TSTP Solution File: SWW386+1 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW386+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:26:05 EDT 2023
% Result : Theorem 47.31s 45.94s
% Output : Proof 47.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW386+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13 % Command : nanocop.sh %s %d
% 0.12/0.32 % Computer : n031.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu May 18 22:27:10 EDT 2023
% 0.12/0.33 % CPUTime :
% 47.31/45.94
% 47.31/45.94 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 47.31/45.94 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.31/45.94 %-----------------------------------------------------
% 47.31/45.94 ncf(matrix, plain, [(51776 ^ _2069884) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, v_pn))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))], !, (19348 ^ _781215) ^ [_1128343, _1128345, _1128347] : [class_Orderings_Olinorder(_1128343), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128343), _1128345)), -(_1128345 = c_Orderings_Obot__class_Obot(tc_fun(_1128343, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1128343, hAPP(hAPP(c_Set_Oinsert(_1128343), _1128347), _1128345)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1128343), _1128347), c_Big__Operators_Olinorder__class_OMin(_1128343, _1128345)))], (6005 ^ _781215) ^ [_876954, _876956, _876958] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_876954, _876956, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_876954)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_876954), _876958), c_Com_Ocom_OSKIP), _876958)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_876954), tc_HOL_Obool)))))], (29268 ^ _781215) ^ [_1314491, _1314493, _1314495] : [class_Fields_Olinordered__field(_1314491), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314491), _1314493), c_Groups_Ozero__class_Ozero(_1314491))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314491), _1314495), c_Groups_Ozero__class_Ozero(_1314491))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314491), c_Groups_Ozero__class_Ozero(_1314491)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314491), _1314493), _1314495))))], (40340 ^ _781215) ^ [_1569871, _1569873, _1569875, _1569877] : [40342 ^ _781215 : [(40345 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1569873, hAPP(_1569875, 40341 ^ [_1569871, _1569873, _1569875, _1569877]))), hAPP(_1569873, 40341 ^ [_1569871, _1569873, _1569875, _1569877])))], (40343 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1569871, 40341 ^ [_1569871, _1569873, _1569875, _1569877])))]], -(c_Wellfounded_Owf(_1569877, hAPP(c_Set_OCollect(tc_prod(_1569877, _1569877)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569877, _1569877, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1569877, tc_HOL_Obool), tc_fun(_1569877, tc_HOL_Obool), _1569877), hAPP(c_COMBS(_1569877, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1569877), c_fconj), _1569871))), hAPP(hAPP(c_COMBC(_1569877, tc_fun(_1569877, _1569877), tc_fun(_1569877, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569877, tc_HOL_Obool), tc_fun(tc_fun(_1569877, _1569877), tc_fun(_1569877, tc_HOL_Obool)), _1569877), c_COMBB(_1569877, tc_HOL_Obool, _1569877)), c_fequal)), _1569875))))))], (5817 ^ _781215) ^ [_873753, _873755, _873757] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_873753, _873755, _873757))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _873755))))], (36049 ^ _781215) ^ [_1458980, _1458982, _1458984] : [class_Rings_Oordered__ring__abs(_1458980), -(hAPP(c_Groups_Oabs__class_Oabs(_1458980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1458980), _1458982), _1458984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1458980), hAPP(c_Groups_Oabs__class_Oabs(_1458980), _1458982)), hAPP(c_Groups_Oabs__class_Oabs(_1458980), _1458984))), 36056 ^ _781215 : [(36059 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458980), _1458982), c_Groups_Ozero__class_Ozero(_1458980)))], (36057 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458980), c_Groups_Ozero__class_Ozero(_1458980)), _1458982))]], 36060 ^ _781215 : [(36063 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458980), _1458984), c_Groups_Ozero__class_Ozero(_1458980)))], (36061 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458980), c_Groups_Ozero__class_Ozero(_1458980)), _1458984))]]], (18998 ^ _781215) ^ [_1121735, _1121737, _1121739, _1121741] : [class_Orderings_Olinorder(_1121735), 19001 ^ _781215 : [(19010 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121735), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1121735), _1121737), _1121739)), _1121741))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121735), _1121737), _1121741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121735), _1121739), _1121741))], (19002 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121735), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1121735), _1121737), _1121739)), _1121741)), 19005 ^ _781215 : [(19008 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121735), _1121739), _1121741)))], (19006 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121735), _1121737), _1121741)))]]]]], (38386 ^ _781215) ^ [_1513183, _1513185, _1513187, _1513189] : [-(hAPP(c_Set_Ovimage(_1513183, _1513185, _1513187), _1513189) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1513185, tc_fun(_1513183, tc_HOL_Obool)), _1513189), hAPP(hAPP(c_COMBB(tc_fun(_1513185, tc_HOL_Obool), tc_fun(_1513183, tc_HOL_Obool), _1513185), c_Set_Ovimage(_1513183, _1513185, _1513187)), hAPP(hAPP(c_COMBC(_1513185, tc_fun(_1513185, tc_HOL_Obool), tc_fun(_1513185, tc_HOL_Obool)), c_Set_Oinsert(_1513185)), c_Orderings_Obot__class_Obot(tc_fun(_1513185, tc_HOL_Obool))))))], (24316 ^ _781215) ^ [_1219715, _1219717] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1219715), hAPP(c_Int_Onumber__class_Onumber__of(_1219715), _1219717)), 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(_1219715), hAPP(c_Int_Onumber__class_Onumber__of(_1219715), _1219717)), hAPP(c_Int_Onumber__class_Onumber__of(_1219715), _1219717))), class_Groups_Omonoid__mult(_1219715), class_Int_Onumber(_1219715)], (23652 ^ _781215) ^ [_1207576, _1207578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207576), _1207578)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1207576, _1207578) = _1207576)], (23194 ^ _781215) ^ [_1198921, _1198923, _1198925] : [class_Divides_Osemiring__div(_1198921), -(_1198923 = c_Groups_Ozero__class_Ozero(_1198921)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1198921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198921), _1198923), _1198925)), _1198923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198921), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1198921), _1198925), _1198923)), c_Groups_Oone__class_Oone(_1198921)))], (31437 ^ _781215) ^ [_1357517] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1357517)) = 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), _1357517))))], (10023 ^ _781215) ^ [_951547, _951549] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951549), _951547))))], (22442 ^ _781215) ^ [_1186636, _1186638] : [class_Divides_Osemiring__div(_1186636), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1186636), _1186638), c_Groups_Oone__class_Oone(_1186636)) = _1186638)], (43682 ^ _781215) ^ [_1653751, _1653753, _1653755] : [-(hAPP(hAPP(c_Map_Omap__of(_1653751, _1653753), c_List_Olist_ONil(tc_prod(_1653751, _1653753))), _1653755) = c_Option_Ooption_ONone(_1653753))], (35158 ^ _781215) ^ [_1441288, _1441290] : [-(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)), _1441288), _1441290))], (23827 ^ _781215) ^ [_1210748, _1210750] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1210748))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1210748)), _1210750) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1210750))], (10040 ^ _781215) ^ [_951873, _951875, _951877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951873), _951875)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951873), _951877))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951875), _951877)))], (51092 ^ _781215) ^ [_1819697, _1819699] : [class_Orderings_Opreorder(_1819697), -(class_Orderings_Opreorder(tc_fun(_1819699, _1819697)))], (50794 ^ _781215) ^ [_1813578] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1813578)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1813578))))], (42893 ^ _781215) ^ [_1634449, _1634451, _1634453, _1634455] : [hBOOL(hAPP(c_List_Odistinct(_1634449), _1634451)), -(hBOOL(hAPP(hAPP(c_member(_1634449), _1634453), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1634449, tc_HOL_Obool)), hAPP(c_List_Oset(_1634449), _1634451)), hAPP(hAPP(c_Set_Oinsert(_1634449), hAPP(hAPP(c_List_Onth(_1634449), _1634451), _1634455)), c_Orderings_Obot__class_Obot(tc_fun(_1634449, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1634449), hAPP(hAPP(c_List_Olist__update(_1634449, _1634451), _1634455), _1634453))))], (3946 ^ _781215) ^ [_841074, _841076, _841078, _841080, _841082, _841084] : [-(c_Map_Odom(_841084, _841080, _841076) = c_Map_Odom(_841082, _841078, _841074)), _841084 = _841082, _841080 = _841078, _841076 = _841074], (16547 ^ _781215) ^ [_1076333, _1076335, _1076337, _1076339, _1076341, _1076343] : [c_Finite__Set_Ofun__left__comm(_1076333, _1076335, _1076337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076333), _1076339)), -(hAPP(hAPP(_1076337, _1076341), hAPP(hAPP(c_Finite__Set_Ofold(_1076333, _1076335, _1076337), _1076343), _1076339)) = hAPP(hAPP(c_Finite__Set_Ofold(_1076333, _1076335, _1076337), hAPP(hAPP(_1076337, _1076341), _1076343)), _1076339))], (26570 ^ _781215) ^ [_1263260, _1263262, _1263264, _1263266] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1263260, tc_fun(_1263262, tc_HOL_Obool))), _1263264), _1263266))], (30327 ^ _781215) ^ [_1336000, _1336002] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1336000), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1336002) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1336000, _1336002))], (46275 ^ _781215) ^ [_1710052, _1710054, _1710056, _1710058] : [hAPP(c_List_Orev(_1710052), _1710054) = hAPP(hAPP(c_List_Olist_OCons(_1710052), _1710056), _1710058), -(_1710054 = hAPP(hAPP(c_List_Oappend(_1710052), hAPP(c_List_Orev(_1710052), _1710058)), hAPP(hAPP(c_List_Olist_OCons(_1710052), _1710056), c_List_Olist_ONil(_1710052))))], (47521 ^ _781215) ^ [_1737468, _1737470, _1737472, _1737474] : [hBOOL(hAPP(c_List_Olistsp(_1737468, _1737470), _1737472)), hBOOL(hAPP(c_List_Olistsp(_1737468, _1737474), _1737472)), -(hBOOL(hAPP(c_List_Olistsp(_1737468, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1737468, tc_HOL_Obool)), _1737470), _1737474)), _1737472)))], (20605 ^ _781215) ^ [_1150997, _1150999, _1151001] : [class_Rings_Olinordered__semidom(_1150997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150997), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150997), _1150999)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150997), _1151001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150999), _1151001)))], (8117 ^ _781215) ^ [_917994, _917996, _917998] : [class_Groups_Ogroup__add(_917994), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917994), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_917994), _917996), _917998)), _917998) = _917996)], (16941 ^ _781215) ^ [_1085375] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1085375) = _1085375)], (11212 ^ _781215) ^ [_975954, _975956, _975958, _975960] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975954), _975956)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _975958), _975956)), _975960)) = 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), _975954), _975958)), _975956)), _975960))], (25348 ^ _781215) ^ [_1238091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1238091)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1238091), c_Int_OMin)))], (15136 ^ _781215) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41237 ^ _781215) ^ [_1590916] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1590916)), -(c_List_Onat__list(_1590916))], (4288 ^ _781215) ^ [_846287, _846289] : [_846289 = _846287, -(c_HOL_OEx(_846289) = c_HOL_OEx(_846287))], (44780 ^ _781215) ^ [_1679710, _1679712, _1679714, _1679716] : [-(_1679710 = c_List_Olist_ONil(_1679712)), -(hAPP(c_List_Ohd(_1679714), hAPP(hAPP(c_List_Omap(_1679712, _1679714), _1679716), _1679710)) = hAPP(_1679716, hAPP(c_List_Ohd(_1679712), _1679710)))], (20370 ^ _781215) ^ [_1146832] : [_1146832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1146832) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (41335 ^ _781215) ^ [_1593423, _1593425, _1593427, _1593429, _1593431, _1593433] : [-(hAPP(c_Set_Oimage(_1593423, _1593425, hAPP(c_Fun_Ocomp(_1593427, _1593425, _1593423, _1593429), _1593431)), _1593433) = hAPP(c_Set_Oimage(_1593427, _1593425, _1593429), hAPP(c_Set_Oimage(_1593423, _1593427, _1593431), _1593433)))], (50406 ^ _781215) ^ [_1806227] : [-(c_Nitpick_Onum(_1806227) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1806227, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1806227)))], (51600 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (42088 ^ _781215) ^ [_1611563, _1611565, _1611567, _1611569] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611563)), _1611565) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611567)), _1611569), -(hAPP(hAPP(c_List_Omap(tc_prod(_1611563, _1611567), _1611563), c_Product__Type_Ofst(_1611563, _1611567)), hAPP(hAPP(c_List_Ozip(_1611563, _1611567), _1611565), _1611569)) = _1611565)], (46315 ^ _781215) ^ [_1711099, _1711101, _1711103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711099), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711101)), _1711103))), -(hAPP(hAPP(c_List_Onth(_1711101), hAPP(c_List_Orev(_1711101), _1711103)), _1711099) = hAPP(hAPP(c_List_Onth(_1711101), _1711103), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711101)), _1711103)), hAPP(c_Nat_OSuc, _1711099))))], (32610 ^ _781215) ^ [_1385188, _1385190, _1385192] : [class_Lattices_Osemilattice__inf(_1385188), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385188), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1385188), _1385190), _1385192)), _1385190)))], (18433 ^ _781215) ^ [_1111260, _1111262, _1111264] : [-(hAPP(c_Nat_Onat_Onat__rec(_1111260, _1111262, _1111264), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1111262)], (43073 ^ _781215) ^ [_1638710, _1638712, _1638714] : [c_Equiv__Relations_Oequiv(_1638710, _1638712, _1638714), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1638710), c_List_Olists(_1638710, _1638712), c_List_Olistrel(_1638710, _1638714)))], (38300 ^ _781215) ^ [_1511138, _1511140, _1511142, _1511144, _1511146] : [hBOOL(hAPP(hAPP(c_member(_1511138), hAPP(_1511140, _1511142)), _1511144)), -(hBOOL(hAPP(hAPP(c_member(_1511146), _1511142), hAPP(c_Set_Ovimage(_1511146, _1511138, _1511140), _1511144))))], (4240 ^ _781215) ^ [_845585, _845587] : [_845587 = _845585, -(c_Random_Orange(_845587) = c_Random_Orange(_845585))], (11960 ^ _781215) ^ [_989035] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989035), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39432 ^ _781215) ^ [_1542337, _1542339, _1542341, _1542343, _1542345, _1542347] : [hBOOL(hAPP(hAPP(c_member(_1542337), _1542339), _1542341)), -(hAPP(c_Fun_Ooverride__on(_1542337, _1542343, _1542345, _1542347, _1542341), _1542339) = hAPP(_1542347, _1542339))], (31371 ^ _781215) ^ [_1355931, _1355933, _1355935, _1355937, _1355939] : [-(hBOOL(hAPP(hAPP(c_member(_1355931), _1355933), hAPP(c_Relation_OImage(_1355935, _1355931, _1355937), _1355939)))), 31372 ^ _781215 : [(31373 ^ _781215) ^ [_1356017] : [hBOOL(hAPP(hAPP(c_member(_1355935), _1356017), _1355939)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1355935, _1355931)), hAPP(hAPP(c_Product__Type_OPair(_1355935, _1355931), _1356017), _1355933)), _1355937))]]], (50408 ^ _781215) ^ [_1806262, _1806264, _1806266, _1806268] : [class_Rings_Olinordered__semidom(_1806262), 50414 ^ _781215 : [(50417 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1806262), c_Groups_Ozero__class_Ozero(_1806262)), hAPP(_1806268, 50413 ^ [_1806262, _1806264, _1806266, _1806268])))], (50415 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806264), 50413 ^ [_1806262, _1806264, _1806266, _1806268]), _1806266)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1806262), c_Groups_Ozero__class_Ozero(_1806262)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1806264, _1806262), _1806268), _1806266))))], (11188 ^ _781215) ^ [_975416, _975418, _975420, _975422] : [class_Rings_Ocomm__semiring__1(_975416), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975416), _975418), _975420)), _975422) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975416), _975418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975416), _975420), _975422)))], (37362 ^ _781215) ^ [_1489955, _1489957] : [c_Equiv__Relations_Oequiv(_1489955, c_Orderings_Otop__class_Otop(tc_fun(_1489955, tc_HOL_Obool)), _1489957), -(c_Equiv__Relations_Oequivp(_1489955, hAPP(hAPP(c_COMBC(_1489955, tc_fun(tc_prod(_1489955, _1489955), tc_HOL_Obool), tc_fun(_1489955, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1489955, tc_fun(tc_fun(tc_prod(_1489955, _1489955), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1489955, _1489955), tc_HOL_Obool), tc_fun(_1489955, tc_HOL_Obool)), _1489955), c_COMBC(_1489955, tc_fun(tc_prod(_1489955, _1489955), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1489955, tc_prod(_1489955, _1489955)), tc_fun(_1489955, tc_fun(tc_fun(tc_prod(_1489955, _1489955), tc_HOL_Obool), tc_HOL_Obool)), _1489955), hAPP(c_COMBB(tc_prod(_1489955, _1489955), tc_fun(tc_fun(tc_prod(_1489955, _1489955), tc_HOL_Obool), tc_HOL_Obool), _1489955), c_member(tc_prod(_1489955, _1489955)))), c_Product__Type_OPair(_1489955, _1489955)))), _1489957)))], (25202 ^ _781215) ^ [] : [c_Int_OPls = c_Int_OMin], (43640 ^ _781215) ^ [_1652819, _1652821, _1652823, _1652825, _1652827] : [c_List_Opartition(_1652819, _1652821, _1652823) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652819), tc_List_Olist(_1652819)), _1652825), _1652827), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1652819, tc_HOL_Obool)), hAPP(c_List_Oset(_1652819), _1652825)), hAPP(c_List_Oset(_1652819), _1652827)) = hAPP(c_List_Oset(_1652819), _1652823))], (43680 ^ _781215) ^ [_1653722] : [-(hBOOL(hAPP(c_List_Odistinct(_1653722), c_List_Olist_ONil(_1653722))))], (28402 ^ _781215) ^ [_1298498, _1298500, _1298502, _1298504] : [class_Fields_Olinordered__field__inverse__zero(_1298498), class_Int_Onumber(_1298498), 28409 ^ _781215 : [(28410 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298498), _1298500), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502))), _1298504)), 28413 ^ _781215 : [(28420 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), c_Groups_Ozero__class_Ozero(_1298498)), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502)))), 28423 ^ _781215 : [(28430 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502)), c_Groups_Ozero__class_Ozero(_1298498)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), c_Groups_Ozero__class_Ozero(_1298498)), _1298504)))], (28424 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502)), c_Groups_Ozero__class_Ozero(_1298498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1298498), _1298504), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502))), _1298500)))]]], (28414 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), c_Groups_Ozero__class_Ozero(_1298498)), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), _1298500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1298498), _1298504), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502)))))]]], (28436 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298498), _1298500), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502))), _1298504))), 28439 ^ _781215 : [(28442 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), _1298500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1298498), _1298504), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502))))], (28440 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), c_Groups_Ozero__class_Ozero(_1298498)), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502))))]], 28443 ^ _781215 : [(28446 ^ _781215) ^ [] : [28447 ^ _781215 : [(28450 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1298498), _1298504), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502))), _1298500))], (28448 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502)), c_Groups_Ozero__class_Ozero(_1298498))))]], 28451 ^ _781215 : [(28454 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), c_Groups_Ozero__class_Ozero(_1298498)), _1298504))], (28452 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502)), c_Groups_Ozero__class_Ozero(_1298498)))]]], (28444 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298498), c_Groups_Ozero__class_Ozero(_1298498)), hAPP(c_Int_Onumber__class_Onumber__of(_1298498), _1298502)))]]]]], (33082 ^ _781215) ^ [_1394973, _1394975, _1394977, _1394979] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1394973, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394973, tc_HOL_Obool)), _1394975), _1394977)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394973, tc_HOL_Obool)), _1394979), _1394977)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1394973, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394973, tc_HOL_Obool)), _1394975), _1394977)), _1394979))], (37542 ^ _781215) ^ [_1494132, _1494134, _1494136] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494132, tc_HOL_Obool)), _1494134), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494132, tc_HOL_Obool), _1494136)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1494132, tc_HOL_Obool), tc_fun(_1494132, tc_HOL_Obool)), _1494136), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494132, tc_HOL_Obool)), _1494134)))], (16201 ^ _781215) ^ [_1067573, _1067575, _1067577, _1067579] : [class_Lattices_Osemilattice__sup(_1067573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067573), _1067575), _1067577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067573), _1067575), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067573), _1067579), _1067577))))], (16127 ^ _781215) ^ [_1066259, _1066261, _1066263, _1066265] : [class_Lattices_Osemilattice__sup(_1066259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066259), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066259), _1066261), _1066263)), _1066265)), 16134 ^ _781215 : [(16137 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066259), _1066263), _1066265)))], (16135 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066259), _1066261), _1066265)))]]], (18235 ^ _781215) ^ [_1107685, _1107687, _1107689] : [class_Orderings_Olinorder(_1107685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107685), _1107687), _1107689)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1107685), _1107689), _1107687) = _1107687)], (7702 ^ _781215) ^ [_910857, _910859, _910861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910857), _910859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _910857), _910861)), _910859)))], (51422 ^ _781215) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (8353 ^ _781215) ^ [_922073, _922075, _922077, _922079] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_922073), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922073), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922073), _922075), _922077)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922073), _922079), _922077))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922073), _922075), _922079)))], (37287 ^ _781215) ^ [] : [-(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))], (46135 ^ _781215) ^ [_1707132, _1707134, _1707136, _1707138] : [-(hAPP(c_List_Orev(_1707132), hAPP(hAPP(c_List_Omap(_1707134, _1707132), _1707136), _1707138)) = hAPP(hAPP(c_List_Omap(_1707134, _1707132), _1707136), hAPP(c_List_Orev(_1707134), _1707138)))], (30762 ^ _781215) ^ [_1344293, _1344295, _1344297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1344293, _1344293), tc_HOL_Obool)), _1344295), _1344297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1344293, tc_HOL_Obool)), hAPP(c_Relation_OField(_1344293), _1344295)), hAPP(c_Relation_OField(_1344293), _1344297))))], (32505 ^ _781215) ^ [_1382842, _1382844, _1382846, _1382848, _1382850, _1382852] : [c_Equiv__Relations_Oequiv(_1382842, _1382844, _1382846), c_Equiv__Relations_Ocongruent(_1382842, tc_fun(_1382848, tc_HOL_Obool), _1382846, _1382850), hBOOL(hAPP(hAPP(c_member(_1382842), _1382852), _1382844)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382842, tc_fun(_1382848, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1382842, _1382842, _1382846), hAPP(hAPP(c_Set_Oinsert(_1382842), _1382852), c_Orderings_Obot__class_Obot(tc_fun(_1382842, tc_HOL_Obool))))), _1382850) = hAPP(_1382850, _1382852))], (26099 ^ _781215) ^ [_1254558] : [class_Rings_Oring__1(_1254558), -(hAPP(c_Int_Oring__1__class_Oof__int(_1254558), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1254558))], (49788 ^ _781215) ^ [_1790313, _1790315, _1790317] : [c_Relation_Ototal__on(_1790313, _1790315, _1790317), -(c_Relation_Ototal__on(_1790313, _1790315, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1790313, _1790313), tc_HOL_Obool)), _1790317), c_Relation_OId(_1790313))))], (27602 ^ _781215) ^ [_1283640, _1283642, _1283644] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1283640, _1283642), _1283644))), _1283640 = 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), _1283644)), _1283642)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1283644)), 27609 ^ _781215 : [(27612 ^ _781215) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1283644) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27610 ^ _781215) ^ [] : [-(_1283642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 27613 ^ _781215 : [(27616 ^ _781215) ^ [] : [27617 ^ _781215 : [(27620 ^ _781215) ^ [] : [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), _1283644))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1283644)), _1283642))], (27618 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1283642)))]], 27625 ^ _781215 : [(27628 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1283642), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1283644))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1283644)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27626 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1283642))]]], (27614 ^ _781215) ^ [] : [_1283642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43515 ^ _781215) ^ [_1649616, _1649618] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1649616), _1649618)), -(c_Nitpick_Ocard_H(_1649616, _1649618) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649616)), c_Hilbert__Choice_OEps(tc_List_Olist(_1649616), hAPP(hAPP(c_COMBS(tc_List_Olist(_1649616), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1649616)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649616), tc_fun(_1649616, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1649616, tc_HOL_Obool), tc_fun(tc_fun(_1649616, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1649616)), c_fequal), c_List_Oset(_1649616))), _1649618))), c_List_Odistinct(_1649616)))))], (11902 ^ _781215) ^ [_988180] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988180), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _988180)], (44952 ^ _781215) ^ [_1682877, _1682879, _1682881, _1682883] : [class_Groups_Osemigroup__add(_1682877), -(hAPP(c_List_Ofoldl(_1682877, _1682877, c_Groups_Oplus__class_Oplus(_1682877), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1682877), _1682879), _1682881)), _1682883) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1682877), _1682879), hAPP(c_List_Ofoldl(_1682877, _1682877, c_Groups_Oplus__class_Oplus(_1682877), _1682881), _1682883)))], (47966 ^ _781215) ^ [_1747097, _1747099, _1747101] : [hBOOL(hAPP(hAPP(c_member(_1747097), _1747099), hAPP(c_List_Oset(_1747097), _1747101))), -(c_List_Oinsert(_1747097, _1747099, _1747101) = _1747101)], (37844 ^ _781215) ^ [_1500545, _1500547, _1500549] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500545, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1500545, tc_HOL_Obool), _1500547)), _1500549) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1500545, tc_HOL_Obool), tc_fun(_1500545, tc_HOL_Obool)), _1500547), hAPP(hAPP(c_COMBC(tc_fun(_1500545, tc_HOL_Obool), tc_fun(_1500545, tc_HOL_Obool), tc_fun(_1500545, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500545, tc_HOL_Obool))), _1500549)))], (29234 ^ _781215) ^ [_1313997, _1313999, _1314001, _1314003] : [class_Fields_Ofield__inverse__zero(_1313997), 29237 ^ _781215 : [(29238 ^ _781215) ^ [] : [_1313999 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313997), _1314001), _1314003), 29241 ^ _781215 : [(29248 ^ _781215) ^ [] : [_1314003 = c_Groups_Ozero__class_Ozero(_1313997), -(_1313999 = c_Groups_Ozero__class_Ozero(_1313997))], (29242 ^ _781215) ^ [] : [-(_1314003 = c_Groups_Ozero__class_Ozero(_1313997)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313997), _1313999), _1314003) = _1314001)]]], (29254 ^ _781215) ^ [] : [-(_1313999 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313997), _1314001), _1314003)), 29257 ^ _781215 : [(29260 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313997), _1313999), _1314003) = _1314001], (29258 ^ _781215) ^ [] : [_1314003 = c_Groups_Ozero__class_Ozero(_1313997)]], 29261 ^ _781215 : [(29264 ^ _781215) ^ [] : [_1313999 = c_Groups_Ozero__class_Ozero(_1313997)], (29262 ^ _781215) ^ [] : [-(_1314003 = c_Groups_Ozero__class_Ozero(_1313997))]]]]], (40889 ^ _781215) ^ [_1582795, _1582797] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1582795, _1582797)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1582797)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17111 ^ _781215) ^ [_1087998, _1088000] : [class_Int_Onumber__ring(_1087998), class_Rings_Olinordered__idom(_1087998), 17118 ^ _781215 : [(17125 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1088000)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087998), c_Groups_Ozero__class_Ozero(_1087998)), hAPP(c_Int_Onumber__class_Onumber__of(_1087998), _1088000))))], (17119 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087998), c_Groups_Ozero__class_Ozero(_1087998)), hAPP(c_Int_Onumber__class_Onumber__of(_1087998), _1088000))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1088000)))]]], (18510 ^ _781215) ^ [_1112723, _1112725, _1112727] : [class_Orderings_Olinorder(_1112723), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112723), _1112725)), -(_1112725 = c_Orderings_Obot__class_Obot(tc_fun(_1112723, tc_HOL_Obool))), 18521 ^ _781215 : [(18531 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112723), hAPP(c_Finite__Set_Ofold1(_1112723, c_Orderings_Oord__class_Omin(_1112723)), _1112725)), _1112727))), 18532 ^ _781215 : [(18533 ^ _781215) ^ [_1113112] : [hBOOL(hAPP(hAPP(c_member(_1112723), _1113112), _1112725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112723), _1113112), _1112727))]]], (18522 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112723), hAPP(c_Finite__Set_Ofold1(_1112723, c_Orderings_Oord__class_Omin(_1112723)), _1112725)), _1112727)), 18526 ^ _781215 : [(18529 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112723), 18525 ^ [_1112723, _1112725, _1112727]), _1112727)))], (18527 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112723), 18525 ^ [_1112723, _1112725, _1112727]), _1112725)))]]]]], (6968 ^ _781215) ^ [_896671, _896673, _896675, _896677, _896679, _896681] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _896671), _896673), _896675), _896677)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _896679), _896677), _896675), _896681)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_896671, _896679)), _896673), _896675), _896681)))], (25536 ^ _781215) ^ [_1240844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240844)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1240844) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (20878 ^ _781215) ^ [_1155480, _1155482, _1155484] : [class_Rings_Oring__1(_1155480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1155482), _1155484)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1155480), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1155484), _1155482)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1155480), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1155480), _1155484)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1155480), _1155482)))], (1178 ^ _781215) ^ [_798910, _798912] : [-(class_Groups_Oab__group__add(_798910)), _798912 = _798910, class_Groups_Oab__group__add(_798912)], (23024 ^ _781215) ^ [_1196329, _1196331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196329)), 23027 ^ _781215 : [(23030 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1196331, _1196329)), _1196329)))], (23028 ^ _781215) ^ [] : [-(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, _1196331, _1196329))))]]], (45909 ^ _781215) ^ [_1701893, _1701895, _1701897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701893), _1701895)), _1701897)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1701893, _1701897)), _1701895) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701893), _1701895))], (6680 ^ _781215) ^ [_890553, _890555, _890557] : [-(hBOOL(hAPP(hAPP(c_member(_890553), _890555), hAPP(hAPP(c_Set_Oinsert(_890553), _890555), _890557))))], (51392 ^ _781215) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (45322 ^ _781215) ^ [_1690453, _1690455, _1690457] : [hAPP(c_List_Ofilter(_1690453, _1690455), _1690457) = c_List_Olist_ONil(_1690453), 45325 ^ _781215 : [(45326 ^ _781215) ^ [_1690550] : [hBOOL(hAPP(hAPP(c_member(_1690453), _1690550), hAPP(c_List_Oset(_1690453), _1690457))), hBOOL(hAPP(_1690455, _1690550))]]], (30840 ^ _781215) ^ [_1345899, _1345901] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1345899), _1345901))))], (24472 ^ _781215) ^ [_1222509, _1222511, _1222513] : [class_Int_Onumber__ring(_1222509), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1222509), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1222509), _1222511), _1222513)), 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(_1222509), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1222509), hAPP(hAPP(c_Power_Opower__class_Opower(_1222509), _1222511), 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(_1222509), _1222513), 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(_1222509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222509), hAPP(c_Int_Onumber__class_Onumber__of(_1222509), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1222511)), _1222513)))], (44012 ^ _781215) ^ [_1661037, _1661039, _1661041, _1661043, _1661045, _1661047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661037)), _1661039)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661041)), _1661043))), -(c_Map_Omap__upds(_1661037, _1661041, _1661045, hAPP(hAPP(c_List_Oappend(_1661037), _1661039), hAPP(hAPP(c_List_Olist_OCons(_1661037), _1661047), c_List_Olist_ONil(_1661037))), _1661043) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1661037, tc_Option_Ooption(_1661041)), c_Map_Omap__upds(_1661037, _1661041, _1661045, _1661039, _1661043)), _1661047), hAPP(c_Option_Ooption_OSome(_1661041), hAPP(hAPP(c_List_Onth(_1661041), _1661043), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661037)), _1661039)))))], (2474 ^ _781215) ^ [_817924, _817926, _817928, _817930, _817932, _817934, _817936, _817938] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_817938, _817934, _817930, _817926) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_817936, _817932, _817928, _817924)), _817938 = _817936, _817934 = _817932, _817930 = _817928, _817926 = _817924], (9419 ^ _781215) ^ [_941758, _941760, _941762] : [class_Orderings_Oorder(_941758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941758), _941760), _941762)), -(_941760 = _941762), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941758), _941760), _941762)))], (6193 ^ _781215) ^ [_880979, _880981, _880983, _880985, _880987] : [c_Finite__Set_Ofolding__one__idem(_880979, _880981, _880983), hBOOL(hAPP(c_Finite__Set_Ofinite(_880979), _880985)), -(_880985 = c_Orderings_Obot__class_Obot(tc_fun(_880979, tc_HOL_Obool))), -(hAPP(_880983, hAPP(hAPP(c_Set_Oinsert(_880979), _880987), _880985)) = hAPP(hAPP(_880981, _880987), hAPP(_880983, _880985)))], (23815 ^ _781215) ^ [_1210514, _1210516] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210514), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210516)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1210514, _1210516)))], (7468 ^ _781215) ^ [_906833, _906835, _906837] : [class_Orderings_Oorder(_906833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906833), _906835), _906837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906833), _906837), _906835))], (47873 ^ _781215) ^ [_1745313, _1745315, _1745317, _1745319] : [47875 ^ _781215 : [(47878 ^ _781215) ^ [] : [hBOOL(hAPP(_1745317, hAPP(hAPP(c_List_Onth(_1745313), _1745315), 47874 ^ [_1745313, _1745315, _1745317, _1745319])))], (47876 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47874 ^ [_1745313, _1745315, _1745317, _1745319]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745313)), _1745315))))]], hBOOL(hAPP(hAPP(c_member(_1745313), _1745319), hAPP(c_List_Oset(_1745313), _1745315))), -(hBOOL(hAPP(_1745317, _1745319)))], (47982 ^ _781215) ^ [_1747362, _1747364, _1747366] : [-(c_List_Omaps(_1747362, _1747364, _1747366, c_List_Olist_ONil(_1747362)) = c_List_Olist_ONil(_1747364))], (31362 ^ _781215) ^ [_1355715, _1355717, _1355719, _1355721, _1355723] : [hBOOL(hAPP(hAPP(c_member(_1355715), _1355717), hAPP(c_Relation_OImage(_1355719, _1355715, _1355721), _1355723))), 31366 ^ _781215 : [(31369 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1355719, _1355715)), hAPP(hAPP(c_Product__Type_OPair(_1355719, _1355715), 31365 ^ [_1355715, _1355717, _1355719, _1355721, _1355723]), _1355717)), _1355721)))], (31367 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1355719), 31365 ^ [_1355715, _1355717, _1355719, _1355721, _1355723]), _1355723)))]]], (50495 ^ _781215) ^ [_1808024, _1808026, _1808028] : [c_List_Olist__all(_1808024, _1808026, hAPP(c_List_Orev(_1808024), _1808028)), -(c_List_Olist__all(_1808024, _1808026, _1808028))], (16385 ^ _781215) ^ [_1070850, _1070852] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1070850, tc_HOL_Obool)), _1070852), c_Orderings_Obot__class_Obot(tc_fun(_1070850, tc_HOL_Obool))) = _1070852)], (40253 ^ _781215) ^ [_1567743, _1567745, _1567747, _1567749] : [c_Wellfounded_Owf(_1567743, _1567745), c_Fun_Oinj__on(_1567743, _1567747, _1567749, c_Orderings_Otop__class_Otop(tc_fun(_1567743, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1567747, hAPP(c_Set_Oimage(tc_prod(_1567743, _1567743), tc_prod(_1567747, _1567747), c_Product__Type_Omap__pair(_1567743, _1567747, _1567743, _1567747, _1567749, _1567749)), _1567745)))], (14916 ^ _781215) ^ [_1042725, _1042727, _1042729, _1042731, _1042733, _1042735] : [c_Com_Ocom_OCond(_1042725, _1042727, _1042729) = c_Com_Ocom_OCall(_1042731, _1042733, _1042735)], (6399 ^ _781215) ^ [_885317, _885319] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _885317), _885319)), -(_885319 = _885317)], (21440 ^ _781215) ^ [_1166008, _1166010] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1166008)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1166010))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1166008), _1166010)))], (26047 ^ _781215) ^ [_1253554, _1253556, _1253558, _1253560] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1253556, _1253554)), _1253558), _1253560) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1253556), hAPP(hAPP(c_COMBC(_1253556, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1253554, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1253556), c_Smallcheck_Osmall__class_Osmall(_1253554)), hAPP(hAPP(c_COMBB(tc_fun(_1253554, tc_prod(_1253556, _1253554)), tc_fun(_1253554, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1253556), hAPP(c_COMBB(tc_prod(_1253556, _1253554), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1253554), _1253558)), c_Product__Type_OPair(_1253556, _1253554)))), _1253560)), _1253560)), class_Smallcheck_Osmall(_1253554), class_Smallcheck_Osmall(_1253556)], (36406 ^ _781215) ^ [_1465527, _1465529, _1465531] : [class_Lattices_Obounded__lattice__top(_1465527), 36409 ^ _781215 : [(36418 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465527), _1465529), _1465531) = c_Orderings_Otop__class_Otop(_1465527)), _1465529 = c_Orderings_Otop__class_Otop(_1465527), _1465531 = c_Orderings_Otop__class_Otop(_1465527)], (36410 ^ _781215) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465527), _1465529), _1465531) = c_Orderings_Otop__class_Otop(_1465527), 36413 ^ _781215 : [(36416 ^ _781215) ^ [] : [-(_1465531 = c_Orderings_Otop__class_Otop(_1465527))], (36414 ^ _781215) ^ [] : [-(_1465529 = c_Orderings_Otop__class_Otop(_1465527))]]]]], (5931 ^ _781215) ^ [_875568, _875570] : [5932 ^ _781215 : [(5933 ^ _781215) ^ [_875616] : [_875568 = hAPP(c_Option_Ooption_OSome(_875570), _875616)]], _875568 = c_Option_Ooption_ONone(_875570)], (10944 ^ _781215) ^ [_969527, _969529, _969531, _969533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969527, tc_HOL_Obool)), _969529), hAPP(hAPP(c_Set_Oinsert(_969527), _969531), _969533))), 10947 ^ _781215 : [(10954 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_969527), _969531), _969529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969527, tc_HOL_Obool)), _969529), _969533)))], (10948 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_969527), _969531), _969529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969527, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969527, tc_HOL_Obool)), _969529), hAPP(hAPP(c_Set_Oinsert(_969527), _969531), c_Orderings_Obot__class_Obot(tc_fun(_969527, tc_HOL_Obool))))), _969533)))]]], (926 ^ _781215) ^ [_795470, _795472, _795474, _795476] : [-(c_Wellfounded_Owf(_795474, _795470)), c_Wellfounded_Owf(_795476, _795472), _795476 = _795474, _795472 = _795470], (15540 ^ _781215) ^ [_1053799, _1053801, _1053803] : [-(c_Map_Omap__add(_1053799, _1053801, hAPP(c_COMBK(tc_Option_Ooption(_1053801), _1053799), c_Option_Ooption_ONone(_1053801)), _1053803) = _1053803)], (28204 ^ _781215) ^ [_1294783, _1294785] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294783), _1294785), hAPP(c_Int_Onumber__class_Onumber__of(_1294783), c_Int_OBit1(c_Int_OPls))) = _1294785), class_Fields_Ofield(_1294783), class_Int_Onumber__ring(_1294783)], (49690 ^ _781215) ^ [_1787903, _1787905, _1787907] : [c_Equiv__Relations_Oequiv(_1787903, _1787905, _1787907), -(hAPP(hAPP(c_Relation_Orel__comp(_1787903, _1787903, _1787903), hAPP(c_Relation_Oconverse(_1787903, _1787903), _1787907)), _1787907) = _1787907)], (13794 ^ _781215) ^ [_1021510, _1021512, _1021514] : [class_Rings_Olinordered__idom(_1021510), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021510), c_Groups_Ozero__class_Ozero(_1021510)), _1021512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021510), c_Groups_Ozero__class_Ozero(_1021510)), _1021514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021510), _1021514), c_Groups_Oone__class_Oone(_1021510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1021510), _1021512), _1021514)), _1021512)))], (25634 ^ _781215) ^ [_1242538, _1242540, _1242542, _1242544] : [hBOOL(hAPP(hAPP(c_member(_1242538), _1242540), c_SetInterval_Oord_OatLeast(_1242538, _1242542, _1242544))), -(hBOOL(hAPP(hAPP(_1242542, _1242544), _1242540)))], (51306 ^ _781215) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (34178 ^ _781215) ^ [_1421114, _1421116, _1421118, _1421120, _1421122] : [class_Groups_Ocomm__monoid__mult(_1421114), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421116), _1421118)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421116), _1421120)), 34192 ^ _781215 : [(34195 ^ _781215) ^ [] : [hAPP(_1421122, 34191 ^ [_1421114, _1421116, _1421118, _1421120, _1421122]) = c_Groups_Oone__class_Oone(_1421114)], (34193 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1421116), 34191 ^ [_1421114, _1421116, _1421118, _1421120, _1421122]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421116, tc_HOL_Obool)), _1421118), _1421120))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1421116, _1421114), _1421122), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421116, tc_HOL_Obool)), _1421118), _1421120)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421114), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1421116, _1421114), _1421122), _1421118)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1421116, _1421114), _1421122), _1421120)))], (27072 ^ _781215) ^ [_1273232, _1273234, _1273236, _1273238] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1273232, _1273234), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1273236), _1273238))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1273232), _1273234) = _1273236)], (43948 ^ _781215) ^ [_1659083, _1659085] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1659083), tc_List_Olist(_1659083), c_List_Olistrel(_1659083, _1659085)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1659083)), c_List_Olist_ONil(_1659083)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1659083), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1659083)), c_List_Olist_ONil(_1659083)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1659083), tc_HOL_Obool))))], (18049 ^ _781215) ^ [_1103661, _1103663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103661)), hAPP(c_Nat_OSuc, _1103663))), -(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(_1103661))), 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)), _1103663)))))], (49678 ^ _781215) ^ [_1787532, _1787534, _1787536, _1787538] : [-(hAPP(c_Relation_Oconverse(_1787532, _1787534), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1787532, _1787534), tc_HOL_Obool)), _1787536), _1787538)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1787534, _1787532), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1787532, _1787534), _1787536)), hAPP(c_Relation_Oconverse(_1787532, _1787534), _1787538)))], (25392 ^ _781215) ^ [_1238707] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1238707) = c_Int_Opred(_1238707))], (35471 ^ _781215) ^ [_1447827, _1447829, _1447831] : [class_Orderings_Olinorder(_1447827), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447827), _1447829), _1447831)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1447827, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1447827, _1447829, _1447831)), hAPP(c_SetInterval_Oord__class_OatLeast(_1447827), _1447831)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1447827), _1447829))], (46738 ^ _781215) ^ [_1720961, _1720963, _1720965, _1720967] : [hBOOL(hAPP(_1720961, _1720963)), -(c_List_OdropWhile(_1720965, _1720961, hAPP(hAPP(c_List_Olist_OCons(_1720965), _1720963), _1720967)) = c_List_OdropWhile(_1720965, _1720961, _1720967))], (46105 ^ _781215) ^ [_1706427, _1706429] : [-(hAPP(c_List_Orev(_1706427), _1706429) = hAPP(c_List_Ofoldl(tc_List_Olist(_1706427), _1706427, hAPP(c_COMBC(_1706427, tc_List_Olist(_1706427), tc_List_Olist(_1706427)), c_List_Olist_OCons(_1706427)), c_List_Olist_ONil(_1706427)), _1706429))], (35451 ^ _781215) ^ [_1447410, _1447412, _1447414] : [class_Orderings_Oorder(_1447410), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447410, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1447410, _1447412, _1447414)), hAPP(c_SetInterval_Oord__class_OatLeast(_1447410), _1447414)) = c_Orderings_Obot__class_Obot(tc_fun(_1447410, tc_HOL_Obool)))], (33122 ^ _781215) ^ [_1396439, _1396441, _1396443, _1396445] : [class_Lattices_Olattice(_1396439), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396439), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1396439), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1396439), _1396441), _1396443)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1396439), _1396441), _1396445))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1396439), _1396441), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1396439), _1396443), _1396445)))))], (49016 ^ _781215) ^ [_1770412] : [-(c_Code__Numeral_OSuc__code__numeral(_1770412) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1770412))))], (44932 ^ _781215) ^ [_1682366, _1682368, _1682370, _1682372] : [44933 ^ _781215 : [(44934 ^ _781215) ^ [_1682463, _1682465] : [_1682366 = hAPP(hAPP(c_List_Olist_OCons(_1682368), _1682465), _1682463)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682368), tc_List_Olist(_1682368))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682368), tc_List_Olist(_1682368)), _1682370), hAPP(hAPP(c_List_Oappend(_1682368), _1682370), _1682366))), c_List_Olexord(_1682368, _1682372))))], (30121 ^ _781215) ^ [_1332167, _1332169, _1332171] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1332167, tc_HOL_Obool)), _1332169), hAPP(c_Set_OPow(_1332167), _1332171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332167, tc_HOL_Obool)), _1332169), _1332171)))], (7602 ^ _781215) ^ [_908916, _908918, _908920, _908922, _908924] : [hAPP(_908916, _908918) = _908920, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_908922, _908924), _908916), _908918), _908920) = _908916)], (10116 ^ _781215) ^ [_953362, _953364, _953366, _953368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953362, tc_HOL_Obool)), _953364), _953366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953362, tc_HOL_Obool)), _953366), _953368)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953362, tc_HOL_Obool)), _953366), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953362, tc_HOL_Obool)), _953368), _953364)) = _953364)], (3148 ^ _781215) ^ [_828577, _828579, _828581, _828583, _828585, _828587, _828589, _828591] : [-(c_Hilbert__Choice_OLeastM(_828591, _828587, _828583, _828579) = c_Hilbert__Choice_OLeastM(_828589, _828585, _828581, _828577)), _828591 = _828589, _828587 = _828585, _828583 = _828581, _828579 = _828577], (47956 ^ _781215) ^ [_1746814, _1746816] : [-(c_List_Oinsert(_1746814, _1746816, c_List_Olist_ONil(_1746814)) = hAPP(hAPP(c_List_Olist_OCons(_1746814), _1746816), c_List_Olist_ONil(_1746814)))], (9725 ^ _781215) ^ [_946350, _946352, _946354, _946356] : [class_Groups_Oordered__ab__semigroup__add(_946350), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946350), _946352), _946354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946350), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946350), _946352), _946356)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946350), _946354), _946356))))], (38622 ^ _781215) ^ [_1520132, _1520134, _1520136, _1520138] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1520132, _1520134)), hAPP(hAPP(c_Product__Type_OSigma(_1520132, _1520134), _1520136), hAPP(c_COMBK(tc_fun(_1520134, tc_HOL_Obool), _1520132), _1520138)))), -(_1520136 = c_Orderings_Obot__class_Obot(tc_fun(_1520132, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1520134), _1520138)))], (48719 ^ _781215) ^ [_1764960, _1764962, _1764964, _1764966, _1764968, _1764970, _1764972] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1764960, _1764962, _1764964, _1764966), _1764968), _1764970), _1764972) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1764962, _1764964, _1764966), _1764970), hAPP(_1764968, _1764972)))], (31636 ^ _781215) ^ [_1362945, _1362947] : [-(hAPP(c_Finite__Set_Ocard(_1362945), _1362947) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362945, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1362945), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1362947))], (22948 ^ _781215) ^ [_1195007, _1195009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195007), 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)), _1195009)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195007), _1195009)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37037 ^ _781215) ^ [_1481162, _1481164, _1481166, _1481168, _1481170] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481162, tc_HOL_Obool)), _1481164), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481166, tc_fun(_1481162, tc_HOL_Obool)), _1481168), _1481170)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481166, tc_fun(_1481162, tc_HOL_Obool)), _1481168), hAPP(hAPP(c_COMBB(tc_fun(_1481162, tc_HOL_Obool), tc_fun(_1481162, tc_HOL_Obool), _1481166), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481162, tc_HOL_Obool)), _1481164)), _1481170)))], (9621 ^ _781215) ^ [_944645, _944647, _944649] : [class_Orderings_Olinorder(_944645), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944645), _944647), _944649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944645), _944649), _944647)))], (50972 ^ _781215) ^ [_1817749, _1817751, _1817753] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1817749, _1817751), _1817753) = c_Lazy__Sequence_Oproduct(_1817749, _1817751, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1817749, _1817753), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1817751, _1817753))), class_Lazy__Sequence_Osmall__lazy(_1817749), class_Lazy__Sequence_Osmall__lazy(_1817751)], (15038 ^ _781215) ^ [_1045307, _1045309] : [class_Rings_Olinordered__idom(_1045307), 15041 ^ _781215 : [(15048 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045307), _1045309), c_Groups_Ozero__class_Ozero(_1045307))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045307), c_Groups_Osgn__class_Osgn(_1045307, _1045309)), c_Groups_Ozero__class_Ozero(_1045307))))], (15042 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045307), c_Groups_Osgn__class_Osgn(_1045307, _1045309)), c_Groups_Ozero__class_Ozero(_1045307))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045307), _1045309), c_Groups_Ozero__class_Ozero(_1045307))))]]], (15990 ^ _781215) ^ [_1063301, _1063303, _1063305, _1063307] : [16004 ^ _781215 : [(16007 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1063307, 16003 ^ [_1063301, _1063303, _1063305, _1063307])))], (16005 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1063301), 16003 ^ [_1063301, _1063303, _1063305, _1063307]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063301, tc_HOL_Obool)), _1063303), _1063305))))]], 15991 ^ _781215 : [(15998 ^ _781215) ^ [_1063510] : [hBOOL(hAPP(hAPP(c_member(_1063301), _1063510), _1063305)), hBOOL(hAPP(_1063307, _1063510))], (15992 ^ _781215) ^ [_1063414] : [hBOOL(hAPP(hAPP(c_member(_1063301), _1063414), _1063303)), hBOOL(hAPP(_1063307, _1063414))]]], (2542 ^ _781215) ^ [_818970, _818972, _818974, _818976] : [-(c_Nitpick_Onat__gcd(_818976, _818972) = c_Nitpick_Onat__gcd(_818974, _818970)), _818976 = _818974, _818972 = _818970], (47172 ^ _781215) ^ [_1730471, _1730473, _1730475] : [class_Enum_Oenum(_1730471), class_Enum_Oenum(_1730473), 47179 ^ _781215 : [(47186 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1730473), hAPP(hAPP(c_COMBB(tc_fun(_1730471, tc_HOL_Obool), tc_HOL_Obool, _1730473), c_Enum_Oenum__class_Oenum__ex(_1730471)), hAPP(hAPP(c_COMBB(tc_fun(_1730471, tc_prod(_1730473, _1730471)), tc_fun(_1730471, tc_HOL_Obool), _1730473), hAPP(c_COMBB(tc_prod(_1730473, _1730471), tc_HOL_Obool, _1730471), _1730475)), c_Product__Type_OPair(_1730473, _1730471))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1730473, _1730471)), _1730475)))], (47180 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1730473, _1730471)), _1730475)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1730473), hAPP(hAPP(c_COMBB(tc_fun(_1730471, tc_HOL_Obool), tc_HOL_Obool, _1730473), c_Enum_Oenum__class_Oenum__ex(_1730471)), hAPP(hAPP(c_COMBB(tc_fun(_1730471, tc_prod(_1730473, _1730471)), tc_fun(_1730471, tc_HOL_Obool), _1730473), hAPP(c_COMBB(tc_prod(_1730473, _1730471), tc_HOL_Obool, _1730471), _1730475)), c_Product__Type_OPair(_1730473, _1730471))))))]]], (18776 ^ _781215) ^ [_1117961] : [class_Orderings_Oord(_1117961), -(c_Orderings_Oord__class_Omax(_1117961) = c_Orderings_Oord_Omax(_1117961, c_Orderings_Oord__class_Oless__eq(_1117961)))], (27122 ^ _781215) ^ [_1274352, _1274354, _1274356] : [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), _1274352), _1274354))), -(hBOOL(hAPP(hAPP(_1274356, _1274352), _1274354))), 27129 ^ _781215 : [(27132 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1274356, 27127 ^ [_1274352, _1274354, _1274356]), 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)))), 27128 ^ [_1274352, _1274354, _1274356])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 27127 ^ [_1274352, _1274354, _1274356]), 27128 ^ [_1274352, _1274354, _1274356]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 27128 ^ [_1274352, _1274354, _1274356]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27142 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1274356, 27127 ^ [_1274352, _1274354, _1274356]), 27128 ^ [_1274352, _1274354, _1274356]))], (27130 ^ _781215) ^ [] : [-(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), 27127 ^ [_1274352, _1274354, _1274356]), 27128 ^ [_1274352, _1274354, _1274356]))))]]], (27169 ^ _781215) ^ [_1275374, _1275376, _1275378, _1275380, _1275382, _1275384] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1275374, _1275376), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1275378), _1275380))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1275374, _1275376), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1275382), _1275384))), -(_1275376 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1275380 = _1275384)], (10400 ^ _781215) ^ [_958567, _958569, _958571, _958573] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_958567, _958569)), c_Sum__Type_OPlus(_958567, _958569, _958571, _958573)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_958567), _958571)), hBOOL(hAPP(c_Finite__Set_Ofinite(_958569), _958573))], (13949 ^ _781215) ^ [_1024266, _1024268, _1024270] : [-(hBOOL(hAPP(_1024266, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1024268), _1024270)))), 13952 ^ _781215 : [(13955 ^ _781215) ^ [] : [hBOOL(hAPP(_1024266, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13953 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1024268), _1024270)))]], 13957 ^ _781215 : [(13960 ^ _781215) ^ [] : [hBOOL(hAPP(_1024266, 13956 ^ [_1024266, _1024268, _1024270]))], (13958 ^ _781215) ^ [] : [-(_1024268 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1024270), 13956 ^ [_1024266, _1024268, _1024270]))]]], (42569 ^ _781215) ^ [_1625935, _1625937, _1625939] : [class_Orderings_Olinorder(_1625935), hBOOL(hAPP(hAPP(c_member(_1625935), _1625937), hAPP(c_List_Oset(_1625935), _1625939))), -(c_List_Olinorder__class_Oinsort__insert__key(_1625935, _1625935, c_COMBI(_1625935), _1625937, _1625939) = _1625939)], (22210 ^ _781215) ^ [_1181900, _1181902] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181900), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181902), _1181900)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181902), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181902, _1181900)))], (44856 ^ _781215) ^ [_1680875, _1680877, _1680879] : [hBOOL(hAPP(c_List_Odistinct(_1680875), hAPP(c_List_Orotate(_1680875, _1680877), _1680879))), -(hBOOL(hAPP(c_List_Odistinct(_1680875), _1680879)))], (51428 ^ _781215) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (20741 ^ _781215) ^ [_1153249] : [class_Int_Onumber__ring(_1153249), -(c_Groups_Oone__class_Oone(_1153249) = hAPP(c_Int_Onumber__class_Onumber__of(_1153249), c_Int_OBit1(c_Int_OPls)))], (32984 ^ _781215) ^ [_1393016, _1393018, _1393020, _1393022] : [class_Lattices_Olattice(_1393016), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393016), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393016), _1393018), _1393020)), _1393022) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393016), _1393018), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393016), _1393020), _1393022)))], (46311 ^ _781215) ^ [_1710800, _1710802, _1710804] : [-(hAPP(c_List_Orotate(_1710800, _1710802), hAPP(c_List_Orev(_1710800), _1710804)) = hAPP(c_List_Orev(_1710800), hAPP(c_List_Orotate(_1710800, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710800)), _1710804)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1710802, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710800)), _1710804)))), _1710804)))], (19128 ^ _781215) ^ [_1124341, _1124343, _1124345, _1124347] : [class_Orderings_Olinorder(_1124341), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124341), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1124341), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1124341), _1124343), _1124345)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1124341), _1124343), _1124347))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1124341), _1124343), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1124341), _1124345), _1124347)))))], (14554 ^ _781215) ^ [_1035841, _1035843, _1035845, _1035847, _1035849] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1035841, _1035843, _1035845)), _1035847), _1035849)), 14559 ^ _781215 : [(14562 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1035843), _1035847), _1035849)))], (14560 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1035841, _1035847)))]], 14563 ^ _781215 : [(14566 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1035845), _1035847), _1035849)))], (14564 ^ _781215) ^ [] : [hBOOL(hAPP(_1035841, _1035847))]]], (43804 ^ _781215) ^ [_1655945, _1655947] : [c_Orderings_Obot__class_Obot(tc_fun(_1655945, tc_HOL_Obool)) = hAPP(c_List_Oset(_1655945), _1655947), -(_1655947 = c_List_Olist_ONil(_1655945))], (21674 ^ _781215) ^ [_1170047, _1170049] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1170047)), c_Int_OBit0(_1170049)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1170047), _1170049)))], (30299 ^ _781215) ^ [_1335375, _1335377, _1335379] : [class_Groups_Oordered__ab__group__add(_1335375), -(hAPP(c_Set_Oimage(_1335375, _1335375, c_Groups_Ouminus__class_Ouminus(_1335375)), c_SetInterval_Oord__class_OatLeastAtMost(_1335375, _1335377, _1335379)) = c_SetInterval_Oord__class_OatLeastAtMost(_1335375, hAPP(c_Groups_Ouminus__class_Ouminus(_1335375), _1335379), hAPP(c_Groups_Ouminus__class_Ouminus(_1335375), _1335377)))], (14918 ^ _781215) ^ [_1042787, _1042789, _1042791, _1042793, _1042795] : [c_Com_Ocom_OSemi(_1042787, _1042789) = c_Com_Ocom_OCond(_1042791, _1042793, _1042795)], (46777 ^ _781215) ^ [_1721694, _1721696, _1721698, _1721700, _1721702] : [-(c_List_OdropWhile(_1721694, _1721696, hAPP(hAPP(c_List_Omap(_1721698, _1721694), _1721700), _1721702)) = hAPP(hAPP(c_List_Omap(_1721698, _1721694), _1721700), c_List_OdropWhile(_1721698, hAPP(c_Fun_Ocomp(_1721694, tc_HOL_Obool, _1721698, _1721696), _1721700), _1721702)))], (15536 ^ _781215) ^ [_1053697, _1053699, _1053701, _1053703] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1053697, tc_Option_Ooption(_1053699)), hAPP(c_COMBK(tc_Option_Ooption(_1053699), _1053697), c_Option_Ooption_ONone(_1053699))), _1053701), c_Option_Ooption_ONone(_1053699)), _1053703) = c_Option_Ooption_ONone(_1053699))], (39336 ^ _781215) ^ [_1538634, _1538636, _1538638, _1538640, _1538642, _1538644] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538634), _1538636)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538638), _1538640)), 39346 ^ _781215 : [(39349 ^ _781215) ^ [] : [hAPP(c_Finite__Set_Ocard(_1538634), hAPP(c_Set_OCollect(_1538634), hAPP(hAPP(c_COMBS(_1538634, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538634), c_fconj), hAPP(hAPP(c_COMBC(_1538634, tc_fun(_1538634, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538634)), _1538636))), hAPP(hAPP(c_COMBC(_1538634, _1538638, tc_HOL_Obool), _1538642), 39345 ^ [_1538634, _1538636, _1538638, _1538640, _1538642, _1538644])))) = _1538644], (39347 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538638), 39345 ^ [_1538634, _1538636, _1538638, _1538640, _1538642, _1538644]), _1538640)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538634, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1538638, tc_HOL_Obool), tc_Nat_Onat, _1538634), c_Finite__Set_Ocard(_1538638)), hAPP(hAPP(c_COMBB(tc_fun(_1538638, tc_HOL_Obool), tc_fun(_1538638, tc_HOL_Obool), _1538634), c_Set_OCollect(_1538638)), hAPP(hAPP(c_COMBB(tc_fun(_1538638, tc_HOL_Obool), tc_fun(_1538638, tc_HOL_Obool), _1538634), hAPP(c_COMBS(_1538638, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538638), c_fconj), hAPP(hAPP(c_COMBC(_1538638, tc_fun(_1538638, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538638)), _1538640)))), _1538642)))), _1538636) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1538644), hAPP(c_Finite__Set_Ocard(_1538638), _1538640)))], (6509 ^ _781215) ^ [_887308, _887310, _887312, _887314] : [hBOOL(hAPP(hAPP(c_member(_887308), _887310), _887312)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887308, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_887308), _887310), _887314)), _887312) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887308, tc_HOL_Obool)), _887314), _887312))], (6156 ^ _781215) ^ [_880216, _880218, _880220, _880222, _880224, _880226, _880228] : [hAPP(_880216, _880218) = hAPP(c_Option_Ooption_OSome(_880220), _880222), -(c_Map_Omap__comp(_880220, _880224, _880226, _880228, _880216, _880218) = hAPP(_880228, _880222))], (17737 ^ _781215) ^ [_1098150, _1098152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1098150)), hAPP(c_Int_Onat, _1098152))), 17740 ^ _781215 : [(17743 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098150), _1098152)))], (17741 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1098152)))]]], (33086 ^ _781215) ^ [_1395141, _1395143, _1395145, _1395147] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1395141, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395141, tc_HOL_Obool)), _1395143), _1395145)), _1395147) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395141, tc_HOL_Obool)), _1395143), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1395141, tc_HOL_Obool)), _1395145), _1395147)))], (22789 ^ _781215) ^ [_1192543] : [22791 ^ _781215 : [(22794 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22790 ^ [_1192543]))], (22792 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 22790 ^ [_1192543]), _1192543)))]], -(c_Nat__Transfer_Onat__set(_1192543))], (21013 ^ _781215) ^ [_1157626] : [-(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, _1157626)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (46273 ^ _781215) ^ [_1709976, _1709978, _1709980] : [-(hAPP(c_List_Ofilter(_1709976, _1709978), c_List_Oconcat(_1709976, _1709980)) = c_List_Oconcat(_1709976, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1709976), tc_List_Olist(_1709976)), c_List_Ofilter(_1709976, _1709978)), _1709980)))], (25308 ^ _781215) ^ [_1237473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1237473))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1237473)))], (50404 ^ _781215) ^ [_1806192] : [-(c_Nitpick_Odenom(_1806192) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1806192, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1806192)))], (22798 ^ _781215) ^ [_1192691, _1192693] : [c_Nat__Transfer_Onat__set(_1192691), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1192693), _1192691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192693)))], (24738 ^ _781215) ^ [_1227640, _1227642, _1227644, _1227646] : [class_Groups_Ocomm__monoid__mult(_1227640), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1227640), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227640), _1227642), _1227644)), _1227646) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227640), hAPP(hAPP(c_Power_Opower__class_Opower(_1227640), _1227642), _1227646)), hAPP(hAPP(c_Power_Opower__class_Opower(_1227640), _1227644), _1227646)))], (10836 ^ _781215) ^ [_967008, _967010, _967012, _967014, _967016, _967018] : [-(c_Map_Omap__add(_967008, _967010, _967012, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_967008, tc_Option_Ooption(_967010)), _967014), _967016), hAPP(c_Option_Ooption_OSome(_967010), _967018))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_967008, tc_Option_Ooption(_967010)), c_Map_Omap__add(_967008, _967010, _967012, _967014)), _967016), hAPP(c_Option_Ooption_OSome(_967010), _967018)))], (19298 ^ _781215) ^ [_1127479, _1127481, _1127483] : [class_Orderings_Olinorder(_1127479), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127479), _1127481)), -(_1127481 = c_Orderings_Obot__class_Obot(tc_fun(_1127479, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127479), _1127483)), -(_1127483 = c_Orderings_Obot__class_Obot(tc_fun(_1127479, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1127479, c_Orderings_Oord__class_Omin(_1127479), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1127479, tc_HOL_Obool)), _1127481), _1127483)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1127479), c_Big__Operators_Olattice_OInf__fin(_1127479, c_Orderings_Oord__class_Omin(_1127479), _1127481)), c_Big__Operators_Olattice_OInf__fin(_1127479, c_Orderings_Oord__class_Omin(_1127479), _1127483)))], (33240 ^ _781215) ^ [_1399256, _1399258] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1399256), _1399258) = 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)), _1399256)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1399258))))], (11894 ^ _781215) ^ [_988118] : [-(_988118 = 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)), _988118)))], (23775 ^ _781215) ^ [_1209858, _1209860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209858)), -(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), _1209858), _1209860))))], (11874 ^ _781215) ^ [_987883] : [-(_987883 = 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)), _987883)))], (15000 ^ _781215) ^ [_1044404, _1044406, _1044408, _1044410] : [class_Int_Onumber__ring(_1044404), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044404), hAPP(c_Int_Onumber__class_Onumber__of(_1044404), _1044406)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044404), hAPP(c_Int_Onumber__class_Onumber__of(_1044404), _1044408)), _1044410)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044404), hAPP(c_Int_Onumber__class_Onumber__of(_1044404), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1044406), _1044408))), _1044410))], (6098 ^ _781215) ^ [_879195, _879197] : [c_Com_Ocom_OSemi(_879195, _879197) = c_Com_Ocom_OSKIP], (41429 ^ _781215) ^ [_1595575, _1595577, _1595579, _1595581, _1595583] : [class_Groups_Ocomm__monoid__add(_1595575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595577), _1595579)), c_Fun_Oinj__on(_1595577, _1595577, _1595581, _1595579), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1595577, _1595575), _1595583), hAPP(c_Set_Oimage(_1595577, _1595577, _1595581), _1595579)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1595577, _1595575), hAPP(c_Fun_Ocomp(_1595577, _1595575, _1595577, _1595583), _1595581)), _1595579))], (32578 ^ _781215) ^ [_1384542, _1384544, _1384546, _1384548] : [hBOOL(hAPP(hAPP(c_member(_1384542), _1384544), _1384546)), hBOOL(hAPP(hAPP(c_member(_1384542), _1384544), _1384548)), -(hBOOL(hAPP(hAPP(c_member(_1384542), _1384544), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384542, tc_HOL_Obool)), _1384546), _1384548))))], (34936 ^ _781215) ^ [_1436123, _1436125, _1436127, _1436129] : [class_Groups_Ocomm__monoid__mult(_1436123), 34939 ^ _781215 : [(34946 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1436125), _1436127))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1436125, _1436123), _1436129), _1436127) = c_Groups_Oone__class_Oone(_1436123))], (34940 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1436125), _1436127)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1436125, _1436123), _1436129), _1436127) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1436123, _1436125, c_Groups_Otimes__class_Otimes(_1436123)), _1436129), c_Groups_Oone__class_Oone(_1436123)), _1436127))]]], (22108 ^ _781215) ^ [_1179659, _1179661, _1179663, _1179665, _1179667] : [-(_1179659 = c_Orderings_Obot__class_Obot(tc_fun(_1179661, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179661, tc_fun(_1179663, tc_HOL_Obool)), _1179659), hAPP(hAPP(c_COMBB(tc_fun(_1179663, tc_HOL_Obool), tc_fun(_1179663, tc_HOL_Obool), _1179661), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1179663, tc_HOL_Obool)), _1179665)), _1179667)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1179663, tc_HOL_Obool)), _1179665), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179661, tc_fun(_1179663, tc_HOL_Obool)), _1179659), _1179667)))], (23559 ^ _781215) ^ [_1205563] : [23561 ^ _781215 : [(23564 ^ _781215) ^ [_1205673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 23560 ^ [_1205563, _1205673]), _1205673))], (23562 ^ _781215) ^ [_1205639] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 23560 ^ [_1205563, _1205639]), _1205563)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1205563)))], (48427 ^ _781215) ^ [_1759059, _1759061, _1759063, _1759065] : [class_Orderings_Olinorder(_1759059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1759059), _1759061)), 48437 ^ _781215 : [(48440 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759059), 48436 ^ [_1759059, _1759061, _1759063, _1759065]), _1759063))], (48438 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759059), 48436 ^ [_1759059, _1759061, _1759063, _1759065]), _1759061)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759059), hAPP(hAPP(c_Finite__Set_Ofold(_1759059, _1759059, c_Orderings_Oord__class_Omax(_1759059)), _1759065), _1759061)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1759059), _1759063), _1759065))))], (46620 ^ _781215) ^ [_1718625, _1718627] : [_1718627 = c_List_Olist_ONil(_1718625), -(c_List_Oremdups(_1718625, _1718627) = c_List_Olist_ONil(_1718625))], (46640 ^ _781215) ^ [_1718958, _1718960] : [c_List_Oremdups(_1718958, _1718960) = _1718960, -(hBOOL(hAPP(c_List_Odistinct(_1718958), _1718960)))], (338 ^ _781215) ^ [_786362, _786364, _786366, _786368, _786370, _786372, _786374, _786376, _786378, _786380, _786382, _786384] : [-(c_Finite__Set_Ofolding__image__simple(_786382, _786378, _786374, _786370, _786366, _786362)), c_Finite__Set_Ofolding__image__simple(_786384, _786380, _786376, _786372, _786368, _786364), _786384 = _786382, _786380 = _786378, _786376 = _786374, _786372 = _786370, _786368 = _786366, _786364 = _786362], (39381 ^ _781215) ^ [_1540598, _1540600] : [-(hAPP(c_Set_OPow(_1540598), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1540598, tc_HOL_Obool)), _1540600)) = hAPP(c_Set_OCollect(tc_fun(_1540598, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1540598, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1540598, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1540598, tc_HOL_Obool), tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1540598, tc_HOL_Obool)), c_COMBS(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1540598, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1540598, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1540598, tc_HOL_Obool), tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_fun(_1540598, tc_HOL_Obool)), tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_fun(_1540598, tc_HOL_Obool)), tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1540598, tc_HOL_Obool)), c_COMBB(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1540598, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1540598, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1540598, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1540598, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1540598, tc_HOL_Obool)), _1540600)), c_Set_OPow(_1540598))))))], (11728 ^ _781215) ^ [_985688, _985690] : [class_Rings_Ocomm__semiring__1(_985688), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985688), _985690), c_Groups_Ozero__class_Ozero(_985688)) = c_Groups_Ozero__class_Ozero(_985688))], (31306 ^ _781215) ^ [] : [-(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)))], (10902 ^ _781215) ^ [_968681, _968683, _968685, _968687, _968689] : [class_Groups_Oab__semigroup__mult(_968681), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_968681, _968681, c_Groups_Otimes__class_Otimes(_968681), _968683, _968685), _968687)), -(hBOOL(hAPP(hAPP(c_member(_968681), _968683), _968685))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_968681, _968681, c_Groups_Otimes__class_Otimes(_968681), _968689, hAPP(hAPP(c_Set_Oinsert(_968681), _968683), _968685)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968681), _968689), _968687))))], (2 ^ _781215) ^ [_781242] : [-(_781242 = _781242)], (21926 ^ _781215) ^ [_1175512, _1175514, _1175516, _1175518, _1175520, _1175522] : [class_Complete__Lattice_Ocomplete__lattice(_1175512), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175514, tc_fun(_1175516, _1175512)), _1175518), _1175520), _1175522) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175514, _1175512), _1175518), hAPP(hAPP(c_COMBC(_1175514, _1175516, _1175512), _1175520), _1175522)))], (18870 ^ _781215) ^ [_1119526, _1119528, _1119530] : [class_Orderings_Olinorder(_1119526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119526), _1119528), _1119530)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1119526), _1119530), _1119528) = _1119530)], (11578 ^ _781215) ^ [_983328, _983330, _983332, _983334, _983336] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983328, tc_HOL_Obool)), _983330), hAPP(c_Set_Oimage(_983332, _983328, _983334), _983336)))), 11579 ^ _781215 : [(11580 ^ _781215) ^ [_983408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983332, tc_HOL_Obool)), _983408), _983336)), _983330 = hAPP(c_Set_Oimage(_983332, _983328, _983334), _983408)]]], (51252 ^ _781215) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (1268 ^ _781215) ^ [_800035, _800037] : [-(class_Rings_Oring__1(_800035)), _800037 = _800035, class_Rings_Oring__1(_800037)], (49686 ^ _781215) ^ [_1787813, _1787815, _1787817] : [-(hAPP(c_Relation_ODomain(_1787813, _1787815), hAPP(c_Relation_Oconverse(_1787815, _1787813), _1787817)) = hAPP(c_Relation_ORange(_1787815, _1787813), _1787817))], (44174 ^ _781215) ^ [_1664382, _1664384, _1664386] : [hAPP(hAPP(c_List_Oappend(_1664382), _1664384), _1664386) = _1664386, -(_1664384 = c_List_Olist_ONil(_1664382))], (7204 ^ _781215) ^ [_902023, _902025, _902027, _902029, _902031] : [hBOOL(hAPP(hAPP(c_member(_902023), _902025), _902027)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_902023, tc_Option_Ooption(_902029)), c_Map_Orestrict__map(_902023, _902029, _902031, _902027)), _902025), c_Option_Ooption_ONone(_902029)) = c_Map_Orestrict__map(_902023, _902029, _902031, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902023, tc_HOL_Obool)), _902027), hAPP(hAPP(c_Set_Oinsert(_902023), _902025), c_Orderings_Obot__class_Obot(tc_fun(_902023, tc_HOL_Obool))))))], (39606 ^ _781215) ^ [_1549479] : [-(c_Int_Oint__ge__less__than(_1549479) = 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), _1549479)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (26904 ^ _781215) ^ [_1270168, _1270170, _1270172, _1270174, _1270176, _1270178] : [-(hAPP(hAPP(c_Product__Type_OPair(_1270168, _1270170), _1270172), _1270174) = hAPP(hAPP(c_Product__Type_OPair(_1270168, _1270170), _1270176), _1270178)), _1270172 = _1270176, _1270174 = _1270178], (20424 ^ _781215) ^ [_1147735, _1147737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147735)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147737))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147735), _1147737)))], (41383 ^ _781215) ^ [_1594488, _1594490, _1594492, _1594494, _1594496, _1594498] : [-(hAPP(hAPP(c_List_Omap(_1594488, _1594490), _1594492), hAPP(hAPP(c_List_Omap(_1594494, _1594488), _1594496), _1594498)) = hAPP(hAPP(c_List_Omap(_1594494, _1594490), hAPP(c_Fun_Ocomp(_1594488, _1594490, _1594494, _1594492), _1594496)), _1594498))], (8225 ^ _781215) ^ [_920039, _920041, _920043] : [class_Rings_Olinordered__idom(_920039), -(_920041 = _920043), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920039), _920041), _920043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920039), _920043), _920041)))], (49377 ^ _781215) ^ [_1779669, _1779671] : [-(c_Transitive__Closure_Ortrancl(_1779669, _1779671) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1779669, _1779669), tc_HOL_Obool)), c_Relation_OId(_1779669)), hAPP(hAPP(c_Relation_Orel__comp(_1779669, _1779669, _1779669), c_Transitive__Closure_Ortrancl(_1779669, _1779671)), _1779671)))], (40827 ^ _781215) ^ [_1581347, _1581349, _1581351, _1581353] : [-(c_Com_Ocom_OWhile(_1581347, _1581349) = c_Com_Ocom_OWhile(_1581351, _1581353)), _1581347 = _1581351, _1581349 = _1581353], (3860 ^ _781215) ^ [_839727, _839729, _839731, _839733, _839735, _839737, _839739, _839741] : [-(c_List_Ofoldl(_839741, _839737, _839733, _839729) = c_List_Ofoldl(_839739, _839735, _839731, _839727)), _839741 = _839739, _839737 = _839735, _839733 = _839731, _839729 = _839727], (4156 ^ _781215) ^ [_844305, _844307, _844309, _844311] : [-(c_Random_Oinc__shift(_844311, _844307) = c_Random_Oinc__shift(_844309, _844305)), _844311 = _844309, _844307 = _844305], (11598 ^ _781215) ^ [_983744, _983746] : [class_Groups_Ocomm__monoid__add(_983744), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983744), c_Groups_Ozero__class_Ozero(_983744)), _983746) = _983746)], (9929 ^ _781215) ^ [_950111, _950113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950111), _950113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _950111)), hAPP(c_Nat_OSuc, _950113))))], (48668 ^ _781215) ^ [_1763910, _1763912, _1763914, _1763916] : [48669 ^ _781215 : [(48672 ^ _781215) ^ [] : [c_List_Olist__ex(_1763910, _1763912, _1763916)], (48670 ^ _781215) ^ [] : [c_List_Olist__ex(_1763910, _1763912, _1763914)]], -(c_List_Olist__ex(_1763910, _1763912, hAPP(hAPP(c_List_Oappend(_1763910), _1763914), _1763916)))], (15098 ^ _781215) ^ [_1046286, _1046288, _1046290] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_1046286, _1046288, _1046290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1046290)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (35755 ^ _781215) ^ [_1453598] : [class_Groups_Oordered__ab__group__add__abs(_1453598), -(hAPP(c_Groups_Oabs__class_Oabs(_1453598), c_Groups_Ozero__class_Ozero(_1453598)) = c_Groups_Ozero__class_Ozero(_1453598))], (37151 ^ _781215) ^ [_1484355, _1484357, _1484359, _1484361, _1484363] : [-(_1484355 = c_Orderings_Obot__class_Obot(tc_fun(_1484357, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484359, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484357, tc_fun(_1484359, tc_HOL_Obool)), _1484355), _1484361)), _1484363) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484357, tc_fun(_1484359, tc_HOL_Obool)), _1484355), hAPP(hAPP(c_COMBC(_1484357, tc_fun(_1484359, tc_HOL_Obool), tc_fun(_1484359, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484359, tc_HOL_Obool), tc_fun(tc_fun(_1484359, tc_HOL_Obool), tc_fun(_1484359, tc_HOL_Obool)), _1484357), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484359, tc_HOL_Obool))), _1484361)), _1484363)))], (39290 ^ _781215) ^ [_1537256, _1537258, _1537260, _1537262] : [-(hAPP(c_Relation_OImage(_1537256, _1537258, _1537260), hAPP(hAPP(c_Set_Oinsert(_1537256), _1537262), c_Orderings_Obot__class_Obot(tc_fun(_1537256, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1537258), hAPP(hAPP(c_COMBC(_1537258, tc_fun(tc_prod(_1537256, _1537258), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1537256, _1537258), tc_fun(tc_fun(tc_prod(_1537256, _1537258), tc_HOL_Obool), tc_HOL_Obool), _1537258), c_member(tc_prod(_1537256, _1537258))), hAPP(c_Product__Type_OPair(_1537256, _1537258), _1537262))), _1537260)))], (45492 ^ _781215) ^ [_1694614, _1694616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1694614), _1694616)), -(c_List_Oupt(_1694614, _1694616) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1694614), c_List_Oupt(hAPP(c_Nat_OSuc, _1694614), _1694616)))], (15773 ^ _781215) ^ [_1058654, _1058656, _1058658, _1058660, _1058662, _1058664] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1058654), _1058656)), _1058658) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1058660), _1058662)), _1058664), 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), _1058660), _1058662)), _1058664))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1058664), _1058660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1058660), _1058654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1058656), _1058662)))], (6503 ^ _781215) ^ [_887219, _887221, _887223] : [c_Hoare__Mirabelle_Otriple__valid(_887219, hAPP(c_Nat_OSuc, _887221), _887223), -(c_Hoare__Mirabelle_Otriple__valid(_887219, _887221, _887223))], (33276 ^ _781215) ^ [_1400139, _1400141, _1400143, _1400145, _1400147, _1400149, _1400151, _1400153] : [c_Equiv__Relations_Oequiv(_1400139, _1400141, _1400143), c_Equiv__Relations_Ocongruent2(_1400139, _1400145, _1400147, _1400143, _1400149, _1400151), hBOOL(hAPP(hAPP(c_member(_1400139), _1400153), _1400141)), -(c_Equiv__Relations_Ocongruent(_1400145, _1400147, _1400149, hAPP(_1400151, _1400153)))], (41031 ^ _781215) ^ [] : [c_Com_OWT__bodies, 41034 ^ _781215 : [(41035 ^ _781215) ^ [_1586295] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1586295), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), _1586295)))]]], (25106 ^ _781215) ^ [_1234409, _1234411, _1234413] : [class_Rings_Olinordered__semidom(_1234409), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234409), c_Groups_Ozero__class_Ozero(_1234409)), _1234411)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234409), _1234411), c_Groups_Oone__class_Oone(_1234409))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234409), hAPP(hAPP(c_Power_Opower__class_Opower(_1234409), _1234411), hAPP(c_Nat_OSuc, _1234413))), c_Groups_Oone__class_Oone(_1234409))))], (42305 ^ _781215) ^ [_1618207, _1618209, _1618211, _1618213] : [c_List_Olistrelp(_1618207, hAPP(hAPP(c_COMBC(_1618207, tc_fun(tc_prod(_1618207, _1618207), tc_HOL_Obool), tc_fun(_1618207, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1618207, tc_fun(tc_fun(tc_prod(_1618207, _1618207), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1618207, _1618207), tc_HOL_Obool), tc_fun(_1618207, tc_HOL_Obool)), _1618207), c_COMBC(_1618207, tc_fun(tc_prod(_1618207, _1618207), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1618207, tc_prod(_1618207, _1618207)), tc_fun(_1618207, tc_fun(tc_fun(tc_prod(_1618207, _1618207), tc_HOL_Obool), tc_HOL_Obool)), _1618207), hAPP(c_COMBB(tc_prod(_1618207, _1618207), tc_fun(tc_fun(tc_prod(_1618207, _1618207), tc_HOL_Obool), tc_HOL_Obool), _1618207), c_member(tc_prod(_1618207, _1618207)))), c_Product__Type_OPair(_1618207, _1618207)))), _1618209), _1618211, _1618213), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618207), tc_List_Olist(_1618207))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618207), tc_List_Olist(_1618207)), _1618211), _1618213)), c_List_Olistrel(_1618207, _1618209))))], (6796 ^ _781215) ^ [_892961, _892963, _892965] : [hBOOL(hAPP(hAPP(c_member(_892961), _892963), hAPP(hAPP(c_Set_Oinsert(_892961), _892965), c_Orderings_Obot__class_Obot(tc_fun(_892961, tc_HOL_Obool))))), -(_892963 = _892965)], (49401 ^ _781215) ^ [_1780230] : [-(c_Relation_Orefl__on(_1780230, c_Orderings_Otop__class_Otop(tc_fun(_1780230, tc_HOL_Obool)), c_Relation_OId(_1780230)))], (11740 ^ _781215) ^ [_985882, _985884] : [class_Groups_Ogroup__add(_985882), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_985882), _985884), _985884) = c_Groups_Ozero__class_Ozero(_985882))], (14642 ^ _781215) ^ [_1037326, _1037328, _1037330] : [class_Int_Onumber__ring(_1037326), class_Int_Oring__char__0(_1037326), 14649 ^ _781215 : [(14656 ^ _781215) ^ [] : [_1037328 = _1037330, -(hAPP(c_Int_Onumber__class_Onumber__of(_1037326), _1037328) = hAPP(c_Int_Onumber__class_Onumber__of(_1037326), _1037330))], (14650 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1037326), _1037328) = hAPP(c_Int_Onumber__class_Onumber__of(_1037326), _1037330), -(_1037328 = _1037330)]]], (50910 ^ _781215) ^ [_1816003] : [-(c_Lazy__Sequence_Oyieldn(_1816003) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1816003), _1816003, c_Lazy__Sequence_Oyield(_1816003)))], (29900 ^ _781215) ^ [_1326419] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1326419)), -(_1326419 = 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))), _1326419)), c_FunDef_Omax__strict)))], (51370 ^ _781215) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (2098 ^ _781215) ^ [_811910, _811912, _811914, _811916] : [-(c_Orderings_Oord_Omin(_811916, _811912) = c_Orderings_Oord_Omin(_811914, _811910)), _811916 = _811914, _811912 = _811910], (41379 ^ _781215) ^ [_1594346, _1594348, _1594350, _1594352, _1594354] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1594346), tc_List_Olist(_1594348), tc_List_Olist(_1594350), hAPP(c_List_Omap(_1594346, _1594348), _1594352)), hAPP(c_List_Omap(_1594350, _1594346), _1594354)) = hAPP(c_List_Omap(_1594350, _1594348), hAPP(c_Fun_Ocomp(_1594346, _1594348, _1594350, _1594352), _1594354)))], (50916 ^ _781215) ^ [_1816169, _1816171, _1816173, _1816175, _1816177] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1816169, _1816171, _1816173) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1816169, _1816175, _1816177), 50919 ^ _781215 : [(50922 ^ _781215) ^ [] : [-(_1816173 = _1816177)], (50920 ^ _781215) ^ [] : [-(_1816171 = _1816175)]]], (45025 ^ _781215) ^ [_1684406, _1684408] : [class_Complete__Lattice_Ocomplete__lattice(_1684406), -(c_Complete__Lattice_OInf__class_OInf(_1684406, hAPP(c_List_Oset(_1684406), _1684408)) = hAPP(c_List_Ofoldl(_1684406, _1684406, c_Lattices_Osemilattice__inf__class_Oinf(_1684406), c_Orderings_Otop__class_Otop(_1684406)), _1684408))], (35699 ^ _781215) ^ [_1452467, _1452469, _1452471] : [class_Fields_Olinordered__field__inverse__zero(_1452467), -(hAPP(c_Groups_Oabs__class_Oabs(_1452467), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1452467), _1452469), _1452471)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1452467), hAPP(c_Groups_Oabs__class_Oabs(_1452467), _1452469)), hAPP(c_Groups_Oabs__class_Oabs(_1452467), _1452471)))], (46361 ^ _781215) ^ [_1712644, _1712646, _1712648, _1712650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712644), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712646)), _1712648))), -(hAPP(c_List_Orev(_1712646), hAPP(hAPP(c_List_Olist__update(_1712646, _1712648), _1712644), _1712650)) = hAPP(hAPP(c_List_Olist__update(_1712646, hAPP(c_List_Orev(_1712646), _1712648)), 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(_1712646)), _1712648)), _1712644)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1712650))], (50848 ^ _781215) ^ [_1814488, _1814490] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1814488)), c_Int_OBit1(_1814490))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1814488), _1814490)))], (42957 ^ _781215) ^ [_1635912, _1635914, _1635916] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635912)), hAPP(hAPP(c_List_Otake(_1635912), _1635914), _1635916)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635912)), _1635916)), _1635914))], (1916 ^ _781215) ^ [_808933, _808935, _808937, _808939, _808941, _808943, _808945, _808947, _808949, _808951] : [-(c_Option_Ooption_Ooption__rec(_808951, _808947, _808943, _808939, _808935) = c_Option_Ooption_Ooption__rec(_808949, _808945, _808941, _808937, _808933)), _808951 = _808949, _808947 = _808945, _808943 = _808941, _808939 = _808937, _808935 = _808933], (41311 ^ _781215) ^ [_1592792, _1592794, _1592796, _1592798, _1592800, _1592802, _1592804] : [-(hAPP(c_Fun_Ocomp(_1592792, _1592794, _1592796, _1592798), hAPP(c_Fun_Ocomp(_1592800, _1592792, _1592796, _1592802), _1592804)) = hAPP(c_Fun_Ocomp(_1592800, _1592794, _1592796, hAPP(c_Fun_Ocomp(_1592792, _1592794, _1592800, _1592798), _1592802)), _1592804))], (986 ^ _781215) ^ [_796326, _796328, _796330, _796332, _796334, _796336] : [-(c_List_Olist__all(_796334, _796330, _796326)), c_List_Olist__all(_796336, _796332, _796328), _796336 = _796334, _796332 = _796330, _796328 = _796326], (27876 ^ _781215) ^ [_1289475, _1289477] : [class_Rings_Odivision__ring__inverse__zero(_1289475), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289475), _1289477), c_Groups_Ozero__class_Ozero(_1289475)) = c_Groups_Ozero__class_Ozero(_1289475))], (3432 ^ _781215) ^ [_833071, _833073, _833075, _833077, _833079, _833081] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_833081, _833077, _833073) = c_SetInterval_Oord__class_OgreaterThanLessThan(_833079, _833075, _833071)), _833081 = _833079, _833077 = _833075, _833073 = _833071], (15879 ^ _781215) ^ [_1060602, _1060604] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), _1060602), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), _1060604)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1060604)), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), _1060604)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _1060602, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), _1060604)))], (50896 ^ _781215) ^ [_1815404] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1815404), _1815404)))], (20229 ^ _781215) ^ [_1144281, _1144283, _1144285, _1144287, _1144289, _1144291] : [hBOOL(hAPP(hAPP(c_member(_1144281), _1144283), _1144285)), hBOOL(hAPP(hAPP(_1144287, _1144283), _1144289)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1144281, tc_fun(_1144291, tc_HOL_Obool)), _1144285), _1144287), _1144289)))], (22448 ^ _781215) ^ [_1186731, _1186733, _1186735] : [class_Divides_Osemiring__div(_1186731), -(c_Divides_Odiv__class_Omod(_1186731, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186731), _1186733), _1186735), _1186735) = c_Groups_Ozero__class_Ozero(_1186731))], (25990 ^ _781215) ^ [_1252641, _1252643, _1252645, _1252647] : [class_Groups_Ocomm__monoid__mult(_1252641), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1252643), _1252645))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1252643, _1252641), _1252647), _1252645) = c_Groups_Oone__class_Oone(_1252641))], (43487 ^ _781215) ^ [_1649146, _1649148] : [43488 ^ _781215 : [(43489 ^ _781215) ^ [_1649192] : [hBOOL(hAPP(_1649146, _1649192))]], -(hBOOL(hAPP(_1649146, c_Hilbert__Choice_OEps(_1649148, _1649146))))], (16431 ^ _781215) ^ [_1071836, _1071838, _1071840, _1071842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1071836, tc_HOL_Obool)), _1071838), _1071840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1071836, tc_HOL_Obool)), _1071842), _1071840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1071836, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071836, tc_HOL_Obool)), _1071838), _1071842)), _1071840)))], (42547 ^ _781215) ^ [_1625395, _1625397, _1625399, _1625401, _1625403, _1625405] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625395), tc_List_Olist(_1625395))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625395), tc_List_Olist(_1625395)), hAPP(hAPP(c_List_Olist_OCons(_1625395), _1625397), _1625399)), hAPP(hAPP(c_List_Olist_OCons(_1625395), _1625401), _1625403))), c_List_Olexord(_1625395, _1625405)))), 42548 ^ _781215 : [(42551 ^ _781215) ^ [] : [_1625397 = _1625401, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625395), tc_List_Olist(_1625395))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625395), tc_List_Olist(_1625395)), _1625399), _1625403)), c_List_Olexord(_1625395, _1625405)))], (42549 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625395, _1625395)), hAPP(hAPP(c_Product__Type_OPair(_1625395, _1625395), _1625397), _1625401)), _1625405))]]], (43826 ^ _781215) ^ [_1656300, _1656302] : [-(_1656300 = c_List_Olist_ONil(_1656302)), hBOOL(hAPP(c_List_Odistinct(_1656302), _1656300)), -(hBOOL(hAPP(c_List_Odistinct(_1656302), c_List_Obutlast(_1656302, _1656300))))], (35687 ^ _781215) ^ [_1452145, _1452147, _1452149, _1452151] : [class_Groups_Oordered__ab__group__add__abs(_1452145), -(hAPP(c_Groups_Oabs__class_Oabs(_1452145), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1452147, _1452145), hAPP(hAPP(c_COMBB(_1452145, _1452145, _1452147), c_Groups_Oabs__class_Oabs(_1452145)), _1452149)), _1452151)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1452147, _1452145), hAPP(hAPP(c_COMBB(_1452145, _1452145, _1452147), c_Groups_Oabs__class_Oabs(_1452145)), _1452149)), _1452151))], (38063 ^ _781215) ^ [_1505256] : [-(c_Nitpick_Oone__frac(_1505256) = c_Nitpick_OAbs__Frac(_1505256, 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))))], (15054 ^ _781215) ^ [_1045575, _1045577] : [class_Rings_Olinordered__idom(_1045575), 15057 ^ _781215 : [(15064 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045575), c_Groups_Ozero__class_Ozero(_1045575)), _1045577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045575), c_Groups_Ozero__class_Ozero(_1045575)), c_Groups_Osgn__class_Osgn(_1045575, _1045577))))], (15058 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045575), c_Groups_Ozero__class_Ozero(_1045575)), c_Groups_Osgn__class_Osgn(_1045575, _1045577))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045575), c_Groups_Ozero__class_Ozero(_1045575)), _1045577)))]]], (20723 ^ _781215) ^ [_1152982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1152982)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1152982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7159 ^ _781215) ^ [_900864, _900866, _900868, _900870] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _900864)), _900866), hAPP(c_Nat_OSuc, _900868)), _900870)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _900864))), _900866), _900868), _900870)))], (7260 ^ _781215) ^ [_903428, _903430, _903432, _903434] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903428), _903430)), hBOOL(hAPP(hAPP(c_member(_903428), _903432), _903430)), hBOOL(hAPP(hAPP(c_member(_903428), _903434), _903430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_903428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903428, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903428, tc_HOL_Obool)), _903430), hAPP(hAPP(c_Set_Oinsert(_903428), _903432), c_Orderings_Obot__class_Obot(tc_fun(_903428, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_903428), _903434), c_Orderings_Obot__class_Obot(tc_fun(_903428, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_903428), _903430))))], (16627 ^ _781215) ^ [_1077805, _1077807, _1077809, _1077811, _1077813, _1077815] : [c_Finite__Set_Ofun__left__comm(_1077805, _1077807, _1077809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077805), _1077811)), -(hBOOL(hAPP(hAPP(c_member(_1077805), _1077813), _1077811))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1077805, _1077807, _1077809), _1077815), hAPP(hAPP(c_Set_Oinsert(_1077805), _1077813), _1077811)) = hAPP(hAPP(c_Finite__Set_Ofold(_1077805, _1077807, _1077809), hAPP(hAPP(_1077809, _1077813), _1077815)), _1077811))], (40389 ^ _781215) ^ [_1571218, _1571220, _1571222] : [c_Wellfounded_OwfP(_1571218, _1571220), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1571218, _1571220), _1571222)))], (5786 ^ _781215) ^ [_872885, _872887, _872889, _872891, _872893] : [c_Hoare__Mirabelle_Ohoare__derivs(_872885, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872885)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872885), _872887), hAPP(c_Com_Ocom_OBODY, _872889)), _872891)), _872893), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872885)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872885), _872887), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _872889))), _872891)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872885), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_872885, _872893, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872885)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872885), _872887), hAPP(c_Com_Ocom_OBODY, _872889)), _872891)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872885), tc_HOL_Obool)))))], (49201 ^ _781215) ^ [_1775280, _1775282, _1775284, _1775286] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775280, _1775280)), hAPP(hAPP(c_Product__Type_OPair(_1775280, _1775280), _1775282), _1775284)), c_Transitive__Closure_Otrancl(_1775280, _1775286))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775280, _1775280)), hAPP(hAPP(c_Product__Type_OPair(_1775280, _1775280), _1775282), _1775284)), c_Transitive__Closure_Ortrancl(_1775280, _1775286))))], (3602 ^ _781215) ^ [_835778, _835780] : [_835780 = _835778, -(c_List_Ohd(_835780) = c_List_Ohd(_835778))], (39791 ^ _781215) ^ [_1555670, _1555672, _1555674] : [hAPP(c_Relation_ORange(_1555670, _1555672), _1555674) = c_Orderings_Obot__class_Obot(tc_fun(_1555672, tc_HOL_Obool)), -(_1555674 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1555670, _1555672), tc_HOL_Obool)))], (47832 ^ _781215) ^ [_1744376, _1744378, _1744380, _1744382, _1744384, _1744386, _1744388, _1744390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744376), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744378)), _1744380))), c_List_Olist__all2(_1744378, _1744382, _1744384, _1744380, _1744386), hBOOL(hAPP(hAPP(_1744384, _1744388), _1744390)), -(c_List_Olist__all2(_1744378, _1744382, _1744384, hAPP(hAPP(c_List_Olist__update(_1744378, _1744380), _1744376), _1744388), hAPP(hAPP(c_List_Olist__update(_1744382, _1744386), _1744376), _1744390)))], (18796 ^ _781215) ^ [_1118264, _1118266, _1118268] : [class_Orderings_Olinorder(_1118264), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118264), _1118266), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1118264), _1118268), _1118266))))], (35491 ^ _781215) ^ [_1448217, _1448219] : [class_Orderings_Olinorder(_1448217), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448217, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1448217), _1448219), c_Orderings_Obot__class_Obot(tc_fun(_1448217, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448217), _1448219)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1448217), _1448219))], (9105 ^ _781215) ^ [_935722, _935724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935722), _935724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935724), _935722)), -(_935722 = _935724)], (51618 ^ _781215) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (29924 ^ _781215) ^ [_1326810, _1326812, _1326814, _1326816] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1326810), _1326812)), 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)), _1326814), _1326810)), 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)), _1326816), _1326812)), 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)), _1326814), _1326816)), _1326812)), c_FunDef_Omax__weak)))], (12050 ^ _781215) ^ [_990463, _990465, _990467, _990469, _990471] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990463, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990463, tc_HOL_Obool)), hAPP(c_Set_Oimage(_990465, _990463, _990467), _990469)), hAPP(c_Set_Oimage(_990465, _990463, _990467), _990471))), hAPP(c_Set_Oimage(_990465, _990463, _990467), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990465, tc_HOL_Obool)), _990469), _990471)))))], (4268 ^ _781215) ^ [_845989, _845991, _845993, _845995] : [-(c_Wellfounded_Oacc(_845995, _845991) = c_Wellfounded_Oacc(_845993, _845989)), _845995 = _845993, _845991 = _845989], (6868 ^ _781215) ^ [_894478, _894480, _894482, _894484, _894486] : [class_Groups_Ominus(_894478), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894480, _894478)), _894482), _894484), _894486) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_894478), hAPP(_894482, _894486)), hAPP(_894484, _894486)))], (3104 ^ _781215) ^ [_827893, _827895, _827897, _827899, _827901, _827903, _827905, _827907] : [-(c_Nitpick_Osetsum_H(_827907, _827903, _827899, _827895) = c_Nitpick_Osetsum_H(_827905, _827901, _827897, _827893)), _827907 = _827905, _827903 = _827901, _827899 = _827897, _827895 = _827893], (34250 ^ _781215) ^ [_1422746, _1422748, _1422750, _1422752, _1422754] : [class_Groups_Ocomm__monoid__add(_1422746), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422748), _1422750)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422748), _1422752)), 34264 ^ _781215 : [(34267 ^ _781215) ^ [] : [hAPP(_1422754, 34263 ^ [_1422746, _1422748, _1422750, _1422752, _1422754]) = c_Groups_Ozero__class_Ozero(_1422746)], (34265 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1422748), 34263 ^ [_1422746, _1422748, _1422750, _1422752, _1422754]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422748, tc_HOL_Obool)), _1422750), _1422752))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422748, _1422746), _1422754), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1422748, tc_HOL_Obool)), _1422750), _1422752)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1422746), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422748, _1422746), _1422754), _1422750)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422748, _1422746), _1422754), _1422752)))], (23474 ^ _781215) ^ [_1204234, _1204236, _1204238, _1204240] : [_1204234 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1204236), _1204238)), _1204240), -(_1204236 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1204234, _1204236) = _1204240), 23481 ^ _781215 : [(23484 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204240), _1204236))], (23482 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204236)))]], 23489 ^ _781215 : [(23492 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204236), _1204240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204240), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23490 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204236))]]], (48852 ^ _781215) ^ [_1767622, _1767624, _1767626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1767622), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767624)), _1767626))), -(hAPP(c_Random_Opick(_1767624, hAPP(hAPP(c_List_Omap(_1767624, tc_prod(tc_Code__Numeral_Ocode__numeral, _1767624)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1767624), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1767626)), hAPP(c_Code__Numeral_Oof__nat, _1767622)) = hAPP(hAPP(c_List_Onth(_1767624), _1767626), _1767622))], (37943 ^ _781215) ^ [_1502729, _1502731] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1502729), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502729, tc_HOL_Obool), _1502731))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1502729, tc_HOL_Obool)), _1502731)))], (42585 ^ _781215) ^ [_1626235, _1626237, _1626239, _1626241, _1626243] : [class_Orderings_Olinorder(_1626235), hBOOL(hAPP(hAPP(c_member(_1626235), hAPP(_1626237, _1626239)), hAPP(c_Set_Oimage(_1626241, _1626235, _1626237), hAPP(c_List_Oset(_1626241), _1626243)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1626241, _1626235, _1626237, _1626239, _1626243) = _1626243)], (11806 ^ _781215) ^ [_986849, _986851] : [class_Groups_Ogroup__add(_986849), 11809 ^ _781215 : [(11816 ^ _781215) ^ [] : [_986851 = c_Groups_Ozero__class_Ozero(_986849), -(hAPP(c_Groups_Ouminus__class_Ouminus(_986849), _986851) = c_Groups_Ozero__class_Ozero(_986849))], (11810 ^ _781215) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_986849), _986851) = c_Groups_Ozero__class_Ozero(_986849), -(_986851 = c_Groups_Ozero__class_Ozero(_986849))]]], (14806 ^ _781215) ^ [_1040608, _1040610, _1040612, _1040614, _1040616, _1040618] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1040608, _1040610, _1040612)), _1040614), _1040616), _1040618))), 14807 ^ _781215 : [(14814 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1040608, _1040614))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1040612), _1040614), _1040616), _1040618))], (14808 ^ _781215) ^ [] : [hBOOL(hAPP(_1040608, _1040614)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1040610), _1040614), _1040616), _1040618))]]], (36442 ^ _781215) ^ [_1466100, _1466102] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466100, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1466100, tc_HOL_Obool))), _1466102) = c_Orderings_Otop__class_Otop(tc_fun(_1466100, tc_HOL_Obool)))], (27936 ^ _781215) ^ [_1290460, _1290462, _1290464, _1290466] : [class_Rings_Odivision__ring(_1290460), -(_1290462 = c_Groups_Ozero__class_Ozero(_1290460)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290460), _1290464), _1290462) = _1290466, -(_1290464 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290460), _1290466), _1290462))], (7636 ^ _781215) ^ [_909510, _909512, _909514, _909516, _909518] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909510, _909512), _909514), _909516), _909518) = _909514, -(hAPP(_909514, _909516) = _909518)], (35821 ^ _781215) ^ [_1454674, _1454676] : [class_Groups_Oordered__ab__group__add__abs(_1454674), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454674), c_Groups_Ozero__class_Ozero(_1454674)), _1454676)), -(hAPP(c_Groups_Oabs__class_Oabs(_1454674), _1454676) = _1454676)], (32292 ^ _781215) ^ [_1378012, _1378014, _1378016, _1378018] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1378012, _1378012)), hAPP(hAPP(c_Product__Type_OPair(_1378012, _1378012), _1378014), _1378016)), c_Relation_OId__on(_1378012, _1378018)))), _1378014 = _1378016, hBOOL(hAPP(hAPP(c_member(_1378012), _1378014), _1378018))], (48974 ^ _781215) ^ [_1769717, _1769719] : [hAPP(c_Code__Numeral_Onat__of, _1769717) = hAPP(c_Code__Numeral_Onat__of, _1769719), -(_1769717 = _1769719)], (14720 ^ _781215) ^ [_1038722, _1038724, _1038726] : [class_Int_Onumber__ring(_1038722), -(hAPP(c_Int_Onumber__class_Onumber__of(_1038722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1038724), _1038726)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038722), hAPP(c_Int_Onumber__class_Onumber__of(_1038722), _1038724)), hAPP(c_Int_Onumber__class_Onumber__of(_1038722), _1038726)))], (20484 ^ _781215) ^ [_1148852, _1148854] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148852)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148854)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1148852), _1148854)))], (39136 ^ _781215) ^ [_1532720, _1532722] : [-(hBOOL(hAPP(_1532722, 39137 ^ [_1532720, _1532722]))), -(hAPP(c_Set_OCollect(_1532720), _1532722) = c_Orderings_Obot__class_Obot(tc_fun(_1532720, tc_HOL_Obool)))], (41245 ^ _781215) ^ [_1591080, _1591082, _1591084] : [-(hAPP(c_Fun_Ocomp(_1591080, _1591082, _1591080, _1591084), c_Fun_Oid(_1591080)) = _1591084)], (23506 ^ _781215) ^ [_1204751] : [c_Nat__Transfer_Onat__set(_1204751), -(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), _1204751)) = _1204751)], (8099 ^ _781215) ^ [_917663, _917665] : [class_Rings_Olinordered__semidom(_917663), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917663), _917665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917663), _917665), c_Groups_Oone__class_Oone(_917663)))))], (51086 ^ _781215) ^ [_1819618, _1819620] : [class_Lattices_Oboolean__algebra(_1819618), -(class_Lattices_Oboolean__algebra(tc_fun(_1819620, _1819618)))], (43140 ^ _781215) ^ [_1640217, _1640219] : [-(c_List_Olists(_1640217, _1640219) = hAPP(c_Set_OCollect(tc_List_Olist(_1640217)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1640217), tc_fun(_1640217, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1640217, tc_HOL_Obool), tc_fun(tc_fun(_1640217, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1640217)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1640217, tc_HOL_Obool))), c_List_Oset(_1640217))), _1640219)))], (13382 ^ _781215) ^ [_1013881, _1013883, _1013885, _1013887] : [_1013881 = c_Finite__Set_Ofold1(_1013883, _1013885), -(hAPP(_1013881, hAPP(hAPP(c_Set_Oinsert(_1013883), _1013887), c_Orderings_Obot__class_Obot(tc_fun(_1013883, tc_HOL_Obool)))) = _1013887)], (22160 ^ _781215) ^ [_1180661, _1180663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180661), 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)))), _1180663))), 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)))), _1180661)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180663), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1180661))], (40976 ^ _781215) ^ [_1584949, _1584951, _1584953] : [c_Fun_Oinj__on(tc_List_Olist(_1584949), tc_List_Olist(_1584951), hAPP(c_List_Omap(_1584949, _1584951), _1584953), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1584949), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1584949, _1584951, _1584953, c_Orderings_Otop__class_Otop(tc_fun(_1584949, tc_HOL_Obool))))], (5918 ^ _781215) ^ [_875407, _875409] : [_875407 = c_Option_Ooption_ONone(_875409), 5921 ^ _781215 : [(5922 ^ _781215) ^ [_875479] : [_875407 = hAPP(c_Option_Ooption_OSome(_875409), _875479)]]], (19854 ^ _781215) ^ [_1137416, _1137418, _1137420] : [class_Orderings_Olinorder(_1137416), hBOOL(hAPP(c_Finite__Set_Ofinite(_1137416), _1137418)), -(_1137418 = c_Orderings_Obot__class_Obot(tc_fun(_1137416, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1137416), _1137420)), -(_1137420 = c_Orderings_Obot__class_Obot(tc_fun(_1137416, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1137416, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1137416, tc_HOL_Obool)), _1137418), _1137420)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1137416), c_Big__Operators_Olinorder__class_OMax(_1137416, _1137418)), c_Big__Operators_Olinorder__class_OMax(_1137416, _1137420)))], (21175 ^ _781215) ^ [_1160192, _1160194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1160192)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1160194)), _1160192) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160194), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160192), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (20380 ^ _781215) ^ [_1146973] : [-(hBOOL(hAPP(_1146973, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20387 ^ [_1146973])))), 20381 ^ _781215 : [(20382 ^ _781215) ^ [_1147025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147025)), hBOOL(hAPP(_1146973, _1147025))]]], (30321 ^ _781215) ^ [_1335867, _1335869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1335867), hAPP(c_Nat_OSuc, _1335869))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1335867, hAPP(c_Nat_OSuc, _1335869)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1335869)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1335867, _1335869)))], (37041 ^ _781215) ^ [_1481361, _1481363, _1481365, _1481367, _1481369, _1481371, _1481373] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481361, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481363, tc_fun(_1481361, tc_HOL_Obool)), _1481365), _1481367)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481369, tc_fun(_1481361, tc_HOL_Obool)), _1481371), _1481373)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481363, tc_fun(_1481361, tc_HOL_Obool)), _1481365), hAPP(hAPP(c_COMBB(tc_fun(_1481369, tc_fun(_1481361, tc_HOL_Obool)), tc_fun(_1481361, tc_HOL_Obool), _1481363), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481369, tc_fun(_1481361, tc_HOL_Obool)), _1481371)), hAPP(hAPP(c_COMBC(_1481363, tc_fun(_1481369, tc_fun(_1481361, tc_HOL_Obool)), tc_fun(_1481369, tc_fun(_1481361, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1481361, tc_HOL_Obool), tc_fun(_1481361, tc_HOL_Obool)), tc_fun(tc_fun(_1481369, tc_fun(_1481361, tc_HOL_Obool)), tc_fun(_1481369, tc_fun(_1481361, tc_HOL_Obool))), _1481363), c_COMBB(tc_fun(_1481361, tc_HOL_Obool), tc_fun(_1481361, tc_HOL_Obool), _1481369)), hAPP(hAPP(c_COMBB(tc_fun(_1481361, tc_HOL_Obool), tc_fun(tc_fun(_1481361, tc_HOL_Obool), tc_fun(_1481361, tc_HOL_Obool)), _1481363), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481361, tc_HOL_Obool))), _1481367))), _1481373))))], (50998 ^ _781215) ^ [_1818245, _1818247] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1818245), _1818247))), -(c_Lazy__Sequence_Osmall__lazy_H(_1818245, _1818247) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1818247), c_Lazy__Sequence_Osmall__lazy_H(_1818245, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1818247), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (45948 ^ _781215) ^ [_1702629, _1702631, _1702633, _1702635, _1702637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702629), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1702631), _1702633))), -(hAPP(hAPP(c_List_Onth(_1702635), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1702635), _1702637), c_List_Oupt(_1702633, _1702631))), _1702629) = hAPP(_1702637, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702633), _1702629)))], (7082 ^ _781215) ^ [_899132, _899134, _899136, _899138] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_899132, _899134, _899136, _899138, c_Orderings_Obot__class_Obot(tc_fun(_899132, tc_HOL_Obool))), _899138)))], (1428 ^ _781215) ^ [_802035, _802037] : [-(class_Lazy__Sequence_Osmall__lazy(_802035)), _802037 = _802035, class_Lazy__Sequence_Osmall__lazy(_802037)], (39214 ^ _781215) ^ [_1534428, _1534430, _1534432] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1534428, tc_HOL_Obool)), _1534430), _1534432) = hAPP(c_Set_OCollect(_1534428), hAPP(hAPP(c_COMBS(_1534428, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534428), c_fconj), hAPP(hAPP(c_COMBC(_1534428, tc_fun(_1534428, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534428)), _1534430))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534428), c_fNot), hAPP(hAPP(c_COMBC(_1534428, tc_fun(_1534428, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534428)), _1534432)))))], (19904 ^ _781215) ^ [_1138199, _1138201, _1138203] : [class_Orderings_Olinorder(_1138199), hBOOL(hAPP(c_Finite__Set_Ofinite(_1138199), _1138201)), 19911 ^ _781215 : [(19918 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1138199, tc_HOL_Obool)), _1138201), hAPP(hAPP(c_Set_Oinsert(_1138199), _1138203), c_Orderings_Obot__class_Obot(tc_fun(_1138199, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1138199, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1138199, c_Orderings_Oord__class_Omax(_1138199), hAPP(hAPP(c_Set_Oinsert(_1138199), _1138203), _1138201)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1138199), _1138203), c_Big__Operators_Olattice_OSup__fin(_1138199, c_Orderings_Oord__class_Omax(_1138199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1138199, tc_HOL_Obool)), _1138201), hAPP(hAPP(c_Set_Oinsert(_1138199), _1138203), c_Orderings_Obot__class_Obot(tc_fun(_1138199, tc_HOL_Obool)))))))], (19912 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1138199, tc_HOL_Obool)), _1138201), hAPP(hAPP(c_Set_Oinsert(_1138199), _1138203), c_Orderings_Obot__class_Obot(tc_fun(_1138199, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1138199, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1138199, c_Orderings_Oord__class_Omax(_1138199), hAPP(hAPP(c_Set_Oinsert(_1138199), _1138203), _1138201)) = _1138203)]]], (31521 ^ _781215) ^ [_1360128, _1360130, _1360132] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360128, tc_Nat_Onat), _1360130), _1360132)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360128, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1360128), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1360130)), _1360132))], (49191 ^ _781215) ^ [_1775060, _1775062, _1775064] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775060, _1775060)), _1775062), _1775064)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775060, _1775060)), _1775062), c_Transitive__Closure_Ortrancl(_1775060, _1775064))))], (2836 ^ _781215) ^ [_823577, _823579, _823581, _823583, _823585, _823587] : [-(c_Com_Ocom_OCall(_823587, _823583, _823579) = c_Com_Ocom_OCall(_823585, _823581, _823577)), _823587 = _823585, _823583 = _823581, _823579 = _823577], (32008 ^ _781215) ^ [_1371424, _1371426, _1371428, _1371430, _1371432] : [class_Groups_Ocomm__monoid__add(_1371424), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371426), _1371428)), hBOOL(hAPP(hAPP(c_member(_1371426), _1371430), _1371428)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371426, _1371424), _1371432), _1371428) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1371424), hAPP(_1371432, _1371430)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371426, _1371424), _1371432), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371426, tc_HOL_Obool)), _1371428), hAPP(hAPP(c_Set_Oinsert(_1371426), _1371430), c_Orderings_Obot__class_Obot(tc_fun(_1371426, tc_HOL_Obool)))))))], (4636 ^ _781215) ^ [_851501, _851503, _851505, _851507] : [-(c_Nitpick_OAbs__Frac(_851507, _851503) = c_Nitpick_OAbs__Frac(_851505, _851501)), _851507 = _851505, _851503 = _851501], (29822 ^ _781215) ^ [_1324938, _1324940, _1324942, _1324944] : [class_Fields_Olinordered__field(_1324938), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324938), c_Groups_Ozero__class_Ozero(_1324938)), _1324940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324938), _1324942), _1324940)), _1324944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324938), _1324942), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324938), _1324944), _1324940))))], (36963 ^ _781215) ^ [_1478925, _1478927, _1478929] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1478925, tc_fun(_1478927, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1478925, tc_HOL_Obool))), _1478929) = c_Orderings_Otop__class_Otop(tc_fun(_1478927, tc_HOL_Obool)))], (22568 ^ _781215) ^ [_1188816] : [-(_1188816 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1188816), _1188816) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (39328 ^ _781215) ^ [_1538365, _1538367] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1538365)), 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)), _1538365))), 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, _1538367))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43521 ^ _781215) ^ [_1649853, _1649855] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1649853), _1649855))), -(c_Nitpick_Ocard_H(_1649853, _1649855) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46872 ^ _781215) ^ [_1724019, _1724021] : [_1724019 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1724021, _1724019, c_List_Olist_ONil(_1724021)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1724021)), c_List_Olist_ONil(_1724021)), c_List_Olist_ONil(tc_List_Olist(_1724021))))], (47695 ^ _781215) ^ [_1741441, _1741443, _1741445, _1741447, _1741449, _1741451] : [c_List_Olist__all2(_1741441, _1741443, _1741445, _1741447, _1741449), -(c_List_Olist__all2(_1741441, _1741443, _1741445, hAPP(hAPP(c_List_Otake(_1741441), _1741451), _1741447), hAPP(hAPP(c_List_Otake(_1741443), _1741451), _1741449)))], (10480 ^ _781215) ^ [_960158, _960160, _960162, _960164, _960166, _960168] : [class_Rings_Oring(_960158), 10483 ^ _781215 : [(10490 ^ _781215) ^ [] : [_960164 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960158), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960158), _960166), _960160)), _960162)), _960168), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960158), _960160), _960162)), _960164) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960158), _960166), _960162)), _960168))], (10484 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960158), _960160), _960162)), _960164) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960158), _960166), _960162)), _960168), -(_960164 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960158), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960158), _960166), _960160)), _960162)), _960168))]]], (35645 ^ _781215) ^ [_1451127, _1451129] : [-(_1451127 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35648 ^ _781215 : [(35655 ^ _781215) ^ [] : [-(_1451129 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1451127, _1451129) = 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, _1451129))), 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)), _1451129)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451127))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451129), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451127), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1451127, _1451129)), 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), _1451129))))), c_Divides_Opdivmod(_1451127, _1451129)))))], (35649 ^ _781215) ^ [] : [_1451129 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1451127, _1451129) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451127))]]], (29446 ^ _781215) ^ [_1317879, _1317881, _1317883, _1317885] : [class_Fields_Olinordered__field(_1317879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317879), _1317881), c_Groups_Ozero__class_Ozero(_1317879))), 29453 ^ _781215 : [(29460 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317879), _1317885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317879), _1317883), _1317881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317879), _1317883), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317879), _1317885), _1317881))))], (29454 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317879), _1317883), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317879), _1317885), _1317881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317879), _1317885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317879), _1317883), _1317881))))]]], (17577 ^ _781215) ^ [_1095769, _1095771, _1095773] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095769), _1095771))), -(c_Smallcheck_Osmall_H(_1095773, _1095769, _1095771) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1095773, _1095769, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1095771), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1095773, _1095771)))], (33563 ^ _781215) ^ [_1406529, _1406531, _1406533] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1406529), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406529, tc_HOL_Obool)), _1406531), _1406533))), -(hAPP(c_Finite__Set_Ocard(_1406529), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1406529, tc_HOL_Obool)), _1406531), _1406533)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1406529), _1406531)), hAPP(c_Finite__Set_Ocard(_1406529), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406529, tc_HOL_Obool)), _1406531), _1406533))))], (42481 ^ _781215) ^ [_1622977, _1622979, _1622981, _1622983, _1622985, _1622987] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622977), tc_List_Olist(_1622977))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622977), tc_List_Olist(_1622977)), hAPP(hAPP(c_List_Olist_OCons(_1622977), _1622979), _1622981)), hAPP(hAPP(c_List_Olist_OCons(_1622977), _1622983), _1622985))), c_List_Olex(_1622977, _1622987)))), 42482 ^ _781215 : [(42489 ^ _781215) ^ [] : [_1622979 = _1622983, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622977), tc_List_Olist(_1622977))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622977), tc_List_Olist(_1622977)), _1622981), _1622985)), c_List_Olex(_1622977, _1622987)))], (42483 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622977, _1622977)), hAPP(hAPP(c_Product__Type_OPair(_1622977, _1622977), _1622979), _1622983)), _1622987)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622977)), _1622981) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622977)), _1622985)]]], (14319 ^ _781215) ^ [_1031705] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1031705) = _1031705)], (49980 ^ _781215) ^ [_1794809, _1794811, _1794813, _1794815] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794809, _1794809), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1794811), _1794813)), _1794815) = hAPP(hAPP(c_Relation_Orel__comp(_1794809, _1794809, _1794809), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794809, _1794809), tc_HOL_Obool), _1794811), _1794815)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794809, _1794809), tc_HOL_Obool), _1794813), _1794815)))], (20 ^ _781215) ^ [_781475, _781477, _781479, _781481] : [-(c_Option_Ois__none(_781479, _781475)), c_Option_Ois__none(_781481, _781477), _781481 = _781479, _781477 = _781475], (30844 ^ _781215) ^ [_1345960, _1345962, _1345964, _1345966, _1345968] : [class_Orderings_Olinorder(_1345960), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1345960, _1345962), _1345964) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1345960, _1345966), _1345968), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345960), _1345962), _1345964)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345960), _1345966), _1345968)), -(_1345964 = _1345968)], (13058 ^ _781215) ^ [_1008640, _1008642] : [class_Groups_Oab__group__add(_1008640), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008640), hAPP(c_Groups_Ouminus__class_Ouminus(_1008640), _1008642)), _1008642) = c_Groups_Ozero__class_Ozero(_1008640))], (22196 ^ _781215) ^ [_1181525, _1181527, _1181529] : [class_Divides_Osemiring__div(_1181525), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181525), c_Divides_Odiv__class_Omod(_1181525, _1181527, _1181529)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181525), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1181525), _1181527), _1181529)), _1181529)) = _1181527)], (33228 ^ _781215) ^ [_1398893, _1398895, _1398897] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398893, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398893, tc_HOL_Obool)), _1398895), _1398897)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398893, tc_HOL_Obool)), _1398895), _1398897)) = _1398895)], (14922 ^ _781215) ^ [_1042899, _1042901, _1042903] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_1042899, _1042901, _1042903)], (26696 ^ _781215) ^ [_1265565, _1265567] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1265565, _1265567) = 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), _1265565), _1265567)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1265565, _1265567)))], (37123 ^ _781215) ^ [_1483750, _1483752, _1483754, _1483756, _1483758] : [hBOOL(hAPP(hAPP(c_member(_1483750), _1483752), _1483754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483756, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483750, tc_fun(_1483756, tc_HOL_Obool)), _1483754), _1483758)), hAPP(_1483758, _1483752))))], (37065 ^ _781215) ^ [_1482412, _1482414, _1482416, _1482418, _1482420] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482412, tc_fun(_1482414, tc_HOL_Obool)), _1482416), hAPP(hAPP(c_COMBS(_1482412, tc_fun(_1482414, tc_HOL_Obool), tc_fun(_1482414, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1482414, tc_HOL_Obool), tc_fun(tc_fun(_1482414, tc_HOL_Obool), tc_fun(_1482414, tc_HOL_Obool)), _1482412), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482414, tc_HOL_Obool))), _1482418)), _1482420)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482414, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482412, tc_fun(_1482414, tc_HOL_Obool)), _1482416), _1482418)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482412, tc_fun(_1482414, tc_HOL_Obool)), _1482416), _1482420)))], (14596 ^ _781215) ^ [_1036622, _1036624, _1036626, _1036628, _1036630, _1036632] : [c_Com_Ocom_OCond(_1036622, _1036624, _1036626) = c_Com_Ocom_OCond(_1036628, _1036630, _1036632), 14599 ^ _781215 : [(14604 ^ _781215) ^ [] : [-(_1036626 = _1036632)], (14602 ^ _781215) ^ [] : [-(_1036624 = _1036630)], (14600 ^ _781215) ^ [] : [-(_1036622 = _1036628)]]], (7548 ^ _781215) ^ [_908102, _908104, _908106, _908108] : [class_Orderings_Oorder(_908102), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908102), _908104), _908106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908102), _908108), _908104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908102), _908108), _908106)))], (6116 ^ _781215) ^ [_879521, _879523] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_879521, _879523))), 6119 ^ _781215 : [(6122 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _879523)))], (6120 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _879521)))]]], (4816 ^ _781215) ^ [_854133, _854135, _854137, _854139, _854141, _854143, _854145, _854147, _854149, _854151, _854153, _854155, _854157, _854159] : [-(c_New__Random__Sequence_Opos__decr__bind(_854159, _854155, _854151, _854147, _854143, _854139, _854135) = c_New__Random__Sequence_Opos__decr__bind(_854157, _854153, _854149, _854145, _854141, _854137, _854133)), _854159 = _854157, _854155 = _854153, _854151 = _854149, _854147 = _854145, _854143 = _854141, _854139 = _854137, _854135 = _854133], (35353 ^ _781215) ^ [_1445349, _1445351, _1445353, _1445355, _1445357] : [35356 ^ _781215 : [(35359 ^ _781215) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1445351, _1445353, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1445351)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1445351), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1445351), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 35355 ^ [_1445349, _1445351, _1445353, _1445355, _1445357]))), _1445355), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1445351), hAPP(_1445357, 35354 ^ [_1445349, _1445351, _1445353, _1445355, _1445357])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1445351), tc_HOL_Obool))))], (35357 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1445349, 35354 ^ [_1445349, _1445351, _1445353, _1445355, _1445357]), 35355 ^ [_1445349, _1445351, _1445353, _1445355, _1445357])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1445351, _1445353, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1445351)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1445351), _1445349), _1445355), _1445357)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1445351), tc_HOL_Obool)))))], (12254 ^ _781215) ^ [_994198, _994200, _994202, _994204] : [class_Rings_Oordered__ring(_994198), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994198), _994200), _994202)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994198), _994204), c_Groups_Ozero__class_Ozero(_994198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994198), _994204), _994202)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994198), _994204), _994200))))], (34011 ^ _781215) ^ [_1415800, _1415802, _1415804, _1415806, _1415808, _1415810] : [c_Equiv__Relations_Ocongruent(_1415800, _1415802, _1415804, _1415806), hBOOL(hAPP(hAPP(c_member(tc_prod(_1415800, _1415800)), hAPP(hAPP(c_Product__Type_OPair(_1415800, _1415800), _1415808), _1415810)), _1415804)), -(hAPP(_1415806, _1415808) = hAPP(_1415806, _1415810))], (27382 ^ _781215) ^ [_1279358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1279358)), 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), _1279358)) = 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), _1279358))))))], (19450 ^ _781215) ^ [_1130136, _1130138, _1130140] : [class_Orderings_Olinorder(_1130136), hBOOL(hAPP(c_Finite__Set_Ofinite(_1130136), _1130138)), -(hBOOL(hAPP(hAPP(c_member(_1130136), _1130140), _1130138))), -(c_Big__Operators_Olattice_OInf__fin(_1130136, c_Orderings_Oord__class_Omin(_1130136), hAPP(hAPP(c_Set_Oinsert(_1130136), _1130140), _1130138)) = hAPP(hAPP(c_Finite__Set_Ofold(_1130136, _1130136, c_Orderings_Oord__class_Omin(_1130136)), _1130140), _1130138))], (51434 ^ _781215) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (5208 ^ _781215) ^ [_860681, _860683, _860685, _860687, _860689, _860691] : [-(c_Lazy__Sequence_Obind(_860691, _860687, _860683) = c_Lazy__Sequence_Obind(_860689, _860685, _860681)), _860691 = _860689, _860687 = _860685, _860683 = _860681], (41385 ^ _781215) ^ [_1594556, _1594558, _1594560, _1594562, _1594564, _1594566] : [-(hAPP(hAPP(c_List_Omap(_1594556, _1594558), _1594560), hAPP(hAPP(c_List_Omap(_1594562, _1594556), _1594564), _1594566)) = hAPP(hAPP(c_List_Omap(_1594562, _1594558), hAPP(c_Fun_Ocomp(_1594556, _1594558, _1594562, _1594560), _1594564)), _1594566))], (51746 ^ _781215) ^ [_1826682, _1826684] : [-(hBOOL(_1826682)), -(hBOOL(hAPP(hAPP(c_fimplies, _1826682), _1826684)))], (36095 ^ _781215) ^ [_1460027, _1460029] : [class_Groups_Oabs__if(_1460027), 36098 ^ _781215 : [(36105 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460027), _1460029), c_Groups_Ozero__class_Ozero(_1460027)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1460027), _1460029) = _1460029)], (36099 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460027), _1460029), c_Groups_Ozero__class_Ozero(_1460027))), -(hAPP(c_Groups_Oabs__class_Oabs(_1460027), _1460029) = hAPP(c_Groups_Ouminus__class_Ouminus(_1460027), _1460029))]]], (4742 ^ _781215) ^ [_853070, _853072] : [_853072 = _853070, -(c_Orderings_Oord__class_Oless__eq(_853072) = c_Orderings_Oord__class_Oless__eq(_853070))], (42683 ^ _781215) ^ [_1628868, _1628870, _1628872] : [42685 ^ _781215 : [(42688 ^ _781215) ^ [] : [hBOOL(hAPP(_1628872, hAPP(hAPP(c_List_Onth(_1628868), _1628870), 42684 ^ [_1628868, _1628870, _1628872])))], (42686 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42684 ^ [_1628868, _1628870, _1628872]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628868)), _1628870))))]], 42689 ^ _781215 : [(42690 ^ _781215) ^ [_1629070] : [hBOOL(hAPP(hAPP(c_member(_1628868), _1629070), hAPP(c_List_Oset(_1628868), _1628870))), -(hBOOL(hAPP(_1628872, _1629070)))]]], (39604 ^ _781215) ^ [_1549351, _1549353, _1549355, _1549357] : [-(c_Nitpick_Oprod(_1549351, _1549353, _1549355, _1549357) = hAPP(c_Set_OCollect(tc_prod(_1549351, _1549353)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549351, _1549353, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1549351, tc_fun(_1549353, tc_HOL_Obool), tc_fun(_1549353, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1549353, tc_HOL_Obool), tc_fun(_1549353, tc_HOL_Obool)), _1549351), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1549353)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549351), c_fconj), hAPP(hAPP(c_COMBC(_1549351, tc_fun(_1549351, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549351)), _1549355)))), hAPP(hAPP(c_COMBC(_1549353, tc_fun(_1549353, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549353)), _1549357)))))], (47689 ^ _781215) ^ [_1741324, _1741326, _1741328, _1741330, _1741332] : [c_List_Olist__all2(_1741324, _1741326, _1741328, _1741330, _1741332), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741324)), _1741330) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741326)), _1741332))], (7626 ^ _781215) ^ [_909307, _909309, _909311, _909313, _909315, _909317] : [-(_909307 = _909309), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909311, _909313), _909315), _909309), _909317), _909307) = hAPP(_909315, _909307))], (6072 ^ _781215) ^ [_878771, _878773] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_878771, _878773))), 6075 ^ _781215 : [(6078 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _878773)))], (6076 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _878771)))]]], (3608 ^ _781215) ^ [_835863, _835865] : [_835865 = _835863, -(c_Set_OPow(_835865) = c_Set_OPow(_835863))], (950 ^ _781215) ^ [_795788, _795790, _795792, _795794, _795796, _795798] : [-(c_Nitpick_Oless__frac(_795796, _795792, _795788)), c_Nitpick_Oless__frac(_795798, _795794, _795790), _795798 = _795796, _795794 = _795792, _795790 = _795788], (34702 ^ _781215) ^ [_1431492, _1431494, _1431496, _1431498, _1431500] : [c_Fun_Oinj__on(_1431492, _1431494, _1431496, _1431498), c_Fun_Oinj__on(_1431492, _1431494, _1431496, _1431500), -(c_Fun_Oinj__on(_1431492, _1431494, _1431496, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431492, tc_HOL_Obool)), _1431498), _1431500)))], (44798 ^ _781215) ^ [_1679953, _1679955, _1679957] : [-(_1679953 = c_List_Olist_ONil(_1679955)), -(hAPP(c_List_Ohd(_1679955), hAPP(hAPP(c_List_Oappend(_1679955), _1679953), _1679957)) = hAPP(c_List_Ohd(_1679955), _1679953))], (14866 ^ _781215) ^ [_1041788, _1041790, _1041792, _1041794, _1041796] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1041788, _1041790, _1041792)), _1041794), _1041796))), 14867 ^ _781215 : [(14874 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1041788, _1041794))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1041792), _1041794), _1041796))], (14868 ^ _781215) ^ [] : [hBOOL(hAPP(_1041788, _1041794)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1041790), _1041794), _1041796))]]], (2874 ^ _781215) ^ [_824168, _824170] : [_824170 = _824168, -(c_Natural_Oevalc(_824170) = c_Natural_Oevalc(_824168))], (2344 ^ _781215) ^ [_815853, _815855, _815857, _815859, _815861, _815863] : [-(c_SetInterval_Oord_OgreaterThan(_815863, _815859, _815855) = c_SetInterval_Oord_OgreaterThan(_815861, _815857, _815853)), _815863 = _815861, _815859 = _815857, _815855 = _815853], (48836 ^ _781215) ^ [_1767244, _1767246, _1767248, _1767250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1767244), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1767246), _1767248))), -(hAPP(c_Random_Opick(_1767246, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1767246)), _1767248), _1767250)), _1767244) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1767246), _1767248))], (6732 ^ _781215) ^ [_891493, _891495, _891497, _891499, _891501] : [c_Finite__Set_Ofolding__one(_891493, _891495, _891497), hBOOL(hAPP(c_Finite__Set_Ofinite(_891493), _891499)), 6739 ^ _781215 : [(6746 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891493, tc_HOL_Obool)), _891499), hAPP(hAPP(c_Set_Oinsert(_891493), _891501), c_Orderings_Obot__class_Obot(tc_fun(_891493, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_891493, tc_HOL_Obool))), -(hAPP(_891497, hAPP(hAPP(c_Set_Oinsert(_891493), _891501), _891499)) = hAPP(hAPP(_891495, _891501), hAPP(_891497, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891493, tc_HOL_Obool)), _891499), hAPP(hAPP(c_Set_Oinsert(_891493), _891501), c_Orderings_Obot__class_Obot(tc_fun(_891493, tc_HOL_Obool)))))))], (6740 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891493, tc_HOL_Obool)), _891499), hAPP(hAPP(c_Set_Oinsert(_891493), _891501), c_Orderings_Obot__class_Obot(tc_fun(_891493, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_891493, tc_HOL_Obool)), -(hAPP(_891497, hAPP(hAPP(c_Set_Oinsert(_891493), _891501), _891499)) = _891501)]]], (51416 ^ _781215) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (6980 ^ _781215) ^ [_896921, _896923, _896925] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _896921), _896923), _896925)), -(_896925 = _896921)], (35637 ^ _781215) ^ [_1451008, _1451010, _1451012] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1451008, _1451010, _1451012, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1451010)], (17131 ^ _781215) ^ [_1088303, _1088305] : [class_Int_Onumber__ring(_1088303), class_Rings_Olinordered__idom(_1088303), 17138 ^ _781215 : [(17145 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088305), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088303), hAPP(c_Int_Onumber__class_Onumber__of(_1088303), _1088305)), c_Groups_Ozero__class_Ozero(_1088303))))], (17139 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088303), hAPP(c_Int_Onumber__class_Onumber__of(_1088303), _1088305)), c_Groups_Ozero__class_Ozero(_1088303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088305), c_Int_OPls)))]]], (42172 ^ _781215) ^ [_1614144, _1614146, _1614148] : [-(_1614144 = _1614146), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614148)), _1614144) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614148)), _1614146), 42178 ^ _781215 : [(42181 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1614148, _1614148, tc_HOL_Obool), c_fequal), 42177 ^ [_1614144, _1614146, _1614148]))], (42179 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614148, _1614148)), 42177 ^ [_1614144, _1614146, _1614148]), hAPP(c_List_Oset(tc_prod(_1614148, _1614148)), hAPP(hAPP(c_List_Ozip(_1614148, _1614148), _1614144), _1614146)))))]]], (8696 ^ _781215) ^ [_928796, _928798] : [class_Rings_Oring__1__no__zero__divisors(_928796), 8699 ^ _781215 : [(8700 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928796), _928798), _928798) = c_Groups_Oone__class_Oone(_928796), -(_928798 = c_Groups_Oone__class_Oone(_928796)), -(_928798 = hAPP(c_Groups_Ouminus__class_Ouminus(_928796), c_Groups_Oone__class_Oone(_928796)))], (8710 ^ _781215) ^ [] : [8711 ^ _781215 : [(8714 ^ _781215) ^ [] : [_928798 = hAPP(c_Groups_Ouminus__class_Ouminus(_928796), c_Groups_Oone__class_Oone(_928796))], (8712 ^ _781215) ^ [] : [_928798 = c_Groups_Oone__class_Oone(_928796)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928796), _928798), _928798) = c_Groups_Oone__class_Oone(_928796))]]], (7770 ^ _781215) ^ [_912225, _912227, _912229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912227), _912229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912225), _912227)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912225), _912229))))], (22408 ^ _781215) ^ [_1185967] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1185967, _1185967) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33362 ^ _781215) ^ [_1401998, _1402000, _1402002, _1402004] : [class_Orderings_Oorder(_1401998), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401998, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1401998, _1402000, _1402002)), c_SetInterval_Oord__class_OatLeastAtMost(_1401998, _1402002, _1402004)) = c_Orderings_Obot__class_Obot(tc_fun(_1401998, tc_HOL_Obool)))], (30037 ^ _781215) ^ [_1330233, _1330235, _1330237, _1330239, _1330241] : [class_Groups_Ocomm__monoid__mult(_1330233), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330235), _1330237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1330235, tc_HOL_Obool)), _1330239), _1330237)), 30051 ^ _781215 : [(30054 ^ _781215) ^ [] : [hAPP(_1330241, 30050 ^ [_1330233, _1330235, _1330237, _1330239, _1330241]) = c_Groups_Oone__class_Oone(_1330233)], (30052 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330235), 30050 ^ [_1330233, _1330235, _1330237, _1330239, _1330241]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330235, tc_HOL_Obool)), _1330237), _1330239))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1330235, _1330233), _1330241), _1330237) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1330235, _1330233), _1330241), _1330239))], (47904 ^ _781215) ^ [_1745976, _1745978, _1745980, _1745982] : [-(_1745976 = _1745978), -(hAPP(c_List_OremoveAll(_1745980, _1745976), hAPP(hAPP(c_List_Olist_OCons(_1745980), _1745978), _1745982)) = hAPP(hAPP(c_List_Olist_OCons(_1745980), _1745978), hAPP(c_List_OremoveAll(_1745980, _1745976), _1745982)))], (7492 ^ _781215) ^ [_907212, _907214, _907216, _907218] : [class_Orderings_Oorder(_907212), _907214 = _907216, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907212), _907218), _907216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907212), _907218), _907214)))], (40045 ^ _781215) ^ [_1562995, _1562997, _1562999] : [c_Wellfounded_Owf(_1562995, _1562997), -(c_Wellfounded_Owf(_1562995, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1562995, _1562995), tc_HOL_Obool)), _1562999), _1562997)))], (36147 ^ _781215) ^ [_1460911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1460911)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1460911 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27706 ^ _781215) ^ [_1285401, _1285403, _1285405, _1285407, _1285409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1285401, _1285403)), hAPP(_1285401, _1285405))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1285407, _1285407)), hAPP(hAPP(c_Product__Type_OPair(_1285407, _1285407), _1285403), _1285405)), c_Wellfounded_Omlex__prod(_1285407, _1285401, _1285409))))], (27388 ^ _781215) ^ [_1279491, _1279493, _1279495] : [-(_1279491 = hAPP(hAPP(c_Product__Type_OPair(_1279493, _1279495), hAPP(c_Product__Type_Ofst(_1279493, _1279495), _1279491)), hAPP(c_Product__Type_Osnd(_1279493, _1279495), _1279491)))], (3252 ^ _781215) ^ [_830225, _830227, _830229, _830231] : [-(c_Big__Operators_Olattice__class_OSup__fin(_830231, _830227) = c_Big__Operators_Olattice__class_OSup__fin(_830229, _830225)), _830231 = _830229, _830227 = _830225], (12768 ^ _781215) ^ [_1003574, _1003576, _1003578, _1003580] : [class_Rings_Olinordered__semiring__strict(_1003574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003574), _1003576), _1003578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003574), c_Groups_Ozero__class_Ozero(_1003574)), _1003580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003574), _1003580), _1003576)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003574), _1003580), _1003578))))], (49802 ^ _781215) ^ [_1790565, _1790567, _1790569] : [c_Relation_Ototal__on(_1790565, _1790567, _1790569), -(c_Relation_Ototal__on(_1790565, _1790567, hAPP(c_Relation_Oconverse(_1790565, _1790565), _1790569)))], (42613 ^ _781215) ^ [_1626989, _1626991, _1626993] : [class_Orderings_Olinorder(_1626989), -(hBOOL(hAPP(hAPP(c_member(_1626989), _1626991), hAPP(c_List_Oset(_1626989), _1626993)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1626989, _1626989, c_COMBI(_1626989), _1626991, _1626993) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1626989, _1626989, c_COMBI(_1626989)), _1626991), _1626993))], (37840 ^ _781215) ^ [_1500365, _1500367, _1500369, _1500371] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1500365, tc_HOL_Obool), tc_fun(_1500367, tc_HOL_Obool)), _1500369), hAPP(hAPP(c_COMBC(tc_fun(_1500365, tc_HOL_Obool), tc_fun(_1500365, tc_fun(_1500367, tc_HOL_Obool)), tc_fun(_1500367, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500365, tc_fun(_1500367, tc_HOL_Obool))), _1500371)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500365, tc_fun(_1500367, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1500365, tc_HOL_Obool), _1500369)), _1500371))], (45564 ^ _781215) ^ [_1695841, _1695843] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1695841), _1695843)) = c_List_Oupt(_1695841, _1695843))], (9957 ^ _781215) ^ [_950567, _950569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _950567), _950569)), 9960 ^ _781215 : [(9963 ^ _781215) ^ [] : [_950567 = _950569], (9961 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950567), _950569)))]]], (9905 ^ _781215) ^ [_949724, _949726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949724), hAPP(c_Nat_OSuc, _949726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949724), _949726))), -(_949724 = hAPP(c_Nat_OSuc, _949726))], (44018 ^ _781215) ^ [_1661312, _1661314, _1661316, _1661318, _1661320] : [hAPP(hAPP(c_List_Oappend(_1661312), _1661314), _1661316) = hAPP(hAPP(c_List_Olist_OCons(_1661312), _1661318), _1661320), 44023 ^ _781215 : [(44026 ^ _781215) ^ [] : [-(_1661316 = hAPP(hAPP(c_List_Olist_OCons(_1661312), _1661318), _1661320))], (44024 ^ _781215) ^ [] : [-(_1661314 = c_List_Olist_ONil(_1661312))]], 44028 ^ _781215 : [(44031 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1661312), 44027 ^ [_1661312, _1661314, _1661316, _1661318, _1661320]), _1661316) = _1661320)], (44029 ^ _781215) ^ [] : [-(_1661314 = hAPP(hAPP(c_List_Olist_OCons(_1661312), _1661318), 44027 ^ [_1661312, _1661314, _1661316, _1661318, _1661320]))]]], (19976 ^ _781215) ^ [_1139614, _1139616, _1139618] : [class_Orderings_Olinorder(_1139614), hBOOL(hAPP(c_Finite__Set_Ofinite(_1139614), _1139616)), -(hBOOL(hAPP(hAPP(c_member(_1139614), _1139618), _1139616))), -(c_Big__Operators_Olinorder__class_OMax(_1139614, hAPP(hAPP(c_Set_Oinsert(_1139614), _1139618), _1139616)) = hAPP(hAPP(c_Finite__Set_Ofold(_1139614, _1139614, c_Orderings_Oord__class_Omax(_1139614)), _1139618), _1139616))], (2050 ^ _781215) ^ [_811170, _811172, _811174, _811176, _811178, _811180] : [-(c_Smallcheck_Oorelse(_811180, _811176, _811172) = c_Smallcheck_Oorelse(_811178, _811174, _811170)), _811180 = _811178, _811176 = _811174, _811172 = _811170], (19060 ^ _781215) ^ [_1122873, _1122875, _1122877] : [class_Orderings_Olinorder(_1122873), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1122873), _1122875), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122873), _1122875), _1122877)) = _1122875)], (10080 ^ _781215) ^ [_952653, _952655, _952657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952653), _952655)), _952657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952655), _952657)))], (50924 ^ _781215) ^ [_1816290, _1816292, _1816294, _1816296, _1816298] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1816290, _1816292, _1816294) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1816290, _1816296, _1816298)), _1816292 = _1816296, _1816294 = _1816298], (32318 ^ _781215) ^ [_1378649, _1378651, _1378653, _1378655] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1378649, tc_HOL_Obool)), _1378651), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378649), _1378653), _1378655))), 32322 ^ _781215 : [(32325 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1378649), 32321 ^ [_1378649, _1378651, _1378653, _1378655]), _1378653)))], (32323 ^ _781215) ^ [] : [-(_1378651 = hAPP(c_Relation_OImage(_1378649, _1378649, _1378655), hAPP(hAPP(c_Set_Oinsert(_1378649), 32321 ^ [_1378649, _1378651, _1378653, _1378655]), c_Orderings_Obot__class_Obot(tc_fun(_1378649, tc_HOL_Obool)))))]]], (9283 ^ _781215) ^ [_939219, _939221, _939223] : [class_Groups_Oab__group__add(_939219), -(hAPP(c_Groups_Ouminus__class_Ouminus(_939219), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939219), _939221), _939223)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939219), hAPP(c_Groups_Ouminus__class_Ouminus(_939219), _939221)), hAPP(c_Groups_Ouminus__class_Ouminus(_939219), _939223)))], (17611 ^ _781215) ^ [_1096227] : [class_Rings_Osemiring__1(_1096227), -(c_Int_Oiszero(_1096227, c_Groups_Ozero__class_Ozero(_1096227)))], (35679 ^ _781215) ^ [_1451944, _1451946, _1451948, _1451950] : [class_Groups_Oordered__ab__group__add__abs(_1451944), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1451944), c_Groups_Ozero__class_Ozero(_1451944)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1451946, _1451944), hAPP(hAPP(c_COMBB(_1451944, _1451944, _1451946), c_Groups_Oabs__class_Oabs(_1451944)), _1451948)), _1451950))))], (49026 ^ _781215) ^ [_1770589, _1770591] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1770589), _1770591) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1770589)), hAPP(c_Code__Numeral_Onat__of, _1770591))))], (4558 ^ _781215) ^ [_850336, _850338, _850340, _850342] : [-(c_Nitpick_Oint__lcm(_850342, _850338) = c_Nitpick_Oint__lcm(_850340, _850336)), _850342 = _850340, _850338 = _850336], (45606 ^ _781215) ^ [_1696467, _1696469, _1696471, _1696473, _1696475] : [class_Orderings_Olinorder(_1696467), 45609 ^ _781215 : [(45616 ^ _781215) ^ [] : [c_List_Olinorder__class_Osorted(_1696467, hAPP(hAPP(c_List_Omap(_1696469, _1696467), _1696471), _1696475)), -(c_List_Olinorder__class_Osorted(_1696467, hAPP(hAPP(c_List_Omap(_1696469, _1696467), _1696471), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696469, _1696467, _1696471), _1696473), _1696475))))], (45610 ^ _781215) ^ [] : [c_List_Olinorder__class_Osorted(_1696467, hAPP(hAPP(c_List_Omap(_1696469, _1696467), _1696471), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696469, _1696467, _1696471), _1696473), _1696475))), -(c_List_Olinorder__class_Osorted(_1696467, hAPP(hAPP(c_List_Omap(_1696469, _1696467), _1696471), _1696475)))]]], (38215 ^ _781215) ^ [_1509185, _1509187, _1509189, _1509191, _1509193] : [-(hAPP(c_Set_Ovimage(_1509185, _1509187, _1509189), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1509187, tc_HOL_Obool)), _1509191), _1509193)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1509185, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1509185, _1509187, _1509189), _1509191)), hAPP(c_Set_Ovimage(_1509185, _1509187, _1509189), _1509193)))], (6134 ^ _781215) ^ [_879808, _879810, _879812, _879814, _879816] : [c_Com_Ocom_OCall(_879808, _879810, _879812) = c_Com_Ocom_OSemi(_879814, _879816)], (46429 ^ _781215) ^ [_1714424, _1714426, _1714428] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714424), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1714424))), _1714426))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714428), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714424))), _1714426))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714424))), hAPP(c_List_Ofilter(tc_List_Olist(_1714424), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714424)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714428)), c_Nat_Osize__class_Osize(tc_List_Olist(_1714424)))), c_List_Otranspose(_1714424, _1714426))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714424)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714424)), _1714426), _1714428)))], (22270 ^ _781215) ^ [_1182989, _1182991, _1182993, _1182995] : [class_Divides_Osemiring__div(_1182989), -(c_Divides_Odiv__class_Omod(_1182989, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182989), _1182991), _1182993), _1182995) = c_Divides_Odiv__class_Omod(_1182989, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182989), c_Divides_Odiv__class_Omod(_1182989, _1182991, _1182995)), _1182993), _1182995))], (13258 ^ _781215) ^ [_1011689, _1011691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1011691), _1011689)), -(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), _1011689), _1011691))))], (51482 ^ _781215) ^ [_1823596, _1823598] : [-(class_HOL_Oequal(tc_sum(_1823596, _1823598)))], (43738 ^ _781215) ^ [_1654701, _1654703, _1654705] : [-(hAPP(hAPP(c_List_Olist__update(_1654701, c_List_Olist_ONil(_1654701)), _1654703), _1654705) = c_List_Olist_ONil(_1654701))], (3798 ^ _781215) ^ [_838758, _838760, _838762, _838764, _838766, _838768] : [-(c_List_Oinsert(_838768, _838764, _838760) = c_List_Oinsert(_838766, _838762, _838758)), _838768 = _838766, _838764 = _838762, _838760 = _838758], (45179 ^ _781215) ^ [_1687548, _1687550, _1687552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1687548), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687550)), _1687552))), -(c_List_Olast(_1687550, hAPP(hAPP(c_List_Odrop(_1687550), _1687548), _1687552)) = c_List_Olast(_1687550, _1687552))], (49231 ^ _781215) ^ [_1776026, _1776028, _1776030, _1776032, _1776034] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776026, _1776026)), hAPP(hAPP(c_Product__Type_OPair(_1776026, _1776026), _1776028), _1776030)), c_Transitive__Closure_Otrancl(_1776026, _1776032))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1776026, _1776026)), hAPP(hAPP(c_Product__Type_OPair(_1776026, _1776026), _1776030), _1776034)), c_Transitive__Closure_Ortrancl(_1776026, _1776032))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776026, _1776026)), hAPP(hAPP(c_Product__Type_OPair(_1776026, _1776026), _1776028), _1776034)), c_Transitive__Closure_Otrancl(_1776026, _1776032))))], (39130 ^ _781215) ^ [_1532612, _1532614] : [hAPP(c_Set_OCollect(_1532612), _1532614) = c_Orderings_Obot__class_Obot(tc_fun(_1532612, tc_HOL_Obool)), 39133 ^ _781215 : [(39134 ^ _781215) ^ [_1532697] : [hBOOL(hAPP(_1532614, _1532697))]]], (4894 ^ _781215) ^ [_855494, _855496, _855498, _855500, _855502, _855504, _855506, _855508] : [-(c_New__DSequence_Opos__bind(_855508, _855504, _855500, _855496) = c_New__DSequence_Opos__bind(_855506, _855502, _855498, _855494)), _855508 = _855506, _855504 = _855502, _855500 = _855498, _855496 = _855494], (36616 ^ _781215) ^ [_1469691, _1469693] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1469691, _1469693)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1469691, _1469693), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1469693), c_Orderings_Otop__class_Otop(tc_fun(_1469693, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1469691), c_Orderings_Otop__class_Otop(tc_fun(_1469691, tc_HOL_Obool)))))], (26632 ^ _781215) ^ [_1264453] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1264453) = 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), _1264453), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (40124 ^ _781215) ^ [_1564613, _1564615, _1564617] : [hAPP(c_Relation_ODomain(_1564613, _1564615), _1564617) = c_Orderings_Obot__class_Obot(tc_fun(_1564613, tc_HOL_Obool)), -(_1564617 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564613, _1564615), tc_HOL_Obool)))], (22611 ^ _781215) ^ [_1189481, _1189483] : [22612 ^ _781215 : [(22613 ^ _781215) ^ [_1189530] : [_1189481 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1189483), _1189530)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189481, _1189483) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33230 ^ _781215) ^ [_1398953, _1398955, _1398957, _1398959] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398953, tc_HOL_Obool)), _1398955), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398953, tc_HOL_Obool)), _1398957), _1398959)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398953, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398953, tc_HOL_Obool)), _1398955), _1398957)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398953, tc_HOL_Obool)), _1398955), _1398959)))], (15518 ^ _781215) ^ [_1053346, _1053348, _1053350] : [class_Orderings_Obot(_1053346), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1053348, _1053346)), _1053350) = c_Orderings_Obot__class_Obot(_1053346))], (46560 ^ _781215) ^ [_1717447, _1717449, _1717451, _1717453, _1717455] : [-(c_Map_Omap__upds(_1717447, _1717449, _1717451, _1717453, _1717455) = c_Map_Omap__add(_1717447, _1717449, _1717451, hAPP(c_Map_Omap__of(_1717447, _1717449), hAPP(c_List_Orev(tc_prod(_1717447, _1717449)), hAPP(hAPP(c_List_Ozip(_1717447, _1717449), _1717453), _1717455)))))], (25232 ^ _781215) ^ [_1236434] : [c_Int_OBit0(_1236434) = c_Int_OMin], (35897 ^ _781215) ^ [_1456124, _1456126, _1456128] : [class_Groups_Oordered__ab__group__add__abs(_1456124), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456124), hAPP(c_Groups_Oabs__class_Oabs(_1456124), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1456124), hAPP(c_Groups_Oabs__class_Oabs(_1456124), _1456126)), hAPP(c_Groups_Oabs__class_Oabs(_1456124), _1456128)))), hAPP(c_Groups_Oabs__class_Oabs(_1456124), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1456124), _1456126), _1456128)))))], (41285 ^ _781215) ^ [_1592061, _1592063, _1592065, _1592067, _1592069] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1592061), tc_Option_Ooption(_1592063), tc_Option_Ooption(_1592065), hAPP(c_Option_Omap(_1592061, _1592063), _1592067)), hAPP(c_Option_Omap(_1592065, _1592061), _1592069)) = hAPP(c_Option_Omap(_1592065, _1592063), hAPP(c_Fun_Ocomp(_1592061, _1592063, _1592065, _1592067), _1592069)))], (19280 ^ _781215) ^ [_1127147, _1127149, _1127151] : [class_Orderings_Olinorder(_1127147), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127147), _1127149)), -(_1127151 = c_Orderings_Obot__class_Obot(tc_fun(_1127147, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1127147, tc_HOL_Obool)), _1127151), _1127149)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1127147), c_Big__Operators_Olattice_OInf__fin(_1127147, c_Orderings_Oord__class_Omin(_1127147), _1127151)), c_Big__Operators_Olattice_OInf__fin(_1127147, c_Orderings_Oord__class_Omin(_1127147), _1127149)) = c_Big__Operators_Olattice_OInf__fin(_1127147, c_Orderings_Oord__class_Omin(_1127147), _1127149))], (15382 ^ _781215) ^ [_1050862] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1050862) = _1050862)], (25166 ^ _781215) ^ [_1235444, _1235446] : [class_Int_Onumber__ring(_1235444), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1235444), hAPP(c_Int_Onumber__class_Onumber__of(_1235444), 