_fun(_1534290, _1534290), tc_fun(_1534290, tc_HOL_Obool)), _1534290), c_COMBB(_1534290, tc_HOL_Obool, _1534290)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1534290), _1534294))))), hAPP(hAPP(c_COMBC(_1534290, tc_fun(_1534290, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534290)), _1534292))))))], (16539 ^ _781404) ^ [_1075562, _1075564, _1075566, _1075568] : [-(c_Sum__Type_OPlus(_1075562, _1075564, _1075566, _1075568) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1075562, _1075564), tc_HOL_Obool))), _1075566 = c_Orderings_Obot__class_Obot(tc_fun(_1075562, tc_HOL_Obool)), _1075568 = c_Orderings_Obot__class_Obot(tc_fun(_1075564, tc_HOL_Obool))], (39003 ^ _781404) ^ [_1526454, _1526456, _1526458] : [-(hAPP(c_Set_OCollect(_1526454), hAPP(hAPP(c_COMBS(_1526454, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526454), c_fdisj), _1526456)), _1526458)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1526454, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1526454), _1526456)), hAPP(c_Set_OCollect(_1526454), _1526458)))], (23914 ^ _781404) ^ [_1210601, _1210603, _1210605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210601)), 23917 ^ _781404 : [(23918 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1210603, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1210605), _1210601)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1210605, _1210601))), 23921 ^ _781404 : [(23922 ^ _781404) ^ [_1210802, _1210804] : [-(hBOOL(hAPP(hAPP(_1210603, _1210804), _1210802))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210802), _1210601)), _1210605 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1210601), _1210804)), _1210802)]]], (23936 ^ _781404) ^ [] : [23939 ^ _781404 : [(23942 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23938 ^ [_1210601, _1210603, _1210605]), _1210601)))], (23944 ^ _781404) ^ [] : [-(_1210605 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1210601), 23937 ^ [_1210601, _1210603, _1210605])), 23938 ^ [_1210601, _1210603, _1210605]))], (23946 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1210603, 23937 ^ [_1210601, _1210603, _1210605]), 23938 ^ [_1210601, _1210603, _1210605]))], (23940 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23938 ^ [_1210601, _1210603, _1210605])))]], -(hBOOL(hAPP(hAPP(_1210603, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1210605), _1210601)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1210605, _1210601))))]]], (49183 ^ _781404) ^ [_1772824, _1772826, _1772828] : [_1772826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1772824) = c_List_Oreplicate(_1772824, _1772826, _1772828))], (19091 ^ _781404) ^ [_1121141, _1121143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121141), _1121143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1121141)), c_Int_OBit1(_1121143))))], (36826 ^ _781404) ^ [_1470538, _1470540, _1470542] : [class_Orderings_Owellorder(_1470538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1470538), _1470540), c_Orderings_Oord__class_OLeast(_1470538, _1470542))), hBOOL(hAPP(_1470542, _1470540))], (19440 ^ _781404) ^ [_1127087, _1127089, _1127091] : [class_Rings_Olinordered__semidom(_1127087), 19443 ^ _781404 : [(19450 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127089), _1127091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127087), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127087), _1127089)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127087), _1127091))))], (19444 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127087), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127087), _1127089)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127087), _1127091))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127089), _1127091)))]]], (35069 ^ _781404) ^ [_1434539, _1434541] : [-(c_Divides_OnegDivAlg(_1434539, _1434541) = hAPP(c_Divides_Oadjust(_1434541), c_Divides_OnegDivAlg(_1434539, 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)))), _1434541)))), -(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), _1434539), _1434541)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434541), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41852 ^ _781404) ^ [_1603603, _1603605, _1603607, _1603609] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1603603, _1603605), tc_fun(_1603603, _1603605)), _1603607), c_Fun_Ocomp(_1603605, _1603605, _1603603, _1603609)) = c_Fun_Ocomp(_1603605, _1603605, _1603603, hAPP(hAPP(c_Nat_Ocompow(_1603605, _1603605), _1603607), _1603609)))], (42125 ^ _781404) ^ [_1611176, _1611178, _1611180] : [-(c_Nitpick_Oplus__frac(_1611176, _1611178, _1611180) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1611176), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1611176), _1611178), hAPP(c_Nitpick_Odenom(_1611176), _1611180))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1611176), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1611176), tc_Int_Oint), c_Nitpick_Ofrac(_1611176)), 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(_1611176), _1611178))), 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(_1611176), _1611178))))), 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(_1611176), _1611180))), 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(_1611176), _1611180)))))), c_COMBI(tc_Int_Oint))))], (37497 ^ _781404) ^ [_1487750, _1487752] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1487750, _1487750)), hAPP(hAPP(c_Product__Type_OPair(_1487750, _1487750), 37498 ^ [_1487750, _1487752]), 37498 ^ [_1487750, _1487752])), _1487752))), -(c_Relation_Oirrefl(_1487750, _1487752))], (17218 ^ _781404) ^ [_1088338, _1088340] : [class_Int_Onumber__ring(_1088338), -(hAPP(c_Int_Onumber__class_Onumber__of(_1088338), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1088340)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1088338), hAPP(c_Int_Onumber__class_Onumber__of(_1088338), _1088340)))], (47603 ^ _781404) ^ [_1738676, _1738678, _1738680, _1738682] : [class_Orderings_Olinorder(_1738676), c_List_Olinorder__class_Osorted(_1738676, hAPP(c_List_Orev(_1738676), _1738678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1738680), _1738682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738682), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738676)), _1738678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1738676), hAPP(hAPP(c_List_Onth(_1738676), _1738678), _1738682)), hAPP(hAPP(c_List_Onth(_1738676), _1738678), _1738680))))], (51626 ^ _781404) ^ [_1826954, _1826956, _1826958, _1826960, _1826962] : [class_Rings_Ocomm__semiring__1(_1826954), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826954), _1826956), _1826958)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826954), _1826960), _1826962)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826954), _1826956), _1826960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826954), _1826958), _1826962))))], (45401 ^ _781404) ^ [_1690702, _1690704, _1690706, _1690708] : [class_Groups_Oab__group__add(_1690702), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1690702), hAPP(c_List_Omonoid__add__class_Olistsum(_1690702), hAPP(hAPP(c_List_Omap(_1690704, _1690702), _1690706), _1690708))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1690702), hAPP(hAPP(c_List_Omap(_1690704, _1690702), hAPP(c_Fun_Ocomp(_1690702, _1690702, _1690704, c_Groups_Ouminus__class_Ouminus(_1690702)), _1690706)), _1690708)))], (10455 ^ _781404) ^ [_959347, _959349, _959351, _959353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959347, tc_HOL_Obool)), _959349), _959351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_959347, tc_HOL_Obool)), _959351), _959353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_959347, tc_HOL_Obool)), _959349), _959353)))], (47555 ^ _781404) ^ [_1737512, _1737514, _1737516] : [-(hAPP(c_List_Orev(_1737512), hAPP(hAPP(c_List_Olist_OCons(_1737512), _1737514), _1737516)) = hAPP(hAPP(c_List_Oappend(_1737512), hAPP(c_List_Orev(_1737512), _1737516)), hAPP(hAPP(c_List_Olist_OCons(_1737512), _1737514), c_List_Olist_ONil(_1737512))))], (52272 ^ _781404) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (45805 ^ _781404) ^ [_1699656, _1699658, _1699660, _1699662] : [-(hBOOL(hAPP(c_List_Olistsp(_1699656, hAPP(hAPP(c_COMBS(_1699656, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1699656), c_fconj), _1699658)), _1699660)), _1699662))), hBOOL(hAPP(c_List_Olistsp(_1699656, _1699658), _1699662)), hBOOL(hAPP(c_List_Olistsp(_1699656, _1699660), _1699662))], (52156 ^ _781404) ^ [_1836179, _1836181] : [class_Lattices_Obounded__lattice(_1836179), -(class_Lattices_Obounded__lattice(tc_fun(_1836181, _1836179)))], (35654 ^ _781404) ^ [_1446876, _1446878] : [35655 ^ _781404 : [(35658 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1446878), _1446876))], (35656 ^ _781404) ^ [] : [_1446876 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1446878, _1446876) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1446878))], (33853 ^ _781404) ^ [_1400872, _1400874, _1400876, _1400878, _1400880] : [c_Finite__Set_Ofun__left__comm(_1400872, _1400874, _1400876), -(hAPP(c_Fun_Ocomp(_1400874, _1400874, _1400874, hAPP(_1400876, _1400878)), hAPP(_1400876, _1400880)) = hAPP(c_Fun_Ocomp(_1400874, _1400874, _1400874, hAPP(_1400876, _1400880)), hAPP(_1400876, _1400878)))], (26417 ^ _781404) ^ [_1252353] : [class_Rings_Oring__1(_1252353), -(hAPP(c_Int_Oring__1__class_Oof__int(_1252353), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1252353))], (2048 ^ _781404) ^ [_811000, _811002, _811004, _811006, _811008, _811010] : [-(c_SetInterval_Oord_OlessThan(_811010, _811006, _811002) = c_SetInterval_Oord_OlessThan(_811008, _811004, _811000)), _811010 = _811008, _811006 = _811004, _811002 = _811000], (45511 ^ _781404) ^ [_1693115, _1693117] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1693115), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1693117), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 45518 ^ _781404 : [(45525 ^ _781404) ^ [] : [_1693115 = _1693117, -(hAPP(c_Code__Numeral_Oof__nat, _1693115) = hAPP(c_Code__Numeral_Oof__nat, _1693117))], (45519 ^ _781404) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1693115) = hAPP(c_Code__Numeral_Oof__nat, _1693117), -(_1693115 = _1693117)]]], (19017 ^ _781404) ^ [_1119909, _1119911] : [class_Int_Onumber__ring(_1119909), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1119909), hAPP(c_Int_Onumber__class_Onumber__of(_1119909), _1119911)), c_Groups_Oone__class_Oone(_1119909)) = hAPP(c_Int_Onumber__class_Onumber__of(_1119909), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1119911), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (32900 ^ _781404) ^ [_1374317, _1374319, _1374321, _1374323] : [class_Orderings_Olinorder(_1374317), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374317), _1374319)), 32910 ^ _781404 : [(32913 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374317), 32909 ^ [_1374317, _1374319, _1374321, _1374323]), _1374321))], (32911 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1374317), 32909 ^ [_1374317, _1374319, _1374321, _1374323]), _1374319)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374317), hAPP(hAPP(c_Finite__Set_Ofold(_1374317, _1374317, c_Orderings_Oord__class_Omax(_1374317)), _1374323), _1374319)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1374317), _1374321), _1374323))))], (49089 ^ _781404) ^ [_1771167, _1771169, _1771171, _1771173] : [49097 ^ _781404 : [(49100 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1771173, 49096 ^ [_1771167, _1771169, _1771171, _1771173])))], (49098 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771167), 49096 ^ [_1771167, _1771169, _1771171, _1771173]), hAPP(c_List_Oset(_1771167), c_List_Oreplicate(_1771167, _1771169, _1771171)))))]], hBOOL(hAPP(_1771173, _1771171)), -(_1771169 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23561 ^ _781404) ^ [_1204375, _1204377, _1204379] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1204375), _1204377)), _1204379) = 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), _1204375), _1204379)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204377), _1204379))), 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, _1204375, _1204379)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1204377, _1204379))), _1204379)))], (33548 ^ _781404) ^ [_1392142, _1392144, _1392146, _1392148] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1392142, tc_HOL_Obool), tc_fun(_1392144, tc_HOL_Obool)), _1392146), hAPP(hAPP(c_COMBC(tc_fun(_1392142, tc_HOL_Obool), tc_fun(_1392142, tc_fun(_1392144, tc_HOL_Obool)), tc_fun(_1392144, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392142, tc_fun(_1392144, tc_HOL_Obool))), _1392148)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392142, tc_fun(_1392144, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1392142, tc_HOL_Obool), _1392146)), _1392148))], (26863 ^ _781404) ^ [_1260803, _1260805, _1260807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1260805), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1260807), 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), _1260807), _1260805))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1260803)))))], (35474 ^ _781404) ^ [_1443232, _1443234, _1443236, _1443238, _1443240, _1443242, _1443244] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1443232, _1443234, tc_fun(_1443236, tc_HOL_Obool)), _1443238), hAPP(hAPP(c_Product__Type_OPair(_1443232, _1443234), _1443240), _1443242)), _1443244)), -(hBOOL(hAPP(hAPP(hAPP(_1443238, _1443240), _1443242), _1443244)))], (34517 ^ _781404) ^ [_1421285, _1421287, _1421289, _1421291] : [-(hAPP(c_Set_Ovimage(_1421285, _1421287, _1421289), _1421291) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1421287, tc_fun(_1421285, tc_HOL_Obool)), _1421291), hAPP(hAPP(c_COMBB(tc_fun(_1421287, tc_HOL_Obool), tc_fun(_1421285, tc_HOL_Obool), _1421287), c_Set_Ovimage(_1421285, _1421287, _1421289)), hAPP(hAPP(c_COMBC(_1421287, tc_fun(_1421287, tc_HOL_Obool), tc_fun(_1421287, tc_HOL_Obool)), c_Set_Oinsert(_1421287)), c_Orderings_Obot__class_Obot(tc_fun(_1421287, tc_HOL_Obool))))))], (19315 ^ _781404) ^ [_1124975, _1124977] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124975)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1124977)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1124975), _1124977)))], (38185 ^ _781404) ^ [_1505255] : [-(c_Relation_Orefl__on(_1505255, c_Orderings_Obot__class_Obot(tc_fun(_1505255, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1505255, _1505255), tc_HOL_Obool))))], (39699 ^ _781404) ^ [_1550869, _1550871, _1550873, _1550875] : [39700 ^ _781404 : [(39701 ^ _781404) ^ [_1550944] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1550873, _1550869)), hAPP(hAPP(c_Product__Type_OPair(_1550873, _1550869), _1550944), _1550871)), _1550875))]], -(hBOOL(hAPP(hAPP(c_member(_1550869), _1550871), hAPP(c_Relation_ORange(_1550873, _1550869), _1550875))))], (33607 ^ _781404) ^ [_1393814, _1393816, _1393818, _1393820, _1393822, _1393824] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393814, tc_fun(_1393816, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393818, tc_fun(_1393814, tc_HOL_Obool)), _1393820), _1393822)), _1393824) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393818, tc_fun(_1393816, tc_HOL_Obool)), _1393820), hAPP(hAPP(c_COMBC(_1393818, tc_fun(_1393814, tc_fun(_1393816, tc_HOL_Obool)), tc_fun(_1393816, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393814, tc_HOL_Obool), tc_fun(tc_fun(_1393814, tc_fun(_1393816, tc_HOL_Obool)), tc_fun(_1393816, tc_HOL_Obool)), _1393818), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393814, tc_fun(_1393816, tc_HOL_Obool))), _1393822)), _1393824)))], (52328 ^ _781404) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (16891 ^ _781404) ^ [_1082138] : [class_Groups_Osgn__if(_1082138), -(c_Groups_Osgn__class_Osgn(_1082138, c_Groups_Ozero__class_Ozero(_1082138)) = c_Groups_Ozero__class_Ozero(_1082138))], (692 ^ _781404) ^ [_791848, _791850, _791852, _791854] : [-(c_List_Olinorder__class_Osorted(_791852, _791848)), c_List_Olinorder__class_Osorted(_791854, _791850), _791854 = _791852, _791850 = _791848], (11928 ^ _781404) ^ [_985831, _985833] : [_985833 = c_Orderings_Obot__class_Obot(tc_fun(_985831, tc_HOL_Obool)), 11931 ^ _781404 : [(11932 ^ _781404) ^ [_985911] : [hBOOL(hAPP(hAPP(c_member(_985831), _985911), _985833))]]], (17777 ^ _781404) ^ [_1098367, _1098369, _1098371, _1098373, _1098375] : [c_Finite__Set_Ofolding__one(_1098367, _1098369, _1098371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098367), _1098373)), -(hBOOL(hAPP(hAPP(c_member(_1098367), _1098375), _1098373))), -(hAPP(_1098371, hAPP(hAPP(c_Set_Oinsert(_1098367), _1098375), _1098373)) = hAPP(hAPP(c_Finite__Set_Ofold(_1098367, _1098367, _1098369), _1098375), _1098373))], (43667 ^ _781404) ^ [_1651637, _1651639, _1651641] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651637), tc_List_Olist(_1651637))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651637), tc_List_Olist(_1651637)), _1651639), c_List_Olist_ONil(_1651637))), c_List_Olexord(_1651637, _1651641)))], (25529 ^ _781404) ^ [_1237652, _1237654] : [hAPP(c_Int_Onat, _1237652) = _1237654, 25532 ^ _781404 : [(25539 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237652))), -(_1237654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25533 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237652)), -(_1237652 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1237654))]]], (11995 ^ _781404) ^ [_986987, _986989, _986991, _986993] : [hBOOL(hAPP(hAPP(c_member(_986987), _986989), _986991)), -(hBOOL(hAPP(hAPP(c_member(_986987), _986989), hAPP(hAPP(c_Set_Oinsert(_986987), _986993), _986991))))], (43905 ^ _781404) ^ [_1657152, _1657154, _1657156, _1657158, _1657160, _1657162] : [hAPP(hAPP(c_List_Olist_OCons(_1657152), _1657154), _1657156) = _1657158, _1657160 = hAPP(hAPP(c_List_Oappend(_1657152), _1657156), _1657162), -(hAPP(hAPP(c_List_Olist_OCons(_1657152), _1657154), _1657160) = hAPP(hAPP(c_List_Oappend(_1657152), _1657158), _1657162))], (21283 ^ _781404) ^ [_1159636, _1159638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159636), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159636)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159638)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16086 ^ _781404) ^ [_1066729, _1066731, _1066733] : [class_Lattices_Olattice(_1066729), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066729), _1066731)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066729), _1066733)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1066729, tc_HOL_Obool)), _1066731), _1066733) = c_Orderings_Obot__class_Obot(tc_fun(_1066729, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066729), c_Big__Operators_Olattice__class_OSup__fin(_1066729, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1066729, tc_HOL_Obool)), _1066731), _1066733))), c_Big__Operators_Olattice__class_OSup__fin(_1066729, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1066729, tc_HOL_Obool)), _1066731), _1066733))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066729), c_Big__Operators_Olattice__class_OSup__fin(_1066729, _1066731)), c_Big__Operators_Olattice__class_OSup__fin(_1066729, _1066733)))], (35535 ^ _781404) ^ [_1444528, _1444530, _1444532, _1444534, _1444536, _1444538] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1444528, _1444530, _1444532), _1444534), hAPP(hAPP(c_Product__Type_OPair(_1444528, _1444530), _1444536), _1444538)) = hAPP(hAPP(_1444534, _1444536), _1444538))], (34079 ^ _781404) ^ [_1407090, _1407092, _1407094, _1407096, _1407098] : [class_Groups_Ocomm__monoid__add(_1407090), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407092), _1407094)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1407092, _1407090), hAPP(hAPP(c_COMBS(_1407092, _1407090, _1407090), hAPP(hAPP(c_COMBB(_1407090, tc_fun(_1407090, _1407090), _1407092), c_Groups_Oplus__class_Oplus(_1407090)), _1407096)), _1407098)), _1407094) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1407090), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1407092, _1407090), _1407096), _1407094)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1407092, _1407090), _1407098), _1407094)))], (11765 ^ _781404) ^ [_982647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982647), _982647))], (46291 ^ _781404) ^ [_1710297, _1710299, _1710301, _1710303] : [-(hAPP(c_List_OremoveAll(_1710297, _1710299), hAPP(hAPP(c_List_Oappend(_1710297), _1710301), _1710303)) = hAPP(hAPP(c_List_Oappend(_1710297), hAPP(c_List_OremoveAll(_1710297, _1710299), _1710301)), hAPP(c_List_OremoveAll(_1710297, _1710299), _1710303)))], (20117 ^ _781404) ^ [_1138636] : [-(c_Int_OBit0(_1138636) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1138636), _1138636))], (52462 ^ _781404) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (15084 ^ _781404) ^ [_1047445, _1047447] : [class_Rings_Ocomm__semiring__1(_1047445), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047445), c_Groups_Ozero__class_Ozero(_1047445)), _1047447) = _1047447)], (24328 ^ _781404) ^ [_1217671, _1217673, _1217675] : [-(hBOOL(hAPP(_1217671, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1217673), _1217675)))), 24331 ^ _781404 : [(24334 ^ _781404) ^ [] : [hBOOL(hAPP(_1217671, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24332 ^ _781404) ^ [] : [-(_1217675 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 24337 ^ _781404 : [(24338 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217675)))], (24344 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24340 ^ [_1217671, _1217673, _1217675]), _1217675)))], (24348 ^ _781404) ^ [] : [hBOOL(hAPP(_1217671, 24339 ^ [_1217671, _1217673, _1217675]))], (24346 ^ _781404) ^ [] : [-(_1217673 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1217675), 24339 ^ [_1217671, _1217673, _1217675])), 24340 ^ [_1217671, _1217673, _1217675]))], (24342 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24340 ^ [_1217671, _1217673, _1217675])))]], 24349 ^ _781404 : [(24350 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217675), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24356 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24352 ^ [_1217671, _1217673, _1217675]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24360 ^ _781404) ^ [] : [hBOOL(hAPP(_1217671, 24351 ^ [_1217671, _1217673, _1217675]))], (24358 ^ _781404) ^ [] : [-(_1217673 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1217675), 24351 ^ [_1217671, _1217673, _1217675])), 24352 ^ [_1217671, _1217673, _1217675]))], (24354 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217675), 24352 ^ [_1217671, _1217673, _1217675])))]]], (45058 ^ _781404) ^ [_1682755, _1682757, _1682759] : [_1682755 = c_List_Olist_ONil(_1682757), -(c_List_Olast(_1682757, hAPP(hAPP(c_List_Oappend(_1682757), _1682759), _1682755)) = c_List_Olast(_1682757, _1682759))], (44262 ^ _781404) ^ [_1665405, _1665407, _1665409, _1665411, _1665413, _1665415] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665405), tc_List_Olist(_1665405))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665405), tc_List_Olist(_1665405)), hAPP(hAPP(c_List_Oappend(_1665405), _1665407), hAPP(hAPP(c_List_Olist_OCons(_1665405), _1665409), c_List_Olist_ONil(_1665405)))), hAPP(hAPP(c_List_Oappend(_1665405), _1665411), hAPP(hAPP(c_List_Olist_OCons(_1665405), _1665413), c_List_Olist_ONil(_1665405))))), c_List_Olistrel1(_1665405, _1665415))), 44267 ^ _781404 : [(44270 ^ _781404) ^ [] : [-(_1665409 = _1665413)], (44268 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665405), tc_List_Olist(_1665405))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665405), tc_List_Olist(_1665405)), _1665407), _1665411)), c_List_Olistrel1(_1665405, _1665415))))]], 44271 ^ _781404 : [(44274 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1665405, _1665405)), hAPP(hAPP(c_Product__Type_OPair(_1665405, _1665405), _1665409), _1665413)), _1665415)))], (44272 ^ _781404) ^ [] : [-(_1665407 = _1665411)]]], (43449 ^ _781404) ^ [_1647748, _1647750, _1647752] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647748), tc_List_Olist(_1647748))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647748), tc_List_Olist(_1647748)), c_List_Olist_ONil(_1647748)), _1647750)), c_List_Olistrel(_1647748, _1647752))), -(_1647750 = c_List_Olist_ONil(_1647748))], (52414 ^ _781404) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (32530 ^ _781404) ^ [_1367395, _1367397, _1367399] : [class_Orderings_Olinorder(_1367395), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367395), _1367397)), -(_1367397 = c_Orderings_Obot__class_Obot(tc_fun(_1367395, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367395), _1367399)), -(_1367399 = c_Orderings_Obot__class_Obot(tc_fun(_1367395, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367395, tc_HOL_Obool)), _1367397), _1367399) = c_Orderings_Obot__class_Obot(tc_fun(_1367395, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1367395, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1367395, tc_HOL_Obool)), _1367397), _1367399)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367395), c_Big__Operators_Olinorder__class_OMax(_1367395, _1367397)), c_Big__Operators_Olinorder__class_OMax(_1367395, _1367399)))], (7171 ^ _781404) ^ [_897592, _897594, _897596] : [class_Lattices_Olattice(_897592), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897592), _897594), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897592), _897596), _897594))))], (8914 ^ _781404) ^ [_932226, _932228] : [8916 ^ _781404 : [(8919 ^ _781404) ^ [] : [hBOOL(hAPP(_932228, 8915 ^ [_932226, _932228]))], (8917 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 8915 ^ [_932226, _932228]), _932226)))]], 8920 ^ _781404 : [(8921 ^ _781404) ^ [_932377] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _932377), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _932226))), -(hBOOL(hAPP(_932228, _932377)))]]], (47855 ^ _781404) ^ [_1743925, _1743927, _1743929, _1743931] : [hBOOL(hAPP(_1743925, _1743927)), -(c_List_OdropWhile(_1743929, _1743925, hAPP(hAPP(c_List_Olist_OCons(_1743929), _1743927), _1743931)) = c_List_OdropWhile(_1743929, _1743925, _1743931))], (38560 ^ _781404) ^ [_1514119, _1514121, _1514123, _1514125, _1514127] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1514119, _1514121), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1514119, tc_HOL_Obool)), _1514123), _1514125)), hAPP(c_COMBK(tc_fun(_1514121, tc_HOL_Obool), _1514119), _1514127)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1514119, _1514121), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1514119, _1514121), _1514123), hAPP(c_COMBK(tc_fun(_1514121, tc_HOL_Obool), _1514119), _1514127))), hAPP(hAPP(c_Product__Type_OSigma(_1514119, _1514121), _1514125), hAPP(c_COMBK(tc_fun(_1514121, tc_HOL_Obool), _1514119), _1514127))))], (42607 ^ _781404) ^ [_1625986, _1625988, _1625990] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1625986)), _1625988), c_Wellfounded_Oacc(tc_List_Olist(_1625986), c_List_Olistrel1(_1625986, _1625990)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1625986)), _1625988), c_List_Olists(_1625986, c_Wellfounded_Oacc(_1625986, _1625990)))))], (42188 ^ _781404) ^ [_1612626, _1612628, _1612630, _1612632, _1612634] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612626), tc_List_Olist(_1612626))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612626), tc_List_Olist(_1612626)), _1612628), _1612630)), hAPP(c_List_Olexn(_1612626, _1612632), _1612634))), 42191 ^ _781404 : [(42194 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612626)), _1612630) = _1612634)], (42192 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612626)), _1612628) = _1612634)]]], (37461 ^ _781404) ^ [_1486596, _1486598, _1486600, _1486602] : [-(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), _1486596), _1486598)), 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), _1486600), _1486602)), 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), _1486596), _1486600)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1486598), _1486602))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (5654 ^ _781404) ^ [_867843, _867845, _867847, _867849, _867851, _867853] : [-(c_COMBS(_867853, _867849, _867845) = c_COMBS(_867851, _867847, _867843)), _867853 = _867851, _867849 = _867847, _867845 = _867843], (13323 ^ _781404) ^ [_1012884, _1012886, _1012888, _1012890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012884), _1012886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012888), _1012890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012884), _1012888)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012886), _1012890))))], (38365 ^ _781404) ^ [_1509248, _1509250, _1509252, _1509254, _1509256, _1509258] : [c_Typedef_Otype__definition(_1509248, _1509250, _1509252, _1509254, _1509256), -(hAPP(_1509254, hAPP(_1509252, _1509258)) = _1509258)], (11048 ^ _781404) ^ [_969015] : [_969015 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969015), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (41477 ^ _781404) ^ [_1594440, _1594442, _1594444, _1594446, _1594448] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594440, _1594440)), hAPP(hAPP(c_Product__Type_OPair(_1594440, _1594440), _1594442), _1594444)), c_Transitive__Closure_Ortrancl(_1594440, _1594446))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1594440, _1594440), tc_HOL_Obool)), _1594446), hAPP(hAPP(c_Product__Type_OSigma(_1594440, _1594440), _1594448), hAPP(c_COMBK(tc_fun(_1594440, tc_HOL_Obool), _1594440), _1594448)))), -(_1594442 = _1594444), -(hBOOL(hAPP(hAPP(c_member(_1594440), _1594442), _1594448)))], (39636 ^ _781404) ^ [_1549198, _1549200, _1549202, _1549204] : [hAPP(hAPP(c_Relation_Orel__comp(_1549198, _1549198, _1549198), _1549200), _1549202) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549198, _1549198), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1549198, _1549198, _1549198), _1549200), _1549204) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549198, _1549198), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1549198, _1549198, _1549198), _1549200), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1549198, _1549198), tc_HOL_Obool)), _1549202), _1549204)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549198, _1549198), tc_HOL_Obool)))], (37708 ^ _781404) ^ [_1493078, _1493080, _1493082, _1493084, _1493086, _1493088, _1493090] : [c_Equiv__Relations_Oequiv(_1493078, _1493080, _1493082), hBOOL(hAPP(hAPP(c_member(tc_fun(_1493078, tc_HOL_Obool)), _1493084), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1493078), _1493080), _1493082))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1493078, tc_HOL_Obool)), _1493086), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1493078), _1493080), _1493082))), hBOOL(hAPP(hAPP(c_member(_1493078), _1493088), _1493084)), hBOOL(hAPP(hAPP(c_member(_1493078), _1493090), _1493086)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1493078, _1493078)), hAPP(hAPP(c_Product__Type_OPair(_1493078, _1493078), _1493088), _1493090)), _1493082)), -(_1493084 = _1493086)], (52732 ^ _781404) ^ [_1842216, _1842218, _1842220, _1842222, _1842224, _1842226] : [-(hAPP(hAPP(hAPP(c_COMBC(_1842216, _1842218, _1842220), _1842222), _1842224), _1842226) = hAPP(hAPP(_1842222, _1842226), _1842224))], (37459 ^ _781404) ^ [_1486552] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1486552) = 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), _1486552), 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))))))], (33349 ^ _781404) ^ [_1385225, _1385227, _1385229, _1385231, _1385233] : [-(hAPP(c_Set_Oimage(_1385225, _1385227, hAPP(hAPP(c_COMBB(_1385229, _1385227, _1385225), _1385231), _1385233)), c_Orderings_Otop__class_Otop(tc_fun(_1385225, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1385229, _1385227, _1385231), hAPP(c_Set_Oimage(_1385225, _1385229, _1385233), c_Orderings_Otop__class_Otop(tc_fun(_1385225, tc_HOL_Obool)))))], (1078 ^ _781404) ^ [_797551, _797553, _797555, _797557, _797559, _797561, _797563, _797565] : [-(c_Equiv__Relations_Ocongruent(_797563, _797559, _797555, _797551)), c_Equiv__Relations_Ocongruent(_797565, _797561, _797557, _797553), _797565 = _797563, _797561 = _797559, _797557 = _797555, _797553 = _797551], (6584 ^ _781404) ^ [_886558, _886560, _886562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886558, tc_HOL_Obool)), _886562), _886560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886558, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886558, tc_HOL_Obool)), _886560)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886558, tc_HOL_Obool)), _886562))))], (43551 ^ _781404) ^ [_1649502, _1649504, _1649506] : [-(hAPP(hAPP(c_List_Ozip(_1649502, _1649504), c_List_Olist_ONil(_1649502)), _1649506) = c_List_Olist_ONil(tc_prod(_1649502, _1649504)))], (16328 ^ _781404) ^ [_1071481] : [class_Rings_Olinordered__semidom(_1071481), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071481), c_Groups_Oone__class_Oone(_1071481)), c_Groups_Ozero__class_Ozero(_1071481)))], (37653 ^ _781404) ^ [_1491937, _1491939, _1491941, _1491943] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1491937, tc_HOL_Obool)), _1491939), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1491937), _1491941), _1491943))), 37657 ^ _781404 : [(37660 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491937), 37656 ^ [_1491937, _1491939, _1491941, _1491943]), _1491941)))], (37658 ^ _781404) ^ [] : [-(_1491939 = hAPP(c_Relation_OImage(_1491937, _1491937, _1491943), hAPP(hAPP(c_Set_Oinsert(_1491937), 37656 ^ [_1491937, _1491939, _1491941, _1491943]), c_Orderings_Obot__class_Obot(tc_fun(_1491937, tc_HOL_Obool)))))]]], (38325 ^ _781404) ^ [_1508574, _1508576, _1508578, _1508580, _1508582, _1508584, _1508586] : [c_Typedef_Otype__definition(_1508574, _1508576, _1508578, _1508580, _1508582), hBOOL(hAPP(hAPP(c_member(_1508576), _1508584), _1508582)), hBOOL(hAPP(hAPP(c_member(_1508576), _1508586), _1508582)), 38336 ^ _781404 : [(38343 ^ _781404) ^ [] : [_1508584 = _1508586, -(hAPP(_1508580, _1508584) = hAPP(_1508580, _1508586))], (38337 ^ _781404) ^ [] : [hAPP(_1508580, _1508584) = hAPP(_1508580, _1508586), -(_1508584 = _1508586)]]], (20165 ^ _781404) ^ [_1139449, _1139451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1139449)), c_Int_OBit1(_1139451))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1139449), _1139451)))], (42967 ^ _781404) ^ [_1636601, _1636603, _1636605, _1636607] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1636601, _1636603))), hAPP(hAPP(c_List_Ozip(_1636601, _1636603), _1636605), _1636607)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636601)), _1636605)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636603)), _1636607)))], (22265 ^ _781404) ^ [_1178256, _1178258, _1178260] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1178256), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1178258), _1178260)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1178256), _1178258)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1178256), _1178260)))], (12702 ^ _781404) ^ [_1001123, _1001125, _1001127, _1001129] : [hBOOL(hAPP(hAPP(_1001127, _1001129), _1001125)), -(hBOOL(hAPP(hAPP(c_member(_1001123), _1001125), c_SetInterval_Oord_OgreaterThan(_1001123, _1001127, _1001129))))], (34389 ^ _781404) ^ [_1418215, _1418217, _1418219, _1418221, _1418223] : [hBOOL(hAPP(hAPP(c_member(_1418215), _1418217), _1418219)), -(hAPP(c_Set_Oimage(_1418215, _1418221, hAPP(c_COMBK(_1418221, _1418215), _1418223)), _1418219) = hAPP(hAPP(c_Set_Oinsert(_1418221), _1418223), c_Orderings_Obot__class_Obot(tc_fun(_1418221, tc_HOL_Obool))))], (47575 ^ _781404) ^ [_1737943, _1737945] : [-(_1737943 = c_List_Olist_ONil(_1737945)), -(hAPP(c_List_Ohd(_1737945), hAPP(c_List_Orev(_1737945), _1737943)) = c_List_Olast(_1737945, _1737943))], (50457 ^ _781404) ^ [_1800578, _1800580, _1800582] : [c_Fun_Oinj__on(_1800578, _1800580, _1800582, c_Orderings_Otop__class_Otop(tc_fun(_1800578, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1800580, _1800578, _1800578, c_Hilbert__Choice_Oinv__into(_1800578, _1800580, c_Orderings_Otop__class_Otop(tc_fun(_1800578, tc_HOL_Obool)), _1800582)), _1800582) = c_Fun_Oid(_1800578))], (21215 ^ _781404) ^ [_1158451, _1158453, _1158455] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158451), _1158453)), _1158455) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158451), _1158455)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158453), _1158455)))], (49693 ^ _781404) ^ [_1784652, _1784654] : [c_Relation_Otrans(_1784652, _1784654), -(c_Relation_Otrans(_1784652, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1784652, _1784652), tc_HOL_Obool)), _1784654), c_Relation_OId(_1784652))))], (43152 ^ _781404) ^ [_1640885, _1640887, _1640889, _1640891, _1640893, _1640895, _1640897] : [-(hAPP(hAPP(c_List_Ozip(_1640885, _1640887), hAPP(hAPP(c_List_Olist__update(_1640885, _1640889), _1640891), _1640893)), hAPP(hAPP(c_List_Olist__update(_1640887, _1640895), _1640891), _1640897)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1640885, _1640887), hAPP(hAPP(c_List_Ozip(_1640885, _1640887), _1640889), _1640895)), _1640891), hAPP(hAPP(c_Product__Type_OPair(_1640885, _1640887), _1640893), _1640897)))], (24220 ^ _781404) ^ [_1215682, _1215684] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215682, _1215684) = 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), _1215682), _1215684) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42776 ^ _781404) ^ [_1630657, _1630659, _1630661] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630657, tc_HOL_Obool)), hAPP(c_List_Oset(_1630657), hAPP(hAPP(c_List_Otake(_1630657), _1630659), _1630661))), hAPP(c_List_Oset(_1630657), _1630661))))], (16416 ^ _781404) ^ [_1073078, _1073080] : [-(_1073078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1073078), _1073080) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073078), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1073080)))], (19257 ^ _781404) ^ [_1123857, _1123859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123857), _1123859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123857)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1123859))))], (50937 ^ _781404) ^ [_1811182, _1811184, _1811186, _1811188] : [c_Fun_Obij__betw(_1811182, _1811184, _1811186, _1811188, c_Orderings_Otop__class_Otop(tc_fun(_1811184, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1811182, _1811184, _1811186), c_Orderings_Otop__class_Otop(tc_fun(_1811182, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1811184, tc_HOL_Obool)))], (31332 ^ _781404) ^ [_1345065, _1345067, _1345069] : [class_Orderings_Olinorder(_1345065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345065), _1345067)), -(_1345067 = c_Orderings_Obot__class_Obot(tc_fun(_1345065, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345065), _1345069)), -(_1345069 = c_Orderings_Obot__class_Obot(tc_fun(_1345065, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1345065, c_Orderings_Oord__class_Omin(_1345065), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1345065, tc_HOL_Obool)), _1345067), _1345069)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345065), c_Big__Operators_Olattice_OInf__fin(_1345065, c_Orderings_Oord__class_Omin(_1345065), _1345067)), c_Big__Operators_Olattice_OInf__fin(_1345065, c_Orderings_Oord__class_Omin(_1345065), _1345069)))], (42236 ^ _781404) ^ [_1614405, _1614407, _1614409] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614405)), hAPP(hAPP(c_List_Olist_OCons(_1614405), _1614407), _1614409)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614405)), _1614409)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43925 ^ _781404) ^ [_1657634, _1657636, _1657638, _1657640] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657634)), hAPP(hAPP(c_List_Oappend(_1657634), _1657636), _1657638)), c_List_Olists(_1657634, _1657640)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657634)), _1657636), c_List_Olists(_1657634, _1657640))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657634)), _1657638), c_List_Olists(_1657634, _1657640)))], (8002 ^ _781404) ^ [_914926, _914928] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _914926), _914928)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _914926)), hAPP(c_Nat_OSuc, _914928)))], (49023 ^ _781404) ^ [_1769248, _1769250, _1769252, _1769254, _1769256] : [-(c_Predicate_Oconversep(_1769248, _1769250, c_Predicate_Opred__comp(_1769248, _1769252, _1769250, _1769254, _1769256)) = c_Predicate_Opred__comp(_1769250, _1769252, _1769248, c_Predicate_Oconversep(_1769252, _1769250, _1769256), c_Predicate_Oconversep(_1769248, _1769252, _1769254)))], (39866 ^ _781404) ^ [_1556371, _1556373] : [c_Wellfounded_Owf(_1556371, _1556373), -(c_Wellfounded_Owf(tc_fun(_1556371, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1556371, _1556373)))], (42268 ^ _781404) ^ [_1615341, _1615343, _1615345] : [-(c_List_Oset__Cons(_1615341, _1615343, _1615345) = hAPP(c_Set_OCollect(tc_List_Olist(_1615341)), hAPP(hAPP(c_COMBB(tc_fun(_1615341, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1615341)), c_HOL_OEx(_1615341)), hAPP(hAPP(c_COMBB(tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool)), tc_fun(_1615341, tc_HOL_Obool), tc_List_Olist(_1615341)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), tc_HOL_Obool, _1615341), c_HOL_OEx(tc_List_Olist(_1615341)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1615341), tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool)), tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1615341, tc_fun(tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool))), tc_fun(tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool)), tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool))), tc_List_Olist(_1615341)), c_COMBS(_1615341, tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1615341, tc_fun(tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool))), tc_List_Olist(_1615341)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1615341), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool)), _1615341), c_COMBS(tc_List_Olist(_1615341), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool)), tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1615341)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), tc_fun(tc_List_Olist(_1615341), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1615341), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1615341)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1615341), tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_List_Olist(_1615341))), tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1615341), tc_List_Olist(_1615341)), tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool)), tc_fun(tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_List_Olist(_1615341))), tc_fun(_1615341, tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool))), tc_List_Olist(_1615341)), c_COMBB(tc_fun(tc_List_Olist(_1615341), tc_List_Olist(_1615341)), tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), _1615341)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1615341), tc_List_Olist(_1615341)), tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool)), tc_List_Olist(_1615341)), c_COMBB(tc_List_Olist(_1615341), tc_HOL_Obool, tc_List_Olist(_1615341))), c_fequal))), c_List_Olist_OCons(_1615341)))))), hAPP(hAPP(c_COMBC(_1615341, tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool)), _1615341), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1615341))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1615341), c_fconj), hAPP(hAPP(c_COMBC(_1615341, tc_fun(_1615341, tc_HOL_Obool), tc_HOL_Obool), c_member(_1615341)), _1615343)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1615341), tc_fun(tc_List_Olist(_1615341), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1615341))), _1615345)))))))], (13872 ^ _781404) ^ [_1023345, _1023347, _1023349] : [class_Groups_Oab__group__add(_1023345), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1023345), _1023347), _1023349) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023345), _1023347), hAPP(c_Groups_Ouminus__class_Ouminus(_1023345), _1023349)))], (19394 ^ _781404) ^ [_1126337] : [class_Rings_Osemiring__1(_1126337), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1126337), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1126337))], (11785 ^ _781404) ^ [_982998, _983000, _983002] : [_983000 = _983002, -(hBOOL(hAPP(hAPP(c_member(_982998), _983000), hAPP(c_fequal, _983002))))], (5903 ^ _781404) ^ [_875007, _875009, _875011] : [class_Orderings_Oorder(_875007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875007), _875009), _875011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875007), _875011), _875009)), -(_875009 = _875011)], (33317 ^ _781404) ^ [_1384308, _1384310] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1384308), hAPP(c_Nat_OSuc, _1384310)) = 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), _1384308), _1384310)))], (19041 ^ _781404) ^ [_1120318, _1120320, _1120322] : [class_Nat_Osemiring__char__0(_1120318), 19044 ^ _781404 : [(19051 ^ _781404) ^ [] : [_1120320 = _1120322, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1120318), _1120320) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1120318), _1120322))], (19045 ^ _781404) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1120318), _1120320) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1120318), _1120322), -(_1120320 = _1120322)]]], (51422 ^ _781404) ^ [_1822960, _1822962, _1822964] : [-(c_Lazy__Sequence_Omap(_1822960, _1822962, _1822964, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1822960)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1822962))], (39007 ^ _781404) ^ [_1526557, _1526559, _1526561] : [-(hAPP(c_Set_OCollect(_1526557), hAPP(hAPP(c_COMBS(_1526557, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526557), c_fconj), _1526559)), _1526561)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1526557, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1526557), _1526559)), hAPP(c_Set_OCollect(_1526557), _1526561)))], (30664 ^ _781404) ^ [_1332658, _1332660, _1332662, _1332664] : [class_Groups_Oordered__ab__group__add(_1332658), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1332658), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332658), _1332660), _1332662)), _1332664) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332658), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1332658), _1332660), _1332664)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1332658), _1332662), _1332664)))], (49701 ^ _781404) ^ [_1784789] : [-(c_Relation_Otrans(_1784789, c_Relation_OId(_1784789)))], (49535 ^ _781404) ^ [_1780682, _1780684] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1780682, _1780684), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1780682)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42770 ^ _781404) ^ [_1630494, _1630496, _1630498, _1630500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1630494), _1630496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630498, tc_HOL_Obool)), hAPP(c_List_Oset(_1630498), hAPP(hAPP(c_List_Otake(_1630498), _1630494), _1630500))), hAPP(c_List_Oset(_1630498), hAPP(hAPP(c_List_Otake(_1630498), _1630496), _1630500)))))], (11250 ^ _781404) ^ [_972309, _972311] : [11252 ^ _781404 : [(11255 ^ _781404) ^ [] : [hBOOL(hAPP(_972311, 11251 ^ [_972309, _972311]))], (11253 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 11251 ^ [_972309, _972311]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972309))))]], 11256 ^ _781404 : [(11257 ^ _781404) ^ [_972462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _972462), _972309)), -(hBOOL(hAPP(_972311, _972462)))]]], (46658 ^ _781404) ^ [_1719079, _1719081] : [-(c_List_Oconcat(tc_List_Olist(_1719079), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719079), tc_List_Olist(tc_List_Olist(_1719079))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1719079)), _1719079, c_List_Olist_ONil(tc_List_Olist(_1719079)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1719079), tc_List_Olist(tc_List_Olist(_1719079))), _1719079), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719079), tc_List_Olist(tc_List_Olist(_1719079)), tc_List_Olist(tc_List_Olist(_1719079))), c_List_Olist_OCons(tc_List_Olist(_1719079))), c_List_Olist_ONil(tc_List_Olist(_1719079)))))), _1719081)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719079), tc_List_Olist(_1719079)), c_List_Otl(_1719079)), hAPP(c_List_Ofilter(tc_List_Olist(_1719079), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1719079)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719079), tc_List_Olist(_1719079), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1719079)))), _1719081)))], (15413 ^ _781404) ^ [_1054054, _1054056] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054054), c_Orderings_Otop__class_Otop(tc_fun(_1054054, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1054054), _1054056) = hAPP(c_Finite__Set_Ocard(_1054054), c_Orderings_Otop__class_Otop(tc_fun(_1054054, tc_HOL_Obool))), -(_1054056 = c_Orderings_Otop__class_Otop(tc_fun(_1054054, tc_HOL_Obool)))], (14127 ^ _781404) ^ [_1027915, _1027917, _1027919] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1027915), _1027917)), 14130 ^ _781404 : [(14131 ^ _781404) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027915, tc_Nat_Onat), _1027919), _1027917) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 14134 ^ _781404 : [(14135 ^ _781404) ^ [_1028077] : [hBOOL(hAPP(hAPP(c_member(_1027915), _1028077), _1027917)), -(hAPP(_1027919, _1028077) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (14141 ^ _781404) ^ [] : [14143 ^ _781404 : [(14146 ^ _781404) ^ [] : [hAPP(_1027919, 14142 ^ [_1027915, _1027917, _1027919]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14144 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1027915), 14142 ^ [_1027915, _1027917, _1027919]), _1027917)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027915, tc_Nat_Onat), _1027919), _1027917) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43713 ^ _781404) ^ [_1652565, _1652567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652565)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652567))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652565), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652567)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652565)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652565)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1652567))))], (23229 ^ _781404) ^ [_1197387, _1197389, _1197391] : [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), _1197387), _1197389)), _1197391)), 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)), _1197391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197389), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40072 ^ _781404) ^ [_1560588] : [class_Orderings_Owellorder(_1560588), -(c_Wellfounded_Owf(_1560588, hAPP(c_Set_OCollect(tc_prod(_1560588, _1560588)), hAPP(c_Product__Type_Oprod_Oprod__case(_1560588, _1560588, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1560588)))))], (20141 ^ _781404) ^ [_1139054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1139054)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1139054), c_Int_OPls)))], (33554 ^ _781404) ^ [_1392350, _1392352, _1392354, _1392356, _1392358, _1392360] : [-(hAPP(hAPP(c_Fun_Ocomp(_1392350, _1392352, _1392354, hAPP(c_COMBK(_1392352, _1392350), _1392356)), _1392358), _1392360) = _1392356)], (6867 ^ _781404) ^ [_891455, _891457, _891459] : [class_Lattices_Osemilattice__sup(_891455), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891455), _891457), _891459) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891455), _891459), _891457))], (38035 ^ _781404) ^ [_1500821, _1500823, _1500825, _1500827, _1500829, _1500831, _1500833, _1500835, _1500837] : [c_Equiv__Relations_Oequiv(_1500821, _1500823, _1500825), c_Equiv__Relations_Oequiv(_1500827, _1500829, _1500831), c_Equiv__Relations_Ocongruent2(_1500821, _1500827, tc_fun(_1500833, tc_HOL_Obool), _1500825, _1500831, _1500835), hBOOL(hAPP(hAPP(c_member(_1500827), _1500837), _1500829)), -(c_Equiv__Relations_Ocongruent(_1500821, tc_fun(_1500833, tc_HOL_Obool), _1500825, hAPP(hAPP(c_COMBB(tc_fun(_1500827, tc_fun(_1500833, tc_HOL_Obool)), tc_fun(_1500833, tc_HOL_Obool), _1500821), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500827, tc_fun(_1500833, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1500827, _1500827, _1500831), hAPP(hAPP(c_Set_Oinsert(_1500827), _1500837), c_Orderings_Obot__class_Obot(tc_fun(_1500827, tc_HOL_Obool)))))), _1500835)))], (41173 ^ _781404) ^ [_1587236, _1587238] : [-(c_Transitive__Closure_Otrancl(_1587236, _1587238) = hAPP(hAPP(c_Relation_Orel__comp(_1587236, _1587236, _1587236), c_Transitive__Closure_Ortrancl(_1587236, _1587238)), _1587238))], (23109 ^ _781404) ^ [_1195143, _1195145, _1195147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1195143)), 23112 ^ _781404 : [(23119 ^ _781404) ^ [] : [_1195145 = _1195147, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195143), _1195145) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195143), _1195147))], (23113 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195143), _1195145) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195143), _1195147), -(_1195145 = _1195147)]]], (27747 ^ _781404) ^ [_1277628, _1277630, _1277632, _1277634, _1277636] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1277628, _1277630, hAPP(hAPP(c_Set_Oinsert(_1277628), _1277632), _1277634)), _1277636))), 27748 ^ _781404 : [(27749 ^ _781404) ^ [_1277732, _1277734] : [hAPP(hAPP(c_Set_Oinsert(_1277628), _1277632), _1277634) = hAPP(hAPP(c_Set_Oinsert(_1277628), _1277734), _1277732), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1277628, _1277628, _1277630, _1277734, _1277732), _1277636)), -(hBOOL(hAPP(hAPP(c_member(_1277628), _1277734), _1277732)))]]], (37114 ^ _781404) ^ [_1477549, _1477551, _1477553, _1477555, _1477557] : [-(hAPP(c_Product__Type_Osnd(_1477549, _1477551), hAPP(c_Product__Type_Oapfst(_1477553, _1477549, _1477551, _1477555), _1477557)) = hAPP(c_Product__Type_Osnd(_1477553, _1477551), _1477557))], (47553 ^ _781404) ^ [_1737455, _1737457, _1737459, _1737461, _1737463] : [-(hAPP(c_List_Ofoldl(_1737455, _1737457, _1737459, _1737461), _1737463) = c_List_Ofoldr(_1737457, _1737455, hAPP(c_COMBC(_1737455, _1737457, _1737455), _1737459), hAPP(c_List_Orev(_1737457), _1737463), _1737461))], (8888 ^ _781404) ^ [_931661, _931663, _931665] : [class_Orderings_Oorder(_931661), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931661, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_931661, _931663), _931665)), hAPP(c_SetInterval_Oord__class_OatLeast(_931661), _931665)) = c_Orderings_Obot__class_Obot(tc_fun(_931661, tc_HOL_Obool)))], (1416 ^ _781404) ^ [_802144, _802146] : [-(class_Orderings_Owellorder(_802144)), _802146 = _802144, class_Orderings_Owellorder(_802146)], (47359 ^ _781404) ^ [_1733268, _1733270, _1733272, _1733274, _1733276] : [class_Orderings_Olinorder(_1733268), c_Fun_Oinj__on(_1733270, _1733268, _1733272, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1733270, tc_HOL_Obool)), hAPP(c_List_Oset(_1733270), _1733274)), hAPP(c_List_Oset(_1733270), _1733276))), c_List_Olinorder__class_Osorted(_1733268, hAPP(hAPP(c_List_Omap(_1733270, _1733268), _1733272), _1733274)), hBOOL(hAPP(c_List_Odistinct(_1733268), hAPP(hAPP(c_List_Omap(_1733270, _1733268), _1733272), _1733274))), c_List_Olinorder__class_Osorted(_1733268, hAPP(hAPP(c_List_Omap(_1733270, _1733268), _1733272), _1733276)), hBOOL(hAPP(c_List_Odistinct(_1733268), hAPP(hAPP(c_List_Omap(_1733270, _1733268), _1733272), _1733276))), hAPP(c_List_Oset(_1733270), _1733274) = hAPP(c_List_Oset(_1733270), _1733276), -(_1733274 = _1733276)], (22151 ^ _781404) ^ [_1175954, _1175956, _1175958] : [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, _1175954)), _1175956)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1175954)), _1175958))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1175956), _1175958)))], (52226 ^ _781404) ^ [_1837098, _1837100] : [class_Orderings_Oorder(_1837098), -(class_Orderings_Oorder(tc_fun(_1837100, _1837098)))], (19975 ^ _781404) ^ [_1136264, _1136266] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136264) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1136266), -(_1136264 = _1136266)], (15220 ^ _781404) ^ [_1049964, _1049966, _1049968, _1049970, _1049972, _1049974, _1049976, _1049978] : [c_Finite__Set_Ofolding__image__simple(_1049964, _1049966, _1049968, _1049970, _1049972, _1049974), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049966), _1049976)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049966), _1049978)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1049966, tc_HOL_Obool)), _1049976), _1049978) = c_Orderings_Obot__class_Obot(tc_fun(_1049966, tc_HOL_Obool)), -(hAPP(_1049974, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1049966, tc_HOL_Obool)), _1049976), _1049978)) = hAPP(hAPP(_1049968, hAPP(_1049974, _1049976)), hAPP(_1049974, _1049978)))], (52396 ^ _781404) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (48484 ^ _781404) ^ [_1758171, _1758173, _1758175] : [class_Orderings_Olinorder(_1758171), 48490 ^ _781404 : [(48493 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1758171), _1758175), 48489 ^ [_1758171, _1758173, _1758175]))], (48491 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758171), 48489 ^ [_1758171, _1758173, _1758175]), hAPP(c_List_Oset(_1758171), _1758173))))]], c_List_Olinorder__class_Osorted(_1758171, _1758173), -(c_List_Olinorder__class_Osorted(_1758171, hAPP(hAPP(c_List_Olist_OCons(_1758171), _1758175), _1758173)))], (39367 ^ _781404) ^ [_1538995, _1538997, _1538999] : [class_Lattices_Odistrib__lattice(_1538995), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538995), _1538997)), -(_1538997 = c_Orderings_Obot__class_Obot(tc_fun(_1538995, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1538995), _1538999), c_Big__Operators_Olattice__class_OInf__fin(_1538995, _1538997)) = c_Big__Operators_Olattice__class_OInf__fin(_1538995, hAPP(c_Set_OCollect(_1538995), hAPP(hAPP(c_COMBB(tc_fun(_1538995, tc_HOL_Obool), tc_HOL_Obool, _1538995), c_HOL_OEx(_1538995)), hAPP(hAPP(c_COMBC(_1538995, tc_fun(_1538995, tc_HOL_Obool), tc_fun(_1538995, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538995, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1538995, tc_HOL_Obool), tc_fun(_1538995, tc_HOL_Obool)), _1538995), c_COMBS(_1538995, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538995, tc_HOL_Obool), tc_fun(_1538995, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1538995), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538995), c_fconj)), hAPP(hAPP(c_COMBC(_1538995, tc_fun(_1538995, _1538995), tc_fun(_1538995, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538995, tc_HOL_Obool), tc_fun(tc_fun(_1538995, _1538995), tc_fun(_1538995, tc_HOL_Obool)), _1538995), c_COMBB(_1538995, tc_HOL_Obool, _1538995)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1538995), _1538999))))), hAPP(hAPP(c_COMBC(_1538995, tc_fun(_1538995, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538995)), _1538997))))))], (42432 ^ _781404) ^ [_1620860, _1620862, _1620864] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620860, _1620860)), hAPP(hAPP(c_Product__Type_OPair(_1620860, _1620860), 42433 ^ [_1620860, _1620862, _1620864]), 42433 ^ [_1620860, _1620862, _1620864])), _1620862))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1620860), tc_List_Olist(_1620860))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1620860), tc_List_Olist(_1620860)), _1620864), _1620864)), c_List_Olexord(_1620860, _1620862)))], (37948 ^ _781404) ^ [_1498787, _1498789, _1498791] : [c_Equiv__Relations_Oequivp(_1498787, _1498789), -(hBOOL(hAPP(hAPP(_1498789, _1498791), _1498791)))], (33185 ^ _781404) ^ [_1380759, _1380761, _1380763] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380759, tc_Nat_Onat), _1380761), _1380763)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380759, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1380759), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1380761)), _1380763))], (42308 ^ _781404) ^ [_1616923, _1616925, _1616927, _1616929] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616923), tc_List_Olist(_1616923))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616923), tc_List_Olist(_1616923)), _1616925), _1616927)), c_List_Olex(_1616923, _1616929))), 42311 ^ _781404 : [(42314 ^ _781404) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616923)), _1616925) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616923)), _1616927))], (42312 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616923), tc_List_Olist(_1616923))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616923), tc_List_Olist(_1616923)), _1616925), _1616927)), c_List_Olexord(_1616923, _1616929))))]]], (6107 ^ _781404) ^ [_878387, _878389, _878391, _878393] : [c_Hoare__Mirabelle_Ohoare__derivs(_878387, _878389, _878391), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_878387), tc_HOL_Obool)), _878389), _878393)), -(c_Hoare__Mirabelle_Ohoare__derivs(_878387, _878393, _878391))], (37964 ^ _781404) ^ [_1499033, _1499035, _1499037, _1499039, _1499041] : [c_Equiv__Relations_Oequivp(_1499033, _1499035), hBOOL(hAPP(hAPP(_1499035, _1499037), _1499039)), hBOOL(hAPP(hAPP(_1499035, _1499039), _1499041)), -(hBOOL(hAPP(hAPP(_1499035, _1499037), _1499041)))], (51148 ^ _781404) ^ [_1815297, _1815299] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1815297), _1815299)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1815297, 51151 ^ [_1815297, _1815299], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1815297), _1815299)), _1815299))], (22251 ^ _781404) ^ [_1178001, _1178003, _1178005] : [class_Rings_Oring__1(_1178001), hBOOL(hAPP(hAPP(c_member(_1178001), _1178003), c_Int_Oring__1__class_OInts(_1178001))), hBOOL(hAPP(hAPP(c_member(_1178001), _1178005), c_Int_Oring__1__class_OInts(_1178001))), -(hBOOL(hAPP(hAPP(c_member(_1178001), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178001), _1178003), _1178005)), c_Int_Oring__1__class_OInts(_1178001))))], (39936 ^ _781404) ^ [_1557612] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1557612)))], (43186 ^ _781404) ^ [_1641789, _1641791, _1641793, _1641795] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1641789, tc_HOL_Obool)), hAPP(c_List_Oset(_1641789), hAPP(hAPP(c_List_Olist__update(_1641789, _1641791), _1641793), _1641795))), hAPP(hAPP(c_Set_Oinsert(_1641789), _1641795), hAPP(c_List_Oset(_1641789), _1641791)))))], (50765 ^ _781404) ^ [_1807617, _1807619] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1807617), _1807619))), -(c_Quickcheck_Obeyond(_1807617, _1807619) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (2884 ^ _781404) ^ [_824176, _824178, _824180, _824182] : [-(c_Relation_ORange(_824182, _824178) = c_Relation_ORange(_824180, _824176)), _824182 = _824180, _824178 = _824176], (47459 ^ _781404) ^ [_1735434, _1735436, _1735438] : [_1735436 = hAPP(hAPP(c_List_Olist_OCons(_1735434), _1735438), c_List_Olist_ONil(_1735434)), -(hAPP(c_List_Orev(_1735434), _1735436) = hAPP(hAPP(c_List_Olist_OCons(_1735434), _1735438), c_List_Olist_ONil(_1735434)))], (39105 ^ _781404) ^ [_1528906, _1528908] : [-(hAPP(c_Set_OCollect(_1528906), hAPP(hAPP(c_COMBC(_1528906, _1528906, tc_HOL_Obool), c_fequal), _1528908)) = hAPP(hAPP(c_Set_Oinsert(_1528906), _1528908), c_Orderings_Obot__class_Obot(tc_fun(_1528906, tc_HOL_Obool))))], (40526 ^ _781404) ^ [_1571282, _1571284, _1571286, _1571288] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1571282, tc_HOL_Obool), tc_fun(_1571282, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1571282, tc_HOL_Obool), tc_fun(_1571282, tc_HOL_Obool)), _1571284), _1571286)), c_Wellfounded_Omax__ext(_1571282, _1571288))), 40529 ^ _781404 : [(40532 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1571282), _1571286)))], (40534 ^ _781404) ^ [] : [_1571286 = c_Orderings_Obot__class_Obot(tc_fun(_1571282, tc_HOL_Obool))], (40536 ^ _781404) ^ [_1571576] : [hBOOL(hAPP(hAPP(c_member(_1571282), _1571576), _1571284)), 40540 ^ _781404 : [(40543 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571282, _1571282)), hAPP(hAPP(c_Product__Type_OPair(_1571282, _1571282), _1571576), 40539 ^ [_1571282, _1571284, _1571286, _1571288, _1571576])), _1571288)))], (40541 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1571282), 40539 ^ [_1571282, _1571284, _1571286, _1571288, _1571576]), _1571286)))]]], (40530 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1571282), _1571284)))]]], (4600 ^ _781404) ^ [_851256, _851258, _851260, _851262, _851264, _851266, _851268, _851270, _851272, _851274] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_851274, _851270, _851266, _851262, _851258) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_851272, _851268, _851264, _851260, _851256)), _851274 = _851272, _851270 = _851268, _851266 = _851264, _851262 = _851260, _851258 = _851256], (30460 ^ _781404) ^ [_1328768, _1328770, _1328772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1328768), _1328770)), -(c_Random_Ominus__shift(_1328772, _1328768, _1328770) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1328772), _1328768)), _1328770))], (12514 ^ _781404) ^ [_997332, _997334, _997336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997332, tc_HOL_Obool)), _997334), _997336)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_997332, tc_HOL_Obool)), _997334), hAPP(c_Set_OPow(_997332), _997336))))], (22987 ^ _781404) ^ [_1192596, _1192598, _1192600, _1192602, _1192604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1192596), _1192598)), 22990 ^ _781404 : [(22997 ^ _781404) ^ [] : [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), _1192598), _1192596)), _1192600)), _1192602)), _1192604)), -(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), _1192598), _1192600)), _1192602)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1192596), _1192600)), _1192604))))], (22991 ^ _781404) ^ [] : [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), _1192598), _1192600)), _1192602)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1192596), _1192600)), _1192604))), -(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), _1192598), _1192596)), _1192600)), _1192602)), _1192604)))]]], (36324 ^ _781404) ^ [_1459755, _1459757] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1459755, _1459757) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1459755, _1459757)))], (37908 ^ _781404) ^ [_1497795, _1497797] : [c_Equiv__Relations_Oequivp(_1497795, hAPP(hAPP(c_COMBC(_1497795, tc_fun(tc_prod(_1497795, _1497795), tc_HOL_Obool), tc_fun(_1497795, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497795, tc_fun(tc_fun(tc_prod(_1497795, _1497795), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1497795, _1497795), tc_HOL_Obool), tc_fun(_1497795, tc_HOL_Obool)), _1497795), c_COMBC(_1497795, tc_fun(tc_prod(_1497795, _1497795), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497795, tc_prod(_1497795, _1497795)), tc_fun(_1497795, tc_fun(tc_fun(tc_prod(_1497795, _1497795), tc_HOL_Obool), tc_HOL_Obool)), _1497795), hAPP(c_COMBB(tc_prod(_1497795, _1497795), tc_fun(tc_fun(tc_prod(_1497795, _1497795), tc_HOL_Obool), tc_HOL_Obool), _1497795), c_member(tc_prod(_1497795, _1497795)))), c_Product__Type_OPair(_1497795, _1497795)))), _1497797)), -(c_Equiv__Relations_Oequiv(_1497795, c_Orderings_Otop__class_Otop(tc_fun(_1497795, tc_HOL_Obool)), _1497797))], (29595 ^ _781404) ^ [_1311350, _1311352, _1311354, _1311356] : [class_Fields_Ofield(_1311350), -(_1311352 = c_Groups_Ozero__class_Ozero(_1311350)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1311350), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311350), _1311354), _1311352)), _1311356) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311350), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1311350), _1311354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311350), _1311352), _1311356))), _1311352))], (6003 ^ _781404) ^ [_876541, _876543, _876545] : [class_Orderings_Oorder(_876541), 6006 ^ _781404 : [(6015 ^ _781404) ^ [] : [-(_876543 = _876545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876541), _876543), _876545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876541), _876545), _876543))], (6007 ^ _781404) ^ [] : [_876543 = _876545, 6010 ^ _781404 : [(6013 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876541), _876545), _876543)))], (6011 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876541), _876543), _876545)))]]]]], (51164 ^ _781404) ^ [_1815591, _1815593, _1815595, _1815597, _1815599] : [51166 ^ _781404 : [(51169 ^ _781404) ^ [] : [c_Relation_Orefl__on(_1815595, hAPP(_1815597, 51165 ^ [_1815591, _1815593, _1815595, _1815597, _1815599]), hAPP(_1815599, 51165 ^ [_1815591, _1815593, _1815595, _1815597, _1815599]))], (51167 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1815591), 51165 ^ [_1815591, _1815593, _1815595, _1815597, _1815599]), _1815593)))]], -(c_Relation_Orefl__on(_1815595, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1815591, tc_fun(_1815595, tc_HOL_Obool)), _1815593), _1815597), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1815591, tc_fun(tc_prod(_1815595, _1815595), tc_HOL_Obool)), _1815593), _1815599)))], (38229 ^ _781404) ^ [_1506103, _1506105, _1506107, _1506109, _1506111] : [c_Relation_Orefl__on(_1506103, _1506105, _1506107), hBOOL(hAPP(hAPP(c_member(tc_prod(_1506103, _1506103)), hAPP(hAPP(c_Product__Type_OPair(_1506103, _1506103), _1506109), _1506111)), _1506107)), -(hBOOL(hAPP(hAPP(c_member(_1506103), _1506111), _1506105)))], (40378 ^ _781404) ^ [_1567698, _1567700, _1567702, _1567704] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1567698), _1567700)), 40384 ^ _781404 : [(40387 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1567702), hAPP(_1567704, 40383 ^ [_1567698, _1567700, _1567702, _1567704])))], (40385 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567698), 40383 ^ [_1567698, _1567700, _1567702, _1567704]), _1567700)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1567702), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1567698, tc_fun(_1567702, tc_HOL_Obool)), _1567700), _1567704))))], (40811 ^ _781404) ^ [_1577441, _1577443, _1577445] : [class_Complete__Lattice_Ocomplete__lattice(_1577441), _1577443 = c_Inductive_Ocomplete__lattice__class_Olfp(_1577441, _1577445), c_Orderings_Oorder__class_Omono(_1577441, _1577441, _1577445), -(_1577443 = hAPP(_1577445, _1577443))], (8592 ^ _781404) ^ [_926253, _926255] : [class_Groups_Olinordered__ab__group__add(_926253), 8595 ^ _781404 : [(8602 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926253), c_Groups_Ozero__class_Ozero(_926253)), _926255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926253), hAPP(c_Groups_Ouminus__class_Ouminus(_926253), _926255)), _926255)))], (8596 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926253), hAPP(c_Groups_Ouminus__class_Ouminus(_926253), _926255)), _926255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926253), c_Groups_Ozero__class_Ozero(_926253)), _926255)))]]], (14589 ^ _781404) ^ [_1037084, _1037086, _1037088] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037084), hAPP(hAPP(c_Set_Oinsert(_1037084), _1037086), _1037088))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1037084), _1037088)))], (36536 ^ _781404) ^ [_1464361, _1464363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1464361), 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)), _1464363)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1464361), _1464363) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1464361, _1464363)))], (44986 ^ _781404) ^ [_1681591, _1681593, _1681595] : [class_Orderings_Olinorder(_1681591), hBOOL(hAPP(hAPP(c_member(_1681591), _1681593), hAPP(c_List_Oset(_1681591), _1681595))), -(c_List_Olinorder__class_Oinsort__insert__key(_1681591, _1681591, c_COMBI(_1681591), _1681593, _1681595) = _1681595)], (17212 ^ _781404) ^ [_1088197, _1088199, _1088201] : [class_Int_Onumber__ring(_1088197), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088197), hAPP(c_Int_Onumber__class_Onumber__of(_1088197), _1088199)), hAPP(c_Int_Onumber__class_Onumber__of(_1088197), _1088201)) = hAPP(c_Int_Onumber__class_Onumber__of(_1088197), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088199), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1088201))))], (37583 ^ _781404) ^ [_1490102, _1490104, _1490106, _1490108] : [hBOOL(hAPP(hAPP(c_member(_1490102), _1490104), _1490106)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1490102, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1490102, _1490102, _1490108), hAPP(hAPP(c_Set_Oinsert(_1490102), _1490104), c_Orderings_Obot__class_Obot(tc_fun(_1490102, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490102), _1490106), _1490108))))], (13273 ^ _781404) ^ [_1012050] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1012050) = _1012050)], (44365 ^ _781404) ^ [_1668170, _1668172, _1668174, _1668176] : [-(hAPP(hAPP(c_List_Odrop(_1668170), _1668172), hAPP(hAPP(c_List_Odrop(_1668170), _1668174), _1668176)) = hAPP(hAPP(c_List_Odrop(_1668170), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1668172), _1668174)), _1668176))], (22687 ^ _781404) ^ [_1186975, _1186977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1186975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1186977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186977), _1186975))))], (7479 ^ _781404) ^ [_903566, _903568, _903570] : [class_Lattices_Olattice(_903566), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903566), _903568), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903566), _903568), _903570)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_903566), _903568), _903570))], (42912 ^ _781404) ^ [_1633766, _1633768, _1633770] : [-(hBOOL(hAPP(hAPP(c_member(_1633766), _1633768), hAPP(c_List_Oset(_1633766), _1633770)))), 42913 ^ _781404 : [(42914 ^ _781404) ^ [_1633840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1633840), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633766)), _1633770))), hAPP(hAPP(c_List_Onth(_1633766), _1633770), _1633840) = _1633768]]], (18035 ^ _781404) ^ [_1102910, _1102912, _1102914] : [class_Rings_Olinordered__semidom(_1102910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102910), c_Groups_Oone__class_Oone(_1102910)), _1102912)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102910), c_Groups_Oone__class_Oone(_1102910)), hAPP(hAPP(c_Power_Opower__class_Opower(_1102910), _1102912), _1102914))))], (760 ^ _781404) ^ [_792856, _792858, _792860, _792862, _792864, _792866] : [-(c_List_Olist__ex1(_792864, _792860, _792856)), c_List_Olist__ex1(_792866, _792862, _792858), _792866 = _792864, _792862 = _792860, _792858 = _792856], (32656 ^ _781404) ^ [_1369717, _1369719] : [class_Orderings_Olinorder(_1369717), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369717), _1369719)), -(c_Big__Operators_Olattice_OSup__fin(_1369717, c_Orderings_Oord__class_Omax(_1369717), _1369719) = hAPP(c_Finite__Set_Ofold1(_1369717, c_Orderings_Oord__class_Omax(_1369717)), _1369719))], (18799 ^ _781404) ^ [_1116486, _1116488] : [class_Int_Onumber__ring(_1116486), class_Rings_Olinordered__idom(_1116486), 18806 ^ _781404 : [(18813 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116488), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116486), hAPP(c_Int_Onumber__class_Onumber__of(_1116486), _1116488)), c_Groups_Ozero__class_Ozero(_1116486))))], (18807 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116486), hAPP(c_Int_Onumber__class_Onumber__of(_1116486), _1116488)), c_Groups_Ozero__class_Ozero(_1116486))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116488), c_Int_OPls)))]]], (42208 ^ _781404) ^ [_1613833, _1613835, _1613837, _1613839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613833)), _1613835)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613833)), _1613837))), _1613835 = hAPP(hAPP(c_List_Olist_OCons(_1613833), _1613839), _1613837)], (30596 ^ _781404) ^ [_1331305] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1331305), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21565 ^ _781404) ^ [_1164822, _1164824, _1164826] : [class_Rings_Olinordered__ring__strict(_1164822), 21568 ^ _781404 : [(21583 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164822), c_Groups_Ozero__class_Ozero(_1164822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164822), _1164824), _1164826)))), 21584 ^ _781404 : [(21591 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164822), _1164824), c_Groups_Ozero__class_Ozero(_1164822))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164822), _1164826), c_Groups_Ozero__class_Ozero(_1164822)))], (21585 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164822), c_Groups_Ozero__class_Ozero(_1164822)), _1164824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164822), c_Groups_Ozero__class_Ozero(_1164822)), _1164826))]]], (21569 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164822), c_Groups_Ozero__class_Ozero(_1164822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164822), _1164824), _1164826))), 21574 ^ _781404 : [(21577 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164822), c_Groups_Ozero__class_Ozero(_1164822)), _1164826)))], (21575 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164822), c_Groups_Ozero__class_Ozero(_1164822)), _1164824)))]], 21578 ^ _781404 : [(21581 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164822), _1164826), c_Groups_Ozero__class_Ozero(_1164822))))], (21579 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164822), _1164824), c_Groups_Ozero__class_Ozero(_1164822))))]]]]], (48542 ^ _781404) ^ [_1759512, _1759514, _1759516, _1759518] : [c_List_Olist__ex(_1759512, _1759514, hAPP(hAPP(c_List_Oappend(_1759512), _1759516), _1759518)), -(c_List_Olist__ex(_1759512, _1759514, _1759516)), -(c_List_Olist__ex(_1759512, _1759514, _1759518))], (26975 ^ _781404) ^ [_1262902, _1262904] : [class_Groups_Oordered__ab__group__add__abs(_1262902), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262902), _1262904), hAPP(c_Groups_Oabs__class_Oabs(_1262902), _1262904))))], (20475 ^ _781404) ^ [_1144750] : [class_Int_Onumber__ring(_1144750), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1144750), c_Groups_Oone__class_Oone(_1144750)), c_Groups_Oone__class_Oone(_1144750)) = hAPP(c_Int_Onumber__class_Onumber__of(_1144750), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (20819 ^ _781404) ^ [_1151136, _1151138] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151136), _1151138) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151138), _1151136))], (22163 ^ _781404) ^ [_1176222, _1176224, _1176226] : [class_Groups_Omonoid__mult(_1176222), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1176222), _1176224), hAPP(c_Nat_OSuc, _1176226)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176222), hAPP(hAPP(c_Power_Opower__class_Opower(_1176222), _1176224), _1176226)), _1176224))], (44395 ^ _781404) ^ [_1668847, _1668849] : [-(hAPP(hAPP(c_List_Odrop(_1668847), _1668849), c_List_Olist_ONil(_1668847)) = c_List_Olist_ONil(_1668847))], (47511 ^ _781404) ^ [_1736669, _1736671, _1736673, _1736675, _1736677] : [c_List_Olist__all2(_1736669, _1736671, _1736673, _1736675, _1736677), -(c_List_Olist__all2(_1736669, _1736671, _1736673, hAPP(c_List_Orev(_1736669), _1736675), hAPP(c_List_Orev(_1736671), _1736677)))], (8940 ^ _781404) ^ [_932751, _932753] : [8948 ^ _781404 : [(8951 ^ _781404) ^ [] : [-(hBOOL(hAPP(_932753, 8947 ^ [_932751, _932753])))], (8949 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 8947 ^ [_932751, _932753]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _932751))))]], 8941 ^ _781404 : [(8942 ^ _781404) ^ [_932820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932820), _932751)), hBOOL(hAPP(_932753, _932820))]]], (40545 ^ _781404) ^ [_1571788, _1571790, _1571792, _1571794] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1571788, tc_HOL_Obool), tc_fun(_1571788, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1571788, tc_HOL_Obool), tc_fun(_1571788, tc_HOL_Obool)), _1571790), _1571792)), c_Wellfounded_Omax__ext(_1571788, _1571794)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571788), _1571790)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571788), _1571792)), -(_1571792 = c_Orderings_Obot__class_Obot(tc_fun(_1571788, tc_HOL_Obool))), 40559 ^ _781404 : [(40562 ^ _781404) ^ [_1572193] : [hBOOL(hAPP(hAPP(c_member(_1571788), _1572193), _1571792)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571788, _1571788)), hAPP(hAPP(c_Product__Type_OPair(_1571788, _1571788), 40558 ^ [_1571788, _1571790, _1571792, _1571794]), _1572193)), _1571794))], (40560 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1571788), 40558 ^ [_1571788, _1571790, _1571792, _1571794]), _1571790)))]]], (40676 ^ _781404) ^ [_1574374, _1574376, _1574378, _1574380] : [c_Orderings_Oorder__class_Omono(tc_fun(_1574374, tc_HOL_Obool), tc_fun(_1574374, tc_HOL_Obool), _1574376), hBOOL(hAPP(hAPP(c_member(_1574374), _1574378), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1574374, tc_HOL_Obool), _1574376))), -(hBOOL(hAPP(hAPP(c_member(_1574374), _1574378), hAPP(_1574376, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574374, tc_HOL_Obool)), _1574380), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1574374, tc_HOL_Obool), _1574376))))))], (7189 ^ _781404) ^ [_897913, _897915, _897917, _897919, _897921] : [c_Orderings_Oorder__class_Omono(tc_fun(_897913, tc_HOL_Obool), tc_fun(_897915, tc_HOL_Obool), _897917), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897915, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897915, tc_HOL_Obool)), hAPP(_897917, _897919)), hAPP(_897917, _897921))), hAPP(_897917, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897913, tc_HOL_Obool)), _897919), _897921)))))], (34743 ^ _781404) ^ [_1426819, _1426821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426819), 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)), _1426821)), -(c_Divides_OnegDivAlg(_1426819, _1426821) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1426819), _1426821)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1426819, _1426821)))], (24678 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (8722 ^ _781404) ^ [_928401, _928403, _928405, _928407] : [class_Orderings_Oorder(_928401), 8725 ^ _781404 : [(8734 ^ _781404) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_928401, _928403, _928405) = hAPP(hAPP(c_Set_Oinsert(_928401), _928407), c_Orderings_Obot__class_Obot(tc_fun(_928401, tc_HOL_Obool)))), _928403 = _928405, _928405 = _928407], (8726 ^ _781404) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_928401, _928403, _928405) = hAPP(hAPP(c_Set_Oinsert(_928401), _928407), c_Orderings_Obot__class_Obot(tc_fun(_928401, tc_HOL_Obool))), 8729 ^ _781404 : [(8732 ^ _781404) ^ [] : [-(_928405 = _928407)], (8730 ^ _781404) ^ [] : [-(_928403 = _928405)]]]]], (50271 ^ _781404) ^ [_1797186, _1797188, _1797190] : [c_Equiv__Relations_Oequiv(_1797186, _1797188, _1797190), 50274 ^ _781404 : [(50279 ^ _781404) ^ [] : [-(c_Relation_Otrans(_1797186, _1797190))], (50277 ^ _781404) ^ [] : [-(c_Relation_Osym(_1797186, _1797190))], (50275 ^ _781404) ^ [] : [-(c_Relation_Orefl__on(_1797186, _1797188, _1797190))]]], (7355 ^ _781404) ^ [_901260, _901262, _901264, _901266] : [class_Orderings_Olinorder(_901260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901260), _901262), _901264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901260), _901264), _901266)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901260, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_901260, _901262, _901264)), c_SetInterval_Oord__class_OgreaterThanAtMost(_901260, _901264, _901266)) = c_SetInterval_Oord__class_OatLeastAtMost(_901260, _901262, _901266))], (44423 ^ _781404) ^ [_1669535, _1669537, _1669539, _1669541] : [hAPP(hAPP(c_List_Oappend(_1669535), _1669537), _1669539) = _1669541, 44426 ^ _781404 : [(44429 ^ _781404) ^ [] : [-(_1669539 = hAPP(hAPP(c_List_Odrop(_1669535), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669535)), _1669537)), _1669541))], (44427 ^ _781404) ^ [] : [-(_1669537 = hAPP(hAPP(c_List_Otake(_1669535), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669535)), _1669537)), _1669541))]]], (1886 ^ _781404) ^ [_808019, _808021] : [-(class_Orderings_Oorder(_808019)), _808021 = _808019, class_Orderings_Oorder(_808021)], (36271 ^ _781404) ^ [_1458423, _1458425, _1458427, _1458429] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1458423, _1458423)), hAPP(hAPP(c_Product__Type_OPair(_1458423, _1458423), _1458425), _1458427)), hAPP(c_Wellfounded_Omeasure(_1458423), _1458429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1458429, _1458425)), hAPP(_1458429, _1458427))))], (25047 ^ _781404) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (7177 ^ _781404) ^ [_897699, _897701, _897703] : [class_Lattices_Osemilattice__sup(_897699), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897699), _897701), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897699), _897701), _897703))))], (30280 ^ _781404) ^ [_1325273, _1325275, _1325277, _1325279, _1325281] : [c_Finite__Set_Ofun__left__comm__idem(_1325273, _1325275, _1325277), -(hAPP(hAPP(_1325277, _1325279), hAPP(hAPP(_1325277, _1325279), _1325281)) = hAPP(hAPP(_1325277, _1325279), _1325281))], (27231 ^ _781404) ^ [_1267621, _1267623, _1267625] : [class_Rings_Oordered__ring__abs(_1267621), -(hAPP(c_Groups_Oabs__class_Oabs(_1267621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267621), _1267623), _1267625)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267621), hAPP(c_Groups_Oabs__class_Oabs(_1267621), _1267623)), hAPP(c_Groups_Oabs__class_Oabs(_1267621), _1267625))), 27238 ^ _781404 : [(27241 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267621), _1267623), c_Groups_Ozero__class_Ozero(_1267621)))], (27239 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267621), c_Groups_Ozero__class_Ozero(_1267621)), _1267623))]], 27242 ^ _781404 : [(27245 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267621), _1267625), c_Groups_Ozero__class_Ozero(_1267621)))], (27243 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267621), c_Groups_Ozero__class_Ozero(_1267621)), _1267625))]]], (9955 ^ _781404) ^ [_951450] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _951450) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14472 ^ _781404) ^ [_1034870, _1034872, _1034874] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1034870), _1034872)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1034870), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1034870, tc_HOL_Obool)), _1034872), _1034874))))], (13333 ^ _781404) ^ [_1013075, _1013077, _1013079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013075), _1013077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013075), _1013079)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013077), _1013079))))], (13167 ^ _781404) ^ [_1009958, _1009960, _1009962, _1009964] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1009958), 13170 ^ _781404 : [(13177 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009958), _1009962), _1009964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009958), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009958), _1009960), _1009962)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009958), _1009960), _1009964))))], (13171 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009958), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009958), _1009960), _1009962)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009958), _1009960), _1009964))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009958), _1009962), _1009964)))]]], (52154 ^ _781404) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (24772 ^ _781404) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26913 ^ _781404) ^ [_1261765] : [class_Rings_Olinordered__idom(_1261765), -(hAPP(c_Groups_Oabs__class_Oabs(_1261765), c_Groups_Oone__class_Oone(_1261765)) = c_Groups_Oone__class_Oone(_1261765))], (15677 ^ _781404) ^ [_1058696, _1058698] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1058696), _1058698)))), -(_1058698 = c_Orderings_Obot__class_Obot(tc_fun(_1058696, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058696), _1058698))], (33482 ^ _781404) ^ [_1390268, _1390270, _1390272, _1390274] : [-(_1390268 = c_Orderings_Obot__class_Obot(tc_fun(_1390270, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390270, tc_fun(_1390272, tc_HOL_Obool)), _1390268), hAPP(c_COMBK(tc_fun(_1390272, tc_HOL_Obool), _1390270), _1390274)) = _1390274)], (52416 ^ _781404) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (23603 ^ _781404) ^ [_1205304, _1205306, _1205308] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1205304), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1205306, _1205308)), _1205308) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1205304), _1205306), _1205308))], (49245 ^ _781404) ^ [_1773897, _1773899] : [class_Lazy__Sequence_Osmall__lazy(_1773897), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1773897), _1773899) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1773897), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1773897)), c_List_Olist_ONil(_1773897)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1773897))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1773899)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1773897, tc_List_Olist(_1773897)), tc_List_Olist(_1773897), c_Lazy__Sequence_Oproduct(_1773897, tc_List_Olist(_1773897), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1773897, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1773899), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1773897), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1773899), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1773897, tc_List_Olist(_1773897), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1773897))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1773897), tc_List_Olist(_1773897)), tc_fun(tc_List_Olist(_1773897), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1773897))), _1773897), hAPP(c_COMBB(tc_List_Olist(_1773897), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1773897)), tc_List_Olist(_1773897)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1773897)))), c_List_Olist_OCons(_1773897))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1773897)))))], (37345 ^ _781404) ^ [_1483618, _1483620] : [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)), _1483618), _1483620)), 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)), _1483618), 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)), _1483620), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (19360 ^ _781404) ^ [_1125764, _1125766] : [class_Rings_Olinordered__semidom(_1125764), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125764), c_Groups_Ozero__class_Ozero(_1125764)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1125764), _1125766))))], (51420 ^ _781404) ^ [_1822908, _1822910, _1822912, _1822914, _1822916] : [-(c_Lazy__Sequence_Omap(_1822908, _1822910, _1822912, c_Lazy__Sequence_Olazy__sequence_OInsert(_1822908, _1822914, _1822916)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1822910, hAPP(_1822912, _1822914), c_Lazy__Sequence_Omap(_1822908, _1822910, _1822912, _1822916)))], (9553 ^ _781404) ^ [_945022, _945024, _945026, _945028] : [class_Orderings_Oorder(_945022), _945024 = _945026, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945022), _945028), _945026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945022), _945028), _945024)))], (20147 ^ _781404) ^ [_1139149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1139149), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1139149)), c_Int_OPls)))], (19227 ^ _781404) ^ [_1123350] : [-(hBOOL(hAPP(_1123350, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 19234 ^ [_1123350])))), 19228 ^ _781404 : [(19229 ^ _781404) ^ [_1123402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1123402)), hBOOL(hAPP(_1123350, _1123402))]]], (22193 ^ _781404) ^ [_1176877, _1176879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176877)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176879)), -(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), _1176877), _1176879))))], (24782 ^ _781404) ^ [_1225790, _1225792] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1225790, _1225792)) = _1225792), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1225790), _1225792) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1225790, _1225792)))], (18295 ^ _781404) ^ [_1107380, _1107382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107380), _1107382)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1107382, _1107380) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (12358 ^ _781404) ^ [_994340, _994342, _994344, _994346] : [-(hBOOL(hAPP(hAPP(c_member(_994340), _994342), _994344))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994340, tc_HOL_Obool)), _994344), hAPP(hAPP(c_Set_Oinsert(_994340), _994342), _994346)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994340, tc_HOL_Obool)), _994344), _994346))], (34217 ^ _781404) ^ [_1412103, _1412105, _1412107, _1412109, _1412111] : [-(_1412103 = c_Orderings_Obot__class_Obot(tc_fun(_1412105, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412105, tc_fun(_1412107, tc_HOL_Obool)), _1412103), hAPP(hAPP(c_COMBB(tc_fun(_1412107, tc_HOL_Obool), tc_fun(_1412107, tc_HOL_Obool), _1412105), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412107, tc_HOL_Obool)), _1412109)), _1412111)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412107, tc_HOL_Obool)), _1412109), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412105, tc_fun(_1412107, tc_HOL_Obool)), _1412103), _1412111)))], (17015 ^ _781404) ^ [_1084272, _1084274, _1084276, _1084278, _1084280, _1084282, _1084284, _1084286] : [c_Finite__Set_Ofolding__image__simple(_1084272, _1084274, _1084276, _1084278, _1084280, _1084282), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084274), _1084284)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084274), _1084286)), 17029 ^ _781404 : [(17032 ^ _781404) ^ [] : [hAPP(_1084280, 17028 ^ [_1084272, _1084274, _1084276, _1084278, _1084280, _1084282, _1084284, _1084286]) = _1084278], (17030 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1084274), 17028 ^ [_1084272, _1084274, _1084276, _1084278, _1084280, _1084282, _1084284, _1084286]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1084274, tc_HOL_Obool)), _1084284), _1084286))))]], -(hAPP(_1084282, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1084274, tc_HOL_Obool)), _1084284), _1084286)) = hAPP(hAPP(_1084276, hAPP(_1084282, _1084284)), hAPP(_1084282, _1084286)))], (42441 ^ _781404) ^ [_1621095, _1621097, _1621099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1621095, _1621095), tc_HOL_Obool)), _1621097), _1621099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1621095), tc_List_Olist(_1621095)), tc_HOL_Obool)), c_List_Olistrel(_1621095, _1621097)), c_List_Olistrel(_1621095, _1621099))))], (38460 ^ _781404) ^ [_1511260, _1511262] : [-(c_Nitpick_Onumber__of__frac(_1511260, _1511262) = c_Nitpick_OAbs__Frac(_1511260, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1511262), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (47726 ^ _781404) ^ [_1741207, _1741209, _1741211, _1741213] : [hBOOL(hAPP(_1741207, _1741209)), -(c_List_OtakeWhile(_1741211, _1741207, hAPP(hAPP(c_List_Olist_OCons(_1741211), _1741209), _1741213)) = hAPP(hAPP(c_List_Olist_OCons(_1741211), _1741209), c_List_OtakeWhile(_1741211, _1741207, _1741213)))], (23757 ^ _781404) ^ [_1207951, _1207953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1207951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1207953)), -(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, _1207951, _1207953))))], (26232 ^ _781404) ^ [_1249542] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1249542)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1249542)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43980 ^ _781404) ^ [_1658931, _1658933, _1658935, _1658937] : [hAPP(hAPP(c_List_Oappend(_1658931), _1658933), _1658935) = hAPP(hAPP(c_List_Oappend(_1658931), _1658937), _1658935), -(_1658933 = _1658937)], (27201 ^ _781404) ^ [_1267029, _1267031] : [class_Rings_Olinordered__idom(_1267029), -(hAPP(c_Groups_Oabs__class_Oabs(_1267029), _1267031) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267029), _1267031), c_Groups_Osgn__class_Osgn(_1267029, _1267031)))], (5224 ^ _781404) ^ [_861126, _861128, _861130, _861132] : [-(c_Quotient_ORespects(_861132, _861128) = c_Quotient_ORespects(_861130, _861126)), _861132 = _861130, _861128 = _861126], (19899 ^ _781404) ^ [_1134916, _1134918] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134916)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1134916)), _1134918)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1134916))), _1134918))], (43162 ^ _781404) ^ [_1641146, _1641148, _1641150, _1641152, _1641154] : [-(hAPP(hAPP(c_List_Olist__update(_1641146, hAPP(hAPP(c_List_Olist__update(_1641146, _1641148), _1641150), _1641152)), _1641150), _1641154) = hAPP(hAPP(c_List_Olist__update(_1641146, _1641148), _1641150), _1641154))], (20089 ^ _781404) ^ [_1138230] : [c_Int_OPls = c_Int_OBit0(_1138230), -(c_Int_OPls = _1138230)], (25111 ^ _781404) ^ [_1230907, _1230909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1230907)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1230909), _1230907)), _1230907) = _1230909)], (31750 ^ _781404) ^ [_1352756, _1352758] : [class_Orderings_Olinorder(_1352756), -(c_Big__Operators_Olinorder__class_OMax(_1352756, hAPP(hAPP(c_Set_Oinsert(_1352756), _1352758), c_Orderings_Obot__class_Obot(tc_fun(_1352756, tc_HOL_Obool)))) = _1352758)], (21161 ^ _781404) ^ [_1157276, _1157278, _1157280, _1157282] : [class_Rings_Ocomm__semiring__1(_1157276), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1157276), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157276), _1157278), _1157280)), _1157282) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157276), hAPP(hAPP(c_Power_Opower__class_Opower(_1157276), _1157278), _1157282)), hAPP(hAPP(c_Power_Opower__class_Opower(_1157276), _1157280), _1157282)))], (40656 ^ _781404) ^ [_1573968, _1573970] : [class_Complete__Lattice_Ocomplete__lattice(_1573968), c_Orderings_Oorder__class_Omono(_1573968, _1573968, _1573970), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1573968), hAPP(_1573970, c_Inductive_Ocomplete__lattice__class_Ogfp(_1573968, _1573970))), c_Inductive_Ocomplete__lattice__class_Ogfp(_1573968, _1573970))))], (22597 ^ _781404) ^ [_1184656, _1184658, _1184660] : [class_Groups_Omonoid__mult(_1184656), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184656), _1184658), 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)))), _1184660))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184656), _1184658), hAPP(hAPP(c_Power_Opower__class_Opower(_1184656), hAPP(hAPP(c_Power_Opower__class_Opower(_1184656), _1184658), _1184660)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (48306 ^ _781404) ^ [_1754095, _1754097, _1754099, _1754101, _1754103] : [class_Orderings_Olinorder(_1754095), 48312 ^ _781404 : [(48315 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1754095), hAPP(_1754101, _1754103)), hAPP(_1754101, 48311 ^ [_1754095, _1754097, _1754099, _1754101, _1754103])))], (48313 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754097), 48311 ^ [_1754095, _1754097, _1754099, _1754101, _1754103]), hAPP(c_List_Oset(_1754097), _1754099))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754097, _1754095, _1754101), _1754103), _1754099) = hAPP(hAPP(c_List_Olist_OCons(_1754097), _1754103), _1754099))], (2894 ^ _781404) ^ [_824325, _824327, _824329, _824331] : [-(c_Relation_ODomain(_824331, _824327) = c_Relation_ODomain(_824329, _824325)), _824331 = _824329, _824327 = _824325], (28921 ^ _781404) ^ [_1299184, _1299186, _1299188, _1299190] : [class_Fields_Olinordered__field(_1299184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299184), _1299186), _1299188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299184), _1299190), c_Groups_Ozero__class_Ozero(_1299184))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299184), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299184), _1299188), _1299190)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299184), _1299186), _1299190))))], (52758 ^ _781404) ^ [_1842619] : [-(hBOOL(_1842619)), -(hBOOL(hAPP(c_fNot, _1842619)))], (24662 ^ _781404) ^ [_1223886, _1223888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1223886), _1223888)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223886, _1223888) = _1223886)], (42804 ^ _781404) ^ [_1631261, _1631263, _1631265, _1631267] : [hBOOL(hAPP(hAPP(c_member(_1631261), _1631263), hAPP(c_List_Oset(_1631261), hAPP(hAPP(c_List_Otake(_1631261), _1631265), _1631267)))), -(hBOOL(hAPP(hAPP(c_member(_1631261), _1631263), hAPP(c_List_Oset(_1631261), _1631267))))], (31056 ^ _781404) ^ [_1339833, _1339835, _1339837] : [class_Orderings_Olinorder(_1339833), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339833), _1339835)), -(_1339835 = c_Orderings_Obot__class_Obot(tc_fun(_1339833, tc_HOL_Obool))), 31067 ^ _781404 : [(31077 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339833), hAPP(c_Finite__Set_Ofold1(_1339833, c_Orderings_Oord__class_Omin(_1339833)), _1339835)), _1339837))), 31078 ^ _781404 : [(31079 ^ _781404) ^ [_1340222] : [hBOOL(hAPP(hAPP(c_member(_1339833), _1340222), _1339835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339833), _1340222), _1339837))]]], (31068 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339833), hAPP(c_Finite__Set_Ofold1(_1339833, c_Orderings_Oord__class_Omin(_1339833)), _1339835)), _1339837)), 31072 ^ _781404 : [(31075 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339833), 31071 ^ [_1339833, _1339835, _1339837]), _1339837)))], (31073 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339833), 31071 ^ [_1339833, _1339835, _1339837]), _1339835)))]]]]], (44639 ^ _781404) ^ [_1674315, _1674317, _1674319] : [-(hAPP(c_List_Oset(_1674315), hAPP(c_List_Orotate(_1674315, _1674317), _1674319)) = hAPP(c_List_Oset(_1674315), _1674319))], (39215 ^ _781404) ^ [_1532972, _1532974] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1532972)), 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)), _1532972))), 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, _1532974))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19125 ^ _781404) ^ [_1121762] : [class_Int_Onumber__ring(_1121762), c_Int_Oiszero(_1121762, hAPP(c_Int_Onumber__class_Onumber__of(_1121762), c_Int_OBit1(c_Int_OPls)))], (38981 ^ _781404) ^ [_1526178, _1526180] : [-(hBOOL(hAPP(_1526180, 38982 ^ [_1526178, _1526180]))), -(hAPP(c_Set_OCollect(_1526178), _1526180) = c_Orderings_Obot__class_Obot(tc_fun(_1526178, tc_HOL_Obool)))], (29937 ^ _781404) ^ [_1318022, _1318024, _1318026, _1318028] : [class_Groups_Ocomm__monoid__mult(_1318022), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1318024), _1318026))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318024, _1318022), _1318028), _1318026) = c_Groups_Oone__class_Oone(_1318022))], (18737 ^ _781404) ^ [_1115449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1115449), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115449))], (47441 ^ _781404) ^ [_1735103, _1735105] : [hAPP(c_List_Orev(_1735103), _1735105) = c_List_Olist_ONil(_1735103), -(_1735105 = c_List_Olist_ONil(_1735103))], (41155 ^ _781404) ^ [_1586806, _1586808, _1586810] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586806, _1586806)), _1586808), _1586810)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586806, _1586806)), _1586808), c_Transitive__Closure_Ortrancl(_1586806, _1586810))))], (6474 ^ _781404) ^ [_884463, _884465] : [class_Orderings_Oorder(_884463), 6477 ^ _781404 : [(6484 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884463), hAPP(_884465, 6485 ^ [_884463, _884465])), hAPP(_884465, hAPP(c_Nat_OSuc, 6485 ^ [_884463, _884465])))), -(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _884463, _884465))], (6478 ^ _781404) ^ [] : [c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _884463, _884465), 6481 ^ _781404 : [(6482 ^ _781404) ^ [_884597] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884463), hAPP(_884465, _884597)), hAPP(_884465, hAPP(c_Nat_OSuc, _884597)))))]]]]], (46237 ^ _781404) ^ [_1709376, _1709378] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709376)), c_List_Oremdups(_1709376, _1709378)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709376)), _1709378), -(c_List_Oremdups(_1709376, _1709378) = _1709378)], (42903 ^ _781404) ^ [_1633578, _1633580, _1633582] : [hBOOL(hAPP(hAPP(c_member(_1633578), _1633580), hAPP(c_List_Oset(_1633578), _1633582))), 42907 ^ _781404 : [(42910 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1633578), _1633582), 42906 ^ [_1633578, _1633580, _1633582]) = _1633580)], (42908 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42906 ^ [_1633578, _1633580, _1633582]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633578)), _1633582))))]]], (52592 ^ _781404) ^ [_1840737] : [-(class_Nat_Osize(tc_Option_Ooption(_1840737)))], (44922 ^ _781404) ^ [_1680479, _1680481, _1680483] : [class_Orderings_Olinorder(_1680479), -(c_List_Oremove1(_1680479, _1680481, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680479, _1680479, c_COMBI(_1680479)), _1680481), _1680483)) = _1680483)], (50628 ^ _781404) ^ [_1804445, _1804447, _1804449, _1804451, _1804453, _1804455, _1804457] : [c_Fun_Oinj__on(_1804445, _1804447, _1804449, hAPP(c_Set_Oimage(_1804451, _1804445, _1804453), _1804455)), c_Fun_Oinj__on(_1804451, _1804445, _1804453, _1804455), hBOOL(hAPP(hAPP(c_member(_1804447), _1804457), hAPP(c_Set_Oimage(_1804445, _1804447, _1804449), hAPP(c_Set_Oimage(_1804451, _1804445, _1804453), _1804455)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1804451, _1804447, _1804455, hAPP(c_Fun_Ocomp(_1804445, _1804447, _1804451, _1804449), _1804453)), _1804457) = hAPP(hAPP(c_Fun_Ocomp(_1804445, _1804451, _1804447, c_Hilbert__Choice_Oinv__into(_1804451, _1804445, _1804455, _1804453)), c_Hilbert__Choice_Oinv__into(_1804445, _1804447, hAPP(c_Set_Oimage(_1804451, _1804445, _1804453), _1804455), _1804449)), _1804457))], (5524 ^ _781404) ^ [_865904, _865906] : [_865906 = _865904, -(c_Groups_Oabs__class_Oabs(_865906) = c_Groups_Oabs__class_Oabs(_865904))], (52750 ^ _781404) ^ [] : [-(hBOOL(c_fTrue))], (15493 ^ _781404) ^ [_1055568, _1055570, _1055572] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055568), _1055570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1055568, tc_HOL_Obool)), _1055572), _1055570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055568), _1055570)), hAPP(c_Finite__Set_Ocard(_1055568), _1055572))), -(_1055572 = _1055570)], (8586 ^ _781404) ^ [_926166, _926168, _926170] : [class_Rings_Osemiring__1(_926166), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_926166, _926168, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _926170) = _926170)], (44389 ^ _781404) ^ [_1668750, _1668752] : [_1668752 = c_List_Olist_ONil(_1668750), -(hAPP(c_List_Orotate1(_1668750), _1668752) = c_List_Olist_ONil(_1668750))], (27189 ^ _781404) ^ [_1266789, _1266791, _1266793] : [class_Rings_Olinordered__idom(_1266789), -(hAPP(c_Groups_Oabs__class_Oabs(_1266789), hAPP(hAPP(c_Power_Opower__class_Opower(_1266789), hAPP(c_Groups_Ouminus__class_Ouminus(_1266789), _1266791)), _1266793)) = hAPP(c_Groups_Oabs__class_Oabs(_1266789), hAPP(hAPP(c_Power_Opower__class_Opower(_1266789), _1266791), _1266793)))], (32348 ^ _781404) ^ [_1364021, _1364023, _1364025, _1364027, _1364029] : [class_Orderings_Olinorder(_1364021), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364021, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1364021, _1364023, _1364025)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1364021, _1364027, _1364029)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1364021, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364021), _1364023), _1364027), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1364021), _1364025), _1364029)))], (42102 ^ _781404) ^ [_1610545, _1610547, _1610549, _1610551] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1610545, _1610547)), _1610549), hAPP(c_Relation_Oconverse(_1610547, _1610545), _1610551))), 42107 ^ _781404 : [(42110 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610547, _1610545)), hAPP(hAPP(c_Product__Type_OPair(_1610547, _1610545), 42105 ^ [_1610545, _1610547, _1610549, _1610551]), 42106 ^ [_1610545, _1610547, _1610549, _1610551])), _1610551)))], (42108 ^ _781404) ^ [] : [-(_1610549 = hAPP(hAPP(c_Product__Type_OPair(_1610545, _1610547), 42106 ^ [_1610545, _1610547, _1610549, _1610551]), 42105 ^ [_1610545, _1610547, _1610549, _1610551]))]]], (52710 ^ _781404) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (25019 ^ _781404) ^ [_1229478] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1229478) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1229478))], (42155 ^ _781404) ^ [_1611931, _1611933, _1611935] : [c_Nitpick_Oless__eq__frac(_1611931, _1611933, _1611935), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1611931), c_Nitpick_Oplus__frac(_1611931, _1611933, c_Nitpick_Ouminus__frac(_1611931, _1611935)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19133 ^ _781404) ^ [_1121864] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1121864) = 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)), _1121864)))], (19027 ^ _781404) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (33941 ^ _781404) ^ [_1404070, _1404072, _1404074, _1404076, _1404078] : [hBOOL(hAPP(hAPP(c_member(_1404070), _1404072), _1404074)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404076, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404070, tc_fun(_1404076, tc_HOL_Obool)), _1404074), _1404078)), hAPP(_1404078, _1404072))))], (40244 ^ _781404) ^ [_1564984, _1564986] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1564984, _1564986), 40245 ^ [_1564984, _1564986])), -(c_Wellfounded_OwfP(_1564984, _1564986))], (31414 ^ _781404) ^ [_1346451, _1346453, _1346455] : [class_Orderings_Olinorder(_1346451), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346451), _1346453)), -(_1346453 = c_Orderings_Obot__class_Obot(tc_fun(_1346451, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346451), _1346455)), -(_1346455 = c_Orderings_Obot__class_Obot(tc_fun(_1346451, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1346451, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1346451, tc_HOL_Obool)), _1346453), _1346455)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346451), c_Big__Operators_Olinorder__class_OMin(_1346451, _1346453)), c_Big__Operators_Olinorder__class_OMin(_1346451, _1346455)))], (43645 ^ _781404) ^ [_1651153, _1651155, _1651157] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1651153, tc_HOL_Obool)), hAPP(c_List_Oset(_1651153), c_List_Oremove1(_1651153, _1651155, _1651157))), hAPP(c_List_Oset(_1651153), _1651157))))], (4766 ^ _781404) ^ [_853945, _853947, _853949, _853951] : [-(c_Product__Type_Osnd(_853951, _853947) = c_Product__Type_Osnd(_853949, _853945)), _853951 = _853949, _853947 = _853945], (19324 ^ _781404) ^ [_1125149, _1125151] : [19325 ^ _781404 : [(19326 ^ _781404) ^ [_1125202] : [_1125151 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1125149), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1125202))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125149), _1125151)))], (35680 ^ _781404) ^ [_1447226, _1447228] : [-(_1447226 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1447228, _1447226) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1447228), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1447226)))], (8351 ^ _781404) ^ [_922228, _922230] : [class_Groups_Olinordered__ab__group__add(_922228), 8354 ^ _781404 : [(8361 ^ _781404) ^ [] : [_922230 = c_Groups_Ozero__class_Ozero(_922228), -(_922230 = hAPP(c_Groups_Ouminus__class_Ouminus(_922228), _922230))], (8355 ^ _781404) ^ [] : [_922230 = hAPP(c_Groups_Ouminus__class_Ouminus(_922228), _922230), -(_922230 = c_Groups_Ozero__class_Ozero(_922228))]]], (48032 ^ _781404) ^ [_1747696, _1747698, _1747700] : [-(hBOOL(hAPP(hAPP(c_member(_1747696), _1747698), hAPP(c_List_Oset(_1747696), _1747700)))), -(c_List_Oinsert(_1747696, _1747698, _1747700) = hAPP(hAPP(c_List_Olist_OCons(_1747696), _1747698), _1747700))], (37132 ^ _781404) ^ [_1478047, _1478049, _1478051, _1478053, _1478055, _1478057, _1478059] : [-(hAPP(c_Product__Type_Oapsnd(_1478047, _1478049, _1478051, _1478053), hAPP(c_Product__Type_Oapfst(_1478055, _1478051, _1478047, _1478057), _1478059)) = hAPP(c_Product__Type_Oapfst(_1478055, _1478051, _1478049, _1478057), hAPP(c_Product__Type_Oapsnd(_1478047, _1478049, _1478055, _1478053), _1478059)))], (1466 ^ _781404) ^ [_802769, _802771] : [-(class_Lattices_Osemilattice__inf(_802769)), _802771 = _802769, class_Lattices_Osemilattice__inf(_802771)], (13277 ^ _781404) ^ [_1012120, _1012122] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1012120), _1012122) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 13280 ^ _781404 : [(13283 ^ _781404) ^ [] : [-(_1012122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13281 ^ _781404) ^ [] : [-(_1012120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (50318 ^ _781404) ^ [_1797902, _1797904] : [-(c_Equiv__Relations_Opart__equivp(_1797902, _1797904)), 50321 ^ _781404 : [(50322 ^ _781404) ^ [_1797979] : [hBOOL(hAPP(hAPP(_1797904, _1797979), _1797979))]], c_Predicate_Osymp(_1797902, _1797904), c_Predicate_Otransp(_1797902, _1797904)], (45126 ^ _781404) ^ [_1683853, _1683855, _1683857] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1683853)), _1683855), c_List_Olists(_1683853, _1683857))), -(_1683855 = c_List_Olist_ONil(_1683853)), 45135 ^ _781404 : [(45140 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1683853)), 45134 ^ [_1683853, _1683855, _1683857]), c_List_Olists(_1683853, _1683857))))], (45138 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1683853), 45133 ^ [_1683853, _1683855, _1683857]), _1683857)))], (45136 ^ _781404) ^ [] : [-(_1683855 = hAPP(hAPP(c_List_Olist_OCons(_1683853), 45133 ^ [_1683853, _1683855, _1683857]), 45134 ^ [_1683853, _1683855, _1683857]))]]], (4296 ^ _781404) ^ [_846468, _846470, _846472, _846474] : [-(c_List_Ofilter(_846474, _846470) = c_List_Ofilter(_846472, _846468)), _846474 = _846472, _846470 = _846468], (34687 ^ _781404) ^ [_1425316] : [-(c_Finite__Set_Ofun__left__comm__idem(_1425316, tc_fun(_1425316, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1425316, tc_HOL_Obool), tc_fun(tc_fun(_1425316, tc_HOL_Obool), tc_fun(_1425316, tc_HOL_Obool)), _1425316), hAPP(c_COMBC(tc_fun(_1425316, tc_HOL_Obool), tc_fun(_1425316, tc_HOL_Obool), tc_fun(_1425316, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1425316, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1425316, tc_fun(_1425316, tc_HOL_Obool), tc_fun(_1425316, tc_HOL_Obool)), c_Set_Oinsert(_1425316)), c_Orderings_Obot__class_Obot(tc_fun(_1425316, tc_HOL_Obool))))))], (44635 ^ _781404) ^ [_1674212, _1674214, _1674216] : [-(c_List_Orotate(_1674212, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1674214), _1674216)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1674212), tc_List_Olist(_1674212), tc_List_Olist(_1674212), c_List_Orotate(_1674212, _1674214)), c_List_Orotate(_1674212, _1674216)))], (43553 ^ _781404) ^ [_1649545] : [class_Groups_Omonoid__add(_1649545), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1649545), c_List_Olist_ONil(_1649545)) = c_Groups_Ozero__class_Ozero(_1649545))], (42551 ^ _781404) ^ [_1624562, _1624564, _1624566, _1624568, _1624570] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1624562), tc_List_Olist(_1624562))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1624562), tc_List_Olist(_1624562)), hAPP(hAPP(c_List_Olist_OCons(_1624562), _1624564), _1624566)), _1624568)), c_List_Olistrel(_1624562, _1624570))), 42556 ^ _781404 : [(42561 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1624562), tc_List_Olist(_1624562))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1624562), tc_List_Olist(_1624562)), _1624566), 42555 ^ [_1624562, _1624564, _1624566, _1624568, _1624570])), c_List_Olistrel(_1624562, _1624570))))], (42559 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624562, _1624562)), hAPP(hAPP(c_Product__Type_OPair(_1624562, _1624562), _1624564), 42554 ^ [_1624562, _1624564, _1624566, _1624568, _1624570])), _1624570)))], (42557 ^ _781404) ^ [] : [-(_1624568 = hAPP(hAPP(c_List_Olist_OCons(_1624562), 42554 ^ [_1624562, _1624564, _1624566, _1624568, _1624570]), 42555 ^ [_1624562, _1624564, _1624566, _1624568, _1624570]))]]], (20207 ^ _781404) ^ [_1140183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1140183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1140183))))], (5518 ^ _781404) ^ [_865819, _865821] : [_865821 = _865819, -(c_Groups_Ozero__class_Ozero(_865821) = c_Groups_Ozero__class_Ozero(_865819))], (42924 ^ _781404) ^ [_1634080, _1634082] : [-(hAPP(c_List_Oset(_1634080), _1634082) = hAPP(c_Set_OCollect(_1634080), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1634080), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1634080, 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)), _1634080), 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)), _1634080), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1634080, tc_fun(tc_Nat_Onat, _1634080), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1634080, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1634080), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1634080), c_COMBB(_1634080, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1634080), _1634082))))), 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(_1634080)), _1634082))))))], (20879 ^ _781404) ^ [_1152119, _1152121, _1152123] : [class_Rings_Ono__zero__divisors(_1152119), -(_1152121 = c_Groups_Ozero__class_Ozero(_1152119)), -(_1152123 = c_Groups_Ozero__class_Ozero(_1152119)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152119), _1152121), _1152123) = c_Groups_Ozero__class_Ozero(_1152119)], (20631 ^ _781404) ^ [_1147234, _1147236] : [class_Int_Onumber__ring(_1147234), 20634 ^ _781404 : [(20641 ^ _781404) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147236)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1147234), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147236)) = hAPP(c_Int_Onumber__class_Onumber__of(_1147234), _1147236))], (20635 ^ _781404) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147236))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1147234), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1147236)) = c_Groups_Ozero__class_Ozero(_1147234))]]], (20701 ^ _781404) ^ [_1148324, _1148326, _1148328] : [class_Rings_Olinordered__idom(_1148324), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148324), _1148326), c_Groups_Ozero__class_Ozero(_1148324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148324), hAPP(hAPP(c_Power_Opower__class_Opower(_1148324), _1148326), 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)))), _1148328)))), c_Groups_Ozero__class_Ozero(_1148324))))], (23868 ^ _781404) ^ [_1209754, _1209756] : [class_Divides_Osemiring__div(_1209754), -(_1209756 = c_Groups_Ozero__class_Ozero(_1209754)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209754), _1209756), _1209756) = c_Groups_Oone__class_Oone(_1209754))], (36719 ^ _781404) ^ [_1468401, _1468403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1468401)), -(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(_1468401), _1468403))), _1468401)))], (45305 ^ _781404) ^ [_1688535, _1688537] : [-(hAPP(hAPP(c_List_Omap(_1688535, _1688535), c_COMBI(_1688535)), _1688537) = _1688537)], (9222 ^ _781404) ^ [_938803, _938805] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_938803, tc_HOL_Obool)), _938805) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938803, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_938803, tc_HOL_Obool))), _938805))], (40626 ^ _781404) ^ [_1573433, _1573435, _1573437] : [class_Complete__Lattice_Ocomplete__lattice(_1573433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1573433), _1573435), hAPP(_1573437, _1573435))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1573433), _1573435), c_Inductive_Ocomplete__lattice__class_Ogfp(_1573433, _1573437))))], (31166 ^ _781404) ^ [_1342021, _1342023, _1342025, _1342027, _1342029, _1342031, _1342033] : [-(c_Nitpick_Ofold__graph_H(_1342021, _1342023, _1342025, _1342027, _1342029, hAPP(hAPP(_1342025, _1342031), _1342033))), 31167 ^ _781404 : [(31174 ^ _781404) ^ [_1342250, _1342252] : [hAPP(hAPP(_1342025, _1342031), _1342033) = hAPP(hAPP(_1342025, _1342252), _1342250), hBOOL(hAPP(hAPP(c_member(_1342021), _1342252), _1342029)), c_Nitpick_Ofold__graph_H(_1342021, _1342023, _1342025, _1342027, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1342021, tc_HOL_Obool)), _1342029), hAPP(hAPP(c_Set_Oinsert(_1342021), _1342252), c_Orderings_Obot__class_Obot(tc_fun(_1342021, tc_HOL_Obool)))), _1342250)], (31168 ^ _781404) ^ [] : [_1342029 = c_Orderings_Obot__class_Obot(tc_fun(_1342021, tc_HOL_Obool)), hAPP(hAPP(_1342025, _1342031), _1342033) = _1342027]]], (27703 ^ _781404) ^ [_1276397, _1276399, _1276401] : [class_Lattices_Oab__semigroup__idem__mult(_1276397), hAPP(_1276399, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276397), 27708 ^ [_1276397, _1276399, _1276401]), 27709 ^ [_1276397, _1276399, _1276401])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276397), hAPP(_1276399, 27708 ^ [_1276397, _1276399, _1276401])), hAPP(_1276399, 27709 ^ [_1276397, _1276399, _1276401])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276397), _1276401)), -(_1276401 = c_Orderings_Obot__class_Obot(tc_fun(_1276397, tc_HOL_Obool))), -(hAPP(_1276399, hAPP(c_Finite__Set_Ofold1(_1276397, c_Groups_Otimes__class_Otimes(_1276397)), _1276401)) = hAPP(c_Finite__Set_Ofold1(_1276397, c_Groups_Otimes__class_Otimes(_1276397)), hAPP(c_Set_Oimage(_1276397, _1276397, _1276399), _1276401)))], (11975 ^ _781404) ^ [_986642, _986644, _986646, _986648] : [-(hBOOL(hAPP(hAPP(c_member(_986642), _986644), _986646))), -(hBOOL(hAPP(hAPP(c_member(_986642), _986644), _986648))), 11982 ^ _781404 : [(11989 ^ _781404) ^ [] : [_986646 = _986648, -(hAPP(hAPP(c_Set_Oinsert(_986642), _986644), _986646) = hAPP(hAPP(c_Set_Oinsert(_986642), _986644), _986648))], (11983 ^ _781404) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_986642), _986644), _986646) = hAPP(hAPP(c_Set_Oinsert(_986642), _986644), _986648), -(_986646 = _986648)]]], (14462 ^ _781404) ^ [_1034662, _1034664] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1034662), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1034662, tc_HOL_Obool), _1034664)))), 14463 ^ _781404 : [(14464 ^ _781404) ^ [_1034726] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1034662, tc_HOL_Obool)), _1034726), _1034664)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034662), _1034726))]]], (24576 ^ _781404) ^ [_1222243, _1222245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1222243)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222245)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1222245), _1222243)), _1222245) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1222245), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1222243), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (46558 ^ _781404) ^ [_1716816] : [-(c_List_Otranspose(_1716816, c_List_Olist_ONil(tc_List_Olist(_1716816))) = c_List_Olist_ONil(tc_List_Olist(_1716816)))], (4906 ^ _781404) ^ [_856173, _856175] : [_856175 = _856173, -(c_Relation_OId(_856175) = c_Relation_OId(_856173))], (27013 ^ _781404) ^ [_1263580, _1263582] : [class_Groups_Oordered__ab__group__add__abs(_1263580), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263580), c_Groups_Ozero__class_Ozero(_1263580)), hAPP(c_Groups_Oabs__class_Oabs(_1263580), _1263582))))], (17168 ^ _781404) ^ [_1087292, _1087294, _1087296] : [class_Int_Onumber__ring(_1087292), class_Rings_Olinordered__idom(_1087292), 17175 ^ _781404 : [(17182 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087294), _1087296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087292), hAPP(c_Int_Onumber__class_Onumber__of(_1087292), _1087294)), hAPP(c_Int_Onumber__class_Onumber__of(_1087292), _1087296))))], (17176 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087292), hAPP(c_Int_Onumber__class_Onumber__of(_1087292), _1087294)), hAPP(c_Int_Onumber__class_Onumber__of(_1087292), _1087296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087294), _1087296)))]]], (25179 ^ _781404) ^ [_1232030, _1232032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1232032, _1232030)), _1232030)))], (26721 ^ _781404) ^ [_1257952, _1257954, _1257956, _1257958, _1257960, _1257962, _1257964] : [c_Finite__Set_Ofolding__image__simple(_1257952, _1257954, _1257956, _1257958, _1257960, _1257962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257954), _1257964)), -(hAPP(_1257962, _1257964) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1257952, _1257954, _1257956), _1257960), _1257958), _1257964))], (34397 ^ _781404) ^ [_1418382, _1418384, _1418386, _1418388, _1418390] : [class_Groups_Ocomm__monoid__mult(_1418382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418384), _1418386)), 34404 ^ _781404 : [(34411 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418384), _1418388), _1418386))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1418384, _1418382), hAPP(hAPP(c_COMBC(_1418384, _1418382, _1418382), hAPP(hAPP(c_COMBS(_1418384, _1418382, tc_fun(_1418382, _1418382)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1418382, tc_fun(_1418382, _1418382)), _1418384), c_If(_1418382)), hAPP(c_fequal, _1418388))), _1418390)), c_Groups_Oone__class_Oone(_1418382))), _1418386) = c_Groups_Oone__class_Oone(_1418382))], (34405 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1418384), _1418388), _1418386)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1418384, _1418382), hAPP(hAPP(c_COMBC(_1418384, _1418382, _1418382), hAPP(hAPP(c_COMBS(_1418384, _1418382, tc_fun(_1418382, _1418382)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1418382, tc_fun(_1418382, _1418382)), _1418384), c_If(_1418382)), hAPP(c_fequal, _1418388))), _1418390)), c_Groups_Oone__class_Oone(_1418382))), _1418386) = hAPP(_1418390, _1418388))]]], (14950 ^ _781404) ^ [_1044337, _1044339, _1044341, _1044343, _1044345] : [class_Groups_Ocomm__monoid__add(_1044337), class_Groups_Oordered__ab__semigroup__add(_1044337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1044339), _1044341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1044339, tc_HOL_Obool)), _1044343), _1044341)), 14968 ^ _781404 : [(14971 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044337), c_Groups_Ozero__class_Ozero(_1044337)), hAPP(_1044345, 14967 ^ [_1044337, _1044339, _1044341, _1044343, _1044345])))], (14969 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1044339), 14967 ^ [_1044337, _1044339, _1044341, _1044343, _1044345]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044339, tc_HOL_Obool)), _1044341), _1044343))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044337), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1044339, _1044337), _1044345), _1044343)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1044339, _1044337), _1044345), _1044341))))], (23968 ^ _781404) ^ [_1211562, _1211564] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211562), _1211564) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23969 ^ _781404 : [(23978 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211562), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211564), _1211562))], (23972 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211562), _1211564))], (23970 ^ _781404) ^ [] : [_1211564 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (400 ^ _781404) ^ [_787518, _787520, _787522, _787524] : [-(c_Nitpick_Owf_H(_787522, _787518)), c_Nitpick_Owf_H(_787524, _787520), _787524 = _787522, _787520 = _787518], (29653 ^ _781404) ^ [_1312378, _1312380, _1312382] : [class_Fields_Olinordered__field(_1312378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312378), _1312380), _1312382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312378), _1312380), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312378), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1312378), _1312380), _1312382)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1312378), c_Groups_Oone__class_Oone(_1312378)), c_Groups_Oone__class_Oone(_1312378))))))], (796 ^ _781404) ^ [_793394, _793396, _793398, _793400, _793402, _793404] : [-(c_List_Oall__interval__int(_793402, _793398, _793394)), c_List_Oall__interval__int(_793404, _793400, _793396), _793404 = _793402, _793400 = _793398, _793396 = _793394], (11313 ^ _781404) ^ [_973757, _973759, _973761, _973763, _973765] : [c_Fun_Oinj__on(_973757, _973759, _973761, c_Orderings_Otop__class_Otop(tc_fun(_973757, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_973757, _973759, _973761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973757, tc_HOL_Obool)), _973763), _973765)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973759, tc_HOL_Obool)), hAPP(c_Set_Oimage(_973757, _973759, _973761), _973763)), hAPP(c_Set_Oimage(_973757, _973759, _973761), _973765)))], (27077 ^ _781404) ^ [_1264565, _1264567, _1264569] : [class_Groups_Oordered__ab__group__add__abs(_1264565), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264565), hAPP(c_Groups_Oabs__class_Oabs(_1264565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264565), _1264567), _1264569))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264565), hAPP(c_Groups_Oabs__class_Oabs(_1264565), _1264567)), hAPP(c_Groups_Oabs__class_Oabs(_1264565), _1264569)))))], (31354 ^ _781404) ^ [_1345432, _1345434, _1345436] : [class_Orderings_Olinorder(_1345432), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1345432, tc_HOL_Obool)), _1345434), _1345436)), -(_1345434 = c_Orderings_Obot__class_Obot(tc_fun(_1345432, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345432), _1345436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345432), c_Big__Operators_Olinorder__class_OMin(_1345432, _1345436)), c_Big__Operators_Olinorder__class_OMin(_1345432, _1345434))))], (39109 ^ _781404) ^ [_1529005, _1529007, _1529009] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1529005, tc_HOL_Obool)), _1529007), _1529009) = hAPP(c_Set_OCollect(_1529005), hAPP(hAPP(c_COMBS(_1529005, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529005), c_fconj), hAPP(hAPP(c_COMBC(_1529005, tc_fun(_1529005, tc_HOL_Obool), tc_HOL_Obool), c_member(_1529005)), _1529007))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1529005), c_fNot), hAPP(hAPP(c_COMBC(_1529005, tc_fun(_1529005, tc_HOL_Obool), tc_HOL_Obool), c_member(_1529005)), _1529009)))))], (52330 ^ _781404) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (33121 ^ _781404) ^ [_1379189, _1379191, _1379193] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1379189, tc_Nat_Onat), _1379191), _1379193) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1379189, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1379189), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1379191)), _1379193)))], (12300 ^ _781404) ^ [_993063, _993065, _993067] : [_993065 = _993067, -(hBOOL(hAPP(hAPP(c_member(_993063), _993065), hAPP(hAPP(c_Set_Oinsert(_993063), _993067), c_Orderings_Obot__class_Obot(tc_fun(_993063, tc_HOL_Obool))))))], (41716 ^ _781404) ^ [_1600273, _1600275] : [-(c_Relation_Ototal__on(_1600273, c_Orderings_Obot__class_Obot(tc_fun(_1600273, tc_HOL_Obool)), _1600275))], (17409 ^ _781404) ^ [_1091967] : [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)), _1091967)), _1091967)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091967), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (4074 ^ _781404) ^ [_843011, _843013, _843015, _843017, _843019, _843021, _843023, _843025] : [-(c_New__Random__Sequence_Oneg__map(_843025, _843021, _843017, _843013) = c_New__Random__Sequence_Oneg__map(_843023, _843019, _843015, _843011)), _843025 = _843023, _843021 = _843019, _843017 = _843015, _843013 = _843011], (51514 ^ _781404) ^ [_1824778, _1824780, _1824782, _1824784] : [class_Rings_Ocomm__ring(_1824778), class_Rings_Odvd(_1824778), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824778), _1824780), _1824782)), 51525 ^ _781404 : [(51532 ^ _781404) ^ [_1825204, _1825206] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824778), _1824780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1824778), _1825206), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824778), _1825204), _1824782))), _1824784))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824778), _1824780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824778), _1825206), _1824784))))], (51526 ^ _781404) ^ [_1825031, _1825033] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824778), _1824780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824778), _1825033), _1824784))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824778), _1824780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1824778), _1825033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824778), _1825031), _1824782))), _1824784))))]]], (7369 ^ _781404) ^ [_901525, _901527] : [class_Lattices_Olattice(_901525), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901525), _901527), _901527) = _901527)], (34857 ^ _781404) ^ [_1429354, _1429356, _1429358, _1429360] : [-(c_Nat_Onat_Onat__case(_1429354, _1429356, _1429358, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429360)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1429354), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1429360))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1429354, _1429354), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1429354, tc_fun(_1429354, _1429354)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1429354, tc_fun(_1429354, _1429354)), tc_Int_Oint), c_If(_1429354)), c_Nat__Numeral_Oneg)), _1429356)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1429354, tc_Int_Oint), _1429358), c_Int_Onat))))], (12762 ^ _781404) ^ [_1002358, _1002360, _1002362, _1002364, _1002366, _1002368] : [hBOOL(hAPP(hAPP(c_member(_1002358), _1002360), c_SetInterval_Oord_OgreaterThanAtMost(_1002358, _1002362, _1002364, _1002366, _1002368))), 12765 ^ _781404 : [(12768 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1002362, _1002360), _1002368)))], (12766 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(_1002364, _1002366), _1002360)))]]], (44028 ^ _781404) ^ [_1660052, _1660054, _1660056] : [hAPP(hAPP(c_List_Oappend(_1660052), _1660054), _1660056) = _1660056, -(_1660054 = c_List_Olist_ONil(_1660052))], (5020 ^ _781404) ^ [_857932, _857934, _857936, _857938, _857940, _857942, _857944, _857946] : [-(c_Fun_Ocomp(_857946, _857942, _857938, _857934) = c_Fun_Ocomp(_857944, _857940, _857936, _857932)), _857946 = _857944, _857942 = _857940, _857938 = _857936, _857934 = _857932], (40161 ^ _781404) ^ [_1563275, _1563277, _1563279, _1563281, _1563283] : [hBOOL(hAPP(hAPP(_1563275, _1563277), _1563279)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1563281, _1563283, _1563275), _1563277)))], (36526 ^ _781404) ^ [_1464028, _1464030] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1464028), _1464030) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1464028, _1464030)))], (8150 ^ _781404) ^ [_918224] : [c_Orderings_Otop__class_Otop(tc_fun(_918224, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_918224, tc_HOL_Obool))], (7657 ^ _781404) ^ [_907319, _907321, _907323] : [class_Lattices_Osemilattice__inf(_907319), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907319), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_907319), _907321), _907323)), _907323)))], (48993 ^ _781404) ^ [_1768669, _1768671, _1768673, _1768675, _1768677] : [hBOOL(hAPP(hAPP(_1768673, _1768677), _1768675)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1768669, _1768671, _1768673), _1768675), _1768677)))], (52288 ^ _781404) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (16823 ^ _781404) ^ [_1081111, _1081113, _1081115, _1081117, _1081119] : [c_Finite__Set_Ofolding__one__idem(_1081111, _1081113, _1081115), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081111), _1081117)), -(_1081117 = c_Orderings_Obot__class_Obot(tc_fun(_1081111, tc_HOL_Obool))), -(hAPP(_1081115, hAPP(hAPP(c_Set_Oinsert(_1081111), _1081119), _1081117)) = hAPP(hAPP(_1081113, _1081119), hAPP(_1081115, _1081117)))], (44729 ^ _781404) ^ [_1676198, _1676200, _1676202] : [class_Groups_Omonoid__add(_1676198), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1676198), _1676200), hAPP(c_List_Ofoldl(_1676198, _1676198, c_Groups_Oplus__class_Oplus(_1676198), c_Groups_Ozero__class_Ozero(_1676198)), _1676202)) = hAPP(c_List_Ofoldl(_1676198, _1676198, c_Groups_Oplus__class_Oplus(_1676198), _1676200), _1676202))], (34034 ^ _781404) ^ [_1406202, _1406204, _1406206, _1406208, _1406210] : [class_Complete__Lattice_Ocomplete__lattice(_1406202), class_Orderings_Olinorder(_1406202), 34041 ^ _781404 : [(34051 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406202), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1406204, _1406202), _1406206), _1406208)), _1406210))), 34052 ^ _781404 : [(34053 ^ _781404) ^ [_1406550] : [hBOOL(hAPP(hAPP(c_member(_1406204), _1406550), _1406206)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406202), hAPP(_1406208, _1406550)), _1406210))]]], (34042 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406202), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1406204, _1406202), _1406206), _1406208)), _1406210)), 34046 ^ _781404 : [(34049 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406202), hAPP(_1406208, 34045 ^ [_1406202, _1406204, _1406206, _1406208, _1406210])), _1406210)))], (34047 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406204), 34045 ^ [_1406202, _1406204, _1406206, _1406208, _1406210]), _1406206)))]]]]], (3872 ^ _781404) ^ [_839546, _839548, _839550, _839552, _839554, _839556] : [-(c_List_OtakeWhile(_839556, _839552, _839548) = c_List_OtakeWhile(_839554, _839550, _839546)), _839556 = _839554, _839552 = _839550, _839548 = _839546], (46425 ^ _781404) ^ [_1712996, _1712998] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712996)), c_List_Oconcat(_1712996, _1712998)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1712996), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1712996))), _1712998)))], (43699 ^ _781404) ^ [_1652300] : [-(c_List_Olists(_1652300, c_Orderings_Obot__class_Obot(tc_fun(_1652300, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1652300)), c_List_Olist_ONil(_1652300)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1652300), tc_HOL_Obool))))], (31816 ^ _781404) ^ [_1353759, _1353761, _1353763] : [class_Orderings_Olinorder(_1353759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353759), _1353761)), hBOOL(hAPP(hAPP(c_member(_1353759), _1353763), _1353761)), 31827 ^ _781404 : [(31834 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353759, tc_HOL_Obool)), _1353761), hAPP(hAPP(c_Set_Oinsert(_1353759), _1353763), c_Orderings_Obot__class_Obot(tc_fun(_1353759, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353759, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1353759, _1353761) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353759), _1353763), c_Big__Operators_Olinorder__class_OMax(_1353759, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353759, tc_HOL_Obool)), _1353761), hAPP(hAPP(c_Set_Oinsert(_1353759), _1353763), c_Orderings_Obot__class_Obot(tc_fun(_1353759, tc_HOL_Obool)))))))], (31828 ^ _781404) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353759, tc_HOL_Obool)), _1353761), hAPP(hAPP(c_Set_Oinsert(_1353759), _1353763), c_Orderings_Obot__class_Obot(tc_fun(_1353759, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353759, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1353759, _1353761) = _1353763)]]], (48579 ^ _781404) ^ [_1760153, _1760155, _1760157] : [c_List_Olist__ex(_1760153, _1760155, hAPP(c_List_Orev(_1760153), _1760157)), -(c_List_Olist__ex(_1760153, _1760155, _1760157))], (12132 ^ _781404) ^ [_989822, _989824, _989826, _989828] : [hBOOL(hAPP(hAPP(c_member(_989822), _989824), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_989822, tc_HOL_Obool)), _989826), _989828))), 12135 ^ _781404 : [(12138 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_989822), _989824), _989828))], (12136 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_989822), _989824), _989826)))]]], (27441 ^ _781404) ^ [_1271398, _1271400] : [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), _1271398)), _1271400))), _1271398 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1271400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45778 ^ _781404) ^ [_1699074, _1699076, _1699078] : [hBOOL(hAPP(c_List_Olistsp(_1699074, _1699076), _1699078)), 45781 ^ _781404 : [(45782 ^ _781404) ^ [_1699163] : [hBOOL(hAPP(hAPP(c_member(_1699074), _1699163), hAPP(c_List_Oset(_1699074), _1699078))), -(hBOOL(hAPP(_1699076, _1699163)))]]], (7183 ^ _781404) ^ [_897806, _897808, _897810] : [class_Lattices_Olattice(_897806), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897806), _897808), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897806), _897808), _897810))))], (3852 ^ _781404) ^ [_839240, _839242, _839244, _839246, _839248, _839250] : [-(c_List_OdropWhile(_839250, _839246, _839242) = c_List_OdropWhile(_839248, _839244, _839240)), _839250 = _839248, _839246 = _839244, _839242 = _839240], (50346 ^ _781404) ^ [_1798312, _1798314] : [c_Equiv__Relations_Oequivp(_1798312, _1798314), -(c_Equiv__Relations_Opart__equivp(_1798312, _1798314))], (37256 ^ _781404) ^ [] : [-(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)))], (19203 ^ _781404) ^ [] : [-(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)))], (38464 ^ _781404) ^ [_1511338, _1511340, _1511342, _1511344, _1511346, _1511348] : [-(hAPP(c_Set_Oimage(_1511338, tc_prod(_1511340, _1511342), hAPP(hAPP(c_COMBS(_1511338, _1511342, tc_prod(_1511340, _1511342)), hAPP(hAPP(c_COMBB(_1511340, tc_fun(_1511342, tc_prod(_1511340, _1511342)), _1511338), c_Product__Type_OPair(_1511340, _1511342)), _1511344)), _1511346)), _1511348) = hAPP(hAPP(c_Product__Type_OSigma(_1511340, _1511342), hAPP(c_Set_Oimage(_1511338, _1511340, _1511344), _1511348)), hAPP(hAPP(c_COMBB(tc_fun(_1511338, tc_HOL_Obool), tc_fun(_1511342, tc_HOL_Obool), _1511340), c_Set_Oimage(_1511338, _1511342, _1511346)), hAPP(hAPP(c_COMBC(_1511340, tc_fun(_1511338, tc_HOL_Obool), tc_fun(_1511338, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511338, tc_HOL_Obool), tc_fun(tc_fun(_1511338, tc_HOL_Obool), tc_fun(_1511338, tc_HOL_Obool)), _1511340), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511338, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1511340, tc_HOL_Obool), tc_fun(_1511338, tc_HOL_Obool), _1511340), c_Set_Ovimage(_1511338, _1511340, _1511344)), hAPP(hAPP(c_COMBC(_1511340, tc_fun(_1511340, tc_HOL_Obool), tc_fun(_1511340, tc_HOL_Obool)), c_Set_Oinsert(_1511340)), c_Orderings_Obot__class_Obot(tc_fun(_1511340, tc_HOL_Obool)))))), _1511348))))], (9497 ^ _781404) ^ [_944118, _944120, _944122, _944124] : [class_Orderings_Oorder(_944118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944118), _944120), _944122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944118), _944124), _944120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944118), _944124), _944122)))], (46000 ^ _781404) ^ [_1704137, _1704139, _1704141] : [c_List_Olist__all2(_1704141, _1704141, c_fequal, _1704137, _1704139), -(_1704137 = _1704139)], (23311 ^ _781404) ^ [_1199182, _1199184] : [_1199182 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1199182, _1199184) = _1199184)], (35249 ^ _781404) ^ [_1437845, _1437847, _1437849, _1437851, _1437853, _1437855] : [hBOOL(hAPP(hAPP(_1437845, _1437847), _1437849)), hBOOL(hAPP(hAPP(_1437851, _1437847), _1437849)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437853, tc_fun(_1437855, tc_HOL_Obool))), _1437845), _1437851), _1437847), _1437849)))], (46678 ^ _781404) ^ [_1720192] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1720192)), c_List_Otranspose__rel(_1720192)), c_List_Olist_ONil(tc_List_Olist(_1720192)))), -(c_List_Otranspose(_1720192, c_List_Olist_ONil(tc_List_Olist(_1720192))) = c_List_Olist_ONil(tc_List_Olist(_1720192)))], (37112 ^ _781404) ^ [_1477482, _1477484, _1477486, _1477488, _1477490, _1477492, _1477494] : [-(hAPP(c_Product__Type_Oapfst(_1477482, _1477484, _1477486, _1477488), hAPP(c_Product__Type_Oapfst(_1477490, _1477482, _1477486, _1477492), _1477494)) = hAPP(c_Product__Type_Oapfst(_1477490, _1477484, _1477486, hAPP(c_Fun_Ocomp(_1477482, _1477484, _1477490, _1477488), _1477492)), _1477494))], (21727 ^ _781404) ^ [_1167734, _1167736, _1167738] : [class_Rings_Olinordered__semiring__strict(_1167734), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167734), c_Groups_Ozero__class_Ozero(_1167734)), _1167736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167734), _1167738), c_Groups_Ozero__class_Ozero(_1167734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167734), _1167738), _1167736)), c_Groups_Ozero__class_Ozero(_1167734))))], (32098 ^ _781404) ^ [_1359172, _1359174, _1359176, _1359178] : [class_Orderings_Olinorder(_1359172), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359172), _1359174), _1359176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359172), _1359174), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359172), _1359178), _1359176))))], (28657 ^ _781404) ^ [_1294224, _1294226, _1294228, _1294230] : [class_Fields_Olinordered__field__inverse__zero(_1294224), 28660 ^ _781404 : [(28661 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294224), _1294226), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294224), _1294228), _1294230))), 28664 ^ _781404 : [(28671 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294224), c_Groups_Ozero__class_Ozero(_1294224)), _1294230))), 28674 ^ _781404 : [(28681 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294224), _1294230), c_Groups_Ozero__class_Ozero(_1294224)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294224), _1294226), c_Groups_Ozero__class_Ozero(_1294224))))], (28675 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294224), _1294230), c_Groups_Ozero__class_Ozero(_1294224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294224), _1294228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294224), _1294226), _1294230))))]]], (28665 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294224), c_Groups_Ozero__class_Ozero(_1294224)), _1294230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294224), _1294226), _1294230)), _1294228)))]]], (28687 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294224), _1294226), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294224), _1294228), _1294230)))), 28690 ^ _781404 : [(28693 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294224), _1294226), _1294230)), _1294228))], (28691 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294224), c_Groups_Ozero__class_Ozero(_1294224)), _1294230)))]], 28694 ^ _781404 : [(28697 ^ _781404) ^ [] : [28698 ^ _781404 : [(28701 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294224), _1294228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294224), _1294226), _1294230)))], (28699 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294224), _1294230), c_Groups_Ozero__class_Ozero(_1294224))))]], 28702 ^ _781404 : [(28705 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294224), _1294226), c_Groups_Ozero__class_Ozero(_1294224)))], (28703 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294224), _1294230), c_Groups_Ozero__class_Ozero(_1294224)))]]], (28695 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294224), c_Groups_Ozero__class_Ozero(_1294224)), _1294230))]]]]], (49011 ^ _781404) ^ [_1769026, _1769028, _1769030, _1769032, _1769034] : [hBOOL(hAPP(hAPP(_1769026, _1769028), _1769030)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1769032, _1769034, _1769026), _1769030), _1769028)))], (41028 ^ _781404) ^ [_1582956, _1582958] : [c_Wellfounded_Oacyclic(_1582956, _1582958), 41031 ^ _781404 : [(41032 ^ _781404) ^ [_1583041] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582956, _1582956)), hAPP(hAPP(c_Product__Type_OPair(_1582956, _1582956), _1583041), _1583041)), c_Transitive__Closure_Otrancl(_1582956, _1582958)))]]], (49055 ^ _781404) ^ [_1770560, _1770562, _1770564] : [-(c_List_Oreplicate(_1770560, hAPP(c_Nat_OSuc, _1770562), _1770564) = hAPP(hAPP(c_List_Olist_OCons(_1770560), _1770564), c_List_Oreplicate(_1770560, _1770562, _1770564)))], (39684 ^ _781404) ^ [_1550532, _1550534, _1550536] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1550532, _1550534)), _1550536)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1550534), hAPP(c_Relation_ORange(_1550532, _1550534), _1550536))))], (20799 ^ _781404) ^ [_1150690, _1150692, _1150694, _1150696] : [class_Rings_Ocomm__semiring__1(_1150690), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150690), _1150692), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150690), _1150694), _1150696)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150690), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150690), _1150692), _1150694)), _1150696))], (41217 ^ _781404) ^ [_1588324, _1588326] : [-(c_Transitive__Closure_Ortrancl(_1588324, c_Transitive__Closure_Ortrancl(_1588324, _1588326)) = c_Transitive__Closure_Ortrancl(_1588324, _1588326))], (42798 ^ _781404) ^ [_1631124, _1631126, _1631128, _1631130] : [hBOOL(hAPP(hAPP(c_member(_1631124), _1631126), hAPP(c_List_Oset(_1631124), c_List_Osublist(_1631124, _1631128, _1631130)))), -(hBOOL(hAPP(hAPP(c_member(_1631124), _1631126), hAPP(c_List_Oset(_1631124), _1631128))))], (34265 ^ _781404) ^ [_1414950, _1414952, _1414954, _1414956] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414950, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1414950, tc_fun(_1414950, tc_HOL_Obool), tc_HOL_Obool), c_member(_1414950)), _1414952)), hAPP(hAPP(c_COMBC(_1414950, tc_fun(_1414950, tc_HOL_Obool), tc_HOL_Obool), c_member(_1414950)), _1414954)), _1414956)), -(hBOOL(hAPP(hAPP(c_member(_1414950), _1414956), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414950, tc_HOL_Obool)), _1414952), _1414954))))], (40319 ^ _781404) ^ [_1566853, _1566855] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1566853, _1566853)), _1566855)), 40322 ^ _781404 : [(40329 ^ _781404) ^ [] : [c_Wellfounded_Oacyclic(_1566853, _1566855), -(c_Wellfounded_Owf(_1566853, _1566855))], (40323 ^ _781404) ^ [] : [c_Wellfounded_Owf(_1566853, _1566855), -(c_Wellfounded_Oacyclic(_1566853, _1566855))]]], (19663 ^ _781404) ^ [_1130907] : [-(c_Int_Osucc(_1130907) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1130907), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (45758 ^ _781404) ^ [_1698116, _1698118] : [-(c_List_Opartition(_1698116, _1698118, c_List_Olist_ONil(_1698116)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1698116), tc_List_Olist(_1698116)), c_List_Olist_ONil(_1698116)), c_List_Olist_ONil(_1698116)))], (24927 ^ _781404) ^ [_1228043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1228043)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228043), c_Int_OMin)))], (10649 ^ _781404) ^ [_962379, _962381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962379)), _962381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962379), _962381)))], (48953 ^ _781404) ^ [_1767789, _1767791, _1767793] : [-(c_List_Osplice(_1767789, hAPP(hAPP(c_List_Olist_OCons(_1767789), _1767791), _1767793), c_List_Olist_ONil(_1767789)) = hAPP(hAPP(c_List_Olist_OCons(_1767789), _1767791), _1767793))], (56 ^ _781404) ^ [_782202, _782204, _782206, _782208, _782210, _782212] : [-(c_Orderings_Oorder__class_Ostrict__mono(_782210, _782206, _782202)), c_Orderings_Oorder__class_Ostrict__mono(_782212, _782208, _782204), _782212 = _782210, _782208 = _782206, _782204 = _782202], (19599 ^ _781404) ^ [_1129817] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1129817)) = 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), _1129817)))], (11497 ^ _781404) ^ [_977929, _977931, _977933, _977935] : [c_Fun_Oinj__on(_977929, _977931, _977933, _977935), -(c_Fun_Oinj__on(_977931, _977929, c_Fun_Othe__inv__into(_977929, _977931, _977935, _977933), hAPP(c_Set_Oimage(_977929, _977931, _977933), _977935)))], (23211 ^ _781404) ^ [_1197038, _1197040, _1197042, _1197044, _1197046] : [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), _1197038), _1197040)), _1197042)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1197038), _1197044)), _1197046))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197042), _1197038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197046), _1197038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197040), _1197044)))], (45447 ^ _781404) ^ [_1691783, _1691785, _1691787, _1691789, _1691791] : [class_Groups_Ocomm__monoid__add(_1691783), hBOOL(hAPP(hAPP(c_member(_1691785), _1691787), hAPP(c_List_Oset(_1691785), _1691789))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1691783), hAPP(hAPP(c_List_Omap(_1691785, _1691783), _1691791), _1691789)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1691783), hAPP(_1691791, _1691787)), hAPP(c_List_Omonoid__add__class_Olistsum(_1691783), hAPP(hAPP(c_List_Omap(_1691785, _1691783), _1691791), c_List_Oremove1(_1691785, _1691787, _1691789)))))], (7635 ^ _781404) ^ [_906890, _906892, _906894] : [-(hAPP(c_Set_OPow(_906890), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_906890, tc_HOL_Obool)), _906892), _906894)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_906890, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_906890), _906892)), hAPP(c_Set_OPow(_906890), _906894)))], (8170 ^ _781404) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39850 ^ _781404) ^ [_1556113, _1556115] : [c_Wellfounded_Owf(_1556113, hAPP(hAPP(c_Relation_Orel__comp(_1556113, _1556113, _1556113), _1556115), _1556115)), -(c_Wellfounded_Owf(_1556113, _1556115))], (19757 ^ _781404) ^ [_1132381, _1132383] : [class_Int_Onumber__ring(_1132381), class_Rings_Olinordered__idom(_1132381), 19764 ^ _781404 : [(19771 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132383), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132381), hAPP(c_Int_Onumber__class_Onumber__of(_1132381), _1132383)), c_Groups_Oone__class_Oone(_1132381))))], (19765 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132381), hAPP(c_Int_Onumber__class_Onumber__of(_1132381), _1132383)), c_Groups_Oone__class_Oone(_1132381))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132383), c_Int_OBit1(c_Int_OPls))))]]], (42063 ^ _781404) ^ [_1609682, _1609684] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609682, _1609682)), _1609684), c_Relation_OId(_1609682))), -(_1609684 = hAPP(hAPP(c_Product__Type_OPair(_1609682, _1609682), 42066 ^ [_1609682, _1609684]), 42066 ^ [_1609682, _1609684]))], (12508 ^ _781404) ^ [_997207, _997209, _997211] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_997207, tc_HOL_Obool)), _997209), hAPP(c_Set_OPow(_997207), _997211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997207, tc_HOL_Obool)), _997209), _997211)))], (25133 ^ _781404) ^ [_1231270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231270), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1231270) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48135 ^ _781404) ^ [_1750134, _1750136, _1750138, _1750140, _1750142] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1750134, _1750134)), hAPP(hAPP(c_Product__Type_OPair(_1750134, _1750134), _1750136), _1750138)), c_List_Omeasures(_1750134, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1750134, tc_Nat_Onat)), _1750140), _1750142))))), 48136 ^ _781404 : [(48139 ^ _781404) ^ [] : [hAPP(_1750140, _1750136) = hAPP(_1750140, _1750138), hBOOL(hAPP(hAPP(c_member(tc_prod(_1750134, _1750134)), hAPP(hAPP(c_Product__Type_OPair(_1750134, _1750134), _1750136), _1750138)), c_List_Omeasures(_1750134, _1750142)))], (48137 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1750140, _1750136)), hAPP(_1750140, _1750138)))]]], (19835 ^ _781404) ^ [_1133681, _1133683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1133681)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1133683)), _1133681) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1133683), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1133681), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (30966 ^ _781404) ^ [_1338201, _1338203, _1338205, _1338207] : [class_Orderings_Olinorder(_1338201), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338201), _1338203)), hBOOL(hAPP(hAPP(c_member(_1338201), _1338205), _1338203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338201), hAPP(hAPP(c_Finite__Set_Ofold(_1338201, _1338201, c_Orderings_Oord__class_Omin(_1338201)), _1338207), _1338203)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338201), _1338205), _1338207))))], (5404 ^ _781404) ^ [_863950, _863952] : [_863952 = _863950, -(c_Finite__Set_Ofinite(_863952) = c_Finite__Set_Ofinite(_863950))], (6705 ^ _781404) ^ [_888733, _888735, _888737] : [class_Groups_Oordered__ab__group__add(_888733), 6708 ^ _781404 : [(6715 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888733), _888737), _888735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888733), hAPP(c_Groups_Ouminus__class_Ouminus(_888733), _888735)), hAPP(c_Groups_Ouminus__class_Ouminus(_888733), _888737))))], (6709 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888733), hAPP(c_Groups_Ouminus__class_Ouminus(_888733), _888735)), hAPP(c_Groups_Ouminus__class_Ouminus(_888733), _888737))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888733), _888737), _888735)))]]], (20057 ^ _781404) ^ [_1137647, _1137649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137647), _1137649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1137647)), c_Int_OBit0(_1137649))))], (3372 ^ _781404) ^ [_831718, _831720, _831722, _831724, _831726, _831728, _831730, _831732] : [-(c_Enum_Oproduct(_831732, _831728, _831724, _831720) = c_Enum_Oproduct(_831730, _831726, _831722, _831718)), _831732 = _831730, _831728 = _831726, _831724 = _831722, _831720 = _831718], (16589 ^ _781404) ^ [_1076533, _1076535, _1076537] : [class_Lattices_Olattice(_1076533), hAPP(_1076535, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076533), 16594 ^ [_1076533, _1076535, _1076537]), 16595 ^ [_1076533, _1076535, _1076537])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076533), hAPP(_1076535, 16594 ^ [_1076533, _1076535, _1076537])), hAPP(_1076535, 16595 ^ [_1076533, _1076535, _1076537])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076533), _1076537)), -(_1076537 = c_Orderings_Obot__class_Obot(tc_fun(_1076533, tc_HOL_Obool))), -(hAPP(_1076535, c_Big__Operators_Olattice__class_OSup__fin(_1076533, _1076537)) = c_Big__Operators_Olattice__class_OSup__fin(_1076533, hAPP(c_Set_Oimage(_1076533, _1076533, _1076535), _1076537)))], (45549 ^ _781404) ^ [_1693871, _1693873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1693871)), hAPP(c_Code__Numeral_Oof__nat, _1693873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1693871), _1693873)))], (15571 ^ _781404) ^ [_1057004, _1057006, _1057008] : [class_Lattices_Olattice(_1057004), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057004), _1057006)), hBOOL(hAPP(hAPP(c_member(_1057004), _1057008), _1057006)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1057004), _1057008), c_Big__Operators_Olattice__class_OSup__fin(_1057004, _1057006)) = c_Big__Operators_Olattice__class_OSup__fin(_1057004, _1057006))], (39991 ^ _781404) ^ [_1558817, _1558819] : [-(hAPP(c_Relation_ODomain(_1558817, _1558819), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1558817, _1558819), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1558817, tc_HOL_Obool)))], (4866 ^ _781404) ^ [_855467, _855469, _855471, _855473, _855475, _855477, _855479, _855481, _855483, _855485, _855487, _855489] : [-(c_Partial__Function_Ofun__lub(_855489, _855485, _855481, _855477, _855473, _855469) = c_Partial__Function_Ofun__lub(_855487, _855483, _855479, _855475, _855471, _855467)), _855489 = _855487, _855485 = _855483, _855481 = _855479, _855477 = _855475, _855473 = _855471, _855469 = _855467], (17551 ^ _781404) ^ [_1094421, _1094423] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094421), _1094423))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094423), _1094421)))], (25083 ^ _781404) ^ [_1230403] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1230403), c_Int_OMin) = c_Int_Osucc(_1230403))], (41950 ^ _781404) ^ [_1606228, _1606230, _1606232, _1606234, _1606236] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606228, _1606228)), hAPP(hAPP(c_Product__Type_OPair(_1606228, _1606228), _1606230), _1606232)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1606228, _1606228), tc_HOL_Obool), _1606234), _1606236))), 41955 ^ _781404 : [(41958 ^ _781404) ^ [] : [-(_1606230 = _1606232)], (41956 ^ _781404) ^ [] : [-(_1606234 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41961 ^ _781404 : [(41966 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606228, _1606228)), hAPP(hAPP(c_Product__Type_OPair(_1606228, _1606228), 41959 ^ [_1606228, _1606230, _1606232, _1606234, _1606236]), _1606232)), _1606236)))], (41964 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606228, _1606228)), hAPP(hAPP(c_Product__Type_OPair(_1606228, _1606228), _1606230), 41959 ^ [_1606228, _1606230, _1606232, _1606234, _1606236])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1606228, _1606228), tc_HOL_Obool), 41960 ^ [_1606228, _1606230, _1606232, _1606234, _1606236]), _1606236))))], (41962 ^ _781404) ^ [] : [-(_1606234 = hAPP(c_Nat_OSuc, 41960 ^ [_1606228, _1606230, _1606232, _1606234, _1606236]))]]], (26521 ^ _781404) ^ [_1254191, _1254193] : [c_Nat__Transfer_Ois__nat(_1254191), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1254191, _1254193)))], (1976 ^ _781404) ^ [_809144, _809146] : [-(class_Nat_Osize(_809144)), _809146 = _809144, class_Nat_Osize(_809146)], (1356 ^ _781404) ^ [_801394, _801396] : [-(class_Groups_Osgn__if(_801394)), _801396 = _801394, class_Groups_Osgn__if(_801396)], (35790 ^ _781404) ^ [_1449630, _1449632, _1449634, _1449636, _1449638, _1449640] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1449630, _1449632, _1449634, _1449636, c_Nitpick_Opair__box_OPairBox(_1449630, _1449632, _1449638, _1449640)) = hAPP(hAPP(_1449636, _1449638), _1449640))], (41504 ^ _781404) ^ [_1595193, _1595195] : [-(c_Transitive__Closure_Ortrancl(_1595193, hAPP(c_Relation_Oconverse(_1595193, _1595193), _1595195)) = hAPP(c_Relation_Oconverse(_1595193, _1595193), c_Transitive__Closure_Ortrancl(_1595193, _1595195)))], (52644 ^ _781404) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (34609 ^ _781404) ^ [_1423425, _1423427] : [-(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)), _1423425)), 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), _1423427), _1423425))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1423425), _1423427))], (9164 ^ _781404) ^ [_937207, _937209, _937211] : [class_Lattices_Oboolean__algebra(_937207), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937207), _937209), _937211) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937207), _937209), hAPP(c_Groups_Ouminus__class_Ouminus(_937207), _937211)))], (3346 ^ _781404) ^ [_831335, _831337] : [_831337 = _831335, -(c_Int_OBit1(_831337) = c_Int_OBit1(_831335))], (39238 ^ _781404) ^ [_1533792, _1533794, _1533796] : [class_Orderings_Olinorder(_1533792), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533792), _1533794)), -(_1533794 = c_Orderings_Obot__class_Obot(tc_fun(_1533792, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1533792), _1533796), c_Big__Operators_Olattice_OInf__fin(_1533792, c_Orderings_Oord__class_Omin(_1533792), _1533794)) = c_Big__Operators_Olattice_OInf__fin(_1533792, c_Orderings_Oord__class_Omin(_1533792), hAPP(c_Set_OCollect(_1533792), hAPP(hAPP(c_COMBB(tc_fun(_1533792, tc_HOL_Obool), tc_HOL_Obool, _1533792), c_HOL_OEx(_1533792)), hAPP(hAPP(c_COMBC(_1533792, tc_fun(_1533792, tc_HOL_Obool), tc_fun(_1533792, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533792, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1533792, tc_HOL_Obool), tc_fun(_1533792, tc_HOL_Obool)), _1533792), c_COMBS(_1533792, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533792, tc_HOL_Obool), tc_fun(_1533792, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1533792), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533792), c_fconj)), hAPP(hAPP(c_COMBC(_1533792, tc_fun(_1533792, _1533792), tc_fun(_1533792, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533792, tc_HOL_Obool), tc_fun(tc_fun(_1533792, _1533792), tc_fun(_1533792, tc_HOL_Obool)), _1533792), c_COMBB(_1533792, tc_HOL_Obool, _1533792)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1533792), _1533796))))), hAPP(hAPP(c_COMBC(_1533792, tc_fun(_1533792, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533792)), _1533794))))))], (7613 ^ _781404) ^ [_906361, _906363] : [class_Lattices_Olattice(_906361), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_906361), _906363), _906363) = _906363)], (14723 ^ _781404) ^ [_1039587, _1039589] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039587), _1039589)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1039587, tc_HOL_Obool)), hAPP(c_Set_OPow(_1039587), _1039589))))], (46967 ^ _781404) ^ [_1726224, _1726226, _1726228] : [class_Orderings_Olinorder(_1726224), c_List_Olinorder__class_Osorted(_1726224, _1726226), -(c_List_Olinorder__class_Osorted(_1726224, hAPP(hAPP(c_List_Otake(_1726224), _1726228), _1726226)))], (19963 ^ _781404) ^ [_1136073, _1136075] : [_1136073 = _1136075, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1136073) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1136075))], (20721 ^ _781404) ^ [_1148714, _1148716, _1148718] : [class_Int_Onumber__ring(_1148714), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1148714), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148714), _1148716), _1148718)), 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(_1148714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148714), hAPP(hAPP(c_Power_Opower__class_Opower(_1148714), _1148716), 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(_1148714), _1148718), 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(_1148714), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148714), hAPP(c_Int_Onumber__class_Onumber__of(_1148714), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1148716)), _1148718)))], (16995 ^ _781404) ^ [_1083837, _1083839, _1083841, _1083843, _1083845] : [c_Finite__Set_Ofolding__one__idem(_1083837, _1083839, _1083841), hAPP(_1083843, hAPP(hAPP(_1083839, 17000 ^ [_1083837, _1083839, _1083841, _1083843, _1083845]), 17001 ^ [_1083837, _1083839, _1083841, _1083843, _1083845])) = hAPP(hAPP(_1083839, hAPP(_1083843, 17000 ^ [_1083837, _1083839, _1083841, _1083843, _1083845])), hAPP(_1083843, 17001 ^ [_1083837, _1083839, _1083841, _1083843, _1083845])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083837), _1083845)), -(_1083845 = c_Orderings_Obot__class_Obot(tc_fun(_1083837, tc_HOL_Obool))), -(hAPP(_1083843, hAPP(_1083841, _1083845)) = hAPP(_1083841, hAPP(c_Set_Oimage(_1083837, _1083837, _1083843), _1083845)))], (15405 ^ _781404) ^ [_1053980] : [-(hAPP(c_Finite__Set_Ocard(_1053980), c_Orderings_Obot__class_Obot(tc_fun(_1053980, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48706 ^ _781404) ^ [_1762575, _1762577] : [-(c_FunDef_Ois__measure(_1762575, _1762577))], (34071 ^ _781404) ^ [_1406911] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1406911) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1406911)))], (38630 ^ _781404) ^ [_1516201, _1516203, _1516205, _1516207] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1516201, _1516203)), hAPP(hAPP(c_Product__Type_OSigma(_1516201, _1516203), hAPP(hAPP(c_Set_Oinsert(_1516201), _1516205), c_Orderings_Obot__class_Obot(tc_fun(_1516201, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1516203, tc_HOL_Obool), _1516201), _1516207))) = hAPP(c_Finite__Set_Ocard(_1516203), _1516207))], (7944 ^ _781404) ^ [_913567, _913569] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913567, tc_HOL_Obool)), _913569), c_Orderings_Otop__class_Otop(tc_fun(_913567, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_913567, tc_HOL_Obool)))], (47491 ^ _781404) ^ [_1736242, _1736244] : [-(hAPP(c_List_Oset(_1736242), hAPP(c_List_Orev(_1736242), _1736244)) = hAPP(c_List_Oset(_1736242), _1736244))], (51054 ^ _781404) ^ [_1813255, _1813257, _1813259] : [_1813257 = _1813259, -(c_Fun_Obij__betw(_1813255, _1813255, c_Fun_Oid(_1813255), _1813257, _1813259))], (18769 ^ _781404) ^ [_1115970, _1115972] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115970)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115972)))), 18772 ^ _781404 : [(18775 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1115972))], (18773 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1115970), _1115972)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1115970), _1115972))], (49699 ^ _781404) ^ [_1784761, _1784763] : [-(c_Relation_Otrans(_1784761, c_Transitive__Closure_Ortrancl(_1784761, _1784763)))], (46939 ^ _781404) ^ [_1725813, _1725815] : [class_Orderings_Olinorder(_1725813), -(c_List_Olinorder__class_Osorted(_1725813, c_List_Olinorder__class_Osort__key(_1725813, _1725813, c_COMBI(_1725813), _1725815)))], (37455 ^ _781404) ^ [_1486470, _1486472] : [-(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), _1486470), _1486472)), 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), _1486472), _1486470)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (12462 ^ _781404) ^ [_996348, _996350, _996352] : [class_Orderings_Oord(_996348), 12465 ^ _781404 : [(12472 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996348), _996350), _996352)), -(hBOOL(hAPP(hAPP(c_member(_996348), _996350), hAPP(c_SetInterval_Oord__class_OatMost(_996348), _996352))))], (12466 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_996348), _996350), hAPP(c_SetInterval_Oord__class_OatMost(_996348), _996352))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996348), _996350), _996352)))]]], (10537 ^ _781404) ^ [_960705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _960705)), _960705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22781 ^ _781404) ^ [_1188658, _1188660, _1188662] : [22782 ^ _781404 : [(22785 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1188660), _1188662))], (22783 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188658)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188658), _1188660)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188658), _1188662))))], (24658 ^ _781404) ^ [_1223792, _1223794] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1223792), _1223794) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223792, _1223794)), _1223794))], (17767 ^ _781404) ^ [_1098182, _1098184, _1098186] : [class_Lattices_Olattice(_1098182), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098182), _1098184)), -(c_Big__Operators_Olattice__class_OInf__fin(_1098182, hAPP(hAPP(c_Set_Oinsert(_1098182), _1098186), _1098184)) = hAPP(hAPP(c_Finite__Set_Ofold(_1098182, _1098182, c_Lattices_Osemilattice__inf__class_Oinf(_1098182)), _1098186), _1098184))], (638 ^ _781404) ^ [_791009, _791011, _791013, _791015, _791017, _791019] : [-(c_Finite__Set_Ofun__left__comm(_791017, _791013, _791009)), c_Finite__Set_Ofun__left__comm(_791019, _791015, _791011), _791019 = _791017, _791015 = _791013, _791011 = _791009], (21011 ^ _781404) ^ [_1154653, _1154655] : [class_Groups_Omonoid__mult(_1154653), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154653), _1154655), c_Groups_Oone__class_Oone(_1154653)) = _1154655)], (28161 ^ _781404) ^ [_1284625, _1284627] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284625), _1284627), hAPP(c_Int_Onumber__class_Onumber__of(_1284625), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1284625), _1284627)), class_Fields_Ofield__inverse__zero(_1284625), class_Int_Onumber__ring(_1284625)], (26461 ^ _781404) ^ [_1253129, _1253131] : [class_Int_Onumber__ring(_1253129), -(hAPP(c_Int_Oring__1__class_Oof__int(_1253129), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1253131)) = hAPP(c_Int_Onumber__class_Onumber__of(_1253129), _1253131))], (35055 ^ _781404) ^ [_1434048, _1434050, _1434052, _1434054] : [class_Rings_Ocomm__semiring__1(_1434048), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434048), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434048), c_Groups_Oone__class_Oone(_1434048)), c_Groups_Oone__class_Oone(_1434048))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1434048), hAPP(hAPP(c_COMBB(_1434048, _1434048, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1434048), _1434050)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1434048, _1434048), hAPP(hAPP(c_COMBB(_1434048, tc_fun(_1434048, _1434048), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1434048)), c_Nat_Osemiring__1__class_Oof__nat(_1434048))), _1434052))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1434054))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434048), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1434048), _1434054)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434048), _1434050), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434048), _1434050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434048), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1434048), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1434054), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1434052)))))], (9401 ^ _781404) ^ [_942581] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942581), hAPP(c_Nat_OSuc, _942581))))], (45214 ^ _781404) ^ [_1686169, _1686171, _1686173, _1686175] : [_1686175 = c_List_Olist_ONil(_1686169), -(hAPP(hAPP(c_List_Omap(_1686169, _1686171), _1686173), _1686175) = c_List_Olist_ONil(_1686171))], (9473 ^ _781404) ^ [_943823, _943825, _943827] : [class_Orderings_Olinorder(_943823), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943823), _943825), _943827))), -(_943825 = _943827), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943823), _943827), _943825)))], (15839 ^ _781404) ^ [_1061880, _1061882, _1061884] : [class_Lattices_Olattice(_1061880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061880), _1061882)), -(_1061882 = c_Orderings_Obot__class_Obot(tc_fun(_1061880, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061880), _1061884)), -(_1061884 = c_Orderings_Obot__class_Obot(tc_fun(_1061880, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1061880, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061880, tc_HOL_Obool)), _1061882), _1061884)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1061880), c_Big__Operators_Olattice__class_OSup__fin(_1061880, _1061882)), c_Big__Operators_Olattice__class_OSup__fin(_1061880, _1061884)))], (39584 ^ _781404) ^ [_1547201, _1547203] : [39585 ^ _781404 : [(39586 ^ _781404) ^ [_1547265, _1547267] : [_1547203 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1547201, _1547265), 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)), _1547267)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1547201), _1547203)))], (49177 ^ _781404) ^ [_1772737, _1772739, _1772741] : [c_List_Olist_ONil(_1772737) = c_List_Oreplicate(_1772737, _1772739, _1772741), -(_1772739 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14649 ^ _781404) ^ [_1038226] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1038226)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1038226), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038226), c_Orderings_Otop__class_Otop(tc_fun(_1038226, tc_HOL_Obool)))))], (24999 ^ _781404) ^ [_1229178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1229178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1229178))))], (43479 ^ _781404) ^ [_1648324] : [-(c_List_Obutlast(_1648324, c_List_Olist_ONil(_1648324)) = c_List_Olist_ONil(_1648324))], (2326 ^ _781404) ^ [_815325, _815327, _815329, _815331] : [-(c_Groups_Osgn__class_Osgn(_815331, _815327) = c_Groups_Osgn__class_Osgn(_815329, _815325)), _815331 = _815329, _815327 = _815325], (36189 ^ _781404) ^ [_1456777] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1456777)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1456777)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51972 ^ _781404) ^ [_1833032, _1833034] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1833032), _1833034)), -(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)))), _1833034, _1833032) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (6281 ^ _781404) ^ [_881306] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _881306)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _881306))], (21105 ^ _781404) ^ [_1156168, _1156170, _1156172] : [class_Rings_Oring(_1156168), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156168), hAPP(c_Groups_Ouminus__class_Ouminus(_1156168), _1156170)), hAPP(c_Groups_Ouminus__class_Ouminus(_1156168), _1156172)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156168), _1156170), _1156172))], (46211 ^ _781404) ^ [_1708945, _1708947] : [c_List_Oremdups(_1708945, _1708947) = _1708947, -(hBOOL(hAPP(c_List_Odistinct(_1708945), _1708947)))], (20745 ^ _781404) ^ [_1149299, _1149301, _1149303] : [class_Rings_Osemiring__1(_1149299), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1149299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1149301), _1149303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149299), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1149299), _1149301)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1149299), _1149303)))], (8684 ^ _781404) ^ [_927789, _927791, _927793] : [class_Orderings_Oorder(_927789), 8687 ^ _781404 : [(8694 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927789), _927791), _927793))), -(c_Orderings_Obot__class_Obot(tc_fun(_927789, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_927789, _927791, _927793))], (8688 ^ _781404) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_927789, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_927789, _927791, _927793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927789), _927791), _927793))]]], (34715 ^ _781404) ^ [_1426136, _1426138, _1426140, _1426142, _1426144, _1426146] : [-(hBOOL(hAPP(hAPP(c_member(_1426136), _1426138), _1426140))), 34718 ^ _781404 : [(34725 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1426136), _1426142), _1426140))), -(hAPP(c_Set_Ovimage(_1426144, _1426136, hAPP(hAPP(c_COMBC(_1426144, _1426136, _1426136), hAPP(hAPP(c_COMBC(_1426144, _1426136, tc_fun(_1426136, _1426136)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1426136, tc_fun(_1426136, _1426136)), _1426144), c_If(_1426136)), hAPP(hAPP(c_COMBC(_1426144, tc_fun(_1426144, tc_HOL_Obool), tc_HOL_Obool), c_member(_1426144)), _1426146))), _1426138)), _1426142)), _1426140) = c_Orderings_Obot__class_Obot(tc_fun(_1426144, tc_HOL_Obool)))], (34719 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1426136), _1426142), _1426140)), -(hAPP(c_Set_Ovimage(_1426144, _1426136, hAPP(hAPP(c_COMBC(_1426144, _1426136, _1426136), hAPP(hAPP(c_COMBC(_1426144, _1426136, tc_fun(_1426136, _1426136)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1426136, tc_fun(_1426136, _1426136)), _1426144), c_If(_1426136)), hAPP(hAPP(c_COMBC(_1426144, tc_fun(_1426144, tc_HOL_Obool), tc_HOL_Obool), c_member(_1426144)), _1426146))), _1426138)), _1426142)), _1426140) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1426144, tc_HOL_Obool)), _1426146))]]], (52174 ^ _781404) ^ [_1836416, _1836418] : [class_Lattices_Obounded__lattice(_1836416), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1836418, _1836416)))], (41083 ^ _781404) ^ [_1584145, _1584147, _1584149, _1584151, _1584153] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584145, _1584145)), hAPP(hAPP(c_Product__Type_OPair(_1584145, _1584145), _1584147), _1584149)), c_Transitive__Closure_Otrancl(_1584145, _1584151))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584145, _1584145)), hAPP(hAPP(c_Product__Type_OPair(_1584145, _1584145), _1584149), _1584153)), _1584151)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584145, _1584145)), hAPP(hAPP(c_Product__Type_OPair(_1584145, _1584145), _1584147), _1584153)), c_Transitive__Closure_Otrancl(_1584145, _1584151))))], (23637 ^ _781404) ^ [_1205931, _1205933, _1205935] : [class_Divides_Osemiring__div(_1205931), -(c_Divides_Odiv__class_Omod(_1205931, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205931), _1205933), _1205935), _1205935) = c_Groups_Ozero__class_Ozero(_1205931))], (738 ^ _781404) ^ [_792503, _792505, _792507, _792509, _792511, _792513, _792515, _792517] : [-(c_Nat__Transfer_Otransfer__morphism(_792515, _792511, _792507, _792503)), c_Nat__Transfer_Otransfer__morphism(_792517, _792513, _792509, _792505), _792517 = _792515, _792513 = _792511, _792509 = _792507, _792505 = _792503], (39395 ^ _781404) ^ [_1539967, _1539969, _1539971] : [class_Lattices_Odistrib__lattice(_1539967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539967), _1539969)), -(_1539969 = c_Orderings_Obot__class_Obot(tc_fun(_1539967, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539967), _1539971)), -(_1539971 = c_Orderings_Obot__class_Obot(tc_fun(_1539967, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1539967), c_Big__Operators_Olattice__class_OSup__fin(_1539967, _1539969)), c_Big__Operators_Olattice__class_OSup__fin(_1539967, _1539971)) = c_Big__Operators_Olattice__class_OSup__fin(_1539967, hAPP(c_Set_OCollect(_1539967), hAPP(hAPP(c_COMBB(tc_fun(_1539967, tc_HOL_Obool), tc_HOL_Obool, _1539967), c_HOL_OEx(_1539967)), hAPP(hAPP(c_COMBB(tc_fun(_1539967, tc_fun(_1539967, tc_HOL_Obool)), tc_fun(_1539967, tc_HOL_Obool), _1539967), hAPP(c_COMBB(tc_fun(_1539967, tc_HOL_Obool), tc_HOL_Obool, _1539967), c_HOL_OEx(_1539967))), hAPP(hAPP(c_COMBC(_1539967, tc_fun(_1539967, tc_fun(_1539967, tc_HOL_Obool)), tc_fun(_1539967, tc_fun(_1539967, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1539967, tc_fun(tc_fun(_1539967, tc_HOL_Obool), tc_fun(_1539967, tc_HOL_Obool))), tc_fun(tc_fun(_1539967, tc_fun(_1539967, tc_HOL_Obool)), tc_fun(_1539967, tc_fun(_1539967, tc_HOL_Obool))), _1539967), c_COMBS(_1539967, tc_fun(_1539967, tc_HOL_Obool), tc_fun(_1539967, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1539967, tc_fun(_1539967, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1539967, tc_fun(tc_fun(_1539967, tc_HOL_Obool), tc_fun(_1539967, tc_HOL_Obool))), _1539967), hAPP(c_COMBB(tc_fun(_1539967, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1539967, tc_HOL_Obool), tc_fun(_1539967, tc_HOL_Obool)), _1539967), c_COMBS(_1539967, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1539967, tc_fun(_1539967, tc_HOL_Obool)), tc_fun(_1539967, tc_fun(_1539967, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1539967), hAPP(c_COMBB(tc_fun(_1539967, tc_HOL_Obool), tc_fun(_1539967, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1539967), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539967), c_fconj))), hAPP(hAPP(c_COMBC(_1539967, tc_fun(_1539967, tc_fun(_1539967, _1539967)), tc_fun(_1539967, tc_fun(_1539967, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1539967, _1539967), tc_fun(_1539967, tc_HOL_Obool)), tc_fun(tc_fun(_1539967, tc_fun(_1539967, _1539967)), tc_fun(_1539967, tc_fun(_1539967, tc_HOL_Obool))), _1539967), c_COMBB(tc_fun(_1539967, _1539967), tc_fun(_1539967, tc_HOL_Obool), _1539967)), hAPP(hAPP(c_COMBB(tc_fun(_1539967, tc_HOL_Obool), tc_fun(tc_fun(_1539967, _1539967), tc_fun(_1539967, tc_HOL_Obool)), _1539967), c_COMBB(_1539967, tc_HOL_Obool, _1539967)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1539967)))))), hAPP(hAPP(c_COMBC(_1539967, tc_fun(_1539967, tc_HOL_Obool), tc_fun(_1539967, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1539967, tc_HOL_Obool), tc_fun(_1539967, tc_HOL_Obool)), _1539967), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1539967)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539967), c_fconj), hAPP(hAPP(c_COMBC(_1539967, tc_fun(_1539967, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539967)), _1539969)))), hAPP(hAPP(c_COMBC(_1539967, tc_fun(_1539967, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539967)), _1539971))))))))], (40666 ^ _781404) ^ [_1574129, _1574131, _1574133, _1574135, _1574137, _1574139] : [hBOOL(hAPP(hAPP(c_member(_1574129), _1574131), _1574133)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1574135, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1574129, _1574135, _1574137), _1574133)), hAPP(_1574139, hAPP(c_Set_Oimage(_1574129, _1574135, _1574137), _1574133)))), -(hBOOL(hAPP(hAPP(c_member(_1574135), hAPP(_1574137, _1574131)), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1574135, tc_HOL_Obool), _1574139))))], (43400 ^ _781404) ^ [_1646620, _1646622] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1646620), _1646622)), -(c_Nitpick_Ocard_H(_1646620, _1646622) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646620)), c_Hilbert__Choice_OEps(tc_List_Olist(_1646620), hAPP(hAPP(c_COMBS(tc_List_Olist(_1646620), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1646620)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1646620), tc_fun(_1646620, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1646620, tc_HOL_Obool), tc_fun(tc_fun(_1646620, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1646620)), c_fequal), c_List_Oset(_1646620))), _1646622))), c_List_Odistinct(_1646620)))))], (20195 ^ _781404) ^ [_1139987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139987), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1139987)), c_Int_OPls)))], (50195 ^ _781404) ^ [_1795993, _1795995] : [-(c_Relation_Osym(_1795993, c_Relation_OId__on(_1795993, _1795995)))], (46253 ^ _781404) ^ [_1709687, _1709689] : [c_List_Olist_ONil(_1709687) = c_List_Oremdups(_1709687, _1709689), -(_1709689 = c_List_Olist_ONil(_1709687))], (19366 ^ _781404) ^ [_1125882, _1125884] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1125882)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1125884), 19369 ^ _781404 : [(19372 ^ _781404) ^ [] : [-(_1125884 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19370 ^ _781404) ^ [] : [-(_1125882 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (51570 ^ _781404) ^ [_1825984, _1825986, _1825988, _1825990] : [class_Divides_Osemiring__div(_1825984), -(_1825986 = c_Groups_Ozero__class_Ozero(_1825984)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825984), _1825986), _1825988)), 51581 ^ _781404 : [(51588 ^ _781404) ^ [] : [_1825988 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825984), _1825990), _1825986), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825984), _1825988), _1825986) = _1825990)], (51582 ^ _781404) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825984), _1825988), _1825986) = _1825990, -(_1825988 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825984), _1825990), _1825986))]]], (52502 ^ _781404) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (38686 ^ _781404) ^ [_1517470, _1517472, _1517474, _1517476] : [_1517470 = c_Orderings_Obot__class_Obot(tc_fun(_1517472, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1517472, _1517474), _1517474, c_Product__Type_Osnd(_1517472, _1517474)), hAPP(hAPP(c_Product__Type_OSigma(_1517472, _1517474), _1517470), hAPP(c_COMBK(tc_fun(_1517474, tc_HOL_Obool), _1517472), _1517476))) = c_Orderings_Obot__class_Obot(tc_fun(_1517474, tc_HOL_Obool)))], (30882 ^ _781404) ^ [_1336529, _1336531, _1336533, _1336535] : [class_Orderings_Olinorder(_1336529), 30885 ^ _781404 : [(30886 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336529), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1336529), _1336531), _1336533)), _1336535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336529), _1336531), _1336535))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336529), _1336533), _1336535)))], (30896 ^ _781404) ^ [] : [30897 ^ _781404 : [(30900 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336529), _1336533), _1336535))], (30898 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336529), _1336531), _1336535))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336529), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1336529), _1336531), _1336533)), _1336535)))]]], (14121 ^ _781404) ^ [_1027754, _1027756, _1027758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027754), _1027756)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1027754), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027756), _1027758)) = 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, _1027754), _1027756)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1027756), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027756), _1027758))))], (50895 ^ _781404) ^ [_1810334, _1810336, _1810338] : [c_Fun_Obij__betw(_1810334, _1810336, _1810338, c_Orderings_Otop__class_Otop(tc_fun(_1810334, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1810336, tc_HOL_Obool))), 50898 ^ _781404 : [(50901 ^ _781404) ^ [] : [-(hAPP(c_Set_Oimage(_1810334, _1810336, _1810338), c_Orderings_Otop__class_Otop(tc_fun(_1810334, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1810336, tc_HOL_Obool)))], (50899 ^ _781404) ^ [] : [-(c_Fun_Oinj__on(_1810334, _1810336, _1810338, c_Orderings_Otop__class_Otop(tc_fun(_1810334, tc_HOL_Obool))))]]], (49195 ^ _781404) ^ [_1773022, _1773024, _1773026] : [_1773024 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1773022, _1773024, _1773026) = c_List_Olist_ONil(_1773022))], (19103 ^ _781404) ^ [_1121364, _1121366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121364), _1121366)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1121364)), c_Int_OBit1(_1121366))))], (7165 ^ _781404) ^ [_897485, _897487, _897489] : [class_Lattices_Osemilattice__sup(_897485), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897485), _897487), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897485), _897489), _897487))))], (47389 ^ _781404) ^ [_1733851, _1733853, _1733855] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733851), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1733851))), _1733853))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1733855), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1733851))), _1733853))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733851), _1733851), hAPP(hAPP(c_COMBC(tc_List_Olist(_1733851), tc_Nat_Onat, _1733851), c_List_Onth(_1733851)), _1733855)), hAPP(c_List_Ofilter(tc_List_Olist(_1733851), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1733851)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1733855)), c_Nat_Osize__class_Osize(tc_List_Olist(_1733851)))), c_List_Otranspose(_1733851, _1733853))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1733851)), _1733853), _1733855))], (25011 ^ _781404) ^ [_1229375] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1229375)), -(hAPP(c_Int_Onat, _1229375) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25515 ^ _781404) ^ [_1237413, _1237415] : [-(_1237413 = hAPP(c_Int_Onat, _1237415)), 25518 ^ _781404 : [(25521 ^ _781404) ^ [] : [_1237415 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1237413)], (25519 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237415)))]], 25522 ^ _781404 : [(25525 ^ _781404) ^ [] : [_1237413 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25523 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237415))]]], (29005 ^ _781404) ^ [_1300742, _1300744, _1300746] : [class_Fields_Olinordered__field__inverse__zero(_1300742), 29008 ^ _781404 : [(29023 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1300742), _1300744), _1300746)), c_Groups_Ozero__class_Ozero(_1300742)))), 29024 ^ _781404 : [(29031 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), _1300744), c_Groups_Ozero__class_Ozero(_1300742))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), c_Groups_Ozero__class_Ozero(_1300742)), _1300746))], (29025 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), c_Groups_Ozero__class_Ozero(_1300742)), _1300744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), _1300746), c_Groups_Ozero__class_Ozero(_1300742)))]]], (29009 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1300742), _1300744), _1300746)), c_Groups_Ozero__class_Ozero(_1300742))), 29014 ^ _781404 : [(29017 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), _1300746), c_Groups_Ozero__class_Ozero(_1300742))))], (29015 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), c_Groups_Ozero__class_Ozero(_1300742)), _1300744)))]], 29018 ^ _781404 : [(29021 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), c_Groups_Ozero__class_Ozero(_1300742)), _1300746)))], (29019 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300742), _1300744), c_Groups_Ozero__class_Ozero(_1300742))))]]]]], (9308 ^ _781404) ^ [_940605, _940607, _940609] : [class_Orderings_Olinorder(_940605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940605), _940607), _940609)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940605, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_940605, _940607, _940609)), hAPP(c_SetInterval_Oord__class_OatLeast(_940605), _940609)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_940605), _940607))], (22875 ^ _781404) ^ [_1190457, _1190459] : [class_Groups_Omonoid__mult(_1190457), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1190457), _1190459), 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(_1190457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190457), _1190459), _1190459)), _1190459))], (46686 ^ _781404) ^ [_1720416, _1720418, _1720420, _1720422] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720416)), _1720418))), c_List_Ofoldr(tc_List_Olist(_1720420), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1720420)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1720420))), _1720422, 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(_1720416)), _1720418)), c_List_Ofoldr(tc_List_Olist(_1720420), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1720420)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1720420), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1720420)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1720420)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1720420), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1720420)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1720420), tc_List_Olist(_1720420), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1720420)))), _1720422), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (20287 ^ _781404) ^ [_1141474] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1141474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141474), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9366 ^ _781404) ^ [_941890, _941892, _941894, _941896] : [class_Orderings_Olinorder(_941890), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941890), _941892), _941894)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941890), _941894), _941896)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941890, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_941890, _941892, _941894)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_941890, _941894), _941896)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_941890, _941892, _941896))], (6491 ^ _781404) ^ [_884770, _884772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _884770)), _884772)), -(_884772 = hAPP(c_Nat_OSuc, 6494 ^ [_884770, _884772]))], (16863 ^ _781404) ^ [_1081724, _1081726, _1081728, _1081730] : [c_Finite__Set_Ofolding__one__idem(_1081724, _1081726, _1081728), -(hAPP(hAPP(_1081726, _1081730), _1081730) = _1081730)], (51438 ^ _781404) ^ [_1823250, _1823252] : [class_Rings_Ocomm__semiring__1(_1823250), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823250), _1823252), c_Groups_Ozero__class_Ozero(_1823250))))], (14330 ^ _781404) ^ [_1031850, _1031852, _1031854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031850), _1031852)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031854), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031852), _1031850))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031854), _1031850)), hAPP(c_Nat_OSuc, _1031852)))], (16953 ^ _781404) ^ [_1083163, _1083165] : [class_Rings_Olinordered__idom(_1083163), 16956 ^ _781404 : [(16963 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083163), c_Groups_Ozero__class_Ozero(_1083163)), _1083165)), -(c_Groups_Osgn__class_Osgn(_1083163, _1083165) = c_Groups_Oone__class_Oone(_1083163))], (16957 ^ _781404) ^ [] : [c_Groups_Osgn__class_Osgn(_1083163, _1083165) = c_Groups_Oone__class_Oone(_1083163), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083163), c_Groups_Ozero__class_Ozero(_1083163)), _1083165)))]]], (35814 ^ _781404) ^ [_1450027, _1450029, _1450031, _1450033, _1450035] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450027, _1450029), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1450031), _1450033))), -(_1450029 = 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)), _1450035)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450027, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1450029), _1450035)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1450031), _1450035)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1450029), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1450031, _1450035))), _1450033)))))], (42816 ^ _781404) ^ [_1631529, _1631531, _1631533] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631529)), hAPP(hAPP(c_List_Otake(_1631529), _1631531), _1631533)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631529)), _1631533)), _1631531))], (12156 ^ _781404) ^ [_990334, _990336, _990338, _990340] : [hBOOL(hAPP(hAPP(c_member(_990334), _990336), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990334, tc_HOL_Obool)), _990338), _990340))), hBOOL(hAPP(hAPP(c_member(_990334), _990336), _990340))], (6673 ^ _781404) ^ [_888167, _888169, _888171] : [class_Groups_Oordered__ab__group__add(_888167), 6676 ^ _781404 : [(6683 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888167), _888171), hAPP(c_Groups_Ouminus__class_Ouminus(_888167), _888169))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888167), _888169), hAPP(c_Groups_Ouminus__class_Ouminus(_888167), _888171))))], (6677 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888167), _888169), hAPP(c_Groups_Ouminus__class_Ouminus(_888167), _888171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888167), _888171), hAPP(c_Groups_Ouminus__class_Ouminus(_888167), _888169))))]]], (42177 ^ _781404) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30414 ^ _781404) ^ [_1327916, _1327918, _1327920, _1327922] : [30416 ^ _781404 : [(30421 ^ _781404) ^ [] : [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(_1327920, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 30415 ^ [_1327916, _1327918, _1327920, _1327922]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1327920, 30415 ^ [_1327916, _1327918, _1327920, _1327922])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30419 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30415 ^ [_1327916, _1327918, _1327920, _1327922]), _1327918)))], (30417 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1327916), 30415 ^ [_1327916, _1327918, _1327920, _1327922])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1327916), _1327918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1327920, _1327916)), _1327922)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1327922), hAPP(_1327920, _1327918))), 30435 ^ _781404 : [(30440 ^ _781404) ^ [] : [-(hAPP(_1327920, 30434 ^ [_1327916, _1327918, _1327920, _1327922]) = _1327922)], (30438 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 30434 ^ [_1327916, _1327918, _1327920, _1327922]), _1327918)))], (30436 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1327916), 30434 ^ [_1327916, _1327918, _1327920, _1327922])))]]], (42354 ^ _781404) ^ [_1618274, _1618276] : [-(c_List_Olistrel1(_1618274, hAPP(c_Relation_Oconverse(_1618274, _1618274), _1618276)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1618274), tc_List_Olist(_1618274)), c_List_Olistrel1(_1618274, _1618276)))], (31280 ^ _781404) ^ [_1344193, _1344195] : [class_Orderings_Olinorder(_1344193), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344193), _1344195)), -(c_Big__Operators_Olattice_OInf__fin(_1344193, c_Orderings_Oord__class_Omin(_1344193), _1344195) = hAPP(c_Finite__Set_Ofold1(_1344193, c_Orderings_Oord__class_Omin(_1344193)), _1344195))], (37619 ^ _781404) ^ [_1490934, _1490936, _1490938] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490934), _1490936)), c_Fun_Oinj__on(_1490934, tc_fun(tc_fun(_1490934, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1490934, tc_fun(tc_prod(_1490934, _1490934), tc_HOL_Obool), tc_fun(tc_fun(_1490934, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490934, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1490934, _1490934), tc_HOL_Obool), tc_fun(tc_fun(_1490934, tc_HOL_Obool), tc_HOL_Obool)), _1490934), c_Equiv__Relations_Oquotient(_1490934)), hAPP(hAPP(c_COMBC(_1490934, tc_fun(_1490934, tc_HOL_Obool), tc_fun(_1490934, tc_HOL_Obool)), c_Set_Oinsert(_1490934)), c_Orderings_Obot__class_Obot(tc_fun(_1490934, tc_HOL_Obool))))), _1490938), _1490936), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1490934, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490934), _1490936), _1490938)) = hAPP(c_Finite__Set_Ocard(_1490934), _1490936))], (19464 ^ _781404) ^ [_1127526] : [class_Rings_Osemiring__1(_1127526), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1127526), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1127526))], (25577 ^ _781404) ^ [_1238384, _1238386] : [hBOOL(hAPP(_1238384, hAPP(c_Int_Onat, _1238386))), 25580 ^ _781404 : [(25587 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238386), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1238384, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25581 ^ _781404) ^ [_1238484] : [_1238386 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1238484), -(hBOOL(hAPP(_1238384, _1238484)))]]], (31638 ^ _781404) ^ [_1350555, _1350557] : [class_Orderings_Olinorder(_1350555), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350555), _1350557)), -(_1350557 = c_Orderings_Obot__class_Obot(tc_fun(_1350555, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1350555), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1350555), 31651 ^ [_1350555, _1350557]), 31652 ^ [_1350555, _1350557])), hAPP(hAPP(c_Set_Oinsert(_1350555), 31651 ^ [_1350555, _1350557]), hAPP(hAPP(c_Set_Oinsert(_1350555), 31652 ^ [_1350555, _1350557]), c_Orderings_Obot__class_Obot(tc_fun(_1350555, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1350555), c_Big__Operators_Olattice_OInf__fin(_1350555, c_Orderings_Oord__class_Omin(_1350555), _1350557)), _1350557)))], (8984 ^ _781404) ^ [_933607, _933609, _933611] : [class_Orderings_Oorder(_933607), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933607, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_933607), _933609)), c_SetInterval_Oord__class_OgreaterThanLessThan(_933607, _933609, _933611)) = c_Orderings_Obot__class_Obot(tc_fun(_933607, tc_HOL_Obool)))], (11299 ^ _781404) ^ [_973422, _973424, _973426, _973428, _973430, _973432] : [c_Fun_Oinj__on(_973422, _973424, _973426, _973428), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973422, tc_HOL_Obool)), _973430), _973428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973422, tc_HOL_Obool)), _973432), _973428)), -(hAPP(c_Set_Oimage(_973422, _973424, _973426), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973422, tc_HOL_Obool)), _973430), _973432)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973424, tc_HOL_Obool)), hAPP(c_Set_Oimage(_973422, _973424, _973426), _973430)), hAPP(c_Set_Oimage(_973422, _973424, _973426), _973432)))], (23549 ^ _781404) ^ [_1204097, _1204099, _1204101, _1204103] : [class_Divides_Osemiring__div(_1204097), -(c_Divides_Odiv__class_Omod(_1204097, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204097), _1204099), _1204101), _1204103) = c_Divides_Odiv__class_Omod(_1204097, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204097), c_Divides_Odiv__class_Omod(_1204097, _1204099, _1204103)), _1204101), _1204103))], (25728 ^ _781404) ^ [_1241179, _1241181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1241179)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1241179), _1241181)), _1241179) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18885 ^ _781404) ^ [_1117821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1117821)), -(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), _1117821))))], (6347 ^ _781404) ^ [_882315, _882317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _882315)), hAPP(c_Nat_OSuc, _882317))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882315), _882317)))], (40458 ^ _781404) ^ [_1569663, _1569665] : [-(c_Hilbert__Choice_OEps(_1569663, hAPP(hAPP(c_COMBC(_1569663, _1569663, tc_HOL_Obool), c_fequal), _1569665)) = _1569665)], (49833 ^ _781404) ^ [_1787465, _1787467, _1787469] : [-(c_List_Olist__ex(_1787465, _1787469, _1787467)), 49834 ^ _781404 : [(49835 ^ _781404) ^ [_1787522] : [hBOOL(hAPP(hAPP(c_member(_1787465), _1787522), hAPP(c_List_Oset(_1787465), _1787467))), hBOOL(hAPP(_1787469, _1787522))]]], (51011 ^ _781404) ^ [_1812543, _1812545, _1812547, _1812549, _1812551] : [c_Fun_Obij__betw(_1812543, _1812545, _1812547, _1812549, _1812551), 51014 ^ _781404 : [(51021 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1812545), _1812551)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1812543), _1812549)))], (51015 ^ _781404) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1812543), _1812549)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1812545), _1812551)))]]], (51786 ^ _781404) ^ [_1829878, _1829880, _1829882] : [class_Rings_Odvd(_1829878), class_Rings_Osemiring__0(_1829878), 51793 ^ _781404 : [(51803 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1829880, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829878), _1829882), 51810 ^ [_1829878, _1829880, _1829882])))), 51804 ^ _781404 : [(51805 ^ _781404) ^ [_1830207] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829878), _1829882), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1829878), _1830207), c_Groups_Ozero__class_Ozero(_1829878)))), hBOOL(hAPP(_1829880, _1830207))]]], (51794 ^ _781404) ^ [] : [51795 ^ _781404 : [(51796 ^ _781404) ^ [_1830070] : [hBOOL(hAPP(_1829880, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829878), _1829882), _1830070)))]], 51798 ^ _781404 : [(51801 ^ _781404) ^ [] : [-(hBOOL(hAPP(_1829880, 51797 ^ [_1829878, _1829880, _1829882])))], (51799 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829878), _1829882), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1829878), 51797 ^ [_1829878, _1829880, _1829882]), c_Groups_Ozero__class_Ozero(_1829878)))))]]]]], (16913 ^ _781404) ^ [_1082493, _1082495] : [class_Rings_Olinordered__idom(_1082493), 16916 ^ _781404 : [(16923 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082493), c_Groups_Ozero__class_Ozero(_1082493)), _1082495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082493), c_Groups_Ozero__class_Ozero(_1082493)), c_Groups_Osgn__class_Osgn(_1082493, _1082495))))], (16917 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082493), c_Groups_Ozero__class_Ozero(_1082493)), c_Groups_Osgn__class_Osgn(_1082493, _1082495))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082493), c_Groups_Ozero__class_Ozero(_1082493)), _1082495)))]]], (35271 ^ _781404) ^ [_1438350, _1438352, _1438354, _1438356, _1438358] : [35273 ^ _781404 : [(35276 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(_1438356, 35272 ^ [_1438350, _1438352, _1438354, _1438356, _1438358]), _1438358))], (35274 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438350), 35272 ^ [_1438350, _1438352, _1438354, _1438356, _1438358]), _1438354)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1438350, tc_fun(_1438352, tc_HOL_Obool)), _1438354), _1438356), _1438358)))], (40732 ^ _781404) ^ [_1575452, _1575454, _1575456, _1575458, _1575460] : [_1575452 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1575454, tc_HOL_Obool), _1575456), c_Orderings_Oorder__class_Omono(tc_fun(_1575454, tc_HOL_Obool), tc_fun(_1575454, tc_HOL_Obool), _1575456), hBOOL(hAPP(hAPP(c_member(_1575454), _1575458), _1575460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575454, tc_HOL_Obool)), _1575460), hAPP(_1575456, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1575454, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1575454, tc_HOL_Obool), tc_fun(_1575454, tc_HOL_Obool), tc_fun(_1575454, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575454, tc_HOL_Obool), tc_fun(tc_fun(_1575454, tc_HOL_Obool), tc_fun(_1575454, tc_HOL_Obool)), tc_fun(_1575454, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1575454, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1575454, tc_HOL_Obool), tc_fun(_1575454, tc_HOL_Obool), tc_fun(_1575454, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575454, tc_HOL_Obool), tc_fun(tc_fun(_1575454, tc_HOL_Obool), tc_fun(_1575454, tc_HOL_Obool)), tc_fun(_1575454, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1575454, tc_HOL_Obool))), _1575456)), _1575460))), _1575452))))), -(hBOOL(hAPP(hAPP(c_member(_1575454), _1575458), _1575452)))], (47913 ^ _781404) ^ [_1745049, _1745051, _1745053, _1745055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1745049), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745051)), c_List_OdropWhile(_1745051, _1745053, _1745055)))), -(hAPP(hAPP(c_List_Onth(_1745051), c_List_OdropWhile(_1745051, _1745053, _1745055)), _1745049) = hAPP(hAPP(c_List_Onth(_1745051), _1745055), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1745049), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745051)), c_List_OtakeWhile(_1745051, _1745053, _1745055)))))], (1896 ^ _781404) ^ [_808144, _808146] : [-(class_Rings_Osemiring(_808144)), _808146 = _808144, class_Rings_Osemiring(_808146)], (45648 ^ _781404) ^ [_1696085] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1696085)) = _1696085)], (3416 ^ _781404) ^ [_832402, _832404, _832406, _832408] : [-(c_Enum_Osublists(_832408, _832404) = c_Enum_Osublists(_832406, _832402)), _832408 = _832406, _832404 = _832402], (31770 ^ _781404) ^ [_1353090, _1353092] : [class_Orderings_Olinorder(_1353090), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353090), _1353092)), -(_1353092 = c_Orderings_Obot__class_Obot(tc_fun(_1353090, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1353090), c_Big__Operators_Olinorder__class_OMax(_1353090, _1353092)), _1353092)))], (34007 ^ _781404) ^ [_1405684, _1405686, _1405688, _1405690, _1405692] : [class_Complete__Lattice_Ocomplete__lattice(_1405684), class_Orderings_Olinorder(_1405684), 34014 ^ _781404 : [(34024 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405684), _1405686), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405688, _1405684), _1405690), _1405692)))), 34025 ^ _781404 : [(34026 ^ _781404) ^ [_1406032] : [hBOOL(hAPP(hAPP(c_member(_1405688), _1406032), _1405690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405684), _1405686), hAPP(_1405692, _1406032)))]]], (34015 ^ _781404) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405684), _1405686), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405688, _1405684), _1405690), _1405692))), 34019 ^ _781404 : [(34022 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405684), _1405686), hAPP(_1405692, 34018 ^ [_1405684, _1405686, _1405688, _1405690, _1405692]))))], (34020 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405688), 34018 ^ [_1405684, _1405686, _1405688, _1405690, _1405692]), _1405690)))]]]]], (33412 ^ _781404) ^ [_1388273, _1388275, _1388277, _1388279, _1388281] : [class_Groups_Oab__group__add(_1388273), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1388275, _1388273), hAPP(hAPP(c_COMBS(_1388275, _1388273, _1388273), hAPP(hAPP(c_COMBB(_1388273, tc_fun(_1388273, _1388273), _1388275), c_Groups_Ominus__class_Ominus(_1388273)), _1388277)), _1388279)), _1388281) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388273), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1388275, _1388273), _1388277), _1388281)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1388275, _1388273), _1388279), _1388281)))], (4632 ^ _781404) ^ [_851794, _851796] : [_851796 = _851794, -(c_Code__Numeral_OSuc__code__numeral(_851796) = c_Code__Numeral_OSuc__code__numeral(_851794))], (6317 ^ _781404) ^ [_881867, _881869] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _881867), _881869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _881869)), _881867)))], (13822 ^ _781404) ^ [_1022494, _1022496] : [class_Groups_Ogroup__add(_1022494), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022494), _1022496), hAPP(c_Groups_Ouminus__class_Ouminus(_1022494), _1022496)) = c_Groups_Ozero__class_Ozero(_1022494))], (32044 ^ _781404) ^ [_1358250, _1358252, _1358254] : [class_Orderings_Olinorder(_1358250), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358250), _1358252), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358250), _1358254), _1358252))))], (16428 ^ _781404) ^ [_1073250, _1073252, _1073254, _1073256] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1073250, _1073252)), c_Sum__Type_OPlus(_1073250, _1073252, _1073254, _1073256))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1073250), _1073254)))], (17917 ^ _781404) ^ [_1100969, _1100971, _1100973] : [class_Rings_Olinordered__semidom(_1100969), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100969), c_Groups_Ozero__class_Ozero(_1100969)), _1100971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100969), _1100971), c_Groups_Oone__class_Oone(_1100969))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1100969), hAPP(hAPP(c_Power_Opower__class_Opower(_1100969), _1100971), hAPP(c_Nat_OSuc, _1100973))), c_Groups_Oone__class_Oone(_1100969))))], (49041 ^ _781404) ^ [_1770285, _1770287, _1770289] : [-(_1770285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1770287), c_List_Oreplicate(_1770287, _1770285, _1770289)) = c_List_Oreplicate(_1770287, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1770285), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1770289))], (15775 ^ _781404) ^ [_1060836, _1060838, _1060840] : [class_Lattices_Olattice(_1060836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060836), _1060838)), -(_1060838 = c_Orderings_Obot__class_Obot(tc_fun(_1060836, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1060836, hAPP(hAPP(c_Set_Oinsert(_1060836), _1060840), _1060838)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1060836), _1060840), c_Big__Operators_Olattice__class_OSup__fin(_1060836, _1060838)))], (9212 ^ _781404) ^ [_938596, _938598, _938600, _938602] : [class_Orderings_Olinorder(_938596), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938596), _938598), _938600)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938596, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_938596, _938598), _938602)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_938596, _938598), _938600)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_938596, _938600), _938602))], (19330 ^ _781404) ^ [_1125281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1125281))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1125281)))], (33394 ^ _781404) ^ [_1387319, _1387321, _1387323, _1387325, _1387327, _1387329] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1387321, _1387323)), hAPP(hAPP(c_Product__Type_OPair(_1387321, _1387323), _1387327), _1387329)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387319, tc_fun(tc_prod(_1387321, _1387323), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1387319, tc_HOL_Obool))), _1387325))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387319, tc_fun(_1387321, tc_fun(_1387323, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1387319, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1387321, _1387323), tc_HOL_Obool), tc_fun(_1387321, tc_fun(_1387323, tc_HOL_Obool)), _1387319), hAPP(c_COMBC(_1387321, tc_fun(tc_prod(_1387321, _1387323), tc_HOL_Obool), tc_fun(_1387323, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1387323, tc_fun(tc_fun(tc_prod(_1387321, _1387323), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1387321, _1387323), tc_HOL_Obool), tc_fun(_1387323, tc_HOL_Obool)), _1387321), c_COMBC(_1387323, tc_fun(tc_prod(_1387321, _1387323), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1387323, tc_prod(_1387321, _1387323)), tc_fun(_1387323, tc_fun(tc_fun(tc_prod(_1387321, _1387323), tc_HOL_Obool), tc_HOL_Obool)), _1387321), hAPP(c_COMBB(tc_prod(_1387321, _1387323), tc_fun(tc_fun(tc_prod(_1387321, _1387323), tc_HOL_Obool), tc_HOL_Obool), _1387323), c_member(tc_prod(_1387321, _1387323)))), c_Product__Type_OPair(_1387321, _1387323))))), _1387325)), _1387327), _1387329)))], (19935 ^ _781404) ^ [_1135519, _1135521, _1135523] : [class_Rings_Olinordered__idom(_1135519), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135519), c_Groups_Ozero__class_Ozero(_1135519)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135519), hAPP(hAPP(c_Power_Opower__class_Opower(_1135519), _1135521), 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(_1135519), _1135523), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (21005 ^ _781404) ^ [_1154558, _1154560] : [class_Groups_Ocomm__monoid__mult(_1154558), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154558), _1154560), c_Groups_Oone__class_Oone(_1154558)) = _1154560)], (42439 ^ _781404) ^ [_1621035, _1621037, _1621039] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621035), tc_List_Olist(_1621035))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621035), tc_List_Olist(_1621035)), _1621037), _1621037)), c_List_Olistrel(_1621035, c_Transitive__Closure_Ortrancl(_1621035, _1621039)))))], (45241 ^ _781404) ^ [_1686875, _1686877, _1686879, _1686881, _1686883, _1686885, _1686887] : [hAPP(hAPP(c_List_Omap(_1686875, _1686877), _1686879), _1686881) = hAPP(hAPP(c_List_Omap(_1686883, _1686877), _1686885), _1686887), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686875)), _1686881) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686883)), _1686887))], (47047 ^ _781404) ^ [_1727416, _1727418, _1727420, _1727422] : [class_Orderings_Olinorder(_1727416), 47050 ^ _781404 : [(47059 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727416, hAPP(hAPP(c_List_Olist_OCons(_1727416), _1727418), hAPP(hAPP(c_List_Olist_OCons(_1727416), _1727420), _1727422)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727416), _1727418), _1727420)), c_List_Olinorder__class_Osorted(_1727416, hAPP(hAPP(c_List_Olist_OCons(_1727416), _1727420), _1727422))], (47051 ^ _781404) ^ [] : [c_List_Olinorder__class_Osorted(_1727416, hAPP(hAPP(c_List_Olist_OCons(_1727416), _1727418), hAPP(hAPP(c_List_Olist_OCons(_1727416), _1727420), _1727422))), 47054 ^ _781404 : [(47057 ^ _781404) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727416, hAPP(hAPP(c_List_Olist_OCons(_1727416), _1727420), _1727422)))], (47055 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727416), _1727418), _1727420)))]]]]], (27351 ^ _781404) ^ [_1269897, _1269899, _1269901, _1269903, _1269905, _1269907] : [c_Finite__Set_Ofun__left__comm(_1269897, _1269899, _1269901), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1269897, _1269899, _1269901, _1269903, _1269905), _1269907)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1269897, _1269899, _1269901), _1269903), _1269905) = _1269907)], (20999 ^ _781404) ^ [_1154463, _1154465] : [class_Rings_Ocomm__semiring__1(_1154463), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154463), c_Groups_Oone__class_Oone(_1154463)), _1154465) = _1154465)], (3918 ^ _781404) ^ [_840243, _840245, _840247, _840249, _840251, _840253, _840255, _840257, _840259, _840261, _840263, _840265, _840267, _840269] : [-(c_New__Random__Sequence_Oneg__decr__bind(_840269, _840265, _840261, _840257, _840253, _840249, _840245) = c_New__Random__Sequence_Oneg__decr__bind(_840267, _840263, _840259, _840255, _840251, _840247, _840243)), _840269 = _840267, _840265 = _840263, _840261 = _840259, _840257 = _840255, _840253 = _840251, _840249 = _840247, _840245 = _840243], (38928 ^ _781404) ^ [_1524812, _1524814, _1524816, _1524818, _1524820, _1524822] : [-(_1524812 = c_Orderings_Obot__class_Obot(tc_fun(_1524814, tc_HOL_Obool))), 38934 ^ _781404 : [(38937 ^ _781404) ^ [] : [c_Fun_Oinj__on(_1524816, _1524818, _1524820, hAPP(_1524822, 38933 ^ [_1524812, _1524814, _1524816, _1524818, _1524820, _1524822]))], (38935 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524814), 38933 ^ [_1524812, _1524814, _1524816, _1524818, _1524820, _1524822]), _1524812)))]], -(c_Fun_Oinj__on(_1524816, _1524818, _1524820, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1524814, tc_fun(_1524816, tc_HOL_Obool)), _1524812), _1524822)))], (52210 ^ _781404) ^ [_1836890, _1836892] : [-(class_Finite__Set_Ofinite(tc_fun(_1836890, _1836892))), class_Finite__Set_Ofinite(_1836890), class_Finite__Set_Ofinite(_1836892)], (41630 ^ _781404) ^ [_1598375, _1598377, _1598379, _1598381, _1598383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598375, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598377, _1598375, _1598379), _1598381)), _1598383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598377, tc_HOL_Obool)), _1598381), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598377, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598375, _1598377, hAPP(c_Relation_Oconverse(_1598377, _1598375), _1598379)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598375, tc_HOL_Obool)), _1598383))))))], (31960 ^ _781404) ^ [_1356567, _1356569, _1356571] : [class_Orderings_Olinorder(_1356567), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356567), _1356569), _1356571) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356567), _1356571), _1356569))], (25949 ^ _781404) ^ [_1245136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1245136)), -(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), _1245136), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (51728 ^ _781404) ^ [_1828785, _1828787, _1828789, _1828791] : [class_Divides_Osemiring__div(_1828785), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828785), _1828787), _1828789)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828785), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1828785), _1828789), _1828787)), _1828791) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1828785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828785), _1828789), _1828791)), _1828787))], (14532 ^ _781404) ^ [_1036042, _1036044, _1036046] : [_1036044 = _1036046, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036042), _1036044) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036042), _1036046))], (46766 ^ _781404) ^ [_1722351, _1722353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1722351), _1722353)), -(c_List_Oupt(_1722353, _1722351) = c_List_Olist_ONil(tc_Nat_Onat))], (44132 ^ _781404) ^ [_1661887, _1661889, _1661891, _1661893] : [-(hAPP(hAPP(c_List_Otake(_1661887), _1661889), hAPP(hAPP(c_List_Oappend(_1661887), _1661891), _1661893)) = hAPP(hAPP(c_List_Oappend(_1661887), hAPP(hAPP(c_List_Otake(_1661887), _1661889), _1661891)), hAPP(hAPP(c_List_Otake(_1661887), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1661889), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661887)), _1661891))), _1661893)))], (44180 ^ _781404) ^ [_1663184, _1663186, _1663188, _1663190, _1663192] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663184), tc_List_Olist(_1663184))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663184), tc_List_Olist(_1663184)), _1663186), _1663188)), c_List_Olexord(_1663184, _1663190))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663184), tc_List_Olist(_1663184))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663184), tc_List_Olist(_1663184)), hAPP(hAPP(c_List_Oappend(_1663184), _1663192), _1663186)), hAPP(hAPP(c_List_Oappend(_1663184), _1663192), _1663188))), c_List_Olexord(_1663184, _1663190))))], (34497 ^ _781404) ^ [_1420855, _1420857, _1420859, _1420861] : [class_Groups_Ocomm__monoid__mult(_1420855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420857), _1420859)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1420857, _1420855), hAPP(c_COMBK(_1420855, _1420857), _1420861)), _1420859) = hAPP(hAPP(c_Power_Opower__class_Opower(_1420855), _1420861), hAPP(c_Finite__Set_Ocard(_1420857), _1420859)))], (43937 ^ _781404) ^ [_1657946, _1657948, _1657950, _1657952, _1657954] : [hAPP(hAPP(c_List_Oappend(_1657946), _1657948), _1657950) = hAPP(hAPP(c_List_Oappend(_1657946), _1657952), _1657954), 43943 ^ _781404 : [(43946 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1657946), 43940 ^ [_1657946, _1657948, _1657950, _1657952, _1657954]), _1657950) = _1657954)], (43944 ^ _781404) ^ [] : [-(_1657948 = hAPP(hAPP(c_List_Oappend(_1657946), _1657952), 43940 ^ [_1657946, _1657948, _1657950, _1657952, _1657954]))]], 43947 ^ _781404 : [(43950 ^ _781404) ^ [] : [-(_1657950 = hAPP(hAPP(c_List_Oappend(_1657946), 43940 ^ [_1657946, _1657948, _1657950, _1657952, _1657954]), _1657954))], (43948 ^ _781404) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1657946), _1657948), 43940 ^ [_1657946, _1657948, _1657950, _1657952, _1657954]) = _1657952)]]], (46147 ^ _781404) ^ [_1707481, _1707483] : [-(c_Enum_On__lists(_1707481, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1707483) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1707481)), c_List_Olist_ONil(_1707481)), c_List_Olist_ONil(tc_List_Olist(_1707481))))], (9328 ^ _781404) ^ [_941019, _941021, _941023, _941025, _941027] : [c_Fun_Oinj__on(_941019, _941021, _941023, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941019, tc_HOL_Obool)), _941025), _941027)), 9331 ^ _781404 : [(9336 ^ _781404) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941021, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941019, _941021, _941023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941019, tc_HOL_Obool)), _941025), _941027))), hAPP(c_Set_Oimage(_941019, _941021, _941023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941019, tc_HOL_Obool)), _941027), _941025))) = c_Orderings_Obot__class_Obot(tc_fun(_941021, tc_HOL_Obool)))], (9334 ^ _781404) ^ [] : [-(c_Fun_Oinj__on(_941019, _941021, _941023, _941027))], (9332 ^ _781404) ^ [] : [-(c_Fun_Oinj__on(_941019, _941021, _941023, _941025))]]], (26623 ^ _781404) ^ [_1255741, _1255743, _1255745, _1255747, _1255749] : [class_Groups_Ocomm__monoid__mult(_1255741), hBOOL(hAPP(c_Finite__Set_Ofinite(_1255743), _1255745)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1255743), _1255747)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1255743, tc_HOL_Obool)), _1255745), _1255747) = c_Orderings_Obot__class_Obot(tc_fun(_1255743, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1255741, _1255743, c_Groups_Otimes__class_Otimes(_1255741)), _1255749), c_Groups_Oone__class_Oone(_1255741)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255743, tc_HOL_Obool)), _1255745), _1255747)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1255741), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1255741, _1255743, c_Groups_Otimes__class_Otimes(_1255741)), _1255749), c_Groups_Oone__class_Oone(_1255741)), _1255745)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1255741, _1255743, c_Groups_Otimes__class_Otimes(_1255741)), _1255749), c_Groups_Oone__class_Oone(_1255741)), _1255747)))], (42234 ^ _781404) ^ [_1614370, _1614372, _1614374] : [_1614370 = hAPP(hAPP(c_List_Olist_OCons(_1614372), _1614374), _1614370)], (16514 ^ _781404) ^ [_1075048, _1075050, _1075052] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075048), _1075050)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075048), _1075052)), 16524 ^ _781404 : [(16527 ^ _781404) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16525 ^ _781404) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1075048), 16523 ^ [_1075048, _1075050, _1075052]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075048, tc_HOL_Obool)), _1075050), _1075052))))]], -(hAPP(c_Finite__Set_Ocard(_1075048), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1075048, tc_HOL_Obool)), _1075050), _1075052)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1075048), _1075050)), hAPP(c_Finite__Set_Ocard(_1075048), _1075052)))], (23243 ^ _781404) ^ [_1197626, _1197628, _1197630] : [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), _1197626), _1197628)), _1197630))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197630), _1197626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197628)))], (7938 ^ _781404) ^ [_913342, _913344, _913346, _913348] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913342, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913342, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913342, tc_HOL_Obool)), _913344), _913346)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913342, tc_HOL_Obool)), _913346), _913348))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913342, tc_HOL_Obool)), _913348), _913344)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913342, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913342, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913342, tc_HOL_Obool)), _913344), _913346)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913342, tc_HOL_Obool)), _913346), _913348))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913342, tc_HOL_Obool)), _913348), _913344)))], (21057 ^ _781404) ^ [_1155341, _1155343, _1155345] : [21058 ^ _781404 : [(21061 ^ _781404) ^ [] : [_1155341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21059 ^ _781404) ^ [] : [_1155343 = _1155345]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155341), _1155343) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155341), _1155345))], (37479 ^ _781404) ^ [_1487221, _1487223, _1487225, _1487227] : [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), _1487221), _1487223)), 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), _1487225), _1487227)), 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), _1487221), _1487227)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1487225), _1487223))))], (22975 ^ _781404) ^ [_1192250, _1192252, _1192254] : [class_Rings_Oring__1(_1192250), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1192250), hAPP(c_Groups_Ouminus__class_Ouminus(_1192250), _1192252)), 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)))), _1192254)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1192250), _1192252), 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)))), _1192254)))], (25750 ^ _781404) ^ [_1241547, _1241549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241547)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1241547), _1241549)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1241547)), _1241549))], (35882 ^ _781404) ^ [_1451219, _1451221, _1451223] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1451219), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1451221)), _1451223)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451219, _1451221), hAPP(c_Divides_OnegateSnd, _1451223))))], (44329 ^ _781404) ^ [_1667388, _1667390, _1667392, _1667394] : [-(hAPP(hAPP(c_List_Odrop(_1667388), hAPP(c_Nat_OSuc, _1667390)), hAPP(hAPP(c_List_Olist_OCons(_1667388), _1667392), _1667394)) = hAPP(hAPP(c_List_Odrop(_1667388), _1667390), _1667394))], (6578 ^ _781404) ^ [_886411, _886413, _886415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886411, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886411, tc_HOL_Obool)), _886413)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886411, tc_HOL_Obool)), _886415))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886411, tc_HOL_Obool)), _886415), _886413)))], (3966 ^ _781404) ^ [_841133, _841135, _841137, _841139, _841141, _841143, _841145, _841147, _841149, _841151, _841153, _841155, _841157, _841159] : [-(c_New__Random__Sequence_Opos__decr__bind(_841159, _841155, _841151, _841147, _841143, _841139, _841135) = c_New__Random__Sequence_Opos__decr__bind(_841157, _841153, _841149, _841145, _841141, _841137, _841133)), _841159 = _841157, _841155 = _841153, _841151 = _841149, _841147 = _841145, _841143 = _841141, _841139 = _841137, _841135 = _841133], (29701 ^ _781404) ^ [_1313368, _1313370, _1313372, _1313374] : [class_Fields_Olinordered__field(_1313368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313368), _1313370), _1313372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313368), c_Groups_Ozero__class_Ozero(_1313368)), _1313374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1313368), c_Groups_Ozero__class_Ozero(_1313368)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313368), _1313372), _1313370))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313368), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313368), _1313374), _1313372)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313368), _1313374), _1313370))))], (6590 ^ _781404) ^ [_886711, _886713, _886715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886711, tc_HOL_Obool)), _886713), _886715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886711, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886711, tc_HOL_Obool)), _886715)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_886711, tc_HOL_Obool)), _886713))))], (45702 ^ _781404) ^ [_1696992, _1696994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1696992)), hAPP(c_Code__Numeral_Onat__of, _1696994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1696992), _1696994)))], (51906 ^ _781404) ^ [_1831879, _1831881] : [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)))), _1831879, _1831881), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831879), _1831881)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831881), _1831879)))]], input).
% 45.81/45.07  ncf('1',plain,[hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), 52838 ^ []), v_G)), -(c_Hoare__Mirabelle_Otriple__valid(t_a, 52831 ^ [], 52838 ^ []))],start(52833 ^ 0,bind([[_2095436], [52838 ^ []]]))).
% 45.81/45.07  ncf('1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), 52838 ^ []), v_G))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_ts), v_G)), hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), 52838 ^ []), v_ts))],extension(12007 ^ 1,bind([[_987221, _987223, _987225, _987227], [tc_Hoare__Mirabelle_Otriple(t_a), v_ts, v_G, 52838 ^ []]]))).
% 45.81/45.07  ncf('1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_ts), v_G)))],extension(52830 ^ 2)).
% 45.81/45.07  ncf('1.1.2',plain,[-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), 52838 ^ []), v_ts)))],extension(52840 ^ 2)).
% 45.81/45.07  ncf('1.2',plain,[c_Hoare__Mirabelle_Otriple__valid(t_a, 52831 ^ [], 52838 ^ [])],extension(52842 ^ 1)).
% 45.81/45.07  %-----------------------------------------------------
% 45.81/45.07  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------