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)))), _1235446))) = hAPP(c_Int_Onumber__class_Onumber__of(_1235444), c_Int_OMin))], (46155 ^ _781215) ^ [_1707498, _1707500] : [_1707500 = c_List_Olist_ONil(_1707498), -(c_List_Olist_ONil(_1707498) = hAPP(c_List_Orev(_1707498), _1707500))], (49846 ^ _781215) ^ [_1791357, _1791359, _1791361] : [c_Relation_Osingle__valued(_1791357, _1791359, _1791361), 49849 ^ _781215 : [(49850 ^ _781215) ^ [_1791478, _1791480] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1791357, _1791359)), hAPP(hAPP(c_Product__Type_OPair(_1791357, _1791359), _1791480), _1791478)), _1791361)), 49853 ^ _781215 : [(49854 ^ _781215) ^ [_1791604] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1791357, _1791359)), hAPP(hAPP(c_Product__Type_OPair(_1791357, _1791359), _1791480), _1791604)), _1791361)), -(_1791478 = _1791604)]]]]], (30978 ^ _781215) ^ [_1348296, _1348298] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348296), hAPP(c_Nat_OSuc, _1348298)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1348296, _1348298))], (11888 ^ _781215) ^ [_988034, _988036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988034), _988036)), _988036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43152 ^ _781215) ^ [_1640574, _1640576, _1640578, _1640580, _1640582] : [-(c_Map_Odom(_1640574, _1640576, c_Map_Omap__upds(_1640574, _1640576, _1640578, _1640580, _1640582)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640574, tc_HOL_Obool)), hAPP(c_List_Oset(_1640574), hAPP(hAPP(c_List_Otake(_1640574), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640576)), _1640582)), _1640580))), c_Map_Odom(_1640574, _1640576, _1640578)))], (26105 ^ _781215) ^ [_1254645, _1254647, _1254649] : [class_Rings_Olinordered__idom(_1254645), 26108 ^ _781215 : [(26115 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254647), _1254649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254645), hAPP(c_Int_Oring__1__class_Oof__int(_1254645), _1254647)), hAPP(c_Int_Oring__1__class_Oof__int(_1254645), _1254649))))], (26109 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254645), hAPP(c_Int_Oring__1__class_Oof__int(_1254645), _1254647)), hAPP(c_Int_Oring__1__class_Oof__int(_1254645), _1254649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254647), _1254649)))]]], (51336 ^ _781215) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (9002 ^ _781215) ^ [_933887, _933889, _933891, _933893] : [class_Orderings_Oord(_933887), 9005 ^ _781215 : [(9012 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933887), hAPP(_933891, 9013 ^ [_933887, _933889, _933891, _933893])), hAPP(_933893, 9013 ^ [_933887, _933889, _933891, _933893]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933889, _933887)), _933891), _933893)))], (9006 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933889, _933887)), _933891), _933893)), 9009 ^ _781215 : [(9010 ^ _781215) ^ [_934044] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933887), hAPP(_933891, _934044)), hAPP(_933893, _934044))))]]]]], (49036 ^ _781215) ^ [_1770774] : [-(_1770774 = 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, _1770774)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1770774))))], (12636 ^ _781215) ^ [_1001139, _1001141, _1001143] : [class_Rings_Olinordered__semiring__strict(_1001139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001139), c_Groups_Ozero__class_Ozero(_1001139)), _1001141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001139), c_Groups_Ozero__class_Ozero(_1001139)), _1001143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001139), c_Groups_Ozero__class_Ozero(_1001139)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001139), _1001141), _1001143))))], (38926 ^ _781215) ^ [_1528214, _1528216, _1528218, _1528220, _1528222] : [c_Relation_Orefl__on(_1528214, _1528216, _1528218), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528214, _1528214)), hAPP(hAPP(c_Product__Type_OPair(_1528214, _1528214), _1528220), _1528222)), _1528218)), -(hBOOL(hAPP(hAPP(c_member(_1528214), _1528222), _1528216)))], (10 ^ _781215) ^ [_781338, _781340, _781342] : [-(_781342 = _781338), _781342 = _781340, _781340 = _781338], (25414 ^ _781215) ^ [_1239002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239002)), -(c_Nat__Transfer_Ois__nat(_1239002))], (47665 ^ _781215) ^ [_1740738, _1740740, _1740742, _1740744, _1740746, _1740748, _1740750] : [c_List_Olist__all2(_1740738, _1740740, _1740742, _1740744, hAPP(hAPP(c_List_Omap(_1740746, _1740740), _1740748), _1740750)), -(c_List_Olist__all2(_1740738, _1740746, hAPP(hAPP(c_COMBC(_1740738, tc_fun(_1740746, _1740740), tc_fun(_1740746, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1740740, tc_HOL_Obool), tc_fun(tc_fun(_1740746, _1740740), tc_fun(_1740746, tc_HOL_Obool)), _1740738), c_COMBB(_1740740, tc_HOL_Obool, _1740746)), _1740742)), _1740748), _1740744, _1740750))], (2032 ^ _781215) ^ [_810869, _810871, _810873, _810875, _810877, _810879, _810881, _810883] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_810883, _810879, _810875, _810871) = c_Hoare__Mirabelle_Otriple_Otriple__case(_810881, _810877, _810873, _810869)), _810883 = _810881, _810879 = _810877, _810875 = _810873, _810871 = _810869], (45674 ^ _781215) ^ [_1697572] : [class_Orderings_Olinorder(_1697572), -(c_List_Olinorder__class_Osorted(_1697572, c_List_Olist_ONil(_1697572)))], (46223 ^ _781215) ^ [_1708808, _1708810, _1708812, _1708814] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708808)), _1708810) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708812)), _1708814), -(hAPP(hAPP(c_List_Ozip(_1708808, _1708812), hAPP(c_List_Orev(_1708808), _1708810)), hAPP(c_List_Orev(_1708812), _1708814)) = hAPP(c_List_Orev(tc_prod(_1708808, _1708812)), hAPP(hAPP(c_List_Ozip(_1708808, _1708812), _1708810), _1708814)))], (31852 ^ _781215) ^ [_1367890, _1367892, _1367894, _1367896, _1367898] : [class_Groups_Ocomm__monoid__add(_1367890), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367892), _1367894)), -(hBOOL(hAPP(hAPP(c_member(_1367892), _1367896), _1367894))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1367892, _1367890), _1367898), hAPP(hAPP(c_Set_Oinsert(_1367892), _1367896), _1367894)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1367890), hAPP(_1367898, _1367896)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1367892, _1367890), _1367898), _1367894)))], (11314 ^ _781215) ^ [_978113, _978115, _978117, _978119] : [-(c_Sum__Type_OPlus(_978113, _978115, _978117, _978119) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_978113, _978115), tc_HOL_Obool))), _978117 = c_Orderings_Obot__class_Obot(tc_fun(_978113, tc_HOL_Obool)), _978119 = c_Orderings_Obot__class_Obot(tc_fun(_978115, tc_HOL_Obool))], (24105 ^ _781215) ^ [_1215916, _1215918, _1215920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1215916)), 24108 ^ _781215 : [(24109 ^ _781215) ^ [] : [-(_1215918 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1215920), _1215916)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215916), _1215918)), _1215920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1215920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215916), hAPP(c_Nat_OSuc, _1215918))))], (24119 ^ _781215) ^ [] : [_1215918 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1215920), _1215916), 24122 ^ _781215 : [(24125 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1215920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215916), hAPP(c_Nat_OSuc, _1215918)))))], (24123 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215916), _1215918)), _1215920)))]]]]], (18099 ^ _781215) ^ [_1105122, _1105124] : [class_Orderings_Olinorder(_1105122), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105122), _1105124), _1105124) = _1105124)], (43105 ^ _781215) ^ [_1639427, _1639429, _1639431] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1639427)), _1639429), c_List_Olists(_1639427, _1639431))), 43108 ^ _781215 : [(43109 ^ _781215) ^ [_1639535] : [hBOOL(hAPP(hAPP(c_member(_1639427), _1639535), hAPP(c_List_Oset(_1639427), _1639429))), -(hBOOL(hAPP(hAPP(c_member(_1639427), _1639535), _1639431)))]]], (18095 ^ _781215) ^ [] : [-(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))))], (29874 ^ _781215) ^ [_1325960, _1325962, _1325964, _1325966] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1325960), _1325962)), 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)), _1325960), _1325964)), 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)), _1325962), _1325966)), 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)), _1325962), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1325964), _1325966))), c_FunDef_Omin__strict)))], (15374 ^ _781215) ^ [_1050691] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050691), _1050691)))], (46594 ^ _781215) ^ [_1718181, _1718183, _1718185, _1718187] : [-(c_List_Oremdups(_1718181, hAPP(hAPP(c_List_Omap(_1718183, _1718181), _1718185), c_List_Oremdups(_1718183, _1718187))) = c_List_Oremdups(_1718181, hAPP(hAPP(c_List_Omap(_1718183, _1718181), _1718185), _1718187)))], (26713 ^ _781215) ^ [_1265972, _1265974, _1265976, _1265978, _1265980, _1265982, _1265984] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1265972, _1265974)), hAPP(hAPP(c_Product__Type_OPair(_1265972, _1265974), _1265976), _1265978)), _1265980)), -(hBOOL(hAPP(hAPP(c_member(_1265982), hAPP(hAPP(_1265984, _1265976), _1265978)), hAPP(c_Set_Oimage(tc_prod(_1265972, _1265974), _1265982, hAPP(c_Product__Type_Oprod_Oprod__case(_1265972, _1265974, _1265982), _1265984)), _1265980))))], (49030 ^ _781215) ^ [_1770681, _1770683] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1770681), _1770683) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1770681), _1770683))], (22685 ^ _781215) ^ [_1190659, _1190661] : [class_Divides_Osemiring__div(_1190659), -(_1190661 = c_Groups_Ozero__class_Ozero(_1190659)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190659), _1190661), _1190661) = c_Groups_Oone__class_Oone(_1190659))], (20346 ^ _781215) ^ [_1146466, _1146468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1146466), _1146468)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1146466)), c_Int_OBit1(_1146468))))], (17393 ^ _781215) ^ [_1092716, _1092718] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092716), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092716)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092718)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1092716), _1092718)))], (51244 ^ _781215) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (45424 ^ _781215) ^ [_1693162, _1693164] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693162))), c_List_Otranspose(_1693162, _1693164)) = c_List_Ofoldr(tc_List_Olist(_1693162), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1693162)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1693162))), _1693164, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49592 ^ _781215) ^ [_1785207, _1785209, _1785211, _1785213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785207, _1785207)), hAPP(hAPP(c_Product__Type_OPair(_1785207, _1785207), _1785209), _1785211)), c_Transitive__Closure_Ortrancl(_1785207, _1785213))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785207, _1785207)), hAPP(hAPP(c_Product__Type_OPair(_1785207, _1785207), _1785211), _1785209)), c_Transitive__Closure_Ortrancl(_1785207, hAPP(c_Relation_Oconverse(_1785207, _1785207), _1785213)))))], (45293 ^ _781215) ^ [_1689746, _1689748, _1689750] : [hAPP(c_List_Ofilter(_1689746, _1689748), _1689750) = _1689750, 45296 ^ _781215 : [(45297 ^ _781215) ^ [_1689837] : [hBOOL(hAPP(hAPP(c_member(_1689746), _1689837), hAPP(c_List_Oset(_1689746), _1689750))), -(hBOOL(hAPP(_1689748, _1689837)))]]], (20776 ^ _781215) ^ [_1153835, _1153837] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1153835) = _1153837), _1153835 = hAPP(c_Int_Onat, _1153837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153837))], (5583 ^ _781215) ^ [_869188, _869190] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_869188, _869190, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_869188), tc_HOL_Obool))))], (9779 ^ _781215) ^ [_947401, _947403] : [class_Groups_Omonoid__mult(_947401), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947401), c_Groups_Oone__class_Oone(_947401)), _947403) = _947403)], (37039 ^ _781215) ^ [_1481252, _1481254, _1481256, _1481258, _1481260] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481252, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481254, tc_fun(_1481252, tc_HOL_Obool)), _1481256), _1481258)), _1481260) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481254, tc_fun(_1481252, tc_HOL_Obool)), _1481256), hAPP(hAPP(c_COMBC(_1481254, tc_fun(_1481252, tc_HOL_Obool), tc_fun(_1481252, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481252, tc_HOL_Obool), tc_fun(tc_fun(_1481252, tc_HOL_Obool), tc_fun(_1481252, tc_HOL_Obool)), _1481254), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481252, tc_HOL_Obool))), _1481258)), _1481260)))], (27416 ^ _781215) ^ [_1280073, _1280075, _1280077, _1280079] : [-(_1280073 = _1280075), hAPP(c_Product__Type_Ofst(_1280077, _1280079), _1280073) = hAPP(c_Product__Type_Ofst(_1280077, _1280079), _1280075), hAPP(c_Product__Type_Osnd(_1280077, _1280079), _1280073) = hAPP(c_Product__Type_Osnd(_1280077, _1280079), _1280075)], (8974 ^ _781215) ^ [_933453, _933455, _933457] : [_933453 = _933455, 8977 ^ _781215 : [(8980 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933457, tc_HOL_Obool)), _933455), _933453)))], (8978 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933457, tc_HOL_Obool)), _933453), _933455)))]]], (16013 ^ _781215) ^ [_1063850, _1063852, _1063854] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063850, tc_HOL_Obool)), _1063852), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063850, tc_HOL_Obool)), _1063852), _1063854)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063850, tc_HOL_Obool)), _1063852), _1063854))], (37341 ^ _781215) ^ [_1489383] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1489383)), c_Int_OInteg)))], (49632 ^ _781215) ^ [_1786494, _1786496, _1786498, _1786500, _1786502] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1786494, _1786496)), hAPP(hAPP(c_Product__Type_OPair(_1786494, _1786496), _1786498), _1786500)), _1786502)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786496, _1786494)), hAPP(hAPP(c_Product__Type_OPair(_1786496, _1786494), _1786500), _1786498)), hAPP(c_Relation_Oconverse(_1786494, _1786496), _1786502))))], (16669 ^ _781215) ^ [_1079369, _1079371, _1079373, _1079375, _1079377, _1079379] : [c_Finite__Set_Ofun__left__comm(_1079369, _1079371, _1079373), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079369), _1079375)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1079369, _1079371, _1079373), _1079377), hAPP(hAPP(c_Set_Oinsert(_1079369), _1079379), _1079375)) = hAPP(hAPP(_1079373, _1079379), hAPP(hAPP(c_Finite__Set_Ofold(_1079369, _1079371, _1079373), _1079377), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079369, tc_HOL_Obool)), _1079375), hAPP(hAPP(c_Set_Oinsert(_1079369), _1079379), c_Orderings_Obot__class_Obot(tc_fun(_1079369, tc_HOL_Obool)))))))], (22002 ^ _781215) ^ [_1177238, _1177240] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1177238, tc_fun(_1177238, tc_HOL_Obool)), _1177240), hAPP(hAPP(c_COMBC(_1177238, tc_fun(_1177238, tc_HOL_Obool), tc_fun(_1177238, tc_HOL_Obool)), c_Set_Oinsert(_1177238)), c_Orderings_Obot__class_Obot(tc_fun(_1177238, tc_HOL_Obool)))) = _1177240)], (41487 ^ _781215) ^ [_1596942, _1596944, _1596946, _1596948, _1596950, _1596952] : [c_Finite__Set_Ofolding(_1596942, _1596944, _1596946, _1596948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596942), _1596950)), hBOOL(hAPP(hAPP(c_member(_1596942), _1596952), _1596950)), -(hAPP(_1596948, _1596950) = hAPP(c_Fun_Ocomp(_1596944, _1596944, _1596944, hAPP(_1596948, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1596942, tc_HOL_Obool)), _1596950), hAPP(hAPP(c_Set_Oinsert(_1596942), _1596952), c_Orderings_Obot__class_Obot(tc_fun(_1596942, tc_HOL_Obool)))))), hAPP(_1596946, _1596952)))], (39032 ^ _781215) ^ [_1530725] : [class_Orderings_Olinorder(_1530725), -(c_Finite__Set_Ofun__left__comm__idem(_1530725, _1530725, c_Orderings_Oord__class_Omin(_1530725)))], (39735 ^ _781215) ^ [_1553948, _1553950, _1553952, _1553954, _1553956] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553948, _1553950)), hAPP(hAPP(c_Product__Type_OPair(_1553948, _1553950), _1553952), _1553954)), _1553956)), -(hBOOL(hAPP(hAPP(c_member(_1553950), _1553954), hAPP(c_Relation_ORange(_1553948, _1553950), _1553956))))], (43902 ^ _781215) ^ [_1657941, _1657943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1657941), _1657943))), -(c_List_Oupto(_1657941, _1657943) = c_List_Olist_ONil(tc_Int_Oint))], (38600 ^ _781215) ^ [_1519529, _1519531, _1519533, _1519535, _1519537, _1519539] : [hBOOL(hAPP(hAPP(c_member(_1519529), _1519531), _1519533)), 38603 ^ _781215 : [(38610 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519535, tc_HOL_Obool)), _1519537), _1519539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519535, _1519529), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519535, _1519529), _1519537), hAPP(c_COMBK(tc_fun(_1519529, tc_HOL_Obool), _1519535), _1519533))), hAPP(hAPP(c_Product__Type_OSigma(_1519535, _1519529), _1519539), hAPP(c_COMBK(tc_fun(_1519529, tc_HOL_Obool), _1519535), _1519533)))))], (38604 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519535, _1519529), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1519535, _1519529), _1519537), hAPP(c_COMBK(tc_fun(_1519529, tc_HOL_Obool), _1519535), _1519533))), hAPP(hAPP(c_Product__Type_OSigma(_1519535, _1519529), _1519539), hAPP(c_COMBK(tc_fun(_1519529, tc_HOL_Obool), _1519535), _1519533)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519535, tc_HOL_Obool)), _1519537), _1519539)))]]], (1398 ^ _781215) ^ [_801660, _801662] : [-(class_Orderings_Otop(_801660)), _801662 = _801660, class_Orderings_Otop(_801662)], (50952 ^ _781215) ^ [_1816815, _1816817, _1816819, _1816821, _1816823, _1816825, _1816827] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1816815, _1816817, _1816819, _1816821, _1816823, _1816825, _1816827) = c_New__DSequence_Oneg__decr__bind(_1816815, _1816817, hAPP(hAPP(hAPP(_1816819, _1816823), _1816825), _1816827), hAPP(hAPP(c_COMBC(_1816815, 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(_1816817)))), hAPP(hAPP(c_COMBC(_1816815, 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(_1816817))))), hAPP(hAPP(c_COMBC(_1816815, 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(_1816817)))))), _1816821), _1816823)), _1816825)), _1816827)))], (44359 ^ _781215) ^ [_1668767, _1668769, _1668771, _1668773] : [-(hBOOL(hAPP(hAPP(c_member(_1668767), _1668769), hAPP(c_List_Oset(_1668767), _1668771)))), -(c_List_Oremove1(_1668767, _1668769, hAPP(hAPP(c_List_Oappend(_1668767), _1668771), _1668773)) = hAPP(hAPP(c_List_Oappend(_1668767), _1668771), c_List_Oremove1(_1668767, _1668769, _1668773)))], (17027 ^ _781215) ^ [_1086601] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086601) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086601), c_Int_OPls)))], (16389 ^ _781215) ^ [_1070950, _1070952, _1070954] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1070950), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1070950, tc_HOL_Obool)), _1070952), _1070954))), 16392 ^ _781215 : [(16395 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1070950), _1070954)))], (16393 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1070950), _1070952)))]]], (34970 ^ _781215) ^ [_1436833, _1436835, _1436837, _1436839, _1436841] : [-(c_Fun_Oinj__on(_1436833, _1436835, _1436837, hAPP(hAPP(c_Set_Oinsert(_1436833), _1436839), _1436841))), c_Fun_Oinj__on(_1436833, _1436835, _1436837, _1436841), -(hBOOL(hAPP(hAPP(c_member(_1436835), hAPP(_1436837, _1436839)), hAPP(c_Set_Oimage(_1436833, _1436835, _1436837), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1436833, tc_HOL_Obool)), _1436841), hAPP(hAPP(c_Set_Oinsert(_1436833), _1436839), c_Orderings_Obot__class_Obot(tc_fun(_1436833, tc_HOL_Obool))))))))], (47398 ^ _781215) ^ [_1734709, _1734711, _1734713, _1734715] : [class_Enum_Oenum(_1734709), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734711)), _1734713) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734709)), c_Enum_Oenum__class_Oenum(_1734709)), -(hAPP(hAPP(c_Map_Omap__of(_1734709, _1734711), hAPP(hAPP(c_List_Ozip(_1734709, _1734711), c_Enum_Oenum__class_Oenum(_1734709)), _1734713)), _1734715) = hAPP(c_Option_Ooption_OSome(_1734711), 47405 ^ [_1734709, _1734711, _1734713, _1734715]))], (7614 ^ _781215) ^ [_909083, _909085, _909087, _909089, _909091, _909093, _909095] : [-(_909083 = _909085), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909087, _909089), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909087, _909089), _909091), _909083), _909093)), _909085), _909095) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909087, _909089), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909087, _909089), _909091), _909085), _909095)), _909083), _909093))], (49207 ^ _781215) ^ [_1775449, _1775451, _1775453] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1775449), tc_List_Olist(_1775449))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1775449), tc_List_Olist(_1775449)), _1775451), _1775451)), c_List_Olistrel(_1775449, c_Transitive__Closure_Ortrancl(_1775449, _1775453)))))], (51440 ^ _781215) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (24326 ^ _781215) ^ [_1219902, _1219904] : [class_Rings_Oring__1__no__zero__divisors(_1219902), 24329 ^ _781215 : [(24330 ^ _781215) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1219902), _1219904), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1219902), -(_1219904 = c_Groups_Oone__class_Oone(_1219902)), -(_1219904 = hAPP(c_Groups_Ouminus__class_Ouminus(_1219902), c_Groups_Oone__class_Oone(_1219902)))], (24340 ^ _781215) ^ [] : [24341 ^ _781215 : [(24344 ^ _781215) ^ [] : [_1219904 = hAPP(c_Groups_Ouminus__class_Ouminus(_1219902), c_Groups_Oone__class_Oone(_1219902))], (24342 ^ _781215) ^ [] : [_1219904 = c_Groups_Oone__class_Oone(_1219902)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1219902), _1219904), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1219902))]]], (32764 ^ _781215) ^ [_1387913, _1387915, _1387917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387913, tc_HOL_Obool)), _1387915), _1387917)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1387913, tc_HOL_Obool)), _1387915), _1387917) = _1387915)], (31501 ^ _781215) ^ [_1359571, _1359573, _1359575, _1359577, _1359579] : [class_Fields_Ofield(_1359571), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359571), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359573, _1359571), _1359575), _1359577)), _1359579) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359573, _1359571), hAPP(hAPP(c_COMBC(_1359573, _1359571, _1359571), hAPP(hAPP(c_COMBB(_1359571, tc_fun(_1359571, _1359571), _1359573), c_Rings_Oinverse__class_Odivide(_1359571)), _1359575)), _1359579)), _1359577))], (37987 ^ _781215) ^ [_1503601] : [class_Complete__Lattice_Ocomplete__lattice(_1503601), -(c_Complete__Lattice_OSup__class_OSup(_1503601, c_Orderings_Otop__class_Otop(tc_fun(_1503601, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1503601))], (7925 ^ _781215) ^ [_914976, _914978] : [7926 ^ _781215 : [(7929 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914978), _914976))], (7927 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914976), _914978))]], _914976 = _914978], (35174 ^ _781215) ^ [_1441641, _1441643, _1441645, _1441647, _1441649, _1441651, _1441653] : [c_Big__Operators_Ocomm__monoid__big(_1441641, _1441643, _1441645, _1441647, _1441649), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1441643), _1441651))), -(hAPP(hAPP(_1441649, _1441653), _1441651) = _1441647)], (39280 ^ _781215) ^ [_1536845, _1536847, _1536849, _1536851, _1536853, _1536855] : [class_Groups_Ocomm__monoid__add(_1536845), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536847), _1536849)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536847, _1536845), _1536851), _1536849) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536853, _1536845), hAPP(hAPP(c_COMBB(tc_fun(_1536847, tc_HOL_Obool), _1536845, _1536853), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536847, _1536845), _1536851)), hAPP(hAPP(c_COMBB(tc_fun(_1536847, tc_HOL_Obool), tc_fun(_1536847, tc_HOL_Obool), _1536853), c_Set_OCollect(_1536847)), hAPP(hAPP(c_COMBB(tc_fun(_1536847, tc_HOL_Obool), tc_fun(_1536847, tc_HOL_Obool), _1536853), hAPP(c_COMBS(_1536847, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536847), c_fconj), hAPP(hAPP(c_COMBC(_1536847, tc_fun(_1536847, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536847)), _1536849)))), hAPP(c_COMBC(_1536847, _1536853, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1536853, tc_fun(_1536853, tc_HOL_Obool), _1536847), c_fequal), _1536855)))))), hAPP(c_Set_Oimage(_1536847, _1536853, _1536855), _1536849)))], (25302 ^ _781215) ^ [_1237360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237360), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1237360)), c_Int_OMin)))], (20900 ^ _781215) ^ [_1155860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155860)), -(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), _1155860))))], (11912 ^ _781215) ^ [_988335, _988337] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988335), _988337) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _988335 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _988337 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21638 ^ _781215) ^ [_1169393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1169393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1169393))))], (44542 ^ _781215) ^ [_1673866, _1673868] : [hAPP(c_List_Orotate1(_1673866), _1673868) = c_List_Olist_ONil(_1673866), -(_1673868 = c_List_Olist_ONil(_1673866))], (25614 ^ _781215) ^ [_1242184, _1242186] : [-(_1242184 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1242184, _1242186) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1242184), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1242186)))], (8570 ^ _781215) ^ [_926613, _926615, _926617] : [class_Groups_Oordered__ab__group__add(_926613), 8573 ^ _781215 : [(8580 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926613), _926617), _926615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926613), hAPP(c_Groups_Ouminus__class_Ouminus(_926613), _926615)), hAPP(c_Groups_Ouminus__class_Ouminus(_926613), _926617))))], (8574 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926613), hAPP(c_Groups_Ouminus__class_Ouminus(_926613), _926615)), hAPP(c_Groups_Ouminus__class_Ouminus(_926613), _926617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926613), _926617), _926615)))]]], (46614 ^ _781215) ^ [_1718538, _1718540] : [c_List_Oremdups(_1718538, _1718540) = c_List_Olist_ONil(_1718538), -(_1718540 = c_List_Olist_ONil(_1718538))], (7782 ^ _781215) ^ [_912461, _912463, _912465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912461), _912463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912461), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912465), _912463))))], (46870 ^ _781215) ^ [_1723966] : [-(c_Enum_Osublists(_1723966, c_List_Olist_ONil(_1723966)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1723966)), c_List_Olist_ONil(_1723966)), c_List_Olist_ONil(tc_List_Olist(_1723966))))], (50802 ^ _781215) ^ [_1813715] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1813715)))], (45171 ^ _781215) ^ [_1687447, _1687449] : [-(_1687447 = c_List_Olist_ONil(_1687449)), -(hBOOL(hAPP(hAPP(c_member(_1687449), c_List_Olast(_1687449, _1687447)), hAPP(c_List_Oset(_1687449), _1687447))))], (20004 ^ _781215) ^ [_1140028, _1140030] : [class_Groups_Olinordered__ab__group__add(_1140028), hBOOL(hAPP(c_Finite__Set_Ofinite(_1140028), _1140030)), -(_1140030 = c_Orderings_Obot__class_Obot(tc_fun(_1140028, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1140028), c_Big__Operators_Olinorder__class_OMax(_1140028, _1140030)) = c_Big__Operators_Olinorder__class_OMin(_1140028, hAPP(c_Set_Oimage(_1140028, _1140028, c_Groups_Ouminus__class_Ouminus(_1140028)), _1140030)))], (46726 ^ _781215) ^ [_1720774, _1720776] : [-(c_List_OdropWhile(_1720774, _1720776, c_List_Olist_ONil(_1720774)) = c_List_Olist_ONil(_1720774))], (23512 ^ _781215) ^ [_1204845, _1204847] : [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), _1204845))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1204847))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1204845))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1204847)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1204845)))], (21297 ^ _781215) ^ [_1162657, _1162659, _1162661, _1162663, _1162665, _1162667] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162657, tc_fun(_1162659, tc_HOL_Obool)), _1162661), hAPP(hAPP(c_COMBC(_1162657, tc_fun(_1162663, tc_fun(_1162659, tc_HOL_Obool)), tc_fun(_1162659, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1162663, tc_HOL_Obool), tc_fun(tc_fun(_1162663, tc_fun(_1162659, tc_HOL_Obool)), tc_fun(_1162659, tc_HOL_Obool)), _1162657), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162663, tc_fun(_1162659, tc_HOL_Obool))), _1162665)), _1162667)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162663, tc_fun(_1162659, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162657, tc_fun(_1162663, tc_HOL_Obool)), _1162661), _1162665)), _1162667))], (31455 ^ _781215) ^ [_1358071, _1358073, _1358075, _1358077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1358071), _1358077)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1358075), _1358073))), -(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), _1358071), _1358073)), 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), _1358075), _1358077)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (10916 ^ _781215) ^ [_968921, _968923, _968925, _968927, _968929] : [c_Finite__Set_Ofolding__one__idem(_968921, _968923, _968925), hBOOL(hAPP(c_Finite__Set_Ofinite(_968921), _968927)), -(_968929 = c_Orderings_Obot__class_Obot(tc_fun(_968921, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968921, tc_HOL_Obool)), _968929), _968927)), -(hAPP(hAPP(_968923, hAPP(_968925, _968929)), hAPP(_968925, _968927)) = hAPP(_968925, _968927))], (51674 ^ _781215) ^ [_1825770, _1825772] : [hBOOL(hAPP(hAPP(c_fequal, _1825770), _1825772)), -(_1825770 = _1825772)], (6574 ^ _781215) ^ [_888608, _888610, _888612, _888614, _888616, _888618, _888620, _888622] : [c_Finite__Set_Ofolding__image__simple__idem(_888608, _888610, _888612, _888614, _888616, _888618), hBOOL(hAPP(c_Finite__Set_Ofinite(_888610), _888620)), hBOOL(hAPP(hAPP(c_member(_888610), _888622), _888620)), -(hAPP(hAPP(_888612, hAPP(_888616, _888622)), hAPP(_888618, _888620)) = hAPP(_888618, _888620))], (38520 ^ _781215) ^ [_1517046, _1517048, _1517050, _1517052, _1517054, _1517056] : [class_Groups_Ocomm__monoid__mult(_1517046), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1517048, _1517046), hAPP(hAPP(c_COMBC(_1517048, tc_fun(_1517050, tc_HOL_Obool), _1517046), hAPP(hAPP(c_COMBB(tc_fun(_1517050, _1517046), tc_fun(tc_fun(_1517050, tc_HOL_Obool), _1517046), _1517048), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1517050, _1517046)), _1517052)), _1517054)), _1517056) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1517048, _1517050), _1517046), hAPP(c_Product__Type_Oprod_Oprod__case(_1517048, _1517050, _1517046), _1517052)), hAPP(hAPP(c_Product__Type_OSigma(_1517048, _1517050), _1517056), hAPP(c_COMBK(tc_fun(_1517050, tc_HOL_Obool), _1517048), _1517054))))], (40813 ^ _781215) ^ [_1581120, _1581122] : [hBOOL(hAPP(c_Com_OWT, _1581120)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_1581122, _1581120))))], (17423 ^ _781215) ^ [_1093213] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093213), 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), _1093213)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1093213)))], (10570 ^ _781215) ^ [_962093, _962095, _962097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962093, tc_HOL_Obool)), _962095), hAPP(hAPP(c_Set_Oinsert(_962093), _962097), c_Orderings_Obot__class_Obot(tc_fun(_962093, tc_HOL_Obool))))), -(_962095 = c_Orderings_Obot__class_Obot(tc_fun(_962093, tc_HOL_Obool))), -(_962095 = hAPP(hAPP(c_Set_Oinsert(_962093), _962097), c_Orderings_Obot__class_Obot(tc_fun(_962093, tc_HOL_Obool))))], (32832 ^ _781215) ^ [_1389579, _1389581, _1389583, _1389585] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389579, tc_HOL_Obool)), _1389581), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389579, tc_HOL_Obool)), _1389583), _1389585)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389579, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389579, tc_HOL_Obool)), _1389581), _1389583)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389579, tc_HOL_Obool)), _1389581), _1389585)))], (9179 ^ _781215) ^ [_937056, _937058, _937060, _937062, _937064, _937066] : [class_Rings_Oordered__ring(_937056), 9182 ^ _781215 : [(9189 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937056), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937056), _937058), _937064)), _937060)), _937062)), _937066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937056), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937056), _937058), _937060)), _937062)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937056), _937064), _937060)), _937066))))], (9183 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937056), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937056), _937058), _937060)), _937062)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937056), _937064), _937060)), _937066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937056), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937056), _937058), _937064)), _937060)), _937062)), _937066)))]]], (25895 ^ _781215) ^ [_1250839, _1250841, _1250843] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250839, tc_Nat_Onat), _1250841), _1250843)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250839, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1250839), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1250841)), _1250843))], (5601 ^ _781215) ^ [_869441, _869443, _869445, _869447] : [c_Hoare__Mirabelle_Ohoare__derivs(_869441, _869443, _869445), c_Hoare__Mirabelle_Ohoare__derivs(_869441, _869447, _869443), -(c_Hoare__Mirabelle_Ohoare__derivs(_869441, _869447, _869445))], (41974 ^ _781215) ^ [_1608935, _1608937, _1608939, _1608941, _1608943, _1608945, _1608947, _1608949] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608935)), _1608937) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608939)), _1608941), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608935)), _1608943) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608939)), _1608941), -(hBOOL(hAPP(hAPP(c_member(_1608939), _1608945), hAPP(c_List_Oset(_1608939), _1608941)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1608939, tc_Option_Ooption(_1608935)), hAPP(c_Map_Omap__of(_1608939, _1608935), hAPP(hAPP(c_List_Ozip(_1608939, _1608935), _1608941), _1608937))), _1608945), hAPP(c_Option_Ooption_OSome(_1608935), _1608947)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1608939, tc_Option_Ooption(_1608935)), hAPP(c_Map_Omap__of(_1608939, _1608935), hAPP(hAPP(c_List_Ozip(_1608939, _1608935), _1608941), _1608943))), _1608945), hAPP(c_Option_Ooption_OSome(_1608935), _1608949)), -(hAPP(c_Map_Omap__of(_1608939, _1608935), hAPP(hAPP(c_List_Ozip(_1608939, _1608935), _1608941), _1608937)) = hAPP(c_Map_Omap__of(_1608939, _1608935), hAPP(hAPP(c_List_Ozip(_1608939, _1608935), _1608941), _1608943)))], (20852 ^ _781215) ^ [_1155041] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1155041)) = 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), _1155041)))], (1328 ^ _781215) ^ [_800785, _800787] : [-(class_Lattices_Obounded__lattice__top(_800785)), _800787 = _800785, class_Lattices_Obounded__lattice__top(_800787)], (51660 ^ _781215) ^ [_1825495] : [-(class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(_1825495)))], (20213 ^ _781215) ^ [_1144041, _1144043] : [class_Int_Onumber__ring(_1144041), 20216 ^ _781215 : [(20223 ^ _781215) ^ [] : [-(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), _1144043)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1144041), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144043)) = c_Groups_Ozero__class_Ozero(_1144041))], (20217 ^ _781215) ^ [] : [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), _1144043))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1144041), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144043)) = hAPP(c_Int_Onumber__class_Onumber__of(_1144041), _1144043))]]], (3334 ^ _781215) ^ [_831484, _831486, _831488, _831490, _831492, _831494, _831496, _831498] : [-(c_List_Omap__filter(_831498, _831494, _831490, _831486) = c_List_Omap__filter(_831496, _831492, _831488, _831484)), _831498 = _831496, _831494 = _831492, _831490 = _831488, _831486 = _831484], (46809 ^ _781215) ^ [_1722402, _1722404, _1722406, _1722408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722402), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722404)), c_List_OdropWhile(_1722404, _1722406, _1722408)))), -(hAPP(hAPP(c_List_Onth(_1722404), c_List_OdropWhile(_1722404, _1722406, _1722408)), _1722402) = hAPP(hAPP(c_List_Onth(_1722404), _1722408), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1722402), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722404)), c_List_OtakeWhile(_1722404, _1722406, _1722408)))))], (26836 ^ _781215) ^ [_1268912, _1268914, _1268916] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1268912, _1268914), _1268916)), 26839 ^ _781215 : [(26840 ^ _781215) ^ [_1268997] : [hBOOL(hAPP(hAPP(_1268914, _1268997), _1268916)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1268912, _1268914), _1268997)))]]], (1748 ^ _781215) ^ [_806035, _806037] : [-(class_Groups_Omonoid__add(_806035)), _806037 = _806035, class_Groups_Omonoid__add(_806037)], (43409 ^ _781215) ^ [_1647351, _1647353, _1647355, _1647357] : [class_Groups_Ocomm__monoid__add(_1647351), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1647351), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1647351), _1647353), c_List_Oupto(_1647355, _1647357))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1647351), _1647353), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1647355, _1647357))))], (25250 ^ _781215) ^ [_1236664] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1236664)))], (49620 ^ _781215) ^ [_1786154, _1786156, _1786158, _1786160, _1786162] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1786154, _1786156)), hAPP(hAPP(c_Product__Type_OPair(_1786154, _1786156), _1786158), _1786160)), hAPP(c_Relation_Oconverse(_1786156, _1786154), _1786162))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786156, _1786154)), hAPP(hAPP(c_Product__Type_OPair(_1786156, _1786154), _1786160), _1786158)), _1786162)))], (41231 ^ _781215) ^ [_1590843] : [c_List_Onat__list(_1590843), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1590843)))], (31110 ^ _781215) ^ [_1350593, _1350595, _1350597, _1350599] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1350593, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1350595)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1350593, tc_HOL_Obool), tc_Nat_Onat), _1350597), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1350599))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1350593, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1350599, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1350595), _1350599))), _1350597))], (21271 ^ _781215) ^ [_1162120, _1162122] : [class_Rings_Osemiring__1(_1162120), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1162120), _1162122) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1162120, hAPP(hAPP(c_COMBC(_1162120, _1162120, _1162120), c_Groups_Oplus__class_Oplus(_1162120)), c_Groups_Oone__class_Oone(_1162120)), _1162122, c_Groups_Ozero__class_Ozero(_1162120)))], (50052 ^ _781215) ^ [_1796774, _1796776, _1796778, _1796780, _1796782] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1796774, _1796774)), hAPP(hAPP(c_Product__Type_OPair(_1796774, _1796774), _1796776), _1796778)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1796774, _1796774), tc_HOL_Obool), _1796780), _1796782))), 50057 ^ _781215 : [(50060 ^ _781215) ^ [] : [-(_1796776 = _1796778)], (50058 ^ _781215) ^ [] : [-(_1796780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 50063 ^ _781215 : [(50068 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1796774, _1796774)), hAPP(hAPP(c_Product__Type_OPair(_1796774, _1796774), 50061 ^ [_1796774, _1796776, _1796778, _1796780, _1796782]), _1796778)), _1796782)))], (50066 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1796774, _1796774)), hAPP(hAPP(c_Product__Type_OPair(_1796774, _1796774), _1796776), 50061 ^ [_1796774, _1796776, _1796778, _1796780, _1796782])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1796774, _1796774), tc_HOL_Obool), 50062 ^ [_1796774, _1796776, _1796778, _1796780, _1796782]), _1796782))))], (50064 ^ _781215) ^ [] : [-(_1796780 = hAPP(c_Nat_OSuc, 50062 ^ [_1796774, _1796776, _1796778, _1796780, _1796782]))]]], (40819 ^ _781215) ^ [_1581232, _1581234, _1581236, _1581238] : [c_Com_Ocom_OWhile(_1581232, _1581234) = c_Com_Ocom_OWhile(_1581236, _1581238), 40822 ^ _781215 : [(40825 ^ _781215) ^ [] : [-(_1581234 = _1581238)], (40823 ^ _781215) ^ [] : [-(_1581232 = _1581236)]]], (7824 ^ _781215) ^ [_913252, _913254, _913256] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _913252), _913254)), _913256) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _913252), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913254), _913256)))], (24360 ^ _781215) ^ [_1220393, _1220395, _1220397] : [class_Rings_Ocomm__semiring__1(_1220393), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1220393), _1220395), 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)))), _1220397)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220393), hAPP(hAPP(c_Power_Opower__class_Opower(_1220393), _1220395), _1220397)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220393), _1220395), _1220397)))], (50800 ^ _781215) ^ [_1813676] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1813676)), c_Int_OMin))], (16965 ^ _781215) ^ [_1085696, _1085698] : [class_Int_Onumber__ring(_1085696), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085696), hAPP(c_Int_Onumber__class_Onumber__of(_1085696), c_Int_OPls)), _1085698) = _1085698)], (13554 ^ _781215) ^ [_1016922, _1016924, _1016926, _1016928] : [class_Rings_Olinordered__semiring__strict(_1016922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016922), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016922), _1016924), _1016926)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016922), _1016924), _1016928))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016922), c_Groups_Ozero__class_Ozero(_1016922)), _1016924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016922), _1016926), _1016928)))], (24216 ^ _781215) ^ [_1217982] : [class_Rings_Osemiring__1(_1217982), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1217982), c_Groups_Oone__class_Oone(_1217982)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1217982))], (29952 ^ _781215) ^ [] : [-(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)))], (32560 ^ _781215) ^ [_1384226, _1384228, _1384230, _1384232] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384226, tc_HOL_Obool)), _1384228), _1384230), _1384232)), 32563 ^ _781215 : [(32566 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1384230, _1384232)))], (32564 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1384228, _1384232)))]]], (12462 ^ _781215) ^ [_997998, _998000] : [class_Rings_Olinordered__ring(_997998), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997998), c_Groups_Ozero__class_Ozero(_997998)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997998), _998000), _998000))))], (31094 ^ _781215) ^ [_1350301, _1350303, _1350305] : [class_Orderings_Oorder(_1350301), 31097 ^ _781215 : [(31104 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350301), _1350303), _1350305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350301, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1350301), _1350303)), hAPP(c_SetInterval_Oord__class_OatMost(_1350301), _1350305))))], (31098 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350301, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1350301), _1350303)), hAPP(c_SetInterval_Oord__class_OatMost(_1350301), _1350305))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350301), _1350303), _1350305)))]]], (51628 ^ _781215) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (44608 ^ _781215) ^ [_1675319, _1675321, _1675323] : [-(hAPP(hAPP(c_List_Odrop(_1675319), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1675319), _1675321), _1675323)) = _1675323)], (42971 ^ _781215) ^ [_1636270, _1636272, _1636274, _1636276, _1636278] : [-(hAPP(hAPP(c_List_Olist__update(_1636270, hAPP(hAPP(c_List_Olist_OCons(_1636270), _1636272), _1636274)), hAPP(c_Nat_OSuc, _1636276)), _1636278) = hAPP(hAPP(c_List_Olist_OCons(_1636270), _1636272), hAPP(hAPP(c_List_Olist__update(_1636270, _1636274), _1636276), _1636278)))], (36831 ^ _781215) ^ [_1475205, _1475207, _1475209, _1475211] : [class_Complete__Lattice_Ocomplete__lattice(_1475205), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475207), _1475209)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1475207, _1475205), _1475209), _1475211) = hAPP(hAPP(c_Finite__Set_Ofold(_1475207, _1475205, hAPP(hAPP(c_COMBB(_1475205, tc_fun(_1475205, _1475205), _1475207), c_Lattices_Osemilattice__inf__class_Oinf(_1475205)), _1475211)), c_Orderings_Otop__class_Otop(_1475205)), _1475209))], (23168 ^ _781215) ^ [_1198506, _1198508] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198506, _1198508) = 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), _1198506), _1198508) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1198508), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198506, _1198508)))], (45526 ^ _781215) ^ [_1695157, _1695159, _1695161, _1695163] : [class_Orderings_Olinorder(_1695157), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695157), _1695159), _1695161)), c_List_Olinorder__class_Osorted(_1695157, hAPP(hAPP(c_List_Olist_OCons(_1695157), _1695161), _1695163)), -(c_List_Olinorder__class_Osorted(_1695157, hAPP(hAPP(c_List_Olist_OCons(_1695157), _1695159), hAPP(hAPP(c_List_Olist_OCons(_1695157), _1695161), _1695163))))], (24574 ^ _781215) ^ [_1224758, _1224760, _1224762] : [class_Rings_Olinordered__idom(_1224758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224758), _1224760), c_Groups_Ozero__class_Ozero(_1224758))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224758), hAPP(hAPP(c_Power_Opower__class_Opower(_1224758), _1224760), 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)))), _1224762)))), c_Groups_Ozero__class_Ozero(_1224758))))], (6285 ^ _781215) ^ [_882847, _882849, _882851, _882853, _882855] : [c_Hoare__Mirabelle_Otriple__valid(_882847, hAPP(c_Nat_OSuc, _882849), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_882847), _882851), hAPP(c_Com_Ocom_OBODY, _882853)), _882855)), -(c_Hoare__Mirabelle_Otriple__valid(_882847, _882849, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_882847), _882851), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _882853))), _882855)))], (5100 ^ _781215) ^ [_858921, _858923, _858925, _858927, _858929, _858931, _858933, _858935] : [-(c_Lazy__Sequence_Ohb__bind(_858935, _858931, _858927, _858923) = c_Lazy__Sequence_Ohb__bind(_858933, _858929, _858925, _858921)), _858935 = _858933, _858931 = _858929, _858927 = _858925, _858923 = _858921], (23879 ^ _781215) ^ [_1211635, _1211637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1211635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1211637), _1211635)), _1211637)))], (30004 ^ _781215) ^ [_1329070, _1329072, _1329074, _1329076] : [c_FunDef_Oreduction__pair(_1329070, _1329072), -(c_FunDef_Oreduction__pair(_1329074, hAPP(hAPP(c_FunDef_Orp__inv__image(_1329070, _1329074), _1329072), _1329076)))], (2074 ^ _781215) ^ [_811540, _811542, _811544, _811546, _811548, _811550] : [-(c_Nat_Onat_Onat__rec(_811550, _811546, _811542) = c_Nat_Onat_Onat__rec(_811548, _811544, _811540)), _811550 = _811548, _811546 = _811544, _811542 = _811540], (2880 ^ _781215) ^ [_824253, _824255] : [_824255 = _824253, -(c_Com_Ocom_Ocom__size(_824255) = c_Com_Ocom_Ocom__size(_824253))], (44728 ^ _781215) ^ [_1678334, _1678336, _1678338, _1678340] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1678334) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1678336), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1678334)), hAPP(hAPP(c_List_Olist_OCons(_1678336), _1678338), _1678340)) = hAPP(hAPP(c_List_Olist_OCons(_1678336), _1678338), _1678340))], (39082 ^ _781215) ^ [_1531511, _1531513, _1531515] : [hBOOL(hAPP(_1531515, _1531513)), -(hBOOL(hAPP(hAPP(c_member(_1531511), _1531513), hAPP(c_Set_OCollect(_1531511), _1531515))))], (10342 ^ _781215) ^ [_957420, _957422, _957424] : [10343 ^ _781215 : [(10346 ^ _781215) ^ [] : [_957422 = _957424], (10344 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957420, tc_HOL_Obool)), _957422), _957424))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957420, tc_HOL_Obool)), _957422), _957424)))], (34292 ^ _781215) ^ [_1423736, _1423738, _1423740] : [class_Lattices_Olattice(_1423736), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423736), _1423738)), hBOOL(hAPP(hAPP(c_member(_1423736), _1423740), _1423738)), 34303 ^ _781215 : [(34310 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1423736, tc_HOL_Obool)), _1423738), hAPP(hAPP(c_Set_Oinsert(_1423736), _1423740), c_Orderings_Obot__class_Obot(tc_fun(_1423736, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1423736, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1423736, _1423738) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423736), _1423740), c_Big__Operators_Olattice__class_OInf__fin(_1423736, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1423736, tc_HOL_Obool)), _1423738), hAPP(hAPP(c_Set_Oinsert(_1423736), _1423740), c_Orderings_Obot__class_Obot(tc_fun(_1423736, tc_HOL_Obool)))))))], (34304 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1423736, tc_HOL_Obool)), _1423738), hAPP(hAPP(c_Set_Oinsert(_1423736), _1423740), c_Orderings_Obot__class_Obot(tc_fun(_1423736, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1423736, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1423736, _1423738) = _1423740)]]], (42995 ^ _781215) ^ [_1636951, _1636953, _1636955, _1636957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1636951), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636953)), _1636955))), -(hAPP(hAPP(c_List_Onth(_1636953), hAPP(hAPP(c_List_Olist__update(_1636953, _1636955), _1636951), _1636957)), _1636951) = _1636957)], (43589 ^ _781215) ^ [_1651764, _1651766] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651764)), c_List_Obutlast(_1651764, _1651766)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651764)), _1651766)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (3578 ^ _781215) ^ [_835438, _835440] : [_835440 = _835438, -(c_Finite__Set_Ocard(_835440) = c_Finite__Set_Ocard(_835438))], (31302 ^ _781215) ^ [_1354581, _1354583, _1354585, _1354587, _1354589] : [-(hAPP(c_Relation_OImage(_1354581, _1354583, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1354581, _1354583), tc_HOL_Obool)), _1354585), _1354587)), _1354589) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1354583, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1354581, _1354583, _1354585), _1354589)), hAPP(c_Relation_OImage(_1354581, _1354583, _1354587), _1354589)))], (42230 ^ _781215) ^ [_1615374, _1615376, _1615378, _1615380] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615374)), _1615376) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615378)), _1615380), hBOOL(hAPP(c_List_Odistinct(_1615374), _1615376)), -(c_Map_Odom(_1615374, _1615378, hAPP(c_Map_Omap__of(_1615374, _1615378), hAPP(hAPP(c_List_Ozip(_1615374, _1615378), _1615376), _1615380))) = hAPP(c_List_Oset(_1615374), _1615376))], (17997 ^ _781215) ^ [_1102518, _1102520, _1102522] : [class_Int_Onumber__ring(_1102518), 18000 ^ _781215 : [(18007 ^ _781215) ^ [] : [c_Int_Oiszero(_1102518, hAPP(c_Int_Onumber__class_Onumber__of(_1102518), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1102520), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1102522)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1102518), _1102520) = hAPP(c_Int_Onumber__class_Onumber__of(_1102518), _1102522))], (18001 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1102518), _1102520) = hAPP(c_Int_Onumber__class_Onumber__of(_1102518), _1102522), -(c_Int_Oiszero(_1102518, hAPP(c_Int_Onumber__class_Onumber__of(_1102518), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1102520), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1102522)))))]]], (30313 ^ _781215) ^ [_1335739, _1335741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335739)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1335739, _1335741)))], (42939 ^ _781215) ^ [_1635512, _1635514, _1635516, _1635518, _1635520, _1635522] : [-(_1635512 = _1635514), -(hAPP(hAPP(c_List_Olist__update(_1635516, hAPP(hAPP(c_List_Olist__update(_1635516, _1635518), _1635512), _1635520)), _1635514), _1635522) = hAPP(hAPP(c_List_Olist__update(_1635516, hAPP(hAPP(c_List_Olist__update(_1635516, _1635518), _1635514), _1635522)), _1635512), _1635520))], (51210 ^ _781215) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (49349 ^ _781215) ^ [_1778942, _1778944, _1778946] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778942, _1778942), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1778942, _1778942), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1778942, _1778944)), c_Transitive__Closure_Ortrancl(_1778942, _1778946))), c_Transitive__Closure_Ortrancl(_1778942, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1778942, _1778942), tc_HOL_Obool)), _1778944), _1778946)))))], (33182 ^ _781215) ^ [_1397733, _1397735, _1397737, _1397739] : [-(hBOOL(hAPP(hAPP(c_member(_1397733), _1397735), _1397737))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397733, tc_HOL_Obool)), _1397737), hAPP(hAPP(c_Set_Oinsert(_1397733), _1397735), _1397739)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397733, tc_HOL_Obool)), _1397737), _1397739))], (51108 ^ _781215) ^ [_1819905, _1819907] : [class_Lattices_Olattice(_1819905), -(class_Lattices_Olattice(tc_fun(_1819907, _1819905)))], (18764 ^ _781215) ^ [_1117675, _1117677, _1117679, _1117681] : [class_Orderings_Olinorder(_1117675), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117675), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117675), _1117677), _1117679)), _1117681) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117675), _1117677), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117675), _1117679), _1117681)))], (5172 ^ _781215) ^ [_860125, _860127, _860129, _860131, _860133, _860135, _860137, _860139] : [-(c_Fun_Ocomp(_860139, _860135, _860131, _860127) = c_Fun_Ocomp(_860137, _860133, _860129, _860125)), _860139 = _860137, _860135 = _860133, _860131 = _860129, _860127 = _860125], (6672 ^ _781215) ^ [_890412, _890414] : [hBOOL(hAPP(hAPP(c_member(_890412), _890414), c_Orderings_Obot__class_Obot(tc_fun(_890412, tc_HOL_Obool))))], (12582 ^ _781215) ^ [_1000152, _1000154, _1000156, _1000158] : [class_Rings_Olinordered__ring__strict(_1000152), 12585 ^ _781215 : [(12600 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000152), _1000154), _1000156)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000152), _1000154), _1000158)))), 12601 ^ _781215 : [(12608 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000152), _1000154), c_Groups_Ozero__class_Ozero(_1000152))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000152), _1000158), _1000156))], (12602 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000152), c_Groups_Ozero__class_Ozero(_1000152)), _1000154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000152), _1000156), _1000158))]]], (12586 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000152), _1000154), _1000156)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000152), _1000154), _1000158))), 12591 ^ _781215 : [(12594 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000152), _1000156), _1000158)))], (12592 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000152), c_Groups_Ozero__class_Ozero(_1000152)), _1000154)))]], 12595 ^ _781215 : [(12598 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000152), _1000158), _1000156)))], (12596 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000152), _1000154), c_Groups_Ozero__class_Ozero(_1000152))))]]]]], (36774 ^ _781215) ^ [_1473070] : [-(c_Fun_Oinj__on(_1473070, tc_fun(_1473070, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1473070, tc_fun(_1473070, tc_HOL_Obool), tc_fun(_1473070, tc_HOL_Obool)), c_Set_Oinsert(_1473070)), c_Orderings_Obot__class_Obot(tc_fun(_1473070, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1473070, tc_HOL_Obool))))], (30986 ^ _781215) ^ [_1348449, _1348451, _1348453] : [class_Orderings_Oorder(_1348449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348449), _1348451), _1348453)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1348449, _1348453), _1348451) = c_Orderings_Obot__class_Obot(tc_fun(_1348449, tc_HOL_Obool)))], (44624 ^ _781215) ^ [_1675718, _1675720, _1675722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675718)), _1675722)), _1675720)), -(hAPP(hAPP(c_List_Odrop(_1675718), _1675720), _1675722) = c_List_Olist_ONil(_1675718))], (23851 ^ _781215) ^ [_1211113, _1211115, _1211117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1211113), _1211115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1211117), _1211115)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1211117), _1211113))))], (10052 ^ _781215) ^ [_952117, _952119, _952121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952117), _952119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952119), _952121))))], (46143 ^ _781215) ^ [_1707295, _1707297] : [_1707297 = c_List_Olist_ONil(_1707295), -(hAPP(c_List_Orev(_1707295), _1707297) = c_List_Olist_ONil(_1707295))], (20571 ^ _781215) ^ [_1150412, _1150414] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150412), _1150414)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150412)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150414)))], (41333 ^ _781215) ^ [_1593373, _1593375, _1593377, _1593379, _1593381, _1593383] : [-(hAPP(hAPP(c_Fun_Ocomp(_1593373, _1593375, _1593377, _1593379), _1593381), _1593383) = hAPP(_1593379, hAPP(_1593381, _1593383)))], (25484 ^ _781215) ^ [_1240084, _1240086] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240084), _1240086) = c_Groups_Oone__class_Oone(tc_Int_Oint), 25489 ^ _781215 : [(25492 ^ _781215) ^ [] : [-(_1240086 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25490 ^ _781215) ^ [] : [-(_1240084 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 25493 ^ _781215 : [(25496 ^ _781215) ^ [] : [-(_1240086 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (25494 ^ _781215) ^ [] : [-(_1240084 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (18894 ^ _781215) ^ [_1119936, _1119938, _1119940, _1119942] : [class_Orderings_Olinorder(_1119936), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119936), _1119938), _1119940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119936), _1119942), _1119940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119936), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1119936), _1119938), _1119942)), _1119940)))], (21596 ^ _781215) ^ [_1168659, _1168661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1168659)), c_Int_OBit1(_1168661))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1168659), _1168661)))], (17915 ^ _781215) ^ [_1101069, _1101071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101069)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101071)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1101069)), hAPP(c_Int_Onat, _1101071)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1101069), _1101071)))], (33002 ^ _781215) ^ [_1393445, _1393447, _1393449, _1393451] : [class_Lattices_Olattice(_1393445), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393445), _1393447), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393445), _1393449), _1393451)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393445), _1393449), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393445), _1393447), _1393451)))], (36598 ^ _781215) ^ [_1469172, _1469174, _1469176, _1469178] : [hBOOL(hAPP(hAPP(c_member(_1469174), _1469178), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1469172, tc_fun(_1469174, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1469172, tc_HOL_Obool))), _1469176))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1469172, tc_fun(_1469174, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1469172, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1469174, tc_HOL_Obool), tc_fun(_1469174, tc_HOL_Obool), _1469172), hAPP(c_COMBC(_1469174, tc_fun(_1469174, tc_HOL_Obool), tc_HOL_Obool), c_member(_1469174))), _1469176)), _1469178)))], (9019 ^ _781215) ^ [_934233, _934235] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_934233, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_934233, tc_HOL_Obool)), _934235)) = _934235)], (16091 ^ _781215) ^ [_1065609, _1065611, _1065613] : [class_Lattices_Olattice(_1065609), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065609), _1065611), _1065613) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065609), _1065613), _1065611))], (31571 ^ _781215) ^ [_1361792, _1361794, _1361796] : [class_Groups_Ocomm__monoid__add(_1361792), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361794, _1361792), _1361796), c_Orderings_Obot__class_Obot(tc_fun(_1361794, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1361792))], (8460 ^ _781215) ^ [_924632, _924634, _924636, _924638] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_924632), _924634)), hBOOL(hAPP(c_Finite__Set_Ofinite(_924636), _924638)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_924632, _924636)), c_Sum__Type_OPlus(_924632, _924636, _924634, _924638)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_924632), _924634)), hAPP(c_Finite__Set_Ocard(_924636), _924638)))], (35531 ^ _781215) ^ [_1448901, _1448903, _1448905] : [class_Orderings_Olinorder(_1448901), 35534 ^ _781215 : [(35541 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1448901), _1448905), _1448903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1448901, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448901), _1448903)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448901), _1448905))))], (35535 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1448901, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448901), _1448903)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448901), _1448905))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1448901), _1448905), _1448903)))]]], (31994 ^ _781215) ^ [_1371099, _1371101, _1371103, _1371105, _1371107] : [class_Groups_Ocomm__monoid__add(_1371099), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371101), _1371103)), hBOOL(hAPP(hAPP(c_member(_1371101), _1371105), _1371103)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371101, _1371099), _1371107), _1371103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1371099), hAPP(_1371107, _1371105)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371101, _1371099), _1371107), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371101, tc_HOL_Obool)), _1371103), hAPP(hAPP(c_Set_Oinsert(_1371101), _1371105), c_Orderings_Obot__class_Obot(tc_fun(_1371101, tc_HOL_Obool)))))))], (42393 ^ _781215) ^ [_1620827, _1620829, _1620831, _1620833, _1620835, _1620837] : [-(c_List_Ofoldr(_1620827, _1620829, _1620831, hAPP(hAPP(c_List_Olist_OCons(_1620827), _1620833), _1620835), _1620837) = hAPP(hAPP(_1620831, _1620833), c_List_Ofoldr(_1620827, _1620829, _1620831, _1620835, _1620837)))], (7855 ^ _781215) ^ [_913890, _913892] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913890), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913892), _913890)))))], (45498 ^ _781215) ^ [_1694725, _1694727] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1694725), _1694727))), -(c_List_Oupt(_1694725, _1694727) = c_List_Olist_ONil(tc_Nat_Onat))], (31320 ^ _781215) ^ [_1354906, _1354908, _1354910] : [class_Orderings_Oord(_1354906), 31323 ^ _781215 : [(31330 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354906), _1354908), _1354910)), -(hBOOL(hAPP(hAPP(c_member(_1354906), _1354908), hAPP(c_SetInterval_Oord__class_OlessThan(_1354906), _1354910))))], (31324 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1354906), _1354908), hAPP(c_SetInterval_Oord__class_OlessThan(_1354906), _1354910))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354906), _1354908), _1354910)))]]], (17073 ^ _781215) ^ [_1087354, _1087356] : [17074 ^ _781215 : [(17077 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1087354), c_Int_OPls))], (17075 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1087354), _1087356))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087354)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087356))))], (16971 ^ _781215) ^ [_1085797, _1085799] : [class_Int_Onumber__ring(_1085797), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085797), _1085799), hAPP(c_Int_Onumber__class_Onumber__of(_1085797), c_Int_OPls)) = _1085799)], (9301 ^ _781215) ^ [_939616, _939618, _939620] : [class_Groups_Ogroup__add(_939616), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939616), hAPP(c_Groups_Ouminus__class_Ouminus(_939616), _939618)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939616), _939618), _939620)) = _939620)], (33969 ^ _781215) ^ [_1414798, _1414800, _1414802] : [class_Orderings_Olinorder(_1414798), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414798), _1414800)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414798), _1414802)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414798, tc_HOL_Obool)), _1414800), _1414802) = c_Orderings_Obot__class_Obot(tc_fun(_1414798, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1414798), c_Big__Operators_Olattice_OSup__fin(_1414798, c_Orderings_Oord__class_Omax(_1414798), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414798, tc_HOL_Obool)), _1414800), _1414802))), c_Big__Operators_Olattice_OSup__fin(_1414798, c_Orderings_Oord__class_Omax(_1414798), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414798, tc_HOL_Obool)), _1414800), _1414802))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1414798), c_Big__Operators_Olattice_OSup__fin(_1414798, c_Orderings_Oord__class_Omax(_1414798), _1414800)), c_Big__Operators_Olattice_OSup__fin(_1414798, c_Orderings_Oord__class_Omax(_1414798), _1414802)))], (10368 ^ _781215) ^ [_957948, _957950, _957952, _957954, _957956] : [hAPP(c_Map_Omap__add(_957948, _957950, _957952, _957954), _957956) = c_Option_Ooption_ONone(_957950), 10371 ^ _781215 : [(10374 ^ _781215) ^ [] : [-(hAPP(_957952, _957956) = c_Option_Ooption_ONone(_957950))], (10372 ^ _781215) ^ [] : [-(hAPP(_957954, _957956) = c_Option_Ooption_ONone(_957950))]]], (5228 ^ _781215) ^ [_860987, _860989, _860991, _860993, _860995, _860997] : [-(c_Product__Type_Oprod_Oprod__case(_860997, _860993, _860989) = c_Product__Type_Oprod_Oprod__case(_860995, _860991, _860987)), _860997 = _860995, _860993 = _860991, _860989 = _860987], (14984 ^ _781215) ^ [_1043986, _1043988, _1043990, _1043992] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043986), hAPP(c_Int_Onumber__class_Onumber__of(_1043986), _1043988)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043986), _1043990), _1043992)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043986), hAPP(c_Int_Onumber__class_Onumber__of(_1043986), _1043988)), _1043990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043986), hAPP(c_Int_Onumber__class_Onumber__of(_1043986), _1043988)), _1043992))), class_Int_Onumber(_1043986), class_Rings_Osemiring(_1043986)], (41607 ^ _781215) ^ [_1599832, _1599834, _1599836, _1599838, _1599840, _1599842] : [c_Finite__Set_Ofolding(_1599832, _1599834, _1599836, _1599838), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599832), _1599840)), -(hAPP(hAPP(_1599838, _1599840), _1599842) = hAPP(hAPP(c_Finite__Set_Ofold(_1599832, _1599834, _1599836), _1599842), _1599840))], (46305 ^ _781215) ^ [_1710622, _1710624] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1710622), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1710622))), c_List_Otranspose(_1710622, _1710624)))))], (41719 ^ _781215) ^ [_1602441, _1602443, _1602445, _1602447, _1602449] : [c_Hoare__Mirabelle_Ohoare__derivs(_1602441, _1602443, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1602441)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1602441), c_Hoare__Mirabelle_Opeek__and(_1602441, _1602445, _1602447)), _1602449), _1602445)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1602441), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1602441, _1602443, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1602441)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1602441), _1602445), c_Com_Ocom_OWhile(_1602447, _1602449)), c_Hoare__Mirabelle_Opeek__and(_1602441, _1602445, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1602447)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1602441), tc_HOL_Obool)))))], (38262 ^ _781215) ^ [_1510268, _1510270] : [-(hAPP(c_Set_Ovimage(_1510268, _1510268, c_COMBI(_1510268)), _1510270) = _1510270)], (47030 ^ _781215) ^ [_1727146, _1727148, _1727150, _1727152, _1727154] : [class_Orderings_Olinorder(_1727146), -(c_List_Olinorder__class_Osort__key(_1727148, _1727146, _1727150, hAPP(hAPP(c_List_Olist_OCons(_1727148), _1727152), _1727154)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1727148, _1727146, _1727150), _1727152), c_List_Olinorder__class_Osort__key(_1727148, _1727146, _1727150, _1727154)))], (51562 ^ _781215) ^ [] : [-(class_HOL_Oequal(tc_Product__Type_Ounit))], (19412 ^ _781215) ^ [_1129399, _1129401, _1129403] : [class_Orderings_Olinorder(_1129399), hBOOL(hAPP(c_Finite__Set_Ofinite(_1129399), _1129401)), -(hBOOL(hAPP(hAPP(c_member(_1129399), _1129403), _1129401))), -(_1129401 = c_Orderings_Obot__class_Obot(tc_fun(_1129399, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1129399, c_Orderings_Oord__class_Omin(_1129399), hAPP(hAPP(c_Set_Oinsert(_1129399), _1129403), _1129401)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1129399), _1129403), c_Big__Operators_Olattice_OInf__fin(_1129399, c_Orderings_Oord__class_Omin(_1129399), _1129401)))], (25566 ^ _781215) ^ [_1241293, _1241295] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1241293, _1241295) = c_Smallcheck_Ofull__small_H(_1241293, hAPP(c_Code__Numeral_Oint__of, _1241295), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1241295))))], (49109 ^ _781215) ^ [_1772126, _1772128, _1772130, _1772132, _1772134] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1772126, _1772126)), hAPP(hAPP(c_Product__Type_OPair(_1772126, _1772126), _1772128), _1772130)), _1772132)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772126, _1772126)), hAPP(hAPP(c_Product__Type_OPair(_1772126, _1772126), _1772130), _1772134)), _1772132)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1772126, _1772126)), hAPP(hAPP(c_Product__Type_OPair(_1772126, _1772126), _1772128), _1772134)), c_Transitive__Closure_Otrancl(_1772126, _1772132))))], (24836 ^ _781215) ^ [_1229380, _1229382, _1229384] : [class_Rings_Olinordered__semidom(_1229380), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229380), c_Groups_Oone__class_Oone(_1229380)), _1229382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229380), c_Groups_Oone__class_Oone(_1229380)), hAPP(hAPP(c_Power_Opower__class_Opower(_1229380), _1229382), _1229384))))], (26674 ^ _781215) ^ [_1265196, _1265198] : [-(c_Divides_OposDivAlg(_1265196, _1265198) = hAPP(c_Divides_Oadjust(_1265198), c_Divides_OposDivAlg(_1265196, 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)))), _1265198)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265196), _1265198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1265198), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6553 ^ _781215) ^ [_888184, _888186, _888188, _888190] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_888184, _888186)), _888188), _888190)), 6557 ^ _781215 : [(6560 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888186), 6556 ^ [_888184, _888186, _888188, _888190]), _888190)))], (6558 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888184), _888188), 6556 ^ [_888184, _888186, _888188, _888190])))]]], (7478 ^ _781215) ^ [_906993, _906995, _906997, _906999] : [class_Orderings_Oord(_906993), _906995 = _906997, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906993), _906997), _906999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906993), _906995), _906999)))], (13698 ^ _781215) ^ [_1019690, _1019692, _1019694, _1019696] : [class_Rings_Olinordered__ring__strict(_1019690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019690), _1019692), c_Groups_Ozero__class_Ozero(_1019690))), 13705 ^ _781215 : [(13712 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019690), _1019696), _1019694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019690), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019690), _1019692), _1019694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019690), _1019692), _1019696))))], (13706 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019690), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019690), _1019692), _1019694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019690), _1019692), _1019696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019690), _1019696), _1019694)))]]], (14620 ^ _781215) ^ [_1036992, _1036994] : [class_Rings_Olinordered__idom(_1036992), -(c_Groups_Osgn__class_Osgn(_1036992, c_Groups_Osgn__class_Osgn(_1036992, _1036994)) = c_Groups_Osgn__class_Osgn(_1036992, _1036994))], (49077 ^ _781215) ^ [_1771412, _1771414, _1771416, _1771418] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1771412, _1771412)), hAPP(hAPP(c_Product__Type_OPair(_1771412, _1771412), _1771414), _1771416)), _1771418)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1771412, _1771412)), hAPP(hAPP(c_Product__Type_OPair(_1771412, _1771412), _1771414), _1771416)), c_Transitive__Closure_Otrancl(_1771412, _1771418))))], (46221 ^ _781215) ^ [_1708768, _1708770] : [-(hAPP(c_List_Oset(_1708768), hAPP(c_List_Orev(_1708768), _1708770)) = hAPP(c_List_Oset(_1708768), _1708770))], (46590 ^ _781215) ^ [_1718102, _1718104] : [-(hBOOL(hAPP(c_List_Odistinct(_1718102), c_List_Oremdups(_1718102, _1718104))))], (16181 ^ _781215) ^ [_1067251, _1067253, _1067255] : [class_Lattices_Osemilattice__sup(_1067251), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067251), _1067253), _1067255)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067251), _1067255), _1067253) = _1067255)], (37572 ^ _781215) ^ [_1494789, _1494791, _1494793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1494789, _1494789), tc_HOL_Obool)), _1494791), _1494793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494789, tc_HOL_Obool)), c_Wellfounded_Oacc(_1494789, _1494793)), c_Wellfounded_Oacc(_1494789, _1494791))))], (34740 ^ _781215) ^ [_1432184, _1432186, _1432188, _1432190] : [c_Fun_Oinj__on(_1432184, _1432186, _1432188, _1432190), -(hAPP(c_Finite__Set_Ocard(_1432186), hAPP(c_Set_Oimage(_1432184, _1432186, _1432188), _1432190)) = hAPP(c_Finite__Set_Ocard(_1432184), _1432190))], (26322 ^ _781215) ^ [_1258819, _1258821, _1258823, _1258825, _1258827] : [class_Groups_Ocomm__monoid__mult(_1258819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1258821), _1258823)), -(hBOOL(hAPP(hAPP(c_member(_1258821), _1258825), _1258823))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1258821, _1258819), _1258827), hAPP(hAPP(c_Set_Oinsert(_1258821), _1258825), _1258823)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1258819), hAPP(_1258827, _1258825)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1258821, _1258819), _1258827), _1258823)))], (11592 ^ _781215) ^ [_983649, _983651] : [class_Groups_Omonoid__add(_983649), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983649), c_Groups_Ozero__class_Ozero(_983649)), _983651) = _983651)], (45281 ^ _781215) ^ [_1689533, _1689535, _1689537, _1689539] : [-(hAPP(c_List_Ofilter(_1689533, _1689535), c_List_Oremove1(_1689533, _1689537, _1689539)) = c_List_Oremove1(_1689533, _1689537, hAPP(c_List_Ofilter(_1689533, _1689535), _1689539)))], (32830 ^ _781215) ^ [_1389495, _1389497, _1389499, _1389501] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389495, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389495, tc_HOL_Obool)), _1389497), _1389499)), _1389501) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389495, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389495, tc_HOL_Obool)), _1389497), _1389501)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389495, tc_HOL_Obool)), _1389499), _1389501)))], (41601 ^ _781215) ^ [_1599727, _1599729, _1599731, _1599733] : [c_Finite__Set_Ofolding(_1599727, _1599729, _1599731, _1599733), -(hAPP(_1599733, c_Orderings_Obot__class_Obot(tc_fun(_1599727, tc_HOL_Obool))) = c_Fun_Oid(_1599729))], (40526 ^ _781215) ^ [_1574896, _1574898, _1574900, _1574902] : [c_Equiv__Relations_Ocongruent(_1574896, _1574898, _1574900, _1574902), 40529 ^ _781215 : [(40530 ^ _781215) ^ [_1575041] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574896, _1574896)), _1575041), _1574900)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1574896, _1574896, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1574896, tc_fun(_1574896, _1574898), tc_fun(_1574896, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574898, tc_HOL_Obool), tc_fun(tc_fun(_1574896, _1574898), tc_fun(_1574896, tc_HOL_Obool)), _1574896), c_COMBB(_1574898, tc_HOL_Obool, _1574896)), hAPP(hAPP(c_COMBB(_1574898, tc_fun(_1574898, tc_HOL_Obool), _1574896), c_fequal), _1574902))), _1574902)), _1575041)))]]], (51616 ^ _781215) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (10386 ^ _781215) ^ [_958276, _958278, _958280, _958282, _958284, _958286] : [hAPP(_958276, _958278) = hAPP(c_Option_Ooption_OSome(_958280), _958282), -(hAPP(c_Map_Omap__add(_958284, _958280, _958286, _958276), _958278) = hAPP(c_Option_Ooption_OSome(_958280), _958282))], (7891 ^ _781215) ^ [_914540] : [_914540 = hAPP(c_Nat_OSuc, _914540)], (14100 ^ _781215) ^ [_1027103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1027103)), -(_1027103 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027103), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (35499 ^ _781215) ^ [_1448392, _1448394, _1448396] : [class_Orderings_Olinorder(_1448392), 35502 ^ _781215 : [(35509 ^ _781215) ^ [] : [_1448394 = _1448396, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448392), _1448394) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448392), _1448396))], (35503 ^ _781215) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448392), _1448394) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448392), _1448396), -(_1448394 = _1448396)]]], (51180 ^ _781215) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (27078 ^ _781215) ^ [_1273347, _1273349] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1273347), _1273349)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1273347), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1273349)))], (51296 ^ _781215) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (39264 ^ _781215) ^ [_1536321, _1536323, _1536325, _1536327] : [_1536321 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1536323, _1536325), 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)), _1536327))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1536323), _1536321)))], (20251 ^ _781215) ^ [_1144740, _1144742] : [-(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, _1144740)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144742))))], (43039 ^ _781215) ^ [_1637851, _1637853, _1637855, _1637857, _1637859, _1637861, _1637863] : [hBOOL(hAPP(hAPP(c_member(_1637851), _1637853), hAPP(c_List_Oset(_1637851), hAPP(hAPP(c_List_Otake(_1637851), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637855)), _1637857)), _1637859)))), -(c_Map_Omap__upds(_1637851, _1637855, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1637851, tc_Option_Ooption(_1637855)), _1637861), _1637853), hAPP(c_Option_Ooption_OSome(_1637855), _1637863)), _1637859, _1637857) = c_Map_Omap__upds(_1637851, _1637855, _1637861, _1637859, _1637857))], (28482 ^ _781215) ^ [_1300077, _1300079, _1300081, _1300083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1300077), _1300079)), -(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), _1300077), _1300081)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1300079), _1300083))), c_FunDef_Opair__less)))], (27840 ^ _781215) ^ [_1288769, _1288771] : [hAPP(c_Int_ORep__Integ, _1288769) = hAPP(c_Int_ORep__Integ, _1288771), -(_1288769 = _1288771)], (44904 ^ _781215) ^ [_1681830, _1681832, _1681834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681830)), _1681832)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1681830, _1681834), _1681832) = _1681832)], (19252 ^ _781215) ^ [_1126660, _1126662, _1126664, _1126666] : [class_Orderings_Olinorder(_1126660), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126660), _1126662)), hBOOL(hAPP(hAPP(c_member(_1126660), _1126664), _1126662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126660), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1126660), _1126664), _1126666)), hAPP(hAPP(c_Finite__Set_Ofold(_1126660, _1126660, c_Orderings_Oord__class_Omax(_1126660)), _1126666), _1126662))))], (5955 ^ _781215) ^ [_876041, _876043, _876045] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_876041, _876043, _876045))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _876043))))], (19772 ^ _781215) ^ [_1136030, _1136032, _1136034] : [class_Orderings_Olinorder(_1136030), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136030), _1136032)), -(_1136032 = c_Orderings_Obot__class_Obot(tc_fun(_1136030, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136030), _1136034)), -(_1136034 = c_Orderings_Obot__class_Obot(tc_fun(_1136030, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1136030, c_Orderings_Oord__class_Omax(_1136030), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1136030, tc_HOL_Obool)), _1136032), _1136034)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1136030), c_Big__Operators_Olattice_OSup__fin(_1136030, c_Orderings_Oord__class_Omax(_1136030), _1136032)), c_Big__Operators_Olattice_OSup__fin(_1136030, c_Orderings_Oord__class_Omax(_1136030), _1136034)))], (282 ^ _781215) ^ [_785566, _785568] : [-(class_Fields_Olinordered__field(_785566)), _785568 = _785566, class_Fields_Olinordered__field(_785568)], (43415 ^ _781215) ^ [_1647494, _1647496, _1647498, _1647500] : [class_Groups_Ocomm__monoid__add(_1647494), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1647494), _1647496), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1647498, _1647500))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1647494), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1647494), _1647496), c_List_Oupto(_1647498, _1647500))))], (43792 ^ _781215) ^ [_1655730, _1655732] : [hAPP(c_List_Oset(_1655730), _1655732) = c_Orderings_Obot__class_Obot(tc_fun(_1655730, tc_HOL_Obool)), -(_1655732 = c_List_Olist_ONil(_1655730))], (29648 ^ _781215) ^ [_1321644, _1321646, _1321648, _1321650] : [class_Fields_Ofield(_1321644), -(_1321646 = c_Groups_Ozero__class_Ozero(_1321644)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1321644), _1321648), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321644), _1321650), _1321646)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321644), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1321644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321644), _1321646), _1321648)), _1321650)), _1321646))], (26704 ^ _781215) ^ [_1265744, _1265746] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1265744, _1265744)), hAPP(hAPP(c_Product__Type_OPair(_1265744, _1265744), 26705 ^ [_1265744, _1265746]), 26705 ^ [_1265744, _1265746])), _1265746)), -(c_Nitpick_Orefl_H(_1265744, _1265746))], (23604 ^ _781215) ^ [_1206524] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1206524))), -(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), _1206524)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15899 ^ _781215) ^ [_1061300, _1061302, _1061304, _1061306, _1061308, _1061310] : [c_Finite__Set_Ofun__left__comm(_1061300, _1061302, _1061304), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061300), _1061306)), hBOOL(hAPP(hAPP(c_member(_1061300), _1061308), _1061306)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1061300, _1061302, _1061304), _1061310), _1061306) = hAPP(hAPP(_1061304, _1061308), hAPP(hAPP(c_Finite__Set_Ofold(_1061300, _1061302, _1061304), _1061310), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1061300, tc_HOL_Obool)), _1061306), hAPP(hAPP(c_Set_Oinsert(_1061300), _1061308), c_Orderings_Obot__class_Obot(tc_fun(_1061300, tc_HOL_Obool)))))))], (38824 ^ _781215) ^ [_1525745, _1525747, _1525749, _1525751, _1525753, _1525755] : [-(c_Product__Type_Omap__pair(_1525745, _1525747, _1525749, _1525751, _1525753, _1525755) = hAPP(c_Product__Type_Oprod_Oprod__case(_1525745, _1525749, tc_prod(_1525747, _1525751)), hAPP(hAPP(c_COMBC(_1525745, tc_fun(_1525749, _1525751), tc_fun(_1525749, tc_prod(_1525747, _1525751))), hAPP(hAPP(c_COMBB(tc_fun(_1525751, tc_prod(_1525747, _1525751)), tc_fun(tc_fun(_1525749, _1525751), tc_fun(_1525749, tc_prod(_1525747, _1525751))), _1525745), c_COMBB(_1525751, tc_prod(_1525747, _1525751), _1525749)), hAPP(hAPP(c_COMBB(_1525747, tc_fun(_1525751, tc_prod(_1525747, _1525751)), _1525745), c_Product__Type_OPair(_1525747, _1525751)), _1525753))), _1525755)))], (23756 ^ _781215) ^ [_1209471, _1209473, _1209475, _1209477] : [class_Rings_Ocomm__semiring__1(_1209471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209471), hAPP(hAPP(c_Power_Opower__class_Opower(_1209471), _1209473), _1209475)), hAPP(hAPP(c_Power_Opower__class_Opower(_1209471), _1209473), _1209477)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1209471), _1209473), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1209475), _1209477)))], (5118 ^ _781215) ^ [_859222, _859224, _859226, _859228, _859230, _859232, _859234, _859236] : [-(c_New__DSequence_Oneg__bind(_859236, _859232, _859228, _859224) = c_New__DSequence_Oneg__bind(_859234, _859230, _859226, _859222)), _859236 = _859234, _859232 = _859230, _859228 = _859226, _859224 = _859222], (44280 ^ _781215) ^ [_1666782, _1666784, _1666786, _1666788] : [hAPP(hAPP(c_List_Oappend(_1666782), _1666784), _1666786) = hAPP(hAPP(c_List_Oappend(_1666782), _1666784), _1666788), -(_1666786 = _1666788)], (38197 ^ _781215) ^ [_1508703, _1508705, _1508707, _1508709] : [c_Fun_Oinj__on(_1508703, _1508705, _1508707, c_Orderings_Otop__class_Otop(tc_fun(_1508703, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508703, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1508703, _1508705, _1508707), hAPP(hAPP(c_Set_Oinsert(_1508705), _1508709), c_Orderings_Obot__class_Obot(tc_fun(_1508705, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1508703), c_HOL_OThe(_1508703, hAPP(hAPP(c_COMBC(_1508703, _1508705, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1508705, tc_fun(_1508705, tc_HOL_Obool), _1508703), c_fequal), _1508707)), _1508709))), c_Orderings_Obot__class_Obot(tc_fun(_1508703, tc_HOL_Obool))))))], (16679 ^ _781215) ^ [_1079640, _1079642] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _1079640, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _1079642)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _1079640, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_Com_Ostate), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies)), c_Natural_Oevalc(_1079642))))), c_fequal))), _1079642), c_fequal)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (49696 ^ _781215) ^ [_1788016, _1788018] : [-(c_List_Olistrel1(_1788016, hAPP(c_Relation_Oconverse(_1788016, _1788016), _1788018)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1788016), tc_List_Olist(_1788016)), c_List_Olistrel1(_1788016, _1788018)))], (40203 ^ _781215) ^ [_1566322] : [class_Orderings_Owellorder(_1566322), -(c_Wellfounded_Owf(_1566322, hAPP(c_Set_OCollect(tc_prod(_1566322, _1566322)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566322, _1566322, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1566322)))))], (14242 ^ _781215) ^ [_1030208, _1030210] : [-(c_Option_Ooption_Ooption__size(_1030208, _1030210, c_Option_Ooption_ONone(_1030208)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51586 ^ _781215) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (4682 ^ _781215) ^ [_852190, _852192] : [_852192 = _852190, -(c_Nitpick_ORep__Frac(_852192) = c_Nitpick_ORep__Frac(_852190))], (25708 ^ _781215) ^ [_1243944, _1243946, _1243948, _1243950, _1243952] : [-(hBOOL(hAPP(hAPP(c_member(_1243944), _1243946), c_SetInterval_Oord_OgreaterThanLessThan(_1243944, _1243948, _1243950, _1243952)))), hBOOL(hAPP(hAPP(_1243948, _1243950), _1243946)), hBOOL(hAPP(hAPP(_1243948, _1243946), _1243952))], (46203 ^ _781215) ^ [_1708467, _1708469, _1708471] : [hAPP(c_List_Orev(_1708467), _1708469) = hAPP(c_List_Orev(_1708467), _1708471), -(_1708469 = _1708471)], (47018 ^ _781215) ^ [_1726936, _1726938] : [class_Enum_Oenum(_1726936), -(hBOOL(hAPP(hAPP(c_member(_1726936), _1726938), hAPP(c_List_Oset(_1726936), c_Enum_Oenum__class_Oenum(_1726936)))))], (11790 ^ _781215) ^ [_986623, _986625] : [class_Groups_Olinordered__ab__group__add(_986623), 11793 ^ _781215 : [(11800 ^ _781215) ^ [] : [_986625 = c_Groups_Ozero__class_Ozero(_986623), -(hAPP(c_Groups_Ouminus__class_Ouminus(_986623), _986625) = _986625)], (11794 ^ _781215) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_986623), _986625) = _986625, -(_986625 = c_Groups_Ozero__class_Ozero(_986623))]]], (39260 ^ _781215) ^ [_1536077, _1536079, _1536081] : [-(hAPP(c_Set_OCollect(_1536077), hAPP(hAPP(c_COMBB(tc_fun(_1536079, tc_HOL_Obool), tc_HOL_Obool, _1536077), c_HOL_OAll(_1536079)), _1536081)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1536079, tc_fun(_1536077, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1536079, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536077, tc_HOL_Obool), tc_fun(_1536077, tc_HOL_Obool), _1536079), c_Set_OCollect(_1536077)), hAPP(c_COMBC(_1536077, _1536079, tc_HOL_Obool), _1536081))))], (3960 ^ _781215) ^ [_841295, _841297] : [_841297 = _841295, -(c_Option_Ooption_ONone(_841297) = c_Option_Ooption_ONone(_841295))], (2174 ^ _781215) ^ [_813062, _813064, _813066, _813068, _813070, _813072] : [-(c_Power_Opower_Opower(_813072, _813068, _813064) = c_Power_Opower_Opower(_813070, _813066, _813062)), _813072 = _813070, _813068 = _813066, _813064 = _813062], (17171 ^ _781215) ^ [_1088922, _1088924] : [class_Int_Onumber__ring(_1088922), class_Rings_Olinordered__idom(_1088922), 17178 ^ _781215 : [(17185 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1088924), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088922), hAPP(c_Int_Onumber__class_Onumber__of(_1088922), _1088924)), c_Groups_Ozero__class_Ozero(_1088922))))], (17179 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088922), hAPP(c_Int_Onumber__class_Onumber__of(_1088922), _1088924)), c_Groups_Ozero__class_Ozero(_1088922))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1088924), c_Int_OPls)))]]], (46848 ^ _781215) ^ [_1723475, _1723477] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1723475), tc_fun(_1723475, tc_HOL_Obool), c_List_Oset(_1723475)), hAPP(c_List_Oset(tc_List_Olist(_1723475)), c_Enum_Osublists(_1723475, _1723477))) = hAPP(c_Set_OPow(_1723475), hAPP(c_List_Oset(_1723475), _1723477)))], (22016 ^ _781215) ^ [_1177571, _1177573, _1177575, _1177577, _1177579] : [class_Complete__Lattice_Ocomplete__lattice(_1177571), 22019 ^ _781215 : [(22020 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177571), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1177573, _1177571), _1177575), _1177577)), _1177579)), 22023 ^ _781215 : [(22024 ^ _781215) ^ [_1177752] : [hBOOL(hAPP(hAPP(c_member(_1177573), _1177752), _1177575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177571), hAPP(_1177577, _1177752)), _1177579)))]]], (22030 ^ _781215) ^ [] : [22032 ^ _781215 : [(22035 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177571), hAPP(_1177577, 22031 ^ [_1177571, _1177573, _1177575, _1177577, _1177579])), _1177579))], (22033 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1177573), 22031 ^ [_1177571, _1177573, _1177575, _1177577, _1177579]), _1177575)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177571), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1177573, _1177571), _1177575), _1177577)), _1177579)))]]], (3376 ^ _781215) ^ [_832155, _832157, _832159, _832161, _832163, _832165, _832167, _832169, _832171, _832173] : [-(c_List_Olinorder__class_Oinsort__insert__key(_832173, _832169, _832165, _832161, _832157) = c_List_Olinorder__class_Oinsort__insert__key(_832171, _832167, _832163, _832159, _832155)), _832173 = _832171, _832169 = _832167, _832165 = _832163, _832161 = _832159, _832157 = _832155], (36263 ^ _781215) ^ [_1462886, _1462888, _1462890, _1462892, _1462894, _1462896, _1462898] : [-(hAPP(c_Product__Type_Oapfst(_1462886, _1462888, _1462890, _1462892), hAPP(c_Product__Type_Oapsnd(_1462894, _1462890, _1462886, _1462896), _1462898)) = hAPP(hAPP(c_Product__Type_OPair(_1462888, _1462890), hAPP(_1462892, hAPP(c_Product__Type_Ofst(_1462886, _1462894), _1462898))), hAPP(_1462896, hAPP(c_Product__Type_Osnd(_1462886, _1462894), _1462898))))], (51258 ^ _781215) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (46299 ^ _781215) ^ [_1710571, _1710573] : [-(_1710571 = c_List_Olist_ONil(_1710573)), -(c_List_Olast(_1710573, hAPP(c_List_Orev(_1710573), _1710571)) = hAPP(c_List_Ohd(_1710573), _1710571))], (19052 ^ _781215) ^ [_1122718, _1122720] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1122718)), hAPP(c_Nat_OSuc, _1122720)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1122718), _1122720)))], (51294 ^ _781215) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (6770 ^ _781215) ^ [_892220, _892222, _892224, _892226] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892220, tc_HOL_Obool)), _892222), hAPP(hAPP(c_Set_Oinsert(_892220), _892224), _892226)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892220, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892220, tc_HOL_Obool)), _892222), _892226)), hAPP(hAPP(c_Set_Oinsert(_892220), _892224), c_Orderings_Obot__class_Obot(tc_fun(_892220, tc_HOL_Obool)))))], (45147 ^ _781215) ^ [_1687184, _1687186, _1687188] : [-(_1687184 = c_List_Olist_ONil(_1687186)), -(c_List_Olast(_1687186, hAPP(hAPP(c_List_Olist_OCons(_1687186), _1687188), _1687184)) = c_List_Olast(_1687186, _1687184))], (22410 ^ _781215) ^ [_1185994] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1185994) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37022 ^ _781215) ^ [_1480625, _1480627, _1480629, _1480631, _1480633] : [37024 ^ _781215 : [(37027 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1480625), _1480627), hAPP(_1480633, 37023 ^ [_1480625, _1480627, _1480629, _1480631, _1480633])))], (37025 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480629), 37023 ^ [_1480625, _1480627, _1480629, _1480631, _1480633]), _1480631)))]], -(hBOOL(hAPP(hAPP(c_member(_1480625), _1480627), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1480629, tc_fun(_1480625, tc_HOL_Obool)), _1480631), _1480633))))], (50940 ^ _781215) ^ [_1816638, _1816640, _1816642, _1816644, _1816646] : [_1816638 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1816640, _1816642, _1816644, _1816646), _1816638) = c_Lazy__Sequence_Ohit__bound(_1816642))], (44910 ^ _781215) ^ [_1681945, _1681947] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681945)), hAPP(c_List_Otl(_1681945), _1681947)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681945)), _1681947)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (49996 ^ _781215) ^ [_1795329, _1795331, _1795333, _1795335, _1795337, _1795339] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1795329, _1795329)), hAPP(hAPP(c_Product__Type_OPair(_1795329, _1795329), _1795331), _1795333)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1795329, _1795329), tc_HOL_Obool), _1795335), _1795337))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1795329, _1795329)), hAPP(hAPP(c_Product__Type_OPair(_1795329, _1795329), _1795333), _1795339)), _1795337)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1795329, _1795329)), hAPP(hAPP(c_Product__Type_OPair(_1795329, _1795329), _1795331), _1795339)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1795329, _1795329), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1795335)), _1795337))))], (9941 ^ _781215) ^ [_950325, _950327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950325), hAPP(c_Nat_OSuc, _950327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950325), _950327))), -(_950325 = hAPP(c_Nat_OSuc, _950327))], (42917 ^ _781215) ^ [_1634913, _1634915, _1634917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634913)), _1634915)), _1634917)), -(hAPP(hAPP(c_List_Otake(_1634913), _1634917), _1634915) = _1634915)], (17327 ^ _781215) ^ [_1091490, _1091492, _1091494] : [class_Lattices_Olattice(_1091490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091490), _1091492)), -(c_Big__Operators_Olattice__class_OSup__fin(_1091490, hAPP(hAPP(c_Set_Oinsert(_1091490), _1091494), _1091492)) = hAPP(hAPP(c_Finite__Set_Ofold(_1091490, _1091490, c_Lattices_Osemilattice__sup__class_Osup(_1091490)), _1091494), _1091492))], (51598 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (38334 ^ _781215) ^ [_1512078, _1512080, _1512082, _1512084, _1512086] : [-(hAPP(c_Set_Ovimage(_1512078, _1512080, _1512082), hAPP(hAPP(c_Set_Oinsert(_1512080), _1512084), _1512086)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1512078, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1512078, _1512080, _1512082), hAPP(hAPP(c_Set_Oinsert(_1512080), _1512084), c_Orderings_Obot__class_Obot(tc_fun(_1512080, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1512078, _1512080, _1512082), _1512086)))], (43654 ^ _781215) ^ [_1653174, _1653176, _1653178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653174), tc_List_Olist(_1653174))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653174), tc_List_Olist(_1653174)), c_List_Olist_ONil(_1653174)), _1653176)), c_List_Olistrel(_1653174, _1653178))), -(_1653176 = c_List_Olist_ONil(_1653174))], (37618 ^ _781215) ^ [_1495757, _1495759, _1495761] : [hBOOL(hAPP(hAPP(c_member(_1495757), _1495759), c_Wellfounded_Oacc(_1495757, _1495761))), 37621 ^ _781215 : [(37622 ^ _781215) ^ [_1495871] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1495757, _1495757)), hAPP(hAPP(c_Product__Type_OPair(_1495757, _1495757), _1495871), _1495759)), _1495761)), -(hBOOL(hAPP(hAPP(c_member(_1495757), _1495871), c_Wellfounded_Oacc(_1495757, _1495761))))]]], (25290 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17039 ^ _781215) ^ [_1086796, _1086798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086796)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086798))), 17042 ^ _781215 : [(17043 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086796), _1086798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1086798)))], (17049 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086796), _1086798)))]]], (19362 ^ _781215) ^ [_1128551, _1128553, _1128555] : [class_Orderings_Olinorder(_1128551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128551), _1128553)), -(_1128555 = c_Orderings_Obot__class_Obot(tc_fun(_1128551, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1128551, tc_HOL_Obool)), _1128555), _1128553)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1128551), c_Big__Operators_Olinorder__class_OMin(_1128551, _1128555)), c_Big__Operators_Olinorder__class_OMin(_1128551, _1128553)) = c_Big__Operators_Olinorder__class_OMin(_1128551, _1128553))], (47567 ^ _781215) ^ [_1738461, _1738463, _1738465, _1738467, _1738469] : [c_List_Olist__all2(_1738461, _1738463, _1738465, _1738467, _1738469), 47570 ^ _781215 : [(47573 ^ _781215) ^ [_1738627] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1738461, _1738463)), _1738627), hAPP(c_List_Oset(tc_prod(_1738461, _1738463)), hAPP(hAPP(c_List_Ozip(_1738461, _1738463), _1738467), _1738469)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1738461, _1738463, tc_HOL_Obool), _1738465), _1738627)))], (47571 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738461)), _1738467) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738463)), _1738469))]]], (42525 ^ _781215) ^ [_1624869, _1624871, _1624873, _1624875, _1624877] : [class_Orderings_Olinorder(_1624869), -(hBOOL(hAPP(hAPP(c_member(_1624869), hAPP(_1624871, _1624873)), hAPP(c_Set_Oimage(_1624875, _1624869, _1624871), hAPP(c_List_Oset(_1624875), _1624877))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1624875, _1624869, _1624871, _1624873, _1624877) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1624875, _1624869, _1624871), _1624873), _1624877))], (31431 ^ _781215) ^ [_1357340, _1357342, _1357344, _1357346, _1357348] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1357344, _1357340)), hAPP(hAPP(c_Product__Type_OPair(_1357344, _1357340), _1357348), _1357342)), _1357346)), -(hBOOL(hAPP(hAPP(c_member(_1357340), _1357342), hAPP(c_Relation_OImage(_1357344, _1357340, _1357346), hAPP(hAPP(c_Set_Oinsert(_1357344), _1357348), c_Orderings_Obot__class_Obot(tc_fun(_1357344, tc_HOL_Obool)))))))], (22096 ^ _781215) ^ [_1179345, _1179347, _1179349, _1179351, _1179353] : [-(_1179345 = c_Orderings_Obot__class_Obot(tc_fun(_1179347, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179347, tc_fun(_1179349, tc_HOL_Obool)), _1179345), hAPP(hAPP(c_COMBC(_1179347, tc_fun(_1179349, tc_HOL_Obool), tc_fun(_1179349, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1179349, tc_HOL_Obool), tc_fun(tc_fun(_1179349, tc_HOL_Obool), tc_fun(_1179349, tc_HOL_Obool)), _1179347), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1179349, tc_HOL_Obool))), _1179351)), _1179353)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1179349, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179347, tc_fun(_1179349, tc_HOL_Obool)), _1179345), _1179351)), _1179353))], (14792 ^ _781215) ^ [_1040322, _1040324, _1040326, _1040328, _1040330, _1040332] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1040322, _1040324, _1040326)), _1040328), _1040330), _1040332)), 14797 ^ _781215 : [(14800 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1040324), _1040328), _1040330), _1040332)))], (14798 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1040322, _1040328)))]], 14801 ^ _781215 : [(14804 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1040326), _1040328), _1040330), _1040332)))], (14802 ^ _781215) ^ [] : [hBOOL(hAPP(_1040322, _1040328))]]], (26801 ^ _781215) ^ [_1268208, _1268210, _1268212, _1268214, _1268216] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1268208, _1268210, tc_HOL_Obool), _1268212), hAPP(hAPP(c_Product__Type_OPair(_1268208, _1268210), _1268214), _1268216))), -(hBOOL(hAPP(hAPP(_1268212, _1268214), _1268216)))], (36506 ^ _781215) ^ [_1467382, _1467384] : [class_Lattices_Obounded__lattice__top(_1467382), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1467382), _1467384), c_Orderings_Otop__class_Otop(_1467382)) = c_Orderings_Otop__class_Otop(_1467382))], (20565 ^ _781215) ^ [_1150281, _1150283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150281)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150283))))], (37313 ^ _781215) ^ [_1488623, _1488625, _1488627, _1488629, _1488631] : [37315 ^ _781215 : [(37318 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1488629, 37314 ^ [_1488623, _1488625, _1488627, _1488629, _1488631]), _1488631))], (37316 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488623), 37314 ^ [_1488623, _1488625, _1488627, _1488629, _1488631]), _1488627)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1488623, tc_fun(_1488625, tc_HOL_Obool)), _1488627), _1488629), _1488631)))], (33767 ^ _781215) ^ [_1410961, _1410963, _1410965] : [class_Lattices_Olattice(_1410961), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410961), _1410963)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410961), _1410965)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410961, tc_HOL_Obool)), _1410963), _1410965) = c_Orderings_Obot__class_Obot(tc_fun(_1410961, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1410961), c_Big__Operators_Olattice__class_OSup__fin(_1410961, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410961, tc_HOL_Obool)), _1410963), _1410965))), c_Big__Operators_Olattice__class_OSup__fin(_1410961, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410961, tc_HOL_Obool)), _1410963), _1410965))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1410961), c_Big__Operators_Olattice__class_OSup__fin(_1410961, _1410963)), c_Big__Operators_Olattice__class_OSup__fin(_1410961, _1410965)))], (15370 ^ _781215) ^ [_1050625, _1050627] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050625), _1050627) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050627), _1050625))], (48784 ^ _781215) ^ [_1766304, _1766306, _1766308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1766304), _1766306)), -(c_Random_Ominus__shift(_1766308, _1766304, _1766306) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1766308), _1766304)), _1766306))], (51632 ^ _781215) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (5804 ^ _781215) ^ [_873501, _873503, _873505, _873507] : [5806 ^ _781215 : [(5809 ^ _781215) ^ [] : [hBOOL(hAPP(_873505, 5805 ^ [_873501, _873503, _873505, _873507]))], (5807 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_873501), 5805 ^ [_873501, _873503, _873505, _873507]), c_Option_Oset(_873501, _873503))))]], _873503 = hAPP(c_Option_Ooption_OSome(_873501), _873507), -(hBOOL(hAPP(_873505, _873507)))], (39030 ^ _781215) ^ [_1530672, _1530674] : [-(hAPP(c_Set_OCollect(_1530672), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1530672), c_fNot), _1530674)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1530672, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1530672), _1530674)))], (35799 ^ _781215) ^ [_1454318, _1454320] : [class_Groups_Oordered__ab__group__add__abs(_1454318), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454318), c_Groups_Ozero__class_Ozero(_1454318)), hAPP(c_Groups_Oabs__class_Oabs(_1454318), _1454320))))], (41287 ^ _781215) ^ [_1592132, _1592134, _1592136, _1592138, _1592140, _1592142] : [-(hAPP(hAPP(c_Option_Omap(_1592132, _1592134), _1592136), hAPP(hAPP(c_Option_Omap(_1592138, _1592132), _1592140), _1592142)) = hAPP(hAPP(c_Option_Omap(_1592138, _1592134), hAPP(c_Fun_Ocomp(_1592132, _1592134, _1592138, _1592136), _1592140)), _1592142))], (13388 ^ _781215) ^ [_1014000, _1014002, _1014004] : [-(hAPP(c_Finite__Set_Ofold1(_1014000, _1014002), hAPP(hAPP(c_Set_Oinsert(_1014000), _1014004), c_Orderings_Obot__class_Obot(tc_fun(_1014000, tc_HOL_Obool)))) = _1014004)], (25666 ^ _781215) ^ [_1243134, _1243136] : [_1243134 = _1243136, -(c_Code__Numeral_OSuc__code__numeral(_1243134) = c_Code__Numeral_OSuc__code__numeral(_1243136))], (42431 ^ _781215) ^ [_1621633, _1621635, _1621637] : [-(hBOOL(hAPP(c_List_Odistinct(_1621633), hAPP(hAPP(c_List_Olist_OCons(_1621633), _1621635), _1621637)))), -(hBOOL(hAPP(hAPP(c_member(_1621633), _1621635), hAPP(c_List_Oset(_1621633), _1621637)))), hBOOL(hAPP(c_List_Odistinct(_1621633), _1621637))], (31134 ^ _781215) ^ [_1351143, _1351145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1351143), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1351145), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1351145), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1351143))))), -(_1351143 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1351145), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1351145), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1351143))))], (41881 ^ _781215) ^ [_1606071, _1606073, _1606075] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1606071, tc_HOL_Obool)), hAPP(c_List_Oset(_1606071), c_List_Oremove1(_1606071, _1606073, _1606075))), hAPP(c_List_Oset(_1606071), _1606075))))], (38312 ^ _781215) ^ [_1511513, _1511515, _1511517, _1511519] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1511513, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1511515, _1511513, _1511517), hAPP(c_Set_Ovimage(_1511515, _1511513, _1511517), _1511519))), _1511519)))], (31523 ^ _781215) ^ [_1360186, _1360188, _1360190, _1360192] : [class_Rings_Osemiring__1(_1360186), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1360186), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360188, tc_Nat_Onat), _1360190), _1360192)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360188, _1360186), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1360186, _1360188), c_Nat_Osemiring__1__class_Oof__nat(_1360186)), _1360190)), _1360192))], (20675 ^ _781215) ^ [_1152169] : [-(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)), _1152169)) = _1152169)], (41303 ^ _781215) ^ [_1592573, _1592575, _1592577, _1592579, _1592581] : [c_Finite__Set_Ofun__left__comm(_1592573, _1592575, _1592577), -(hAPP(c_Fun_Ocomp(_1592575, _1592575, _1592575, hAPP(_1592577, _1592579)), hAPP(_1592577, _1592581)) = hAPP(c_Fun_Ocomp(_1592575, _1592575, _1592575, hAPP(_1592577, _1592581)), hAPP(_1592577, _1592579)))], (8916 ^ _781215) ^ [_932354, _932356, _932358] : [_932354 = _932356, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932358, tc_HOL_Obool)), _932356), _932354)))], (13410 ^ _781215) ^ [_1014374, _1014376] : [_1014374 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014374), _1014376), -(_1014376 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1014374 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44292 ^ _781215) ^ [_1667030, _1667032, _1667034, _1667036, _1667038] : [hAPP(hAPP(c_List_Oappend(_1667030), _1667032), _1667034) = hAPP(hAPP(c_List_Oappend(_1667030), _1667036), _1667038), 44298 ^ _781215 : [(44301 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1667030), 44295 ^ [_1667030, _1667032, _1667034, _1667036, _1667038]), _1667034) = _1667038)], (44299 ^ _781215) ^ [] : [-(_1667032 = hAPP(hAPP(c_List_Oappend(_1667030), _1667036), 44295 ^ [_1667030, _1667032, _1667034, _1667036, _1667038]))]], 44302 ^ _781215 : [(44305 ^ _781215) ^ [] : [-(_1667034 = hAPP(hAPP(c_List_Oappend(_1667030), 44295 ^ [_1667030, _1667032, _1667034, _1667036, _1667038]), _1667038))], (44303 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1667030), _1667032), 44295 ^ [_1667030, _1667032, _1667034, _1667036, _1667038]) = _1667036)]]], (35004 ^ _781215) ^ [_1437715, _1437717, _1437719, _1437721, _1437723] : [c_Fun_Oinj__on(_1437715, _1437717, _1437719, _1437721), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437717, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1437715, _1437717, _1437719), _1437721)), _1437723)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1437717), _1437723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1437715), _1437721)), hAPP(c_Finite__Set_Ocard(_1437717), _1437723))))], (50898 ^ _781215) ^ [_1815432, _1815434, _1815436, _1815438] : [-(c_New__Random__Sequence_Opos__empty(_1815432, _1815434, _1815436, _1815438) = c_New__DSequence_Opos__empty(_1815432))], (28976 ^ _781215) ^ [_1309454, _1309456, _1309458, _1309460] : [class_Fields_Olinordered__field__inverse__zero(_1309454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309454), _1309456), _1309458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309454), c_Groups_Ozero__class_Ozero(_1309454)), _1309460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309454), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309454), _1309456), _1309460)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309454), _1309458), _1309460))))], (1568 ^ _781215) ^ [_803785, _803787] : [-(class_Groups_Ocancel__semigroup__add(_803785)), _803787 = _803785, class_Groups_Ocancel__semigroup__add(_803787)], (2064 ^ _781215) ^ [_811391, _811393, _811395, _811397] : [-(c_Int_Onat__aux(_811397, _811393) = c_Int_Onat__aux(_811395, _811391)), _811397 = _811395, _811393 = _811391], (1208 ^ _781215) ^ [_799285, _799287] : [-(class_Groups_Ogroup__add(_799285)), _799287 = _799285, class_Groups_Ogroup__add(_799287)], (21249 ^ _781215) ^ [_1161622, _1161624, _1161626, _1161628] : [-(hAPP(c_Set_Oimage(_1161622, _1161624, _1161626), _1161628) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1161622, tc_fun(_1161624, tc_HOL_Obool)), _1161628), hAPP(hAPP(c_COMBC(_1161622, tc_fun(_1161624, tc_HOL_Obool), tc_fun(_1161624, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1161624, tc_fun(tc_fun(_1161624, tc_HOL_Obool), tc_fun(_1161624, tc_HOL_Obool)), _1161622), c_Set_Oinsert(_1161624)), _1161626)), c_Orderings_Obot__class_Obot(tc_fun(_1161624, tc_HOL_Obool)))))], (41775 ^ _781215) ^ [_1603964, _1603966, _1603968, _1603970, _1603972, _1603974] : [c_Finite__Set_Ofolding__idem(_1603964, _1603966, _1603968, _1603970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1603964), _1603972)), hBOOL(hAPP(hAPP(c_member(_1603964), _1603974), _1603972)), -(hAPP(c_Fun_Ocomp(_1603966, _1603966, _1603966, hAPP(_1603970, _1603972)), hAPP(_1603968, _1603974)) = hAPP(_1603970, _1603972))], (42036 ^ _781215) ^ [_1610432, _1610434, _1610436, _1610438, _1610440, _1610442, _1610444] : [hAPP(hAPP(c_List_Omap(_1610432, _1610434), _1610436), _1610438) = hAPP(hAPP(c_List_Omap(_1610440, _1610434), _1610442), _1610444), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610432)), _1610438) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610440)), _1610444))], (11206 ^ _781215) ^ [_975845, _975847, _975849] : [class_Rings_Ocomm__semiring__1(_975845), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975845), _975847), _975849) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975845), _975849), _975847))], (2000 ^ _781215) ^ [_810299, _810301] : [_810301 = _810299, -(c_HOL_Obool_Obool__size(_810301) = c_HOL_Obool_Obool__size(_810299))], (6235 ^ _781215) ^ [_881797, _881799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_881797), _881799)), -(_881799 = c_Orderings_Obot__class_Obot(tc_fun(_881797, tc_HOL_Obool))), 6244 ^ _781215 : [(6247 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_881797), 6242 ^ [_881797, _881799])))], (6245 ^ _781215) ^ [] : [-(_881799 = hAPP(hAPP(c_Set_Oinsert(_881797), 6243 ^ [_881797, _881799]), 6242 ^ [_881797, _881799]))]]], (36450 ^ _781215) ^ [_1466256, _1466258] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466256), c_Orderings_Otop__class_Otop(tc_fun(_1466256, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466258), c_Orderings_Otop__class_Otop(tc_fun(_1466258, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1466256, _1466258)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1466256, _1466258), tc_HOL_Obool)))))], (20756 ^ _781215) ^ [_1153488, _1153490] : [20757 ^ _781215 : [(20758 ^ _781215) ^ [_1153544] : [_1153490 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153488), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1153544)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1153488), _1153490)))], (21353 ^ _781215) ^ [_1164166, _1164168, _1164170, _1164172, _1164174] : [21355 ^ _781215 : [(21358 ^ _781215) ^ [] : [hBOOL(hAPP(_1164174, 21354 ^ [_1164166, _1164168, _1164170, _1164172, _1164174]))], (21356 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1164166), 21354 ^ [_1164166, _1164168, _1164170, _1164172, _1164174]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1164168, tc_fun(_1164166, tc_HOL_Obool)), _1164170), _1164172))))]], 21359 ^ _781215 : [(21360 ^ _781215) ^ [_1164388] : [hBOOL(hAPP(hAPP(c_member(_1164168), _1164388), _1164170)), 21363 ^ _781215 : [(21364 ^ _781215) ^ [_1164485] : [hBOOL(hAPP(hAPP(c_member(_1164166), _1164485), hAPP(_1164172, _1164388))), -(hBOOL(hAPP(_1164174, _1164485)))]]]]], (21948 ^ _781215) ^ [_1176144] : [-(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)))), _1176144) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1176144)))], (41573 ^ _781215) ^ [_1599121, _1599123, _1599125, _1599127, _1599129, _1599131] : [c_Finite__Set_Ofolding(_1599121, _1599123, _1599125, _1599127), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599121), _1599129)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599121), _1599131)), -(hAPP(c_Fun_Ocomp(_1599123, _1599123, _1599123, hAPP(_1599127, _1599131)), hAPP(_1599127, _1599129)) = hAPP(c_Fun_Ocomp(_1599123, _1599123, _1599123, hAPP(_1599127, _1599129)), hAPP(_1599127, _1599131)))], (45031 ^ _781215) ^ [_1684521, _1684523, _1684525] : [class_Lattices_Olattice(_1684521), -(c_Big__Operators_Olattice__class_OSup__fin(_1684521, hAPP(c_List_Oset(_1684521), hAPP(hAPP(c_List_Olist_OCons(_1684521), _1684523), _1684525))) = hAPP(c_List_Ofoldl(_1684521, _1684521, c_Lattices_Osemilattice__sup__class_Osup(_1684521), _1684523), _1684525))], (5030 ^ _781215) ^ [_857712, _857714] : [_857714 = _857712, -(c_Lazy__Sequence_Ohit__bound(_857714) = c_Lazy__Sequence_Ohit__bound(_857712))], (21782 ^ _781215) ^ [_1171962, _1171964, _1171966, _1171968] : [class_Rings_Osemiring__1(_1171962), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1171962, _1171964, hAPP(c_Nat_OSuc, _1171966), _1171968) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1171962, _1171964, _1171966, hAPP(_1171964, _1171968)))], (1488 ^ _781215) ^ [_802785, _802787] : [-(class_Rings_Olinordered__comm__semiring__strict(_802785)), _802787 = _802785, class_Rings_Olinordered__comm__semiring__strict(_802787)], (27058 ^ _781215) ^ [_1272993, _1272995] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1272993, _1272995), c_Divides_Odivmod__nat(_1272993, _1272995))))], (44830 ^ _781215) ^ [_1680297, _1680299, _1680301] : [-(hAPP(c_List_Otl(_1680297), hAPP(hAPP(c_List_Odrop(_1680297), _1680299), _1680301)) = hAPP(hAPP(c_List_Odrop(_1680297), _1680299), hAPP(c_List_Otl(_1680297), _1680301)))], (16937 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (39292 ^ _781215) ^ [_1537359, _1537361, _1537363, _1537365, _1537367, _1537369] : [class_Groups_Ocomm__monoid__add(_1537359), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537361), _1537363)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537361, _1537359), hAPP(hAPP(c_COMBS(_1537361, _1537359, _1537359), hAPP(hAPP(c_COMBS(_1537361, _1537359, tc_fun(_1537359, _1537359)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1537359, tc_fun(_1537359, _1537359)), _1537361), c_If(_1537359)), _1537365)), _1537367)), _1537369)), _1537363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1537359), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537361, _1537359), _1537367), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1537361, tc_HOL_Obool)), _1537363), hAPP(c_Set_OCollect(_1537361), _1537365)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537361, _1537359), _1537369), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1537361, tc_HOL_Obool)), _1537363), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1537361, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1537361), _1537365))))))], (37067 ^ _781215) ^ [_1482533, _1482535, _1482537, _1482539, _1482541] : [class_Complete__Lattice_Ocomplete__lattice(_1482533), 37070 ^ _781215 : [(37071 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482533), _1482535), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482537, _1482533), _1482539), _1482541))), 37074 ^ _781215 : [(37075 ^ _781215) ^ [_1482714] : [hBOOL(hAPP(hAPP(c_member(_1482537), _1482714), _1482539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482533), _1482535), hAPP(_1482541, _1482714))))]]], (37081 ^ _781215) ^ [] : [37083 ^ _781215 : [(37086 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482533), _1482535), hAPP(_1482541, 37082 ^ [_1482533, _1482535, _1482537, _1482539, _1482541])))], (37084 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482537), 37082 ^ [_1482533, _1482535, _1482537, _1482539, _1482541]), _1482539)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482533), _1482535), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482537, _1482533), _1482539), _1482541))))]]], (49211 ^ _781215) ^ [_1775550, _1775552] : [-(c_Transitive__Closure_Otrancl(_1775550, _1775552) = hAPP(hAPP(c_Relation_Orel__comp(_1775550, _1775550, _1775550), _1775552), c_Transitive__Closure_Ortrancl(_1775550, _1775552)))], (46496 ^ _781215) ^ [_1716301, _1716303, _1716305] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716301)), c_List_OtakeWhile(_1716301, _1716303, _1716305))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716301)), _1716305))))], (9151 ^ _781215) ^ [_936449] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936449), _936449))))], (51758 ^ _781215) ^ [_1826809, _1826811] : [hBOOL(hAPP(hAPP(c_fimplies, _1826809), _1826811)), hBOOL(_1826809), -(hBOOL(_1826811))], (40837 ^ _781215) ^ [_1581510, _1581512] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_1581510, _1581512)], (19266 ^ _781215) ^ [_1126927, _1126929, _1126931] : [class_Orderings_Olinorder(_1126927), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126927), _1126929)), -(_1126929 = c_Orderings_Obot__class_Obot(tc_fun(_1126927, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1126927, c_Orderings_Oord__class_Omin(_1126927), hAPP(hAPP(c_Set_Oinsert(_1126927), _1126931), _1126929)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1126927), _1126931), c_Big__Operators_Olattice_OInf__fin(_1126927, c_Orderings_Oord__class_Omin(_1126927), _1126929)))], (14248 ^ _781215) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20822 ^ _781215) ^ [_1154544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1154544)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154544), c_Int_OPls)))], (36592 ^ _781215) ^ [_1468953, _1468955, _1468957, _1468959] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1468953, tc_fun(_1468955, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1468953, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1468955, tc_HOL_Obool), tc_fun(_1468955, tc_HOL_Obool), _1468953), hAPP(c_COMBC(_1468955, tc_fun(_1468955, tc_HOL_Obool), tc_HOL_Obool), c_member(_1468955))), _1468957)), _1468959)), -(hBOOL(hAPP(hAPP(c_member(_1468955), _1468959), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1468953, tc_fun(_1468955, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1468953, tc_HOL_Obool))), _1468957))))], (23787 ^ _781215) ^ [_1210015, _1210017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1210015), _1210017)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1210015, _1210017) = _1210015)], (48808 ^ _781215) ^ [_1766603, _1766605, _1766607] : [-(_1766603 = c_List_Olist_ONil(_1766605)), -(hBOOL(hAPP(hAPP(c_member(_1766605), hAPP(c_Product__Type_Ofst(_1766605, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1766605, _1766603), _1766607))), hAPP(c_List_Oset(_1766605), _1766603))))], (39927 ^ _781215) ^ [_1560823, _1560825, _1560827, _1560829] : [39928 ^ _781215 : [(39929 ^ _781215) ^ [_1560877] : [hBOOL(hAPP(hAPP(_1560827, _1560877), _1560829))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1560823, _1560825, _1560827), _1560829)))], (46890 ^ _781215) ^ [_1724506, _1724508] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1724506))), c_Enum_Osublists(_1724506, _1724508)) = 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(_1724506)), _1724508)))], (7562 ^ _781215) ^ [_908335, _908337, _908339] : [class_Orderings_Opreorder(_908335), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908335), _908337), _908339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908335), _908339), _908337))], (14226 ^ _781215) ^ [_1029967, _1029969] : [class_Groups_Olinordered__ab__group__add(_1029967), 14229 ^ _781215 : [(14236 ^ _781215) ^ [] : [_1029969 = c_Groups_Ozero__class_Ozero(_1029967), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029967), _1029969), _1029969) = c_Groups_Ozero__class_Ozero(_1029967))], (14230 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029967), _1029969), _1029969) = c_Groups_Ozero__class_Ozero(_1029967), -(_1029969 = c_Groups_Ozero__class_Ozero(_1029967))]]], (4736 ^ _781215) ^ [_852985, _852987] : [_852987 = _852985, -(c_Set_OCollect(_852987) = c_Set_OCollect(_852985))], (14514 ^ _781215) ^ [_1035033] : [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), _1035033))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1035033) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1035033)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41106 ^ _781215) ^ [_1587784, _1587786, _1587788] : [-(c_Map_Odom(_1587784, _1587786, hAPP(c_Map_Omap__of(_1587784, _1587786), _1587788)) = hAPP(c_Set_Oimage(tc_prod(_1587784, _1587786), _1587784, c_Product__Type_Ofst(_1587784, _1587786)), hAPP(c_List_Oset(tc_prod(_1587784, _1587786)), _1587788)))], (44286 ^ _781215) ^ [_1666891, _1666893, _1666895, _1666897] : [_1666895 = _1666897, -(hAPP(hAPP(c_List_Oappend(_1666891), _1666893), _1666895) = hAPP(hAPP(c_List_Oappend(_1666891), _1666893), _1666897))], (7588 ^ _781215) ^ [_908676, _908678, _908680, _908682, _908684] : [hBOOL(hAPP(hAPP(c_member(_908676), _908678), _908680)), -(hAPP(c_Map_Orestrict__map(_908676, _908682, _908684, _908680), _908678) = hAPP(_908684, _908678))], (40994 ^ _781215) ^ [_1585307] : [-(hAPP(c_List_Omap(_1585307, _1585307), c_COMBI(_1585307)) = c_Fun_Oid(tc_List_Olist(_1585307)))], (44576 ^ _781215) ^ [_1674623, _1674625, _1674627, _1674629] : [-(hAPP(hAPP(c_List_Odrop(_1674623), _1674625), hAPP(hAPP(c_List_Otake(_1674623), _1674627), _1674629)) = hAPP(hAPP(c_List_Otake(_1674623), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1674627), _1674625)), hAPP(hAPP(c_List_Odrop(_1674623), _1674625), _1674629)))], (23446 ^ _781215) ^ [_1203704, _1203706, _1203708, _1203710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203706), _1203708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203708), 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), _1203706), _1203704)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1203706), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1203710, _1203704))), _1203708))))], (5646 ^ _781215) ^ [_870202] : [5647 ^ _781215 : [(5648 ^ _781215) ^ [_870250] : [hAPP(c_Com_Obody, _870202) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _870250)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _870202))))], (292 ^ _781215) ^ [_785691, _785693] : [-(class_Fields_Olinordered__field__inverse__zero(_785691)), _785693 = _785691, class_Fields_Olinordered__field__inverse__zero(_785693)], (43764 ^ _781215) ^ [_1655207, _1655209, _1655211] : [-(hAPP(hAPP(c_List_Omap(_1655207, _1655209), _1655211), c_List_Olist_ONil(_1655207)) = c_List_Olist_ONil(_1655209))], (35395 ^ _781215) ^ [_1446280, _1446282, _1446284] : [class_Orderings_Oorder(_1446280), 35398 ^ _781215 : [(35405 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446280), _1446284), _1446282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1446280, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1446280), _1446282)), hAPP(c_SetInterval_Oord__class_OatLeast(_1446280), _1446284))))], (35399 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1446280, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1446280), _1446282)), hAPP(c_SetInterval_Oord__class_OatLeast(_1446280), _1446284))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446280), _1446284), _1446282)))]]], (5800 ^ _781215) ^ [_873414, _873416, _873418, _873420, _873422] : [-(c_Option_Ooption_Ooption__rec(_873414, _873416, _873418, _873420, hAPP(c_Option_Ooption_OSome(_873416), _873422)) = hAPP(_873420, _873422))], (37628 ^ _781215) ^ [_1496010, _1496012, _1496014] : [37630 ^ _781215 : [(37633 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1496010), 37629 ^ [_1496010, _1496012, _1496014]), c_Wellfounded_Oacc(_1496010, _1496014)))], (37631 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1496010, _1496010)), hAPP(hAPP(c_Product__Type_OPair(_1496010, _1496010), 37629 ^ [_1496010, _1496012, _1496014]), _1496012)), _1496014)))]], -(hBOOL(hAPP(hAPP(c_member(_1496010), _1496012), c_Wellfounded_Oacc(_1496010, _1496014))))], (12016 ^ _781215) ^ [_989870, _989872, _989874] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989870), _989872) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989870), _989874), -(_989870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_989872 = _989874)], (4330 ^ _781215) ^ [_846904, _846906, _846908, _846910] : [-(c_List_Olistrel1(_846910, _846906) = c_List_Olistrel1(_846908, _846904)), _846910 = _846908, _846906 = _846904], (16467 ^ _781215) ^ [_1072603, _1072605, _1072607] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072603, tc_HOL_Obool)), _1072605), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072603, tc_HOL_Obool)), _1072605), _1072607))))], (24704 ^ _781215) ^ [_1227075, _1227077] : [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), _1227075), _1227077))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227075))), -(_1227077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31936 ^ _781215) ^ [_1369832, _1369834, _1369836, _1369838] : [-(hBOOL(hAPP(hAPP(c_member(_1369832), _1369834), _1369836))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1369832, tc_Nat_Onat), _1369838), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369832, tc_HOL_Obool)), _1369836), hAPP(hAPP(c_Set_Oinsert(_1369832), _1369834), c_Orderings_Obot__class_Obot(tc_fun(_1369832, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1369832, tc_Nat_Onat), _1369838), _1369836))], (48802 ^ _781215) ^ [_1766560, _1766562] : [-(_1766560 = _1766562), -(c_Random_Oinc__shift(_1766560, _1766562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1766562), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (20521 ^ _781215) ^ [_1149543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149543), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1149543)), c_Int_OPls)))], (41643 ^ _781215) ^ [_1600572, _1600574, _1600576, _1600578, _1600580, _1600582] : [c_Finite__Set_Ofolding(_1600572, _1600574, _1600576, _1600578), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600572), _1600580)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600572), _1600582)), -(hAPP(c_Fun_Ocomp(_1600574, _1600574, _1600574, hAPP(_1600578, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1600572, tc_HOL_Obool)), _1600580), _1600582))), hAPP(_1600578, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1600572, tc_HOL_Obool)), _1600580), _1600582))) = hAPP(c_Fun_Ocomp(_1600574, _1600574, _1600574, hAPP(_1600578, _1600580)), hAPP(_1600578, _1600582)))], (14530 ^ _781215) ^ [_1035344, _1035346, _1035348, _1035350, _1035352, _1035354] : [hBOOL(hAPP(_1035344, _1035346)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1035348), _1035346), _1035350), _1035352)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1035344, _1035348, _1035354)), _1035346), _1035350), _1035352)))], (4630 ^ _781215) ^ [_851416, _851418] : [_851418 = _851416, -(c_Nitpick_Ofrac(_851418) = c_Nitpick_Ofrac(_851416))], (33256 ^ _781215) ^ [_1399744, _1399746, _1399748, _1399750] : [class_Orderings_Oorder(_1399744), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399744, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1399744, _1399746, _1399748)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1399744, _1399748, _1399750)) = c_Orderings_Obot__class_Obot(tc_fun(_1399744, tc_HOL_Obool)))], (9555 ^ _781215) ^ [_943654, _943656, _943658] : [class_Orderings_Oorder(_943654), 9558 ^ _781215 : [(9559 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943654), _943656), _943658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943654), _943656), _943658))), -(_943656 = _943658)], (9569 ^ _781215) ^ [] : [9570 ^ _781215 : [(9573 ^ _781215) ^ [] : [_943656 = _943658], (9571 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943654), _943656), _943658))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943654), _943656), _943658)))]]], (24490 ^ _781215) ^ [_1222994, _1222996, _1222998] : [class_Rings_Ocomm__semiring__1(_1222994), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1222994), _1222996), 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)))), _1222998))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222994), _1222996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222994), hAPP(hAPP(c_Power_Opower__class_Opower(_1222994), _1222996), _1222998)), hAPP(hAPP(c_Power_Opower__class_Opower(_1222994), _1222996), _1222998))))], (24176 ^ _781215) ^ [_1217303, _1217305] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1217303))), _1217305) = 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)))), _1217303), _1217305))], (22148 ^ _781215) ^ [_1180383, _1180385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180383), 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)))), _1180385)), 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)))), _1180383)) = 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), _1180385), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1180383))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (41917 ^ _781215) ^ [_1607329, _1607331, _1607333, _1607335] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607329, _1607329)), hAPP(hAPP(c_Product__Type_OPair(_1607329, _1607329), _1607331), _1607333)), hAPP(c_List_Oset(tc_prod(_1607329, _1607329)), hAPP(hAPP(c_List_Ozip(_1607329, _1607329), _1607335), _1607335))))), hBOOL(hAPP(hAPP(c_member(_1607329), _1607331), hAPP(c_List_Oset(_1607329), _1607335))), _1607331 = _1607333], (51696 ^ _781215) ^ [_1826066] : [-(hBOOL(_1826066)), -(hBOOL(hAPP(c_fNot, _1826066)))], (14036 ^ _781215) ^ [_1025885, _1025887, _1025889, _1025891, _1025893, _1025895] : [class_Rings_Olinordered__semiring__1(_1025885), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025885), _1025887), _1025889)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025885), _1025891), _1025889)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025885), c_Groups_Ozero__class_Ozero(_1025885)), _1025893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025885), c_Groups_Ozero__class_Ozero(_1025885)), _1025895)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025885), _1025893), _1025895) = c_Groups_Oone__class_Oone(_1025885), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025885), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025885), _1025893), _1025887)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025885), _1025895), _1025891))), _1025889)))], (19678 ^ _781215) ^ [_1134508, _1134510] : [class_Orderings_Olinorder(_1134508), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134508), _1134510)), -(_1134510 = c_Orderings_Obot__class_Obot(tc_fun(_1134508, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1134508), c_Big__Operators_Olinorder__class_OMax(_1134508, _1134510)), _1134510)))], (8079 ^ _781215) ^ [_917376, _917378, _917380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917376), _917378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917378), _917380)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _917376)), _917380)))], (16869 ^ _781215) ^ [_1084224, _1084226] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084224))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084224)), _1084226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1084226))], (25138 ^ _781215) ^ [_1235015] : [_1235015 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1235015) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45716 ^ _781215) ^ [_1698205, _1698207, _1698209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1698205), _1698207)), -(c_List_Oupt(_1698205, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1698207), _1698209)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1698205, _1698207)), c_List_Oupt(_1698207, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1698207), _1698209))))], (25568 ^ _781215) ^ [] : [-(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))], (19430 ^ _781215) ^ [_1129648, _1129650, _1129652] : [class_Orderings_Olinorder(_1129648), hBOOL(hAPP(c_Finite__Set_Ofinite(_1129648), _1129650)), 19437 ^ _781215 : [(19444 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1129648, tc_HOL_Obool)), _1129650), hAPP(hAPP(c_Set_Oinsert(_1129648), _1129652), c_Orderings_Obot__class_Obot(tc_fun(_1129648, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1129648, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1129648, c_Orderings_Oord__class_Omin(_1129648), hAPP(hAPP(c_Set_Oinsert(_1129648), _1129652), _1129650)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1129648), _1129652), c_Big__Operators_Olattice_OInf__fin(_1129648, c_Orderings_Oord__class_Omin(_1129648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1129648, tc_HOL_Obool)), _1129650), hAPP(hAPP(c_Set_Oinsert(_1129648), _1129652), c_Orderings_Obot__class_Obot(tc_fun(_1129648, tc_HOL_Obool)))))))], (19438 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1129648, tc_HOL_Obool)), _1129650), hAPP(hAPP(c_Set_Oinsert(_1129648), _1129652), c_Orderings_Obot__class_Obot(tc_fun(_1129648, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1129648, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1129648, c_Orderings_Oord__class_Omin(_1129648), hAPP(hAPP(c_Set_Oinsert(_1129648), _1129652), _1129650)) = _1129652)]]], (15468 ^ _781215) ^ [_1052484, _1052486] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052484), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1052486)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052484), _1052486))], (476 ^ _781215) ^ [_788617, _788619, _788621, _788623, _788625, _788627] : [-(c_Hoare__Mirabelle_Otriple__valid(_788625, _788621, _788617)), c_Hoare__Mirabelle_Otriple__valid(_788627, _788623, _788619), _788627 = _788625, _788623 = _788621, _788619 = _788617], (24166 ^ _781215) ^ [_1217075, _1217077] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1217075)))), _1217077) = 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)))), _1217075)), _1217077))], (38242 ^ _781215) ^ [_1509787, _1509789, _1509791, _1509793, _1509795] : [-(hAPP(hAPP(c_Option_Omap(_1509787, _1509789), _1509791), _1509793) = hAPP(c_Option_Ooption_OSome(_1509789), _1509795)), 38243 ^ _781215 : [(38244 ^ _781215) ^ [_1509855] : [_1509793 = hAPP(c_Option_Ooption_OSome(_1509787), _1509855), hAPP(_1509791, _1509855) = _1509795]]], (27636 ^ _781215) ^ [_1284258, _1284260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284258), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1284260, _1284258) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1284260), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1284258)))], (7877 ^ _781215) ^ [_914279] : [-(hAPP(c_Nat_OSuc, _914279) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914279), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (38219 ^ _781215) ^ [_1509320, _1509322, _1509324, _1509326] : [hAPP(hAPP(c_Option_Omap(_1509320, _1509322), _1509324), _1509326) = c_Option_Ooption_ONone(_1509322), -(_1509326 = c_Option_Ooption_ONone(_1509320))], (6533 ^ _781215) ^ [_887809, _887811, _887813, _887815, _887817, _887819, _887821] : [c_Finite__Set_Ofolding__image__simple__idem(_887809, _887811, _887813, _887815, _887817, _887819), -(hAPP(hAPP(_887813, _887821), _887821) = _887821)], (47350 ^ _781215) ^ [_1733507, _1733509, _1733511] : [class_Enum_Oenum(_1733507), class_Enum_Oenum(_1733509), class_HOL_Oequal(_1733509), 47361 ^ _781215 : [(47368 ^ _781215) ^ [] : [c_Enum_Oex__n__lists(_1733507, hAPP(hAPP(c_COMBB(tc_fun(_1733509, _1733507), tc_HOL_Obool, tc_List_Olist(_1733507)), _1733511), hAPP(hAPP(c_COMBB(tc_fun(_1733509, tc_Option_Ooption(_1733507)), tc_fun(_1733509, _1733507), tc_List_Olist(_1733507)), c_Fun_Ocomp(tc_Option_Ooption(_1733507), _1733507, _1733509, c_Option_Othe(_1733507))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1733509, _1733507)), tc_fun(_1733509, tc_Option_Ooption(_1733507)), tc_List_Olist(_1733507)), c_Map_Omap__of(_1733509, _1733507)), hAPP(c_List_Ozip(_1733509, _1733507), c_Enum_Oenum__class_Oenum(_1733509))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733509)), c_Enum_Oenum__class_Oenum(_1733509))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1733509, _1733507)), _1733511)))], (47362 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1733509, _1733507)), _1733511)), -(c_Enum_Oex__n__lists(_1733507, hAPP(hAPP(c_COMBB(tc_fun(_1733509, _1733507), tc_HOL_Obool, tc_List_Olist(_1733507)), _1733511), hAPP(hAPP(c_COMBB(tc_fun(_1733509, tc_Option_Ooption(_1733507)), tc_fun(_1733509, _1733507), tc_List_Olist(_1733507)), c_Fun_Ocomp(tc_Option_Ooption(_1733507), _1733507, _1733509, c_Option_Othe(_1733507))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1733509, _1733507)), tc_fun(_1733509, tc_Option_Ooption(_1733507)), tc_List_Olist(_1733507)), c_Map_Omap__of(_1733509, _1733507)), hAPP(c_List_Ozip(_1733509, _1733507), c_Enum_Oenum__class_Oenum(_1733509))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733509)), c_Enum_Oenum__class_Oenum(_1733509))))]]], (14108 ^ _781215) ^ [_1027246, _1027248] : [class_Rings_Olinordered__idom(_1027246), 14111 ^ _781215 : [(14118 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027246), _1027248), c_Groups_Ozero__class_Ozero(_1027246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027246), _1027248), _1027248)), c_Groups_Ozero__class_Ozero(_1027246))))], (14112 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027246), _1027248), _1027248)), c_Groups_Ozero__class_Ozero(_1027246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027246), _1027248), c_Groups_Ozero__class_Ozero(_1027246))))]]], (7316 ^ _781215) ^ [_904882, _904884, _904886] : [class_Orderings_Olinorder(_904882), 7319 ^ _781215 : [(7320 ^ _781215) ^ [] : [-(_904884 = _904886), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904882), _904884), _904886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904882), _904886), _904884)))], (7330 ^ _781215) ^ [] : [7331 ^ _781215 : [(7334 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904882), _904886), _904884))], (7332 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904882), _904884), _904886))]], _904884 = _904886]]], (11176 ^ _781215) ^ [_975096, _975098, _975100, _975102, _975104] : [class_Rings_Ocomm__semiring__1(_975096), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975096), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975096), _975098), _975100)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975096), _975102), _975104)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975096), _975098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975096), _975100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975096), _975102), _975104))))], (382 ^ _781215) ^ [_787100, _787102, _787104, _787106, _787108, _787110, _787112, _787114, _787116, _787118, _787120, _787122, _787124, _787126] : [-(c_Predicate_Opred__comp(_787124, _787120, _787116, _787112, _787108, _787104, _787100)), c_Predicate_Opred__comp(_787126, _787122, _787118, _787114, _787110, _787106, _787102), _787126 = _787124, _787122 = _787120, _787118 = _787116, _787114 = _787112, _787110 = _787108, _787106 = _787104, _787102 = _787100], (30982 ^ _781215) ^ [_1348363, _1348365] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348363), _1348365)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1348365), _1348363))], (26846 ^ _781215) ^ [_1269098, _1269100, _1269102] : [26848 ^ _781215 : [(26851 ^ _781215) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1269098, _1269100), 26847 ^ [_1269098, _1269100, _1269102]))], (26849 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1269100, 26847 ^ [_1269098, _1269100, _1269102]), _1269102)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1269098, _1269100), _1269102)))], (13610 ^ _781215) ^ [_1017998, _1018000, _1018002, _1018004, _1018006] : [class_Rings_Olinordered__semiring__strict(_1017998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017998), _1018000), _1018002)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017998), _1018004), _1018006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017998), c_Groups_Ozero__class_Ozero(_1017998)), _1018000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017998), c_Groups_Ozero__class_Ozero(_1017998)), _1018004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017998), _1018000), _1018004)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017998), _1018002), _1018006))))], (37033 ^ _781215) ^ [_1480963, _1480965, _1480967, _1480969, _1480971] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1480963, tc_fun(_1480965, tc_HOL_Obool)), _1480967), hAPP(hAPP(c_COMBC(_1480963, tc_fun(_1480965, tc_HOL_Obool), tc_fun(_1480965, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1480965, tc_HOL_Obool), tc_fun(tc_fun(_1480965, tc_HOL_Obool), tc_fun(_1480965, tc_HOL_Obool)), _1480963), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480965, tc_HOL_Obool))), _1480969)), _1480971)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480965, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1480963, tc_fun(_1480965, tc_HOL_Obool)), _1480967), _1480969)), _1480971))], (25336 ^ _781215) ^ [_1237907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1237907))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1237907)))], (51412 ^ _781215) ^ [] : [-(class_HOL_Oequal(tc_Nat_Onat))], (15236 ^ _781215) ^ [_1048501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048501)), -(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)), _1048501))))], (23867 ^ _781215) ^ [_1211399, _1211401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211399)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211401), _1211399)), _1211399) = _1211401)], (18275 ^ _781215) ^ [_1108365, _1108367, _1108369, _1108371] : [class_Orderings_Olinorder(_1108365), 18278 ^ _781215 : [(18287 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108365), _1108367), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1108365), _1108369), _1108371)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108365), _1108367), _1108369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108365), _1108367), _1108371))], (18279 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108365), _1108367), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1108365), _1108369), _1108371))), 18282 ^ _781215 : [(18285 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108365), _1108367), _1108371)))], (18283 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108365), _1108367), _1108369)))]]]]], (40671 ^ _781215) ^ [_1578207, _1578209, _1578211, _1578213, _1578215] : [c_Com_Ocom_OCond(_1578207, _1578209, _1578211) = c_Com_Ocom_OWhile(_1578213, _1578215)], (20144 ^ _781215) ^ [_1142841] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1142841)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1142841)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142841)), 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)))))], (25200 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (34682 ^ _781215) ^ [_1430987, _1430989, _1430991, _1430993] : [34684 ^ _781215 : [(34688 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1430987), 34686 ^ [_1430987, _1430989, _1430991, _1430993]), _1430993)))], (34690 ^ _781215) ^ [] : [-(hAPP(_1430991, 34683 ^ [_1430987, _1430989, _1430991, _1430993]) = hAPP(_1430991, 34686 ^ [_1430987, _1430989, _1430991, _1430993]))], (34692 ^ _781215) ^ [] : [34683 ^ [_1430987, _1430989, _1430991, _1430993] = 34686 ^ [_1430987, _1430989, _1430991, _1430993]], (34685 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1430987), 34683 ^ [_1430987, _1430989, _1430991, _1430993]), _1430993)))]], -(c_Fun_Oinj__on(_1430987, _1430989, _1430991, _1430993))], (45634 ^ _781215) ^ [_1696997, _1696999, _1697001] : [class_Orderings_Olinorder(_1696997), c_List_Olinorder__class_Osorted(_1696997, _1696999), hBOOL(hAPP(c_List_Odistinct(_1696997), _1696999)), c_List_Olinorder__class_Osorted(_1696997, _1697001), hBOOL(hAPP(c_List_Odistinct(_1696997), _1697001)), hAPP(c_List_Oset(_1696997), _1696999) = hAPP(c_List_Oset(_1696997), _1697001), -(_1696999 = _1697001)], (40659 ^ _781215) ^ [_1577865, _1577867, _1577869, _1577871, _1577873] : [c_Com_Ocom_OCall(_1577865, _1577867, _1577869) = c_Com_Ocom_OWhile(_1577871, _1577873)], (28908 ^ _781215) ^ [_1308274, _1308276, _1308278] : [class_Fields_Olinordered__field__inverse__zero(_1308274), 28911 ^ _781215 : [(28926 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308274), c_Groups_Ozero__class_Ozero(_1308274)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308274), _1308276), _1308278)))), 28927 ^ _781215 : [(28934 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308274), _1308276), c_Groups_Ozero__class_Ozero(_1308274))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308274), _1308278), c_Groups_Ozero__class_Ozero(_1308274)))], (28928 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308274), c_Groups_Ozero__class_Ozero(_1308274)), _1308276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308274), c_Groups_Ozero__class_Ozero(_1308274)), _1308278))]]], (28912 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308274), c_Groups_Ozero__class_Ozero(_1308274)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308274), _1308276), _1308278))), 28917 ^ _781215 : [(28920 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308274), c_Groups_Ozero__class_Ozero(_1308274)), _1308278)))], (28918 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308274), c_Groups_Ozero__class_Ozero(_1308274)), _1308276)))]], 28921 ^ _781215 : [(28924 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308274), _1308278), c_Groups_Ozero__class_Ozero(_1308274))))], (28922 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308274), _1308276), c_Groups_Ozero__class_Ozero(_1308274))))]]]]], (14224 ^ _781215) ^ [_1029921, _1029923] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_1029921, _1029923)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1029921)), c_Com_Ocom_Ocom__size(_1029923))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20816 ^ _781215) ^ [_1154443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1154443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1154443))))], (4192 ^ _781215) ^ [_844837, _844839, _844841, _844843] : [-(c_Random_Opick(_844843, _844839) = c_Random_Opick(_844841, _844837)), _844843 = _844841, _844839 = _844837], (20362 ^ _781215) ^ [] : [-(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)))], (2788 ^ _781215) ^ [_822821, _822823, _822825, _822827, _822829, _822831, _822833, _822835] : [-(c_Recdef_Osame__fst(_822835, _822831, _822827, _822823) = c_Recdef_Osame__fst(_822833, _822829, _822825, _822821)), _822835 = _822833, _822831 = _822829, _822827 = _822825, _822823 = _822821], (6009 ^ _781215) ^ [_877066, _877068, _877070, _877072, _877074, _877076] : [c_Hoare__Mirabelle_Ohoare__derivs(_877066, _877068, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877066)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877066), _877070), _877072), _877074)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877066), tc_HOL_Obool)))), 6016 ^ _781215 : [(6019 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_877076, 6014 ^ [_877066, _877068, _877070, _877072, _877074, _877076]), 6015 ^ [_877066, _877068, _877070, _877072, _877074, _877076]))], (6017 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_877074, 6014 ^ [_877066, _877068, _877070, _877072, _877074, _877076]), 6015 ^ [_877066, _877068, _877070, _877072, _877074, _877076])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_877066, _877068, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877066)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877066), _877070), _877072), _877076)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877066), tc_HOL_Obool)))))], (26857 ^ _781215) ^ [_1269322, _1269324] : [26858 ^ _781215 : [(26861 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1269324), _1269322))], (26859 ^ _781215) ^ [] : [_1269322 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1269324, _1269322) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1269324))], (44912 ^ _781215) ^ [_1681995, _1681997, _1681999] : [-(hAPP(c_List_Otl(_1681995), hAPP(hAPP(c_List_Otake(_1681995), _1681997), _1681999)) = hAPP(hAPP(c_List_Otake(_1681995), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1681997), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1681995), _1681999)))], (39236 ^ _781215) ^ [_1534964, _1534966, _1534968, _1534970] : [-(hAPP(c_Set_Ovimage(_1534964, _1534966, _1534968), _1534970) = hAPP(c_Set_OCollect(_1534964), hAPP(hAPP(c_COMBC(_1534964, tc_fun(_1534966, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1534966, tc_fun(tc_fun(_1534966, tc_HOL_Obool), tc_HOL_Obool), _1534964), c_member(_1534966)), _1534968)), _1534970)))], (40311 ^ _781215) ^ [] : [-(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))))], (42702 ^ _781215) ^ [_1629365, _1629367] : [hBOOL(hAPP(c_List_Odistinct(_1629365), _1629367)), 42705 ^ _781215 : [(42706 ^ _781215) ^ [_1629497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1629497), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629365)), _1629367))), 42709 ^ _781215 : [(42710 ^ _781215) ^ [_1629624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1629624), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629365)), _1629367))), -(_1629497 = _1629624), hAPP(hAPP(c_List_Onth(_1629365), _1629367), _1629497) = hAPP(hAPP(c_List_Onth(_1629365), _1629367), _1629624)]]]]], (9173 ^ _781215) ^ [_936919, _936921, _936923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936921), _936923)), -(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, _936919)), _936921)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _936919)), _936923))))], (4032 ^ _781215) ^ [_842375, _842377, _842379, _842381, _842383, _842385] : [-(c_Finite__Set_Ofold__image(_842385, _842381, _842377) = c_Finite__Set_Ofold__image(_842383, _842379, _842375)), _842385 = _842383, _842381 = _842379, _842377 = _842375], (25406 ^ _781215) ^ [_1238886] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1238886), c_Int_OMin) = c_Int_Osucc(_1238886))], (19502 ^ _781215) ^ [_1131063, _1131065, _1131067] : [class_Orderings_Olinorder(_1131063), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131063), _1131065)), -(hBOOL(hAPP(hAPP(c_member(_1131063), _1131067), _1131065))), -(c_Big__Operators_Olinorder__class_OMin(_1131063, hAPP(hAPP(c_Set_Oinsert(_1131063), _1131067), _1131065)) = hAPP(hAPP(c_Finite__Set_Ofold(_1131063, _1131063, c_Orderings_Oord__class_Omin(_1131063)), _1131067), _1131065))], (41553 ^ _781215) ^ [_1598655, _1598657, _1598659, _1598661, _1598663, _1598665] : [c_Finite__Set_Ofolding(_1598655, _1598657, _1598659, _1598661), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598655), _1598663)), -(hAPP(c_Fun_Ocomp(_1598657, _1598657, _1598657, hAPP(_1598659, _1598665)), hAPP(_1598661, _1598663)) = hAPP(c_Fun_Ocomp(_1598657, _1598657, _1598657, hAPP(_1598661, _1598663)), hAPP(_1598659, _1598665)))], (20703 ^ _781215) ^ [] : [-(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))))], (36237 ^ _781215) ^ [_1462401, _1462403] : [_1462401 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1462401, _1462403) = 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)))], (21578 ^ _781215) ^ [_1168359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1168359), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1168359)), c_Int_OPls)))], (6437 ^ _781215) ^ [_886044, _886046, _886048] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886044, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886044, tc_HOL_Obool)), _886046), _886048)), _886048) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886044, tc_HOL_Obool)), _886046), _886048))], (22039 ^ _781215) ^ [_1178065, _1178067, _1178069, _1178071, _1178073] : [class_Complete__Lattice_Ocomplete__lattice(_1178065), class_Orderings_Olinorder(_1178065), 22046 ^ _781215 : [(22056 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178065), _1178067), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1178069, _1178065), _1178071), _1178073)))), 22057 ^ _781215 : [(22058 ^ _781215) ^ [_1178413] : [hBOOL(hAPP(hAPP(c_member(_1178069), _1178413), _1178071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178065), _1178067), hAPP(_1178073, _1178413)))]]], (22047 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178065), _1178067), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1178069, _1178065), _1178071), _1178073))), 22051 ^ _781215 : [(22054 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178065), _1178067), hAPP(_1178073, 22050 ^ [_1178065, _1178067, _1178069, _1178071, _1178073]))))], (22052 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1178069), 22050 ^ [_1178065, _1178067, _1178069, _1178071, _1178073]), _1178071)))]]]]], (30133 ^ _781215) ^ [_1332423, _1332425, _1332427] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1332423, tc_HOL_Obool)), _1332425), hAPP(c_Set_OPow(_1332423), _1332427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332423, tc_HOL_Obool)), _1332425), _1332427)))], (24164 ^ _781215) ^ [_1217020, _1217022] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1217020)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1217022)) = 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)))), _1217020)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1217022)))], (37685 ^ _781215) ^ [_1497257, _1497259, _1497261, _1497263, _1497265, _1497267, _1497269] : [c_Typedef_Otype__definition(_1497257, _1497259, _1497261, _1497263, _1497265), hBOOL(hAPP(hAPP(c_member(_1497259), _1497267), _1497265)), hBOOL(hAPP(hAPP(c_member(_1497259), _1497269), _1497265)), 37696 ^ _781215 : [(37703 ^ _781215) ^ [] : [_1497267 = _1497269, -(hAPP(_1497263, _1497267) = hAPP(_1497263, _1497269))], (37697 ^ _781215) ^ [] : [hAPP(_1497263, _1497267) = hAPP(_1497263, _1497269), -(_1497267 = _1497269)]]], (32666 ^ _781215) ^ [_1386145, _1386147, _1386149, _1386151] : [class_Lattices_Osemilattice__inf(_1386145), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386145), _1386147), _1386149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386145), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1386145), _1386147), _1386151)), _1386149)))], (34438 ^ _781215) ^ [_1426212, _1426214, _1426216] : [class_Lattices_Olattice(_1426212), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426212), _1426214)), -(hBOOL(hAPP(hAPP(c_member(_1426212), _1426216), _1426214))), -(_1426214 = c_Orderings_Obot__class_Obot(tc_fun(_1426212, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1426212, hAPP(hAPP(c_Set_Oinsert(_1426212), _1426216), _1426214)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426212), _1426216), c_Big__Operators_Olattice__class_OInf__fin(_1426212, _1426214)))], (39723 ^ _781215) ^ [_1553586, _1553588, _1553590] : [-(hAPP(c_Relation_ORange(_1553586, _1553588), hAPP(c_Set_OCollect(tc_prod(_1553586, _1553588)), hAPP(c_Product__Type_Oprod_Oprod__case(_1553586, _1553588, tc_HOL_Obool), _1553590))) = hAPP(c_Set_OCollect(_1553588), hAPP(hAPP(c_COMBB(tc_fun(_1553586, tc_HOL_Obool), tc_HOL_Obool, _1553588), c_HOL_OEx(_1553586)), hAPP(c_COMBC(_1553586, _1553588, tc_HOL_Obool), _1553590))))], (19886 ^ _781215) ^ [_1137950, _1137952, _1137954] : [class_Orderings_Olinorder(_1137950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1137950), _1137952)), -(hBOOL(hAPP(hAPP(c_member(_1137950), _1137954), _1137952))), -(_1137952 = c_Orderings_Obot__class_Obot(tc_fun(_1137950, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1137950, c_Orderings_Oord__class_Omax(_1137950), hAPP(hAPP(c_Set_Oinsert(_1137950), _1137954), _1137952)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1137950), _1137954), c_Big__Operators_Olattice_OSup__fin(_1137950, c_Orderings_Oord__class_Omax(_1137950), _1137952)))], (37929 ^ _781215) ^ [_1502410, _1502412, _1502414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1502410, tc_HOL_Obool), tc_HOL_Obool)), _1502412), _1502414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502410, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502410, tc_HOL_Obool), _1502412)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502410, tc_HOL_Obool), _1502414))))], (36648 ^ _781215) ^ [_1470238] : [class_Lattices_Oboolean__algebra(_1470238), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1470238), c_Orderings_Otop__class_Otop(_1470238)) = c_Orderings_Obot__class_Obot(_1470238))], (48950 ^ _781215) ^ [_1769288] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1769288)) = _1769288)], (50956 ^ _781215) ^ [_1816980, _1816982, _1816984] : [-(hAPP(c_New__DSequence_Opos__single(_1816980, _1816982), _1816984) = hAPP(c_Lazy__Sequence_Osingle(_1816980), _1816982))], (51568 ^ _781215) ^ [] : [-(class_HOL_Oequal(tc_Code__Evaluation_Oterm))], (45426 ^ _781215) ^ [_1693223, _1693225, _1693227, _1693229, _1693231] : [-(hAPP(hAPP(c_List_Omap(_1693223, _1693225), _1693227), hAPP(c_List_Ofilter(_1693223, _1693229), _1693231)) = c_List_Omap__filter(_1693223, _1693225, hAPP(hAPP(c_COMBC(_1693223, tc_Option_Ooption(_1693225), tc_Option_Ooption(_1693225)), hAPP(hAPP(c_COMBS(_1693223, tc_Option_Ooption(_1693225), tc_fun(tc_Option_Ooption(_1693225), tc_Option_Ooption(_1693225))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1693225), tc_fun(tc_Option_Ooption(_1693225), tc_Option_Ooption(_1693225))), _1693223), c_If(tc_Option_Ooption(_1693225))), _1693229)), hAPP(hAPP(c_COMBB(_1693225, tc_Option_Ooption(_1693225), _1693223), c_Option_Ooption_OSome(_1693225)), _1693227))), c_Option_Ooption_ONone(_1693225)), _1693231))], (19204 ^ _781215) ^ [_1125925, _1125927] : [class_Orderings_Olinorder(_1125925), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125925), _1125927)), -(_1125927 = c_Orderings_Obot__class_Obot(tc_fun(_1125925, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1125925), c_Big__Operators_Olinorder__class_OMin(_1125925, _1125927)), _1125927)))], (41863 ^ _781215) ^ [_1605706, _1605708, _1605710, _1605712] : [-(_1605706 = _1605708), 41866 ^ _781215 : [(41873 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1605710), _1605706), hAPP(c_List_Oset(_1605710), _1605712))), -(hBOOL(hAPP(hAPP(c_member(_1605710), _1605706), hAPP(c_List_Oset(_1605710), c_List_Oremove1(_1605710, _1605708, _1605712)))))], (41867 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1605710), _1605706), hAPP(c_List_Oset(_1605710), c_List_Oremove1(_1605710, _1605708, _1605712)))), -(hBOOL(hAPP(hAPP(c_member(_1605710), _1605706), hAPP(c_List_Oset(_1605710), _1605712))))]]], (44656 ^ _781215) ^ [_1676463, _1676465, _1676467, _1676469] : [-(hAPP(hAPP(c_List_Odrop(_1676463), _1676465), hAPP(hAPP(c_List_Olist_OCons(_1676463), _1676467), _1676469)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1676463), hAPP(hAPP(c_List_Olist_OCons(_1676463), _1676467), _1676469), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1676463), tc_List_Olist(_1676463)), c_List_Odrop(_1676463)), _1676469), _1676465))], (13252 ^ _781215) ^ [_1011590, _1011592] : [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), _1011590), _1011592))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1011592), _1011590)))], (41851 ^ _781215) ^ [_1605530, _1605532, _1605534] : [-(hBOOL(hAPP(hAPP(c_member(_1605530), _1605532), hAPP(c_List_Oset(_1605530), _1605534)))), -(c_List_Oremove1(_1605530, _1605532, _1605534) = _1605534)], (11922 ^ _781215) ^ [_988478, _988480] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988478), _988480) = _988478, -(_988480 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21902 ^ _781215) ^ [_1174884, _1174886, _1174888, _1174890, _1174892, _1174894] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174884, tc_fun(_1174886, tc_HOL_Obool)), _1174888), hAPP(hAPP(c_COMBB(_1174890, tc_fun(_1174886, tc_HOL_Obool), _1174884), _1174892), _1174894)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174890, tc_fun(_1174886, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1174884, _1174890, _1174894), _1174888)), _1174892))], (9535 ^ _781215) ^ [_943414, _943416, _943418] : [class_Orderings_Olinorder(_943414), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943414), _943416), _943418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943414), _943418), _943416)))], (31012 ^ _781215) ^ [_1348841, _1348843, _1348845] : [class_Orderings_Oorder(_1348841), 31015 ^ _781215 : [(31022 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348841), _1348843), _1348845))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1348841, _1348843), _1348845) = c_Orderings_Obot__class_Obot(tc_fun(_1348841, tc_HOL_Obool)))], (31016 ^ _781215) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1348841, _1348843), _1348845) = c_Orderings_Obot__class_Obot(tc_fun(_1348841, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348841), _1348843), _1348845))]]], (33106 ^ _781215) ^ [_1395778, _1395780, _1395782, _1395784, _1395786] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395778, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395780, tc_fun(_1395778, tc_HOL_Obool)), _1395782), _1395784)), _1395786) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395780, tc_fun(_1395778, tc_HOL_Obool)), _1395782), hAPP(hAPP(c_COMBC(_1395780, tc_fun(_1395778, tc_HOL_Obool), tc_fun(_1395778, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395778, tc_HOL_Obool), tc_fun(tc_fun(_1395778, tc_HOL_Obool), tc_fun(_1395778, tc_HOL_Obool)), _1395780), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395778, tc_HOL_Obool))), _1395784)), _1395786)))], (39761 ^ _781215) ^ [_1554798, _1554800, _1554802, _1554804, _1554806, _1554808] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1554798, _1554800, _1554802), _1554804), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554800, _1554802), tc_HOL_Obool)), _1554806), _1554808)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554798, _1554802), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1554798, _1554800, _1554802), _1554804), _1554806)), hAPP(hAPP(c_Relation_Orel__comp(_1554798, _1554800, _1554802), _1554804), _1554808)))], (13933 ^ _781215) ^ [_1023982, _1023984, _1023986] : [hBOOL(hAPP(_1023982, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1023984), _1023986))), 13936 ^ _781215 : [(13943 ^ _781215) ^ [_1024167] : [_1023984 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1023986), _1024167), -(hBOOL(hAPP(_1023982, _1024167)))], (13937 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1023984), _1023986)), -(hBOOL(hAPP(_1023982, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (19580 ^ _781215) ^ [_1132677, _1132679] : [class_Orderings_Olinorder(_1132677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132677), _1132679)), -(_1132679 = c_Orderings_Obot__class_Obot(tc_fun(_1132677, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132677), c_Big__Operators_Olattice_OInf__fin(_1132677, c_Orderings_Oord__class_Omin(_1132677), _1132679)), c_Big__Operators_Olattice_OSup__fin(_1132677, c_Orderings_Oord__class_Omax(_1132677), _1132679))))], (45692 ^ _781215) ^ [_1697792, _1697794] : [45693 ^ _781215 : [(45696 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1697794), _1697792))], (45694 ^ _781215) ^ [] : [_1697794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1697792, _1697794) = c_List_Olist_ONil(tc_Nat_Onat))], (45255 ^ _781215) ^ [_1689106, _1689108, _1689110, _1689112] : [hBOOL(hAPP(_1689106, _1689108)), -(hAPP(c_List_Ofilter(_1689110, _1689106), hAPP(hAPP(c_List_Olist_OCons(_1689110), _1689108), _1689112)) = hAPP(hAPP(c_List_Olist_OCons(_1689110), _1689108), hAPP(c_List_Ofilter(_1689110, _1689106), _1689112)))], (44345 ^ _781215) ^ [_1668351, _1668353, _1668355, _1668357, _1668359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668351), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668353)), _1668355))), -(hAPP(hAPP(c_List_Olist__update(_1668353, hAPP(hAPP(c_List_Oappend(_1668353), _1668355), _1668357)), _1668351), _1668359) = hAPP(hAPP(c_List_Oappend(_1668353), hAPP(hAPP(c_List_Olist__update(_1668353, _1668355), _1668351), _1668359)), _1668357))], (39951 ^ _781215) ^ [_1561310, _1561312, _1561314, _1561316] : [c_Wellfounded_Owf(_1561310, _1561312), -(c_Wellfounded_Owf(_1561314, hAPP(hAPP(c_Relation_Oinv__image(_1561310, _1561314), _1561312), _1561316)))], (27570 ^ _781215) ^ [_1283104, _1283106, _1283108] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1283104, _1283106), _1283108)), 27573 ^ _781215 : [(27582 ^ _781215) ^ [] : [-(_1283106 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 27585 ^ _781215 : [(27594 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1283106))), 27597 ^ _781215 : [(27600 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1283108)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27598 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1283106), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1283108))))]]], (27586 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1283106)), 27589 ^ _781215 : [(27592 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1283108)), _1283106)))], (27590 ^ _781215) ^ [] : [-(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), _1283108))))]]]]], (27576 ^ _781215) ^ [] : [_1283106 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1283108) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27574 ^ _781215) ^ [] : [-(_1283104 = 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), _1283108)), _1283106)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1283108)))]]], (45871 ^ _781215) ^ [_1701088, _1701090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701088), _1701090)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1701088, _1701090)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1701090), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (33252 ^ _781215) ^ [_1399630, _1399632, _1399634] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399630, tc_HOL_Obool)), _1399632), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1399630, tc_HOL_Obool)), _1399634)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399630, tc_HOL_Obool)), _1399632), _1399634))], (37959 ^ _781215) ^ [_1503115, _1503117, _1503119] : [class_Complete__Lattice_Ocomplete__lattice(_1503115), hBOOL(hAPP(hAPP(c_member(_1503115), _1503117), _1503119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1503115), _1503117), c_Complete__Lattice_OSup__class_OSup(_1503115, _1503119))))], (45343 ^ _781215) ^ [_1690810, _1690812, _1690814, _1690816] : [-(hAPP(c_List_Ofilter(_1690810, _1690812), hAPP(hAPP(c_List_Oappend(_1690810), _1690814), _1690816)) = hAPP(hAPP(c_List_Oappend(_1690810), hAPP(c_List_Ofilter(_1690810, _1690812), _1690814)), hAPP(c_List_Ofilter(_1690810, _1690812), _1690816)))], (3452 ^ _781215) ^ [_833377, _833379, _833381, _833383] : [-(c_List_Oupt(_833383, _833379) = c_List_Oupt(_833381, _833377)), _833383 = _833381, _833379 = _833377], (37043 ^ _781215) ^ [_1481564, _1481566, _1481568, _1481570, _1481572, _1481574] : [class_Complete__Lattice_Ocomplete__lattice(_1481564), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481566, tc_fun(_1481568, _1481564)), _1481570), _1481572), _1481574) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481566, _1481564), _1481570), hAPP(hAPP(c_COMBC(_1481566, _1481568, _1481564), _1481572), _1481574)))], (46281 ^ _781215) ^ [_1710201, _1710203, _1710205, _1710207] : [_1710203 = hAPP(hAPP(c_List_Oappend(_1710201), hAPP(c_List_Orev(_1710201), _1710207)), hAPP(hAPP(c_List_Olist_OCons(_1710201), _1710205), c_List_Olist_ONil(_1710201))), -(hAPP(c_List_Orev(_1710201), _1710203) = hAPP(hAPP(c_List_Olist_OCons(_1710201), _1710205), _1710207))], (51462 ^ _781215) ^ [_1823344] : [class_Lazy__Sequence_Osmall__lazy(_1823344), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1823344)))], (17845 ^ _781215) ^ [_1099924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1099924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1099924))))], (18770 ^ _781215) ^ [_1117818, _1117820, _1117822, _1117824] : [class_Orderings_Olinorder(_1117818), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117818), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117818), _1117820), _1117822)), _1117824) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117818), _1117820), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117818), _1117822), _1117824)))], (34554 ^ _781215) ^ [_1428402, _1428404, _1428406] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1428402), _1428404)), c_Fun_Oinj__on(_1428402, tc_fun(tc_fun(_1428402, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1428402, tc_fun(tc_prod(_1428402, _1428402), tc_HOL_Obool), tc_fun(tc_fun(_1428402, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428402, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1428402, _1428402), tc_HOL_Obool), tc_fun(tc_fun(_1428402, tc_HOL_Obool), tc_HOL_Obool)), _1428402), c_Equiv__Relations_Oquotient(_1428402)), hAPP(hAPP(c_COMBC(_1428402, tc_fun(_1428402, tc_HOL_Obool), tc_fun(_1428402, tc_HOL_Obool)), c_Set_Oinsert(_1428402)), c_Orderings_Obot__class_Obot(tc_fun(_1428402, tc_HOL_Obool))))), _1428406), _1428404), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1428402, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1428402), _1428404), _1428406)) = hAPP(c_Finite__Set_Ocard(_1428402), _1428404))], (43924 ^ _781215) ^ [_1658666, _1658668, _1658670, _1658672] : [_1658666 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1658668), _1658666), hAPP(hAPP(c_List_Olist_OCons(_1658668), _1658670), _1658672)) = c_List_Olist_ONil(_1658668))], (6481 ^ _781215) ^ [_886791, _886793, _886795, _886797] : [hBOOL(hAPP(hAPP(c_member(_886791), _886793), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886791, tc_HOL_Obool)), _886795), _886797))), -(hBOOL(hAPP(hAPP(c_member(_886791), _886793), _886795)))], (26161 ^ _781215) ^ [_1255657, _1255659, _1255661] : [class_Rings_Oring__1(_1255657), -(hAPP(c_Int_Oring__1__class_Oof__int(_1255657), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1255659), _1255661)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1255657), hAPP(c_Int_Oring__1__class_Oof__int(_1255657), _1255659)), hAPP(c_Int_Oring__1__class_Oof__int(_1255657), _1255661)))], (15372 ^ _781215) ^ [_1050662] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1050662)) = _1050662)], (14126 ^ _781215) ^ [_1027576, _1027578] : [class_Groups_Oab__semigroup__mult(_1027576), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027576), _1027578)), -(_1027578 = c_Orderings_Obot__class_Obot(tc_fun(_1027576, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1027576), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1027576), 14139 ^ [_1027576, _1027578]), 14140 ^ [_1027576, _1027578])), hAPP(hAPP(c_Set_Oinsert(_1027576), 14139 ^ [_1027576, _1027578]), hAPP(hAPP(c_Set_Oinsert(_1027576), 14140 ^ [_1027576, _1027578]), c_Orderings_Obot__class_Obot(tc_fun(_1027576, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1027576), hAPP(c_Finite__Set_Ofold1(_1027576, c_Groups_Otimes__class_Otimes(_1027576)), _1027578)), _1027578)))], (39743 ^ _781215) ^ [_1554199, _1554201, _1554203, _1554205, _1554207, _1554209, _1554211] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1554199, _1554201, _1554203), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1554205, tc_fun(tc_prod(_1554199, _1554201), tc_HOL_Obool)), _1554207), _1554209)), _1554211) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1554205, tc_fun(tc_prod(_1554199, _1554203), tc_HOL_Obool)), _1554207), hAPP(hAPP(c_COMBC(_1554205, tc_fun(tc_prod(_1554201, _1554203), tc_HOL_Obool), tc_fun(tc_prod(_1554199, _1554203), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1554199, _1554201), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1554201, _1554203), tc_HOL_Obool), tc_fun(tc_prod(_1554199, _1554203), tc_HOL_Obool)), _1554205), c_Relation_Orel__comp(_1554199, _1554201, _1554203)), _1554209)), _1554211)))], (31246 ^ _781215) ^ [_1353398, _1353400] : [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)), _1353398), 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)), _1353400), 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)), _1353398), _1353400)), c_Int_Ointrel)))], (8432 ^ _781215) ^ [_923950, _923952, _923954, _923956, _923958] : [-(c_Map_Orestrict__map(_923950, _923952, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_923950, tc_Option_Ooption(_923952)), _923954), _923956), hAPP(c_Option_Ooption_OSome(_923952), _923958)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_923950, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_923950), _923956), c_Orderings_Obot__class_Obot(tc_fun(_923950, tc_HOL_Obool))))) = c_Map_Orestrict__map(_923950, _923952, _923954, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_923950, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_923950), _923956), c_Orderings_Obot__class_Obot(tc_fun(_923950, tc_HOL_Obool))))))], (9221 ^ _781215) ^ [_938125, _938127, _938129] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_938125), _938127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938125, tc_HOL_Obool)), _938129), _938127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_938125), _938127)), hAPP(c_Finite__Set_Ocard(_938125), _938129))), -(_938129 = _938127)], (38001 ^ _781215) ^ [_1504077, _1504079, _1504081] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1504077, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1504077, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1504077, tc_HOL_Obool), tc_HOL_Obool)), _1504079), _1504081))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1504077, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1504077, tc_HOL_Obool), _1504079)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1504077, tc_HOL_Obool), _1504081)))))], (41889 ^ _781215) ^ [_1606512, _1606514, _1606516, _1606518, _1606520, _1606522] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606512, _1606514)), hAPP(hAPP(c_Product__Type_OPair(_1606512, _1606514), _1606516), _1606518)), hAPP(c_List_Oset(tc_prod(_1606512, _1606514)), hAPP(hAPP(c_List_Ozip(_1606512, _1606514), _1606520), _1606522)))), 41892 ^ _781215 : [(41895 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606514), _1606518), hAPP(c_List_Oset(_1606514), _1606522))))], (41893 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606512), _1606516), hAPP(c_List_Oset(_1606512), _1606520))))]]], (41301 ^ _781215) ^ [_1592506, _1592508, _1592510, _1592512, _1592514, _1592516, _1592518] : [-(hAPP(c_Product__Type_Oapfst(_1592506, _1592508, _1592510, _1592512), hAPP(c_Product__Type_Oapfst(_1592514, _1592506, _1592510, _1592516), _1592518)) = hAPP(c_Product__Type_Oapfst(_1592514, _1592508, _1592510, hAPP(c_Fun_Ocomp(_1592506, _1592508, _1592514, _1592512), _1592516)), _1592518))], (15402 ^ _781215) ^ [_1051283, _1051285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1051283)), _1051285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051283), _1051285)))], (37169 ^ _781215) ^ [_1484759, _1484761, _1484763, _1484765, _1484767] : [_1484759 = c_Orderings_Obot__class_Obot(tc_fun(_1484761, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484761, tc_fun(_1484763, tc_HOL_Obool)), _1484759), hAPP(hAPP(c_COMBB(tc_fun(_1484763, tc_HOL_Obool), tc_fun(_1484763, tc_HOL_Obool), _1484761), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484763, tc_HOL_Obool)), _1484765)), _1484767)) = c_Orderings_Otop__class_Otop(tc_fun(_1484763, tc_HOL_Obool)))], (31381 ^ _781215) ^ [_1356197, _1356199, _1356201] : [class_Orderings_Olinorder(_1356197), 31384 ^ _781215 : [(31391 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356197), _1356199), _1356201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1356197, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1356197), _1356199)), hAPP(c_SetInterval_Oord__class_OlessThan(_1356197), _1356201))))], (31385 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1356197, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1356197), _1356199)), hAPP(c_SetInterval_Oord__class_OlessThan(_1356197), _1356201))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356197), _1356199), _1356201)))]]], (4370 ^ _781215) ^ [_847500, _847502, _847504, _847506, _847508, _847510] : [-(c_Relation_OImage(_847510, _847506, _847502) = c_Relation_OImage(_847508, _847504, _847500)), _847510 = _847508, _847506 = _847504, _847502 = _847500], (5442 ^ _781215) ^ [_864316, _864318, _864320, _864322] : [-(tc_sum(_864322, _864318) = tc_sum(_864320, _864316)), _864322 = _864320, _864318 = _864316], (39240 ^ _781215) ^ [_1535117, _1535119, _1535121] : [-(c_Map_Odom(_1535117, _1535119, _1535121) = hAPP(c_Set_OCollect(_1535117), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1535117), c_fNot), hAPP(hAPP(c_COMBC(_1535117, tc_Option_Ooption(_1535119), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1535119), tc_fun(tc_Option_Ooption(_1535119), tc_HOL_Obool), _1535117), c_fequal), _1535121)), c_Option_Ooption_ONone(_1535119)))))], (48506 ^ _781215) ^ [_1760681, _1760683, _1760685, _1760687, _1760689, _1760691] : [class_Groups_Oab__semigroup__mult(_1760681), hBOOL(hAPP(c_Finite__Set_Ofinite(_1760683), _1760685)), 48516 ^ _781215 : [(48519 ^ _781215) ^ [] : [hAPP(_1760687, 48515 ^ [_1760681, _1760683, _1760685, _1760687, _1760689, _1760691]) = hAPP(_1760689, 48515 ^ [_1760681, _1760683, _1760685, _1760687, _1760689, _1760691])], (48517 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760683), 48515 ^ [_1760681, _1760683, _1760685, _1760687, _1760689, _1760691]), _1760685)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1760681, _1760683, c_Groups_Otimes__class_Otimes(_1760681)), _1760687), _1760691), _1760685) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1760681, _1760683, c_Groups_Otimes__class_Otimes(_1760681)), _1760689), _1760691), _1760685))], (13766 ^ _781215) ^ [_1020991, _1020993, _1020995] : [class_Rings_Olinordered__ring(_1020991), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020991), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020991), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020991), _1020993), _1020993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020991), _1020995), _1020995))), c_Groups_Ozero__class_Ozero(_1020991)))], (41943 ^ _781215) ^ [_1608188, _1608190, _1608192, _1608194, _1608196, _1608198, _1608200, _1608202] : [class_Groups_Ocomm__monoid__mult(_1608188), c_Fun_Oinj__on(_1608190, _1608192, _1608194, _1608196), _1608198 = hAPP(c_Set_Oimage(_1608190, _1608192, _1608194), _1608196), 41957 ^ _781215 : [(41960 ^ _781215) ^ [] : [hAPP(_1608200, 41956 ^ [_1608188, _1608190, _1608192, _1608194, _1608196, _1608198, _1608200, _1608202]) = hAPP(hAPP(c_Fun_Ocomp(_1608192, _1608188, _1608190, _1608202), _1608194), 41956 ^ [_1608188, _1608190, _1608192, _1608194, _1608196, _1608198, _1608200, _1608202])], (41958 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608190), 41956 ^ [_1608188, _1608190, _1608192, _1608194, _1608196, _1608198, _1608200, _1608202]), _1608196)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1608192, _1608188), _1608202), _1608198) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1608190, _1608188), _1608200), _1608196))], (20181 ^ _781215) ^ [_1143523, _1143525] : [class_Int_Onumber__ring(_1143523), 20184 ^ _781215 : [(20191 ^ _781215) ^ [] : [c_Int_Oiszero(_1143523, hAPP(c_Int_Onumber__class_Onumber__of(_1143523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1143525), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1143523), _1143525) = c_Groups_Oone__class_Oone(_1143523))], (20185 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1143523), _1143525) = c_Groups_Oone__class_Oone(_1143523), -(c_Int_Oiszero(_1143523, hAPP(c_Int_Onumber__class_Onumber__of(_1143523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1143525), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (33234 ^ _781215) ^ [_1399121, _1399123, _1399125, _1399127] : [class_Orderings_Oorder(_1399121), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399121, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1399121, _1399123), _1399125)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1399121, _1399125), _1399127)) = c_Orderings_Obot__class_Obot(tc_fun(_1399121, tc_HOL_Obool)))], (1898 ^ _781215) ^ [_807906, _807908, _807910, _807912, _807914, _807916] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_807914, _807910, _807906)), c_Hoare__Mirabelle_Ohoare__derivs(_807916, _807912, _807908), _807916 = _807914, _807912 = _807910, _807908 = _807906], (25674 ^ _781215) ^ [_1243264] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1243264)], (33262 ^ _781215) ^ [_1399871, _1399873, _1399875, _1399877] : [-(c_Map_Odom(_1399871, _1399873, c_Map_Orestrict__map(_1399871, _1399873, _1399875, _1399877)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399871, tc_HOL_Obool)), c_Map_Odom(_1399871, _1399873, _1399875)), _1399877))], (6932 ^ _781215) ^ [_896004, _896006, _896008, _896010, _896012, _896014, _896016, _896018] : [c_Finite__Set_Ofolding__image__simple(_896004, _896006, _896008, _896010, _896012, _896014), hBOOL(hAPP(c_Finite__Set_Ofinite(_896006), _896016)), -(hBOOL(hAPP(hAPP(c_member(_896006), _896018), _896016))), -(hAPP(_896014, hAPP(hAPP(c_Set_Oinsert(_896006), _896018), _896016)) = hAPP(hAPP(_896008, hAPP(_896012, _896018)), hAPP(_896014, _896016)))], (11288 ^ _781215) ^ [_977522, _977524] : [class_Rings_Ocomm__semiring__1(_977522), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977522), _977524), _977524) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977522), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977522), c_Groups_Oone__class_Oone(_977522)), c_Groups_Oone__class_Oone(_977522))), _977524))], (30087 ^ _781215) ^ [_1331379, _1331381, _1331383, _1331385] : [class_Orderings_Olinorder(_1331379), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331379), _1331381), _1331383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331379), _1331383), _1331385)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1331379, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1331379, _1331381, _1331383)), c_SetInterval_Oord__class_OatLeastAtMost(_1331379, _1331383, _1331385)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1331379, _1331381, _1331385))], (19134 ^ _781215) ^ [_1124514, _1124516, _1124518, _1124520] : [class_Orderings_Olinorder(_1124514), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124514), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1124514), _1124516), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1124514), _1124518), _1124520))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1124514), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1124514), _1124516), _1124518)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1124514), _1124516), _1124520)))))], (39128 ^ _781215) ^ [_1532567, _1532569] : [-(hAPP(c_Set_OCollect(_1532567), _1532569) = _1532569)], (35857 ^ _781215) ^ [_1455199, _1455201] : [class_Groups_Oordered__ab__group__add__abs(_1455199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455199), hAPP(c_Groups_Oabs__class_Oabs(_1455199), _1455201)), c_Groups_Ozero__class_Ozero(_1455199)))], (31112 ^ _781215) ^ [_1350675] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1350675), hAPP(c_Nat_OSuc, _1350675)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1350675), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (50467 ^ _781215) ^ [_1807536, _1807538, _1807540, _1807542] : [-(c_List_Olist__all(_1807536, _1807538, hAPP(hAPP(c_List_Olist_OCons(_1807536), _1807540), _1807542))), hBOOL(hAPP(_1807538, _1807540)), c_List_Olist__all(_1807536, _1807538, _1807542)], (6700 ^ _781215) ^ [_890914, _890916, _890918, _890920] : [-(hBOOL(hAPP(hAPP(c_member(_890914), _890916), _890918))), -(hBOOL(hAPP(hAPP(c_member(_890914), _890916), _890920))), 6707 ^ _781215 : [(6714 ^ _781215) ^ [] : [_890918 = _890920, -(hAPP(hAPP(c_Set_Oinsert(_890914), _890916), _890918) = hAPP(hAPP(c_Set_Oinsert(_890914), _890916), _890920))], (6708 ^ _781215) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_890914), _890916), _890918) = hAPP(hAPP(c_Set_Oinsert(_890914), _890916), _890920), -(_890918 = _890920)]]], (48717 ^ _781215) ^ [_1764898, _1764900, _1764902, _1764904, _1764906, _1764908, _1764910] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1764898, _1764900, _1764902, _1764904), _1764906), _1764908), _1764910) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1764900, _1764902, _1764904), _1764908), hAPP(_1764906, _1764910)))], (10654 ^ _781215) ^ [_963566, _963568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963566), _963568)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963568)), _963566) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963568), _963566)))], (50027 ^ _781215) ^ [_1796173, _1796175] : [-(hAPP(hAPP(c_Nat_Ocompow(_1796173, _1796173), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1796175) = c_Fun_Oid(_1796173))], (26755 ^ _781215) ^ [_1267281, _1267283] : [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), _1267281), _1267283))), 26758 ^ _781215 : [(26767 ^ _781215) ^ [] : [-(c_Divides_OnegDivAlg(_1267281, _1267283) = hAPP(c_Divides_Oadjust(_1267283), c_Divides_OnegDivAlg(_1267281, 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)))), _1267283)))), -(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), _1267281), _1267283)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1267283), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26759 ^ _781215) ^ [] : [26760 ^ _781215 : [(26763 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1267283), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (26761 ^ _781215) ^ [] : [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), _1267281), _1267283)))]], -(c_Divides_OnegDivAlg(_1267281, _1267283) = 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), _1267281), _1267283)))]]], (16557 ^ _781215) ^ [_1076552, _1076554, _1076556, _1076558, _1076560] : [c_Finite__Set_Ofolding__one__idem(_1076552, _1076554, _1076556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076552), _1076558)), -(_1076558 = c_Orderings_Obot__class_Obot(tc_fun(_1076552, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076552), _1076560)), -(_1076560 = c_Orderings_Obot__class_Obot(tc_fun(_1076552, tc_HOL_Obool))), -(hAPP(_1076556, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1076552, tc_HOL_Obool)), _1076558), _1076560)) = hAPP(hAPP(_1076554, hAPP(_1076556, _1076558)), hAPP(_1076556, _1076560)))], (7210 ^ _781215) ^ [_902214, _902216, _902218, _902220, _902222] : [-(hBOOL(hAPP(hAPP(c_member(_902214), _902216), _902218))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_902214, tc_Option_Ooption(_902220)), c_Map_Orestrict__map(_902214, _902220, _902222, _902218)), _902216), c_Option_Ooption_ONone(_902220)) = c_Map_Orestrict__map(_902214, _902220, _902222, _902218))], (15174 ^ _781215) ^ [_1047588, _1047590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1047588), _1047590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047588)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047590))))], (43746 ^ _781215) ^ [_1654865, _1654867, _1654869, _1654871] : [_1654867 = c_List_Olist_ONil(_1654865), -(hAPP(hAPP(c_List_Olist__update(_1654865, _1654867), _1654869), _1654871) = c_List_Olist_ONil(_1654865))], (40263 ^ _781215) ^ [_1567934, _1567936, _1567938] : [-(hAPP(c_Relation_ODomain(_1567934, _1567936), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1567934, _1567936), tc_HOL_Obool), _1567938)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1567934, _1567936), tc_HOL_Obool), tc_fun(_1567934, tc_HOL_Obool)), _1567938), c_Relation_ODomain(_1567934, _1567936)))], (48739 ^ _781215) ^ [_1765449, _1765451, _1765453, _1765455, _1765457, _1765459, _1765461, _1765463] : [class_Groups_Ocomm__monoid__add(_1765449), class_Orderings_Oord(_1765451), _1765453 = _1765455, _1765457 = _1765459, 48757 ^ _781215 : [(48762 ^ _781215) ^ [] : [hAPP(_1765461, 48756 ^ [_1765449, _1765451, _1765453, _1765455, _1765457, _1765459, _1765461, _1765463]) = hAPP(_1765463, 48756 ^ [_1765449, _1765451, _1765453, _1765455, _1765457, _1765459, _1765461, _1765463])], (48760 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1765451), 48756 ^ [_1765449, _1765451, _1765453, _1765455, _1765457, _1765459, _1765461, _1765463]), _1765459)))], (48758 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1765451), _1765455), 48756 ^ [_1765449, _1765451, _1765453, _1765455, _1765457, _1765459, _1765461, _1765463])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1765451, _1765449), _1765461), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1765451, _1765453), _1765457)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1765451, _1765449), _1765463), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1765451, _1765455), _1765459)))], (35439 ^ _781215) ^ [_1447124, _1447126, _1447128, _1447130] : [class_Orderings_Olinorder(_1447124), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447124, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1447124, _1447126, _1447128)), hAPP(c_SetInterval_Oord__class_OatLeast(_1447124), _1447130)) = c_SetInterval_Oord__class_OatLeastAtMost(_1447124, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1447124), _1447126), _1447130), _1447128))], (10444 ^ _781215) ^ [_959387, _959389, _959391] : [class_Groups_Ogroup__add(_959387), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959387), _959389), _959391) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959387), _959389), hAPP(c_Groups_Ouminus__class_Ouminus(_959387), _959391)))], (44884 ^ _781215) ^ [_1681341, _1681343, _1681345] : [-(hAPP(hAPP(c_List_Otake(_1681341), _1681343), hAPP(c_List_Otl(_1681341), _1681345)) = hAPP(c_List_Otl(_1681341), hAPP(hAPP(c_List_Otake(_1681341), hAPP(c_Nat_OSuc, _1681343)), _1681345)))], (41223 ^ _781215) ^ [_1590682, _1590684] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1590682, _1590684)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1590682, _1590684))], (46506 ^ _781215) ^ [_1716500, _1716502, _1716504, _1716506, _1716508] : [-(hBOOL(hAPP(_1716500, _1716502))), -(c_List_OtakeWhile(_1716504, _1716500, hAPP(hAPP(c_List_Oappend(_1716504), _1716506), hAPP(hAPP(c_List_Olist_OCons(_1716504), _1716502), _1716508))) = c_List_OtakeWhile(_1716504, _1716500, _1716506))], (21011 ^ _781215) ^ [_1157592] : [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, _1157592)))))], (36977 ^ _781215) ^ [_1479215, _1479217, _1479219, _1479221] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479215, tc_fun(_1479217, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1479215, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1479217, tc_HOL_Obool), tc_fun(_1479217, tc_HOL_Obool), _1479215), hAPP(c_COMBC(_1479217, tc_fun(_1479217, tc_HOL_Obool), tc_HOL_Obool), c_member(_1479217))), _1479219)), _1479221)), -(hBOOL(hAPP(hAPP(c_member(_1479217), _1479221), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479215, tc_fun(_1479217, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1479215, tc_HOL_Obool))), _1479219))))], (1788 ^ _781215) ^ [_806535, _806537] : [-(class_Orderings_Oorder(_806535)), _806537 = _806535, class_Orderings_Oorder(_806537)], (18019 ^ _781215) ^ [_1102939, _1102941] : [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(_1102941))), 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)), _1102939))))), -(hAPP(c_Nat_OSuc, _1102939) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102941))], (45970 ^ _781215) ^ [_1703048, _1703050, _1703052] : [class_Orderings_Olinorder(_1703048), hBOOL(hAPP(hAPP(c_member(_1703048), _1703050), hAPP(c_List_Oset(_1703048), _1703052))), c_List_Olinorder__class_Osorted(_1703048, _1703052), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1703048, _1703048, c_COMBI(_1703048)), _1703050), c_List_Oremove1(_1703048, _1703050, _1703052)) = _1703052)], (34662 ^ _781215) ^ [_1430552, _1430554] : [-(c_Fun_Oinj__on(_1430552, _1430552, c_COMBI(_1430552), _1430554))], (7989 ^ _781215) ^ [_915931, _915933, _915935] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_915931), _915933)), -(hAPP(c_Finite__Set_Ocard(_915931), hAPP(hAPP(c_Set_Oinsert(_915931), _915935), _915933)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_915931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915931, tc_HOL_Obool)), _915933), hAPP(hAPP(c_Set_Oinsert(_915931), _915935), c_Orderings_Obot__class_Obot(tc_fun(_915931, tc_HOL_Obool)))))))], (19066 ^ _781215) ^ [_1122982, _1122984, _1122986, _1122988] : [class_Orderings_Olinorder(_1122982), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122982), _1122984), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1122982), _1122986), _1122988)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1122982), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122982), _1122984), _1122986)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122982), _1122984), _1122988)))], (49093 ^ _781215) ^ [_1771811, _1771813] : [-(hAPP(c_Relation_ODomain(_1771811, _1771811), c_Transitive__Closure_Otrancl(_1771811, _1771813)) = hAPP(c_Relation_ODomain(_1771811, _1771811), _1771813))], (29948 ^ _781215) ^ [] : [-(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)))))], (19184 ^ _781215) ^ [_1125585, _1125587, _1125589] : [class_Orderings_Olinorder(_1125585), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125585), _1125587)), hBOOL(hAPP(hAPP(c_member(_1125585), _1125589), _1125587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125585), c_Big__Operators_Olinorder__class_OMin(_1125585, _1125587)), _1125589)))], (18085 ^ _781215) ^ [_1104507, _1104509, _1104511, _1104513, _1104515] : [-(c_Nat_Onat_Onat__case(_1104507, _1104509, _1104511, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104513)), _1104515)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1104507), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1104513))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1104507, _1104507), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1104507, tc_fun(_1104507, _1104507)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1104507, tc_fun(_1104507, _1104507)), tc_Int_Oint), c_If(_1104507)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1104507, _1104509, _1104511, _1104515))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1104507, tc_Int_Oint), _1104511), 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)), _1104515)))))], (5190 ^ _781215) ^ [_860426, _860428] : [_860428 = _860426, -(c_List_Olist_ONil(_860428) = c_List_Olist_ONil(_860426))], (31044 ^ _781215) ^ [_1349347, _1349349, _1349351, _1349353] : [class_Orderings_Olinorder(_1349347), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349347), _1349349), _1349351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349347), _1349351), _1349353)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1349347, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349347, _1349349), _1349351)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349347, _1349351), _1349353)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349347, _1349349), _1349353))], (50810 ^ _781215) ^ [_1813849] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1813849), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1813849)), c_Int_OPls)))], (51358 ^ _781215) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (27980 ^ _781215) ^ [_1291106, _1291108] : [class_Rings_Odivision__ring__inverse__zero(_1291106), 27983 ^ _781215 : [(27990 ^ _781215) ^ [] : [-(_1291108 = c_Groups_Ozero__class_Ozero(_1291106)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291106), _1291108), _1291108) = c_Groups_Oone__class_Oone(_1291106))], (27984 ^ _781215) ^ [] : [_1291108 = c_Groups_Ozero__class_Ozero(_1291106), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291106), _1291108), _1291108) = c_Groups_Ozero__class_Ozero(_1291106))]]], (11460 ^ _781215) ^ [_980964, _980966, _980968, _980970, _980972, _980974] : [_980964 = hAPP(_980966, _980968), hBOOL(hAPP(hAPP(c_member(_980970), _980968), _980972)), -(hBOOL(hAPP(hAPP(c_member(_980974), _980964), hAPP(c_Set_Oimage(_980970, _980974, _980966), _980972))))], (27696 ^ _781215) ^ [_1285154, _1285156, _1285158, _1285160, _1285162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1285154, _1285156)), hAPP(_1285154, _1285158))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1285160, _1285160)), hAPP(hAPP(c_Product__Type_OPair(_1285160, _1285160), _1285156), _1285158)), _1285162)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1285160, _1285160)), hAPP(hAPP(c_Product__Type_OPair(_1285160, _1285160), _1285156), _1285158)), c_Wellfounded_Omlex__prod(_1285160, _1285154, _1285162))))], (28544 ^ _781215) ^ [_1301328, _1301330, _1301332, _1301334] : [class_Fields_Olinordered__field__inverse__zero(_1301328), class_Int_Onumber(_1301328), 28551 ^ _781215 : [(28552 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301328), hAPP(c_Int_Onumber__class_Onumber__of(_1301328), _1301330)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301328), _1301332), _1301334))), 28555 ^ _781215 : [(28562 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301328), c_Groups_Ozero__class_Ozero(_1301328)), _1301334))), 28565 ^ _781215 : [(28572 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301328), _1301334), c_Groups_Ozero__class_Ozero(_1301328)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301328), hAPP(c_Int_Onumber__class_Onumber__of(_1301328), _1301330)), c_Groups_Ozero__class_Ozero(_1301328))))], (28566 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301328), _1301334), c_Groups_Ozero__class_Ozero(_1301328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301328), _1301332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301328), hAPP(c_Int_Onumber__class_Onumber__of(_1301328), _1301330)), _1301334))))]]], (28556 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301328), c_Groups_Ozero__class_Ozero(_1301328)), _1301334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301328), hAPP(c_Int_Onumber__class_Onumber__of(_1301328), _1301330)), _1301334)), _1301332)))]]], (28578 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301328), hAPP(c_Int_Onumber__class_Onumber__of(_1301328), _1301330)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301328), _1301332), _1301334)))), 28581 ^ _781215 : [(28584 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301328), hAPP(c_Int_Onumber__class_Onumber__of(_1301328), _1301330)), _1301334)), _1301332))], (28582 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301328), c_Groups_Ozero__class_Ozero(_1301328)), _1301334)))]], 28585 ^ _781215 : [(28588 ^ _781215) ^ [] : [28589 ^ _781215 : [(28592 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301328), _1301332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301328), hAPP(c_Int_Onumber__class_Onumber__of(_1301328), _1301330)), _1301334)))], (28590 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301328), _1301334), c_Groups_Ozero__class_Ozero(_1301328))))]], 28593 ^ _781215 : [(28596 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301328), hAPP(c_Int_Onumber__class_Onumber__of(_1301328), _1301330)), c_Groups_Ozero__class_Ozero(_1301328)))], (28594 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301328), _1301334), c_Groups_Ozero__class_Ozero(_1301328)))]]], (28586 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301328), c_Groups_Ozero__class_Ozero(_1301328)), _1301334))]]]]], (47713 ^ _781215) ^ [_1741811, _1741813, _1741815, _1741817] : [_1741817 = c_List_Olist_ONil(_1741813), -(c_List_Olist__all2(_1741811, _1741813, _1741815, c_List_Olist_ONil(_1741811), _1741817))], (14393 ^ _781215) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37519 ^ _781215) ^ [_1493698, _1493700, _1493702] : [class_Complete__Lattice_Ocomplete__lattice(_1493698), 37522 ^ _781215 : [(37523 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493698), _1493700), c_Complete__Lattice_OInf__class_OInf(_1493698, _1493702))), 37526 ^ _781215 : [(37527 ^ _781215) ^ [_1493856] : [hBOOL(hAPP(hAPP(c_member(_1493698), _1493856), _1493702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493698), _1493700), _1493856)))]]], (37533 ^ _781215) ^ [] : [37535 ^ _781215 : [(37538 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493698), _1493700), 37534 ^ [_1493698, _1493700, _1493702]))], (37536 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493698), 37534 ^ [_1493698, _1493700, _1493702]), _1493702)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493698), _1493700), c_Complete__Lattice_OInf__class_OInf(_1493698, _1493702))))]]], (15843 ^ _781215) ^ [_1060013] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1060013) = _1060013)], (41515 ^ _781215) ^ [_1597544, _1597546, _1597548, _1597550, _1597552, _1597554] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1597544, _1597546), _1597546, tc_prod(_1597548, _1597550), c_Product__Type_Osnd(_1597544, _1597546)), c_Product__Type_Omap__pair(_1597548, _1597544, _1597550, _1597546, _1597552, _1597554)) = hAPP(c_Fun_Ocomp(_1597550, _1597546, tc_prod(_1597548, _1597550), _1597554), c_Product__Type_Osnd(_1597548, _1597550)))], (29514 ^ _781215) ^ [_1319179, _1319181, _1319183, _1319185] : [class_Fields_Olinordered__field(_1319179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319179), c_Groups_Ozero__class_Ozero(_1319179)), _1319181)), 29521 ^ _781215 : [(29528 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319179), _1319183), _1319181)), _1319185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319179), _1319183), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319179), _1319185), _1319181))))], (29522 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319179), _1319183), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319179), _1319185), _1319181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319179), _1319183), _1319181)), _1319185)))]]], (16762 ^ _781215) ^ [_1082091, _1082093, _1082095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1082091, tc_HOL_Obool)), _1082093), _1082095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1082091, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1082091, tc_fun(_1082091, tc_HOL_Obool), tc_HOL_Obool), c_member(_1082091)), _1082093)), hAPP(hAPP(c_COMBC(_1082091, tc_fun(_1082091, tc_HOL_Obool), tc_HOL_Obool), c_member(_1082091)), _1082095))))], (32902 ^ _781215) ^ [_1391223, _1391225, _1391227] : [32904 ^ _781215 : [(32910 ^ _781215) ^ [] : [-(32903 ^ [_1391223, _1391225, _1391227] = 32906 ^ [_1391223, _1391225, _1391227])], (32908 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391223), 32906 ^ [_1391223, _1391225, _1391227]), _1391227)))], (32905 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391223), 32903 ^ [_1391223, _1391225, _1391227]), _1391225)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1391223, tc_HOL_Obool)), _1391225), _1391227) = c_Orderings_Obot__class_Obot(tc_fun(_1391223, tc_HOL_Obool)))], (25726 ^ _781215) ^ [_1244304, _1244306, _1244308, _1244310, _1244312] : [-(hBOOL(hAPP(hAPP(c_member(_1244304), _1244306), c_SetInterval_Oord_OatLeastAtMost(_1244304, _1244308, _1244310, _1244312)))), hBOOL(hAPP(hAPP(_1244308, _1244310), _1244306)), hBOOL(hAPP(hAPP(_1244308, _1244306), _1244312))], (4688 ^ _781215) ^ [_852275, _852277] : [_852277 = _852275, -(c_List_Onth(_852277) = c_List_Onth(_852275))], (21392 ^ _781215) ^ [_1165147, _1165149] : [_1165147 = _1165149, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1165147) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1165149))], (44724 ^ _781215) ^ [_1678222, _1678224, _1678226, _1678228] : [-(hAPP(c_List_Orotate1(_1678222), c_List_Olist_ONil(_1678222)) = c_List_Olist_ONil(_1678222))], (49369 ^ _781215) ^ [_1779461, _1779463] : [-(c_Transitive__Closure_Ortrancl(_1779461, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1779461, _1779461), tc_HOL_Obool)), _1779463), c_Relation_OId(_1779461))) = c_Transitive__Closure_Ortrancl(_1779461, _1779463))], (9577 ^ _781215) ^ [_943952, _943954, _943956] : [class_Orderings_Opreorder(_943952), 9580 ^ _781215 : [(9589 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943952), _943954), _943956))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943952), _943954), _943956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943952), _943956), _943954)))], (9581 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943952), _943954), _943956)), 9584 ^ _781215 : [(9587 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943952), _943956), _943954))], (9585 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943952), _943954), _943956)))]]]]], (46910 ^ _781215) ^ [_1724948, _1724950, _1724952, _1724954] : [class_Enum_Oenum(_1724948), class_Enum_Oenum(_1724950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724950)), _1724952) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724948)), c_Enum_Oenum__class_Oenum(_1724948)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724950)), _1724954) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724948)), c_Enum_Oenum__class_Oenum(_1724948)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1724950), _1724950, _1724948, c_Option_Othe(_1724950)), hAPP(c_Map_Omap__of(_1724948, _1724950), hAPP(hAPP(c_List_Ozip(_1724948, _1724950), c_Enum_Oenum__class_Oenum(_1724948)), _1724952))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1724950), _1724950, _1724948, c_Option_Othe(_1724950)), hAPP(c_Map_Omap__of(_1724948, _1724950), hAPP(hAPP(c_List_Ozip(_1724948, _1724950), c_Enum_Oenum__class_Oenum(_1724948)), _1724954))), -(_1724952 = _1724954)], (37249 ^ _781215) ^ [_1487032, _1487034, _1487036, _1487038, _1487040] : [-(_1487032 = c_Orderings_Obot__class_Obot(tc_fun(_1487034, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1487036, tc_HOL_Obool)), _1487038), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1487034, tc_fun(_1487036, tc_HOL_Obool)), _1487032), _1487040)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1487034, tc_fun(_1487036, tc_HOL_Obool)), _1487032), hAPP(hAPP(c_COMBB(tc_fun(_1487036, tc_HOL_Obool), tc_fun(_1487036, tc_HOL_Obool), _1487034), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1487036, tc_HOL_Obool)), _1487038)), _1487040)))], (940 ^ _781215) ^ [_795663, _795665] : [-(class_Rings_Oinverse(_795663)), _795665 = _795663, class_Rings_Oinverse(_795665)], (36590 ^ _781215) ^ [_1468883, _1468885] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468883, tc_HOL_Obool)), _1468885) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468883, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1468883, tc_HOL_Obool))), _1468885))], (28026 ^ _781215) ^ [_1291802, _1291804, _1291806] : [class_Fields_Ofield__inverse__zero(_1291802), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291802), c_Groups_Oone__class_Oone(_1291802)), hAPP(hAPP(c_Power_Opower__class_Opower(_1291802), _1291804), _1291806)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1291802), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291802), c_Groups_Oone__class_Oone(_1291802)), _1291804)), _1291806))], (12782 ^ _781215) ^ [_1003843, _1003845, _1003847, _1003849] : [class_Rings_Olinordered__comm__semiring__strict(_1003843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003843), _1003845), _1003847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003843), c_Groups_Ozero__class_Ozero(_1003843)), _1003849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003843), _1003849), _1003845)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003843), _1003849), _1003847))))], (32796 ^ _781215) ^ [_1388619, _1388621, _1388623, _1388625] : [hBOOL(hAPP(hAPP(c_member(_1388619), _1388621), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388619, tc_HOL_Obool)), _1388623), _1388625))), -(hBOOL(hAPP(hAPP(c_member(_1388619), _1388621), _1388625)))], (18389 ^ _781215) ^ [_1110302, _1110304, _1110306, _1110308] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1110302), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110302), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1110302), _1110304), _1110306)), _1110308) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1110302), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110302), _1110304), _1110308)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110302), _1110306), _1110308)))], (39058 ^ _781215) ^ [_1531097] : [class_Lattices_Oab__semigroup__idem__mult(_1531097), -(c_Finite__Set_Ofun__left__comm__idem(_1531097, _1531097, c_Groups_Otimes__class_Otimes(_1531097)))], (13208 ^ _781215) ^ [_1010981, _1010983] : [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), _1010981), _1010983))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1010981))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1010983)))], (21716 ^ _781215) ^ [_1170725] : [-(c_Int_Osucc(c_Int_OBit0(_1170725)) = c_Int_OBit1(_1170725))], (11547 ^ _781215) ^ [_982592, _982594, _982596] : [-(hAPP(c_Set_Oimage(_982592, _982594, _982596), c_Orderings_Obot__class_Obot(tc_fun(_982592, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_982594, tc_HOL_Obool)))], (51602 ^ _781215) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (14626 ^ _781215) ^ [_1037085, _1037087, _1037089] : [class_Int_Onumber(_1037085), 14629 ^ _781215 : [(14636 ^ _781215) ^ [] : [_1037089 = hAPP(c_Int_Onumber__class_Onumber__of(_1037085), _1037087), -(hAPP(c_Int_Onumber__class_Onumber__of(_1037085), _1037087) = _1037089)], (14630 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1037085), _1037087) = _1037089, -(_1037089 = hAPP(c_Int_Onumber__class_Onumber__of(_1037085), _1037087))]]], (29726 ^ _781215) ^ [_1323028, _1323030, _1323032] : [class_Fields_Olinordered__field(_1323028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323028), _1323030), _1323032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323028), _1323030), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323028), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323028), _1323030), _1323032)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323028), c_Groups_Oone__class_Oone(_1323028)), c_Groups_Oone__class_Oone(_1323028))))))], (23975 ^ _781215) ^ [_1213447, _1213449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213447)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213447), _1213449)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1213447)), hAPP(c_Int_Onat, _1213449)))], (23130 ^ _781215) ^ [_1197940, _1197942] : [c_Nat__Transfer_Onat__set(_1197940), c_Nat__Transfer_Onat__set(_1197942), 23137 ^ _781215 : [(23144 ^ _781215) ^ [] : [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), _1197940)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1197940), _1197942)))], (23138 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1197940), _1197942)), -(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), _1197940)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197942))))]]], (11276 ^ _781215) ^ [_977332, _977334] : [class_Rings_Ocomm__semiring__1(_977332), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977332), _977334), c_Groups_Oone__class_Oone(_977332)) = _977334)], (11300 ^ _781215) ^ [_977798, _977800, _977802] : [class_Rings_Ocomm__semiring__1(_977798), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977798), _977800), _977802)), _977802) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977798), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977798), _977800), c_Groups_Oone__class_Oone(_977798))), _977802))], (31128 ^ _781215) ^ [_1350982, _1350984, _1350986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1350982), _1350984)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1350982), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1350984), _1350986)) = 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, _1350982), _1350984)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1350984), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1350984), _1350986))))], (15152 ^ _781215) ^ [_1047156] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047156)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1047156)))], (39568 ^ _781215) ^ [_1547736, _1547738, _1547740] : [class_Orderings_Olinorder(_1547736), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547736), _1547738)), -(_1547738 = c_Orderings_Obot__class_Obot(tc_fun(_1547736, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547736), _1547740)), -(_1547740 = c_Orderings_Obot__class_Obot(tc_fun(_1547736, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1547736), c_Big__Operators_Olattice_OSup__fin(_1547736, c_Orderings_Oord__class_Omax(_1547736), _1547738)), c_Big__Operators_Olattice_OSup__fin(_1547736, c_Orderings_Oord__class_Omax(_1547736), _1547740)) = c_Big__Operators_Olattice_OSup__fin(_1547736, c_Orderings_Oord__class_Omax(_1547736), hAPP(c_Set_OCollect(_1547736), hAPP(hAPP(c_COMBB(tc_fun(_1547736, tc_HOL_Obool), tc_HOL_Obool, _1547736), c_HOL_OEx(_1547736)), hAPP(hAPP(c_COMBB(tc_fun(_1547736, tc_fun(_1547736, tc_HOL_Obool)), tc_fun(_1547736, tc_HOL_Obool), _1547736), hAPP(c_COMBB(tc_fun(_1547736, tc_HOL_Obool), tc_HOL_Obool, _1547736), c_HOL_OEx(_1547736))), hAPP(hAPP(c_COMBC(_1547736, tc_fun(_1547736, tc_fun(_1547736, tc_HOL_Obool)), tc_fun(_1547736, tc_fun(_1547736, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1547736, tc_fun(tc_fun(_1547736, tc_HOL_Obool), tc_fun(_1547736, tc_HOL_Obool))), tc_fun(tc_fun(_1547736, tc_fun(_1547736, tc_HOL_Obool)), tc_fun(_1547736, tc_fun(_1547736, tc_HOL_Obool))), _1547736), c_COMBS(_1547736, tc_fun(_1547736, tc_HOL_Obool), tc_fun(_1547736, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1547736, tc_fun(_1547736, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1547736, tc_fun(tc_fun(_1547736, tc_HOL_Obool), tc_fun(_1547736, tc_HOL_Obool))), _1547736), hAPP(c_COMBB(tc_fun(_1547736, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1547736, tc_HOL_Obool), tc_fun(_1547736, tc_HOL_Obool)), _1547736), c_COMBS(_1547736, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1547736, tc_fun(_1547736, tc_HOL_Obool)), tc_fun(_1547736, tc_fun(_1547736, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1547736), hAPP(c_COMBB(tc_fun(_1547736, tc_HOL_Obool), tc_fun(_1547736, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1547736), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547736), c_fconj))), hAPP(hAPP(c_COMBC(_1547736, tc_fun(_1547736, tc_fun(_1547736, _1547736)), tc_fun(_1547736, tc_fun(_1547736, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1547736, _1547736), tc_fun(_1547736, tc_HOL_Obool)), tc_fun(tc_fun(_1547736, tc_fun(_1547736, _1547736)), tc_fun(_1547736, tc_fun(_1547736, tc_HOL_Obool))), _1547736), c_COMBB(tc_fun(_1547736, _1547736), tc_fun(_1547736, tc_HOL_Obool), _1547736)), hAPP(hAPP(c_COMBB(tc_fun(_1547736, tc_HOL_Obool), tc_fun(tc_fun(_1547736, _1547736), tc_fun(_1547736, tc_HOL_Obool)), _1547736), c_COMBB(_1547736, tc_HOL_Obool, _1547736)), c_fequal))), c_Orderings_Oord__class_Omin(_1547736)))))), hAPP(hAPP(c_COMBC(_1547736, tc_fun(_1547736, tc_HOL_Obool), tc_fun(_1547736, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1547736, tc_HOL_Obool), tc_fun(_1547736, tc_HOL_Obool)), _1547736), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1547736)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547736), c_fconj), hAPP(hAPP(c_COMBC(_1547736, tc_fun(_1547736, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547736)), _1547738)))), hAPP(hAPP(c_COMBC(_1547736, tc_fun(_1547736, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547736)), _1547740))))))))], (22102 ^ _781215) ^ [_1179490, _1179492, _1179494, _1179496, _1179498] : [_1179490 = c_Orderings_Obot__class_Obot(tc_fun(_1179492, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179492, tc_fun(_1179494, tc_HOL_Obool)), _1179490), hAPP(hAPP(c_COMBB(tc_fun(_1179494, tc_HOL_Obool), tc_fun(_1179494, tc_HOL_Obool), _1179492), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1179494, tc_HOL_Obool)), _1179496)), _1179498)) = c_Orderings_Obot__class_Obot(tc_fun(_1179494, tc_HOL_Obool)))], (36217 ^ _781215) ^ [_1462022, _1462024] : [36218 ^ _781215 : [(36221 ^ _781215) ^ [] : [_1462024 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36219 ^ _781215) ^ [] : [-(_1462022 = 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), _1462022)), _1462024))))], (38264 ^ _781215) ^ [_1510326, _1510328, _1510330, _1510332, _1510334] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1510326, _1510328, _1510330), _1510332), _1510334)), -(hBOOL(hAPP(_1510332, hAPP(_1510330, _1510334))))], (5392 ^ _781215) ^ [_863593, _863595] : [_863595 = _863593, -(c_Groups_Ouminus__class_Ouminus(_863595) = c_Groups_Ouminus__class_Ouminus(_863593))], (51242 ^ _781215) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (614 ^ _781215) ^ [_790784, _790786] : [-(class_Lattices_Oab__semigroup__idem__mult(_790784)), _790786 = _790784, class_Lattices_Oab__semigroup__idem__mult(_790786)], (43864 ^ _781215) ^ [_1656862, _1656864, _1656866] : [-(hAPP(hAPP(c_List_Otake(_1656862), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1656862), _1656864), _1656866)) = hAPP(hAPP(c_List_Olist_OCons(_1656862), _1656864), c_List_Olist_ONil(_1656862)))], (11778 ^ _781215) ^ [_986459] : [class_Rings_Ozero__neq__one(_986459), c_Groups_Oone__class_Oone(_986459) = c_Groups_Ozero__class_Ozero(_986459)], (36287 ^ _781215) ^ [_1463581, _1463583] : [_1463581 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1463583, _1463581) = _1463583)], (33290 ^ _781215) ^ [_1400390, _1400392, _1400394, _1400396] : [class_Lattices_Osemilattice__inf(_1400390), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400390), _1400392)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1400390, _1400390, c_Lattices_Osemilattice__inf__class_Oinf(_1400390)), _1400394), hAPP(hAPP(c_Set_Oinsert(_1400390), _1400396), _1400392)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1400390), _1400396), hAPP(hAPP(c_Finite__Set_Ofold(_1400390, _1400390, c_Lattices_Osemilattice__inf__class_Oinf(_1400390)), _1400394), _1400392)))], (7676 ^ _781215) ^ [_910339] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910339), hAPP(c_Nat_OSuc, _910339))))], (21768 ^ _781215) ^ [_1171721, _1171723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171721), _1171723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1171721)), c_Int_OBit1(_1171723))))], (42154 ^ _781215) ^ [_1613512, _1613514, _1613516] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1613512), _1613514)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1613512)), hAPP(c_Set_OCollect(tc_List_Olist(_1613512)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1613512), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1613512)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613512), tc_fun(_1613512, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1613512, tc_HOL_Obool), tc_fun(tc_fun(_1613512, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1613512)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1613512, tc_HOL_Obool))), c_List_Oset(_1613512))), _1613514))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613512), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1613512)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1613512)))), _1613516))))))], (1308 ^ _781215) ^ [_800535, _800537] : [-(class_Orderings_Owellorder(_800535)), _800537 = _800535, class_Orderings_Owellorder(_800537)], (5792 ^ _781215) ^ [_873150, _873152, _873154, _873156, _873158] : [c_Hoare__Mirabelle_Ohoare__derivs(_873150, _873152, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873150)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873150), _873154), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _873156))), _873158)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873150), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_873150, _873152, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873150)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873150), _873154), hAPP(c_Com_Ocom_OBODY, _873156)), _873158)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873150), tc_HOL_Obool)))))], (5692 ^ _781215) ^ [_871185, _871187, _871189] : [hAPP(hAPP(c_Set_Oinsert(_871185), _871187), c_Orderings_Obot__class_Obot(tc_fun(_871185, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_871185), _871189), c_Orderings_Obot__class_Obot(tc_fun(_871185, tc_HOL_Obool))), -(_871187 = _871189)], (2746 ^ _781215) ^ [_822196, _822198, _822200, _822202] : [-(c_Wellfounded_Omin__ext(_822202, _822198) = c_Wellfounded_Omin__ext(_822200, _822196)), _822202 = _822200, _822198 = _822196], (42395 ^ _781215) ^ [_1620901, _1620903, _1620905, _1620907] : [_1620901 = _1620903, -(c_List_Oremove1(_1620905, _1620901, hAPP(hAPP(c_List_Olist_OCons(_1620905), _1620903), _1620907)) = _1620907)], (51456 ^ _781215) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (21756 ^ _781215) ^ [_1171498, _1171500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171498), _1171500)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1171498)), c_Int_OBit1(_1171500))))], (47922 ^ _781215) ^ [_1746256, _1746258, _1746260] : [-(c_List_Oinsert(_1746256, _1746258, c_List_Oremdups(_1746256, _1746260)) = c_List_Oremdups(_1746256, c_List_Oinsert(_1746256, _1746258, _1746260)))], (38233 ^ _781215) ^ [_1509607, _1509609, _1509611, _1509613, _1509615] : [hAPP(hAPP(c_Option_Omap(_1509607, _1509609), _1509611), _1509613) = hAPP(c_Option_Ooption_OSome(_1509609), _1509615), 38237 ^ _781215 : [(38240 ^ _781215) ^ [] : [-(hAPP(_1509611, 38236 ^ [_1509607, _1509609, _1509611, _1509613, _1509615]) = _1509615)], (38238 ^ _781215) ^ [] : [-(_1509613 = hAPP(c_Option_Ooption_OSome(_1509607), 38236 ^ [_1509607, _1509609, _1509611, _1509613, _1509615]))]]], (11746 ^ _781215) ^ [_985977, _985979, _985981] : [class_Groups_Oab__group__add(_985977), 11749 ^ _781215 : [(11756 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_985977), _985979), _985981) = c_Groups_Ozero__class_Ozero(_985977), -(_985979 = _985981)], (11750 ^ _781215) ^ [] : [_985979 = _985981, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_985977), _985979), _985981) = c_Groups_Ozero__class_Ozero(_985977))]]], (39797 ^ _781215) ^ [_1555783, _1555785, _1555787] : [_1555787 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1555783, _1555785), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1555783, _1555785), _1555787) = c_Orderings_Obot__class_Obot(tc_fun(_1555785, tc_HOL_Obool)))], (49447 ^ _781215) ^ [_1781462, _1781464] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1781462), tc_List_Olist(_1781462)), tc_HOL_Obool)), c_List_Olistrel(_1781462, _1781464)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1781462), c_List_Olistrel1(_1781462, _1781464)))))], (19692 ^ _781215) ^ [_1134688, _1134690, _1134692] : [class_Orderings_Olinorder(_1134688), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134688), _1134690)), hBOOL(hAPP(hAPP(c_member(_1134688), _1134692), _1134690)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1134688), _1134692), c_Big__Operators_Olinorder__class_OMax(_1134688, _1134690)) = c_Big__Operators_Olinorder__class_OMax(_1134688, _1134690))], (21027 ^ _781215) ^ [_1157864, _1157866] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157864) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1157866)), _1157864 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1157866)), 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), _1157866)))], (21990 ^ _781215) ^ [_1176973, _1176975, _1176977, _1176979, _1176981] : [_1176973 = c_Orderings_Obot__class_Obot(tc_fun(_1176975, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1176975, tc_fun(_1176977, tc_HOL_Obool)), _1176973), hAPP(hAPP(c_COMBB(tc_fun(_1176977, tc_HOL_Obool), tc_fun(_1176977, tc_HOL_Obool), _1176975), hAPP(c_Set_Oinsert(_1176977), _1176979)), _1176981)) = c_Orderings_Obot__class_Obot(tc_fun(_1176977, tc_HOL_Obool)))], (36923 ^ _781215) ^ [_1477216, _1477218, _1477220, _1477222] : [36925 ^ _781215 : [(36928 ^ _781215) ^ [] : [hAPP(_1477222, 36924 ^ [_1477216, _1477218, _1477220, _1477222]) = c_Orderings_Otop__class_Otop(tc_fun(_1477216, tc_HOL_Obool))], (36926 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477218), 36924 ^ [_1477216, _1477218, _1477220, _1477222]), _1477220)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1477216, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477218, tc_fun(_1477216, tc_HOL_Obool)), _1477220), _1477222))], (50501 ^ _781215) ^ [_1808113, _1808115, _1808117] : [c_List_Olist__all(_1808113, _1808115, _1808117), -(c_List_Olist__all(_1808113, _1808115, hAPP(c_List_Orev(_1808113), _1808117)))], (15970 ^ _781215) ^ [_1062902, _1062904, _1062906, _1062908] : [15971 ^ _781215 : [(15972 ^ _781215) ^ [_1063012] : [hBOOL(hAPP(hAPP(c_member(_1062902), _1063012), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062902, tc_HOL_Obool)), _1062904), _1062906))), hBOOL(hAPP(_1062908, _1063012))]], 15980 ^ _781215 : [(15983 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1062908, 15979 ^ [_1062902, _1062904, _1062906, _1062908])))], (15981 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062902), 15979 ^ [_1062902, _1062904, _1062906, _1062908]), _1062904)))]], 15985 ^ _781215 : [(15988 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1062908, 15984 ^ [_1062902, _1062904, _1062906, _1062908])))], (15986 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062902), 15984 ^ [_1062902, _1062904, _1062906, _1062908]), _1062906)))]]], (14886 ^ _781215) ^ [_1042207, _1042209, _1042211] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1042207, _1042209, _1042211))), 14889 ^ _781215 : [(14892 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1042211)))], (14890 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1042209)))]]], (7945 ^ _781215) ^ [_915200, _915202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915200), _915202)), _915202 = _915200], (40321 ^ _781215) ^ [_1569498, _1569500] : [-(c_List_Olex(_1569498, _1569500) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1569498), tc_List_Olist(_1569498)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1569498, _1569500)))], (19146 ^ _781215) ^ [_1124826, _1124828, _1124830] : [class_Groups_Olinordered__ab__group__add(_1124826), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1124826), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1124826), _1124828), _1124830)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1124826), hAPP(c_Groups_Ouminus__class_Ouminus(_1124826), _1124828)), hAPP(c_Groups_Ouminus__class_Ouminus(_1124826), _1124830)))], (20352 ^ _781215) ^ [_1146582] : [c_Int_OBit1(_1146582) = c_Int_OPls], (21750 ^ _781215) ^ [_1171397, _1171399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1171397)), c_Int_OBit1(_1171399))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171397), _1171399)))], (18117 ^ _781215) ^ [_1105499, _1105501, _1105503, _1105505] : [class_Orderings_Olinorder(_1105499), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105499), _1105501), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105499), _1105503), _1105505)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105499), _1105503), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105499), _1105501), _1105505)))], (15180 ^ _781215) ^ [_1047699, _1047701] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047699)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047701)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1047699), _1047701)))], (11126 ^ _781215) ^ [_973847, _973849] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973847), _973849) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973849), _973847))], (42643 ^ _781215) ^ [_1627834, _1627836, _1627838] : [-(_1627834 = _1627836), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627838)), _1627834) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627838)), _1627836), 42649 ^ _781215 : [(42652 ^ _781215) ^ [] : [hAPP(hAPP(c_List_Onth(_1627838), _1627834), 42648 ^ [_1627834, _1627836, _1627838]) = hAPP(hAPP(c_List_Onth(_1627838), _1627836), 42648 ^ [_1627834, _1627836, _1627838])], (42650 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42648 ^ [_1627834, _1627836, _1627838]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627838)), _1627834))))]]], (51324 ^ _781215) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (39725 ^ _781215) ^ [_1553661, _1553663, _1553665, _1553667, _1553669, _1553671, _1553673, _1553675] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553661, _1553663)), hAPP(hAPP(c_Product__Type_OPair(_1553661, _1553663), _1553665), _1553667)), _1553669)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1553663, _1553671)), hAPP(hAPP(c_Product__Type_OPair(_1553663, _1553671), _1553667), _1553673)), _1553675)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1553661, _1553671)), hAPP(hAPP(c_Product__Type_OPair(_1553661, _1553671), _1553665), _1553673)), hAPP(hAPP(c_Relation_Orel__comp(_1553661, _1553663, _1553671), _1553669), _1553675))))], (7840 ^ _781215) ^ [_913602, _913604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_913602, tc_HOL_Obool)), _913604), c_Orderings_Obot__class_Obot(tc_fun(_913602, tc_HOL_Obool))))], (9071 ^ _781215) ^ [_935137, _935139, _935141, _935143] : [class_Groups_Ouminus(_935137), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_935139, _935137)), _935141), _935143) = hAPP(c_Groups_Ouminus__class_Ouminus(_935137), hAPP(_935141, _935143)))], (36390 ^ _781215) ^ [_1465255, _1465257] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465255, tc_HOL_Obool)), _1465257), c_Orderings_Otop__class_Otop(tc_fun(_1465255, tc_HOL_Obool))) = _1465257)], (46582 ^ _781215) ^ [_1717955] : [c_List_Onat__list(_1717955), -(c_List_Oembed__list(c_List_Oreturn__list(_1717955)) = _1717955)], (9211 ^ _781215) ^ [_937934, _937936, _937938] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_937934), _937936)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937934, tc_HOL_Obool)), _937938), _937936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_937934), _937938)), hAPP(c_Finite__Set_Ocard(_937934), _937936))))], (51690 ^ _781215) ^ [_1825990] : [hBOOL(hAPP(c_fNot, _1825990)), hBOOL(_1825990)], (35271 ^ _781215) ^ [_1443549, _1443551, _1443553, _1443555, _1443557] : [hBOOL(hAPP(hAPP(c_member(_1443549), _1443551), hAPP(c_Relation_OImage(_1443553, _1443549, _1443555), _1443557))), 35275 ^ _781215 : [(35278 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1443553), 35274 ^ [_1443549, _1443551, _1443553, _1443555, _1443557]), _1443557)))], (35276 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1443553, _1443549)), hAPP(hAPP(c_Product__Type_OPair(_1443553, _1443549), 35274 ^ [_1443549, _1443551, _1443553, _1443555, _1443557]), _1443551)), _1443555)))]]], (34590 ^ _781215) ^ [_1429311, _1429313, _1429315, _1429317, _1429319] : [c_Fun_Oinj__on(_1429311, _1429313, _1429315, _1429317), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429311, tc_HOL_Obool)), _1429319), _1429317)), -(c_Fun_Oinj__on(_1429311, _1429313, _1429315, _1429319))], (19170 ^ _781215) ^ [_1125338, _1125340, _1125342] : [class_Orderings_Olinorder(_1125338), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125338), _1125340)), hBOOL(hAPP(hAPP(c_member(_1125338), _1125342), _1125340)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1125338), _1125342), c_Big__Operators_Olattice_OInf__fin(_1125338, c_Orderings_Oord__class_Omin(_1125338), _1125340)) = c_Big__Operators_Olattice_OInf__fin(_1125338, c_Orderings_Oord__class_Omin(_1125338), _1125340))], (5764 ^ _781215) ^ [_872448, _872450, _872452] : [-(hAPP(hAPP(c_Set_Oinsert(_872448), _872450), hAPP(hAPP(c_Set_Oinsert(_872448), _872450), _872452)) = hAPP(hAPP(c_Set_Oinsert(_872448), _872450), _872452))], (51302 ^ _781215) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (15466 ^ _781215) ^ [_1052444, _1052446] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052444), _1052446) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052444), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1052446)))], (34850 ^ _781215) ^ [_1434406, _1434408, _1434410, _1434412, _1434414, _1434416] : [c_Fun_Oinj__on(_1434406, _1434408, _1434410, _1434412), -(hBOOL(hAPP(hAPP(c_member(_1434408), _1434414), hAPP(c_Set_Oimage(_1434406, _1434408, _1434410), _1434412)))), -(c_Fun_Oinj__on(_1434406, _1434408, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1434406, _1434408), _1434410), _1434416), _1434414), _1434412))], (11510 ^ _781215) ^ [_981786, _981788, _981790, _981792, _981794] : [hBOOL(hAPP(hAPP(c_member(_981786), _981788), _981790)), -(hBOOL(hAPP(hAPP(c_member(_981792), hAPP(_981794, _981788)), hAPP(c_Set_Oimage(_981786, _981792, _981794), _981790))))], (45318 ^ _781215) ^ [_1690336, _1690338, _1690340] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690336)), hAPP(c_List_Ofilter(_1690336, _1690338), _1690340))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690336)), _1690340))))], (45764 ^ _781215) ^ [_1699060, _1699062, _1699064] : [class_Orderings_Olinorder(_1699060), 45767 ^ _781215 : [(45780 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1699060, hAPP(hAPP(c_List_Olist_OCons(_1699060), _1699062), _1699064))), c_List_Olinorder__class_Osorted(_1699060, _1699064), 45786 ^ _781215 : [(45789 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699060), _1699062), 45785 ^ [_1699060, _1699062, _1699064]))], (45787 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699060), 45785 ^ [_1699060, _1699062, _1699064]), hAPP(c_List_Oset(_1699060), _1699064))))]]], (45768 ^ _781215) ^ [] : [c_List_Olinorder__class_Osorted(_1699060, hAPP(hAPP(c_List_Olist_OCons(_1699060), _1699062), _1699064)), 45771 ^ _781215 : [(45774 ^ _781215) ^ [_1699246] : [hBOOL(hAPP(hAPP(c_member(_1699060), _1699246), hAPP(c_List_Oset(_1699060), _1699064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699060), _1699062), _1699246)))], (45772 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1699060, _1699064))]]]]], (14278 ^ _781215) ^ [_1030844, _1030846] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_1030844, _1030846)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1030844)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1030846))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17507 ^ _781215) ^ [_1094520, _1094522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094520), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094522)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094520)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094522))], (22466 ^ _781215) ^ [_1187096, _1187098, _1187100, _1187102] : [class_Divides_Osemiring__div(_1187096), -(c_Divides_Odiv__class_Omod(_1187096, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187096), _1187098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187096), _1187100), _1187102)), _1187100) = c_Divides_Odiv__class_Omod(_1187096, _1187098, _1187100))], (16303 ^ _781215) ^ [_1069353, _1069355, _1069357] : [class_Lattices_Obounded__lattice__bot(_1069353), 16306 ^ _781215 : [(16315 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069353), _1069355), _1069357) = c_Orderings_Obot__class_Obot(_1069353)), _1069355 = c_Orderings_Obot__class_Obot(_1069353), _1069357 = c_Orderings_Obot__class_Obot(_1069353)], (16307 ^ _781215) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069353), _1069355), _1069357) = c_Orderings_Obot__class_Obot(_1069353), 16310 ^ _781215 : [(16313 ^ _781215) ^ [] : [-(_1069357 = c_Orderings_Obot__class_Obot(_1069353))], (16311 ^ _781215) ^ [] : [-(_1069355 = c_Orderings_Obot__class_Obot(_1069353))]]]]], (6774 ^ _781215) ^ [_892386, _892388, _892390] : [-(hAPP(hAPP(c_Set_Oinsert(_892386), _892388), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892386, tc_HOL_Obool)), _892390), hAPP(hAPP(c_Set_Oinsert(_892386), _892388), c_Orderings_Obot__class_Obot(tc_fun(_892386, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_892386), _892388), _892390))], (31076 ^ _781215) ^ [_1349992] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1349992)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1349992)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1349992)))], (45013 ^ _781215) ^ [_1684146, _1684148, _1684150, _1684152, _1684154] : [c_Finite__Set_Ofun__left__comm__idem(_1684146, _1684148, _1684150), -(hAPP(hAPP(c_Finite__Set_Ofold(_1684146, _1684148, _1684150), _1684152), hAPP(c_List_Oset(_1684146), _1684154)) = hAPP(c_List_Ofoldl(_1684148, _1684146, hAPP(c_COMBC(_1684146, _1684148, _1684148), _1684150), _1684152), _1684154))], (34660 ^ _781215) ^ [_1430503, _1430505, _1430507, _1430509, _1430511] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1430503, _1430505, _1430507), _1430509), _1430511), c_Orderings_Obot__class_Obot(tc_fun(_1430505, tc_HOL_Obool))) = _1430511)], (5346 ^ _781215) ^ [_862904, _862906] : [_862906 = _862904, -(c_Lazy__Sequence_Oempty(_862906) = c_Lazy__Sequence_Oempty(_862904))], (25660 ^ _781215) ^ [_1243053, _1243055] : [c_Code__Numeral_OSuc__code__numeral(_1243053) = c_Code__Numeral_OSuc__code__numeral(_1243055), -(_1243053 = _1243055)], (10852 ^ _781215) ^ [_967372, _967374, _967376, _967378, _967380, _967382] : [class_Rings_Oordered__ring(_967372), 10855 ^ _781215 : [(10862 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967372), _967378), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967372), _967380), _967374)), _967376)), _967382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967372), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967372), _967374), _967376)), _967378)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967372), _967380), _967376)), _967382))))], (10856 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967372), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967372), _967374), _967376)), _967378)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967372), _967380), _967376)), _967382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967372), _967378), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967372), _967380), _967374)), _967376)), _967382))))]]], (22226 ^ _781215) ^ [_1182235, _1182237] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182235, _1182237)), _1182237) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (688 ^ _781215) ^ [_791841, _791843, _791845, _791847, _791849, _791851] : [-(c_Enum_Oall__n__lists(_791849, _791845, _791841)), c_Enum_Oall__n__lists(_791851, _791847, _791843), _791851 = _791849, _791847 = _791845, _791843 = _791841], (27566 ^ _781215) ^ [_1283014, _1283016] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1283014), _1283016) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1283014, _1283016)))], (2582 ^ _781215) ^ [_819590, _819592] : [_819592 = _819590, -(c_Nitpick_Ozero__frac(_819592) = c_Nitpick_Ozero__frac(_819590))], (9999 ^ _781215) ^ [_951203, _951205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951203), _951205)), -(_951203 = _951205), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _951203), _951205)))], (42006 ^ _781215) ^ [_1609789, _1609791, _1609793, _1609795] : [class_Orderings_Olinorder(_1609789), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1609789, _1609789, c_COMBI(_1609789)), _1609791), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1609789, _1609789, c_COMBI(_1609789)), _1609793), _1609795)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1609789, _1609789, c_COMBI(_1609789)), _1609793), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1609789, _1609789, c_COMBI(_1609789)), _1609791), _1609795)))], (25580 ^ _781215) ^ [_1241580, _1241582, _1241584, _1241586, _1241588, _1241590] : [-(hBOOL(hAPP(hAPP(c_member(_1241580), _1241582), c_SetInterval_Oord_OgreaterThanAtMost(_1241580, _1241584, _1241586, _1241588, _1241590)))), hBOOL(hAPP(hAPP(_1241586, _1241588), _1241582)), hBOOL(hAPP(hAPP(_1241584, _1241582), _1241590))], (8363 ^ _781215) ^ [_922268, _922270, _922272, _922274, _922276] : [hBOOL(hAPP(hAPP(c_member(_922268), _922270), c_Map_Oran(_922272, _922268, c_Map_Orestrict__map(_922272, _922268, _922274, _922276)))), 8367 ^ _781215 : [(8370 ^ _781215) ^ [] : [-(hAPP(_922274, 8366 ^ [_922268, _922270, _922272, _922274, _922276]) = hAPP(c_Option_Ooption_OSome(_922268), _922270))], (8368 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_922272), 8366 ^ [_922268, _922270, _922272, _922274, _922276]), _922276)))]]], (50248 ^ _781215) ^ [_1802250, _1802252, _1802254] : [-(hBOOL(hAPP(hAPP(c_member(_1802250), _1802252), hAPP(c_List_Oset(_1802250), _1802254)))), 50249 ^ _781215 : [(50250 ^ _781215) ^ [_1802339, _1802341] : [_1802254 = hAPP(hAPP(c_List_Oappend(_1802250), _1802341), hAPP(hAPP(c_List_Olist_OCons(_1802250), _1802252), _1802339)), -(hBOOL(hAPP(hAPP(c_member(_1802250), _1802252), hAPP(c_List_Oset(_1802250), _1802339))))]]], (36538 ^ _781215) ^ [_1467911, _1467913] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467911, tc_HOL_Obool)), _1467913), c_Orderings_Otop__class_Otop(tc_fun(_1467911, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1467911, tc_HOL_Obool)))], (26855 ^ _781215) ^ [_1269284] : [-(c_Divides_Odivmod__nat(_1269284, 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)), _1269284))], (36512 ^ _781215) ^ [_1467481, _1467483] : [class_Lattices_Obounded__lattice__top(_1467481), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1467481), c_Orderings_Otop__class_Otop(_1467481)), _1467483) = c_Orderings_Otop__class_Otop(_1467481))], (24015 ^ _781215) ^ [_1214200, _1214202, _1214204] : [-(hBOOL(hAPP(_1214200, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1214202, _1214204)))), 24018 ^ _781215 : [(24021 ^ _781215) ^ [] : [hBOOL(hAPP(_1214200, _1214202))], (24019 ^ _781215) ^ [] : [-(_1214204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 24022 ^ _781215 : [(24027 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24025 ^ [_1214200, _1214202, _1214204]), _1214204)))], (24029 ^ _781215) ^ [] : [-(_1214202 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214204), 24024 ^ [_1214200, _1214202, _1214204])), 24025 ^ [_1214200, _1214202, _1214204]))], (24031 ^ _781215) ^ [] : [hBOOL(hAPP(_1214200, 24025 ^ [_1214200, _1214202, _1214204]))], (24023 ^ _781215) ^ [] : [_1214204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (21970 ^ _781215) ^ [] : [-(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))))], (5841 ^ _781215) ^ [_874127] : [-(c_Option_Ois__none(_874127, c_Option_Ooption_ONone(_874127)))], (40663 ^ _781215) ^ [_1577974, _1577976, _1577978, _1577980] : [c_Com_Ocom_OWhile(_1577974, _1577976) = c_Com_Ocom_OSemi(_1577978, _1577980)], (18089 ^ _781215) ^ [_1104662, _1104664, _1104666, _1104668] : [-(c_Nat_Onat_Onat__case(_1104662, _1104664, _1104666, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104668)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1104662), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1104668))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1104662, _1104662), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1104662, tc_fun(_1104662, _1104662)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1104662, tc_fun(_1104662, _1104662)), tc_Int_Oint), c_If(_1104662)), c_Nat__Numeral_Oneg)), _1104664)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1104662, tc_Int_Oint), _1104666), c_Int_Onat))))], (51290 ^ _781215) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (34039 ^ _781215) ^ [_1416426, _1416428, _1416430, _1416432, _1416434, _1416436, _1416438] : [c_Equiv__Relations_Oequiv(_1416426, _1416428, _1416430), c_Equiv__Relations_Ocongruent(_1416426, tc_fun(_1416432, tc_HOL_Obool), _1416430, _1416434), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416426, tc_fun(_1416432, tc_HOL_Obool)), _1416436), _1416434) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416426, tc_fun(_1416432, tc_HOL_Obool)), _1416438), _1416434), hBOOL(hAPP(hAPP(c_member(tc_fun(_1416426, tc_HOL_Obool)), _1416436), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1416426), _1416428), _1416430))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1416426, tc_HOL_Obool)), _1416438), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1416426), _1416428), _1416430))), 34061 ^ _781215 : [(34065 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416426), 34063 ^ [_1416426, _1416428, _1416430, _1416432, _1416434, _1416436, _1416438]), _1416428)))], (34067 ^ _781215) ^ [] : [-(hAPP(_1416434, 34060 ^ [_1416426, _1416428, _1416430, _1416432, _1416434, _1416436, _1416438]) = hAPP(_1416434, 34063 ^ [_1416426, _1416428, _1416430, _1416432, _1416434, _1416436, _1416438]))], (34069 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1416426, _1416426)), hAPP(hAPP(c_Product__Type_OPair(_1416426, _1416426), 34060 ^ [_1416426, _1416428, _1416430, _1416432, _1416434, _1416436, _1416438]), 34063 ^ [_1416426, _1416428, _1416430, _1416432, _1416434, _1416436, _1416438])), _1416430))], (34062 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416426), 34060 ^ [_1416426, _1416428, _1416430, _1416432, _1416434, _1416436, _1416438]), _1416428)))]], -(_1416436 = _1416438)], (16947 ^ _781215) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (2202 ^ _781215) ^ [_813504, _813506, _813508, _813510, _813512, _813514] : [-(c_Smallcheck_Ofull__small_H(_813514, _813510, _813506) = c_Smallcheck_Ofull__small_H(_813512, _813508, _813504)), _813514 = _813512, _813510 = _813508, _813506 = _813504], (45377 ^ _781215) ^ [_1691844] : [-(c_List_Otranspose(_1691844, c_List_Olist_ONil(tc_List_Olist(_1691844))) = c_List_Olist_ONil(tc_List_Olist(_1691844)))], (39661 ^ _781215) ^ [_1551987, _1551989] : [-(c_Product__Type_Oapfst(_1551987, _1551987, _1551989, c_Fun_Oid(_1551987)) = c_Fun_Oid(tc_prod(_1551987, _1551989)))], (51338 ^ _781215) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (47000 ^ _781215) ^ [_1726633, _1726635, _1726637, _1726639] : [class_Orderings_Olinorder(_1726633), -(hAPP(c_List_Oset(_1726635), c_List_Olinorder__class_Osort__key(_1726635, _1726633, _1726637, _1726639)) = hAPP(c_List_Oset(_1726635), _1726639))], (34896 ^ _781215) ^ [_1435378, _1435380, _1435382, _1435384, _1435386, _1435388] : [class_Groups_Oab__semigroup__mult(_1435378), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435380), _1435382)), -(hBOOL(hAPP(hAPP(c_member(_1435380), _1435384), _1435382))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435378, _1435380, c_Groups_Otimes__class_Otimes(_1435378)), _1435386), _1435388), hAPP(hAPP(c_Set_Oinsert(_1435380), _1435384), _1435382)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435378), hAPP(_1435386, _1435384)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435378, _1435380, c_Groups_Otimes__class_Otimes(_1435378)), _1435386), _1435388), _1435382)))], (40896 ^ _781215) ^ [_1582899] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40892 ^ [_1582899]), c_Int_OInteg)))], (7438 ^ _781215) ^ [_906381, _906383, _906385] : [class_Orderings_Oorder(_906381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906381), _906383), _906385)), _906383 = _906385], (7762 ^ _781215) ^ [_912052, _912054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912052), _912054)), _912054))], (51446 ^ _781215) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (45400 ^ _781215) ^ [_1692334, _1692336, _1692338, _1692340] : [-(c_List_Otranspose(_1692334, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692336), tc_List_Olist(_1692334)), hAPP(c_List_Omap(_1692336, _1692334), _1692338)), _1692340)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692336), tc_List_Olist(_1692334)), hAPP(c_List_Omap(_1692336, _1692334), _1692338)), c_List_Otranspose(_1692336, _1692340)))], (51400 ^ _781215) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (48980 ^ _781215) ^ [_1769802, _1769804] : [_1769802 = _1769804, -(hAPP(c_Code__Numeral_Onat__of, _1769802) = hAPP(c_Code__Numeral_Onat__of, _1769804))], (16471 ^ _781215) ^ [_1072725, _1072727, _1072729, _1072731] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1072725, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072725, tc_HOL_Obool)), _1072727), _1072729)), _1072731) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072725, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1072725, tc_HOL_Obool)), _1072727), _1072731)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1072725, tc_HOL_Obool)), _1072729), _1072731)))], (11182 ^ _781215) ^ [_975273, _975275, _975277, _975279] : [class_Rings_Ocomm__semiring__1(_975273), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975273), _975275), _975277)), _975279) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975273), _975275), _975279)), _975277))], (36504 ^ _781215) ^ [] : [-(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))], (24196 ^ _781215) ^ [_1217634] : [class_Rings_Osemiring__1(_1217634), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1217634), c_Groups_Ozero__class_Ozero(_1217634)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1217634))], (3286 ^ _781215) ^ [_830744, _830746, _830748, _830750, _830752, _830754] : [-(c_Big__Operators_Olattice_OSup__fin(_830754, _830750, _830746) = c_Big__Operators_Olattice_OSup__fin(_830752, _830748, _830744)), _830754 = _830752, _830750 = _830748, _830746 = _830744], (5196 ^ _781215) ^ [_860511, _860513] : [_860513 = _860511, -(c_If(_860513) = c_If(_860511))], (34664 ^ _781215) ^ [_1430602, _1430604, _1430606, _1430608] : [c_Fun_Oinj__on(_1430602, _1430604, _1430606, _1430608), 34667 ^ _781215 : [(34668 ^ _781215) ^ [_1430710] : [hBOOL(hAPP(hAPP(c_member(_1430602), _1430710), _1430608)), 34671 ^ _781215 : [(34672 ^ _781215) ^ [_1430812] : [hBOOL(hAPP(hAPP(c_member(_1430602), _1430812), _1430608)), hAPP(_1430606, _1430710) = hAPP(_1430606, _1430812), -(_1430710 = _1430812)]]]]], (47964 ^ _781215) ^ [_1747018, _1747020, _1747022] : [-(hAPP(c_List_Oset(_1747018), hAPP(c_List_OremoveAll(_1747018, _1747020), _1747022)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1747018, tc_HOL_Obool)), hAPP(c_List_Oset(_1747018), _1747022)), hAPP(hAPP(c_Set_Oinsert(_1747018), _1747020), c_Orderings_Obot__class_Obot(tc_fun(_1747018, tc_HOL_Obool)))))], (10306 ^ _781215) ^ [_956761, _956763, _956765, _956767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_956761, tc_HOL_Obool)), _956763), _956765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_956761, tc_HOL_Obool)), _956765), _956767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_956761, tc_HOL_Obool)), _956763), _956767)))], (33943 ^ _781215) ^ [_1414303, _1414305, _1414307] : [class_Orderings_Olinorder(_1414303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414303), _1414305)), -(_1414305 = c_Orderings_Obot__class_Obot(tc_fun(_1414303, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414303), _1414307)), -(_1414307 = c_Orderings_Obot__class_Obot(tc_fun(_1414303, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1414303, tc_HOL_Obool)), _1414305), _1414307) = c_Orderings_Obot__class_Obot(tc_fun(_1414303, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1414303, c_Orderings_Oord__class_Omax(_1414303), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414303, tc_HOL_Obool)), _1414305), _1414307)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1414303), c_Big__Operators_Olattice_OSup__fin(_1414303, c_Orderings_Oord__class_Omax(_1414303), _1414305)), c_Big__Operators_Olattice_OSup__fin(_1414303, c_Orderings_Oord__class_Omax(_1414303), _1414307)))], (26167 ^ _781215) ^ [_1255792, _1255794] : [class_Rings_Oring__1(_1255792), -(hAPP(c_Int_Oring__1__class_Oof__int(_1255792), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255794)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1255792), _1255794))], (27106 ^ _781215) ^ [_1274066, _1274068, _1274070] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1274066), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1274068), _1274070)))), 27109 ^ _781215 : [(27116 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1274068), _1274070))), -(c_Smallcheck_Osmall_H(_1274066, _1274068, _1274070) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1274066, _1274068, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1274070), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1274066, _1274070)))], (27110 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1274068), _1274070)), -(c_Smallcheck_Osmall_H(_1274066, _1274068, _1274070) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))]]], (51402 ^ _781215) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (5893 ^ _781215) ^ [_875007, _875009, _875011, _875013, _875015, _875017, _875019] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_875007), _875009), _875011), _875013) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_875007), _875015), _875017), _875019)), _875009 = _875015, _875011 = _875017, _875013 = _875019], (23648 ^ _781215) ^ [_1207482, _1207484] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207482), _1207484) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1207482, _1207484)), _1207484))], (17961 ^ _781215) ^ [_1101917, _1101919] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1101917)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1101919)), hAPP(c_Int_Onat, _1101917)) = hAPP(c_Int_Onat, _1101919))], (22258 ^ _781215) ^ [_1182745, _1182747, _1182749] : [class_Divides_Osemiring__div(_1182745), -(c_Divides_Odiv__class_Omod(_1182745, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182745), _1182747), _1182749), _1182747) = c_Divides_Odiv__class_Omod(_1182745, _1182749, _1182747))], (24083 ^ _781215) ^ [_1215478, _1215480] : [-(_1215478 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1215480), _1215478) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215480), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1215480), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1215478), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (20316 ^ _781215) ^ [_1145919, _1145921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1145919)), c_Int_OBit1(_1145921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145919), _1145921)))], (26994 ^ _781215) ^ [_1271806, _1271808] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1271806))), 26997 ^ _781215 : [(27004 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1271808))), -(c_Divides_Odivmod__int(_1271806, _1271808) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1271806), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1271808))))], (26998 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1271808)), -(c_Divides_Odivmod__int(_1271806, _1271808) = c_Divides_OnegDivAlg(_1271806, _1271808))]]], (46690 ^ _781215) ^ [_1719839, _1719841, _1719843, _1719845, _1719847] : [c_Finite__Set_Ofun__left__comm(_1719839, _1719841, _1719843), -(hAPP(hAPP(c_Finite__Set_Ofold(_1719839, _1719841, _1719843), _1719845), hAPP(c_List_Oset(_1719839), _1719847)) = hAPP(c_List_Ofoldl(_1719841, _1719839, hAPP(c_COMBC(_1719839, _1719841, _1719841), _1719843), _1719845), c_List_Oremdups(_1719839, _1719847)))], (27408 ^ _781215) ^ [_1279922, _1279924, _1279926, _1279928] : [_1279922 = _1279924, 27411 ^ _781215 : [(27414 ^ _781215) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1279926, _1279928), _1279922) = hAPP(c_Product__Type_Osnd(_1279926, _1279928), _1279924))], (27412 ^ _781215) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1279926, _1279928), _1279922) = hAPP(c_Product__Type_Ofst(_1279926, _1279928), _1279924))]]], (21572 ^ _781215) ^ [_1168264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1168264)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1168264), c_Int_OPls)))], (34220 ^ _781215) ^ [_1422104, _1422106, _1422108, _1422110, _1422112, _1422114] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422104, tc_fun(_1422106, tc_HOL_Obool))), _1422108), _1422110), _1422112), _1422114)), 34223 ^ _781215 : [(34226 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1422110, _1422112), _1422114)))], (34224 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1422108, _1422112), _1422114)))]]], (16283 ^ _781215) ^ [_1068995, _1068997, _1068999, _1069001] : [class_Lattices_Osemilattice__sup(_1068995), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068995), _1068997), _1068999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068995), _1068997), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068995), _1069001), _1068999))))], (37492 ^ _781215) ^ [_1493238, _1493240, _1493242] : [class_Complete__Lattice_Ocomplete__lattice(_1493238), class_Orderings_Olinorder(_1493238), 37499 ^ _781215 : [(37509 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1493238), c_Complete__Lattice_OInf__class_OInf(_1493238, _1493240)), _1493242))), 37510 ^ _781215 : [(37511 ^ _781215) ^ [_1493544] : [hBOOL(hAPP(hAPP(c_member(_1493238), _1493544), _1493240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1493238), _1493544), _1493242))]]], (37500 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1493238), c_Complete__Lattice_OInf__class_OInf(_1493238, _1493240)), _1493242)), 37504 ^ _781215 : [(37507 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1493238), 37503 ^ [_1493238, _1493240, _1493242]), _1493242)))], (37505 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493238), 37503 ^ [_1493238, _1493240, _1493242]), _1493240)))]]]]], (32284 ^ _781215) ^ [_1377851, _1377853, _1377855, _1377857] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1377851, _1377851)), hAPP(hAPP(c_Product__Type_OPair(_1377851, _1377851), _1377853), _1377855)), c_Relation_OId__on(_1377851, _1377857))), 32287 ^ _781215 : [(32290 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377851), _1377853), _1377857)))], (32288 ^ _781215) ^ [] : [-(_1377853 = _1377855)]]], (18701 ^ _781215) ^ [_1116418, _1116420, _1116422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116418)), 18707 ^ _781215 : [(18710 ^ _781215) ^ [] : [hBOOL(hAPP(_1116420, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 18706 ^ [_1116418, _1116420, _1116422]), _1116418)))], (18708 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1116420, 18706 ^ [_1116418, _1116420, _1116422])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116422)), 18715 ^ _781215 : [(18716 ^ _781215) ^ [_1116707] : [hBOOL(hAPP(_1116420, _1116707)), -(hBOOL(hAPP(_1116420, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1116707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116422), _1116418)))))]]], (48383 ^ _781215) ^ [_1757920, _1757922, _1757924, _1757926] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1757920, tc_HOL_Obool), tc_fun(_1757920, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1757920, tc_HOL_Obool), tc_fun(_1757920, tc_HOL_Obool)), _1757922), _1757924)), c_Wellfounded_Omax__ext(_1757920, _1757926))), 48386 ^ _781215 : [(48389 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1757920), _1757924)))], (48391 ^ _781215) ^ [] : [_1757924 = c_Orderings_Obot__class_Obot(tc_fun(_1757920, tc_HOL_Obool))], (48393 ^ _781215) ^ [_1758214] : [hBOOL(hAPP(hAPP(c_member(_1757920), _1758214), _1757922)), 48397 ^ _781215 : [(48400 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757920, _1757920)), hAPP(hAPP(c_Product__Type_OPair(_1757920, _1757920), _1758214), 48396 ^ [_1757920, _1757922, _1757924, _1757926, _1758214])), _1757926)))], (48398 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757920), 48396 ^ [_1757920, _1757922, _1757924, _1757926, _1758214]), _1757924)))]]], (48387 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1757920), _1757922)))]]], (50431 ^ _781215) ^ [_1806790, _1806792, _1806794] : [50433 ^ _781215 : [(50436 ^ _781215) ^ [] : [hBOOL(hAPP(_1806792, hAPP(hAPP(c_List_Onth(_1806790), _1806794), 50432 ^ [_1806790, _1806792, _1806794])))], (50434 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50432 ^ [_1806790, _1806792, _1806794]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806790)), _1806794))))]], -(c_List_Olist__all(_1806790, _1806792, _1806794))], (43646 ^ _781215) ^ [_1652988, _1652990] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1652988)), c_List_Olist_ONil(_1652988)), c_List_Olists(_1652988, _1652990))))], (39765 ^ _781215) ^ [_1554944, _1554946, _1554948, _1554950] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1554944, _1554946, _1554948), _1554950), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1554946, _1554948), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1554944, _1554948), tc_HOL_Obool)))], (36013 ^ _781215) ^ [_1458361, _1458363] : [-(c_Divides_Opdivmod(_1458361, _1458363) = 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), _1458361)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458363))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458361), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458363))))], (6894 ^ _781215) ^ [_895101, _895103, _895105] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895101), _895103)), hBOOL(hAPP(_895105, _895103)), 6905 ^ _781215 : [(6908 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895101), 6903 ^ [_895101, _895103, _895105]), 6904 ^ [_895101, _895103, _895105])))], (6910 ^ _781215) ^ [] : [-(hBOOL(hAPP(_895105, 6904 ^ [_895101, _895103, _895105])))], (6912 ^ _781215) ^ [] : [hBOOL(hAPP(_895105, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895101, tc_HOL_Obool)), 6904 ^ [_895101, _895103, _895105]), hAPP(hAPP(c_Set_Oinsert(_895101), 6903 ^ [_895101, _895103, _895105]), c_Orderings_Obot__class_Obot(tc_fun(_895101, tc_HOL_Obool))))))], (6906 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_895101), 6904 ^ [_895101, _895103, _895105])))]], -(hBOOL(hAPP(_895105, c_Orderings_Obot__class_Obot(tc_fun(_895101, tc_HOL_Obool)))))], (30072 ^ _781215) ^ [_1331122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331122)), 30076 ^ _781215 : [(30079 ^ _781215) ^ [] : [-(_1331122 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 30075 ^ [_1331122]))], (30077 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 30075 ^ [_1331122])))]]], (49437 ^ _781215) ^ [_1781101, _1781103, _1781105, _1781107, _1781109, _1781111] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1781101, _1781101)), hAPP(hAPP(c_Product__Type_OPair(_1781101, _1781101), _1781103), _1781105)), c_Transitive__Closure_Ortrancl(_1781101, _1781107))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1781101), tc_List_Olist(_1781101))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1781101), tc_List_Olist(_1781101)), _1781109), _1781111)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1781101), c_List_Olistrel1(_1781101, _1781107)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1781101), tc_List_Olist(_1781101))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1781101), tc_List_Olist(_1781101)), hAPP(hAPP(c_List_Olist_OCons(_1781101), _1781103), _1781109)), hAPP(hAPP(c_List_Olist_OCons(_1781101), _1781105), _1781111))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1781101), c_List_Olistrel1(_1781101, _1781107)))))], (51736 ^ _781215) ^ [_1826588, _1826590] : [hBOOL(hAPP(hAPP(c_fdisj, _1826588), _1826590)), -(hBOOL(_1826588)), -(hBOOL(_1826590))], (19380 ^ _781215) ^ [_1128865, _1128867, _1128869] : [class_Orderings_Olinorder(_1128865), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128865), _1128867)), -(_1128867 = c_Orderings_Obot__class_Obot(tc_fun(_1128865, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128865), _1128869)), -(_1128869 = c_Orderings_Obot__class_Obot(tc_fun(_1128865, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1128865, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1128865, tc_HOL_Obool)), _1128867), _1128869)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1128865), c_Big__Operators_Olinorder__class_OMin(_1128865, _1128867)), c_Big__Operators_Olinorder__class_OMin(_1128865, _1128869)))], (36942 ^ _781215) ^ [_1477696, _1477698, _1477700, _1477702] : [36944 ^ _781215 : [(36947 ^ _781215) ^ [] : [hAPP(_1477702, 36943 ^ [_1477696, _1477698, _1477700, _1477702]) = c_Orderings_Otop__class_Otop(tc_fun(_1477698, tc_HOL_Obool))], (36945 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477696), 36943 ^ [_1477696, _1477698, _1477700, _1477702]), _1477700)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477696, tc_fun(_1477698, tc_HOL_Obool)), _1477700), _1477702) = c_Orderings_Otop__class_Otop(tc_fun(_1477698, tc_HOL_Obool)))], (41008 ^ _781215) ^ [_1585624, _1585626, _1585628, _1585630] : [-(hAPP(c_List_Oset(_1585624), hAPP(hAPP(c_List_Omap(_1585626, _1585624), _1585628), _1585630)) = hAPP(c_Set_Oimage(_1585626, _1585624, _1585628), hAPP(c_List_Oset(_1585626), _1585630)))], (32848 ^ _781215) ^ [_1390065, _1390067, _1390069, _1390071] : [class_Lattices_Odistrib__lattice(_1390065), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1390065), _1390067), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1390065), _1390069), _1390071)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1390065), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1390065), _1390067), _1390069)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1390065), _1390067), _1390071)))], (36460 ^ _781215) ^ [_1466463] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1466463)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1466463), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1466463), c_Orderings_Otop__class_Otop(tc_fun(_1466463, tc_HOL_Obool)))))], (12468 ^ _781215) ^ [_998107, _998109, _998111] : [class_Groups_Oordered__comm__monoid__add(_998107), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998107), _998109), c_Groups_Ozero__class_Ozero(_998107))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998107), _998111), c_Groups_Ozero__class_Ozero(_998107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998107), _998109), _998111)), c_Groups_Ozero__class_Ozero(_998107))))], (46674 ^ _781215) ^ [_1719555] : [-(c_List_Oembed__list(_1719555) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1719555))], (1188 ^ _781215) ^ [_799035, _799037] : [-(class_Rings_Oordered__ring(_799035)), _799037 = _799035, class_Rings_Oordered__ring(_799037)], (8678 ^ _781215) ^ [_928443, _928445, _928447] : [class_Rings_Oring(_928443), -(hAPP(c_Groups_Ouminus__class_Ouminus(_928443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928443), _928445), _928447)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928443), hAPP(c_Groups_Ouminus__class_Ouminus(_928443), _928445)), _928447))], (26456 ^ _781215) ^ [_1261234, _1261236, _1261238, _1261240] : [class_Orderings_Olinorder(_1261234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261234), _1261236), _1261238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261234), _1261238), _1261240)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261234, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1261234, _1261236, _1261238)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1261234, _1261238, _1261240)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1261234, _1261236, _1261240))], (49034 ^ _781215) ^ [_1770736, _1770738] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1770736, _1770738) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1770736), hAPP(c_Code__Numeral_Onat__of, _1770738))))], (43551 ^ _781215) ^ [_1650615, _1650617, _1650619] : [-(c_Hilbert__Choice_OEps(tc_prod(_1650615, _1650617), _1650619) = c_Hilbert__Choice_OEps(tc_prod(_1650615, _1650617), hAPP(c_Product__Type_Oprod_Oprod__case(_1650615, _1650617, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1650617, tc_prod(_1650615, _1650617)), tc_fun(_1650617, tc_HOL_Obool), _1650615), hAPP(c_COMBB(tc_prod(_1650615, _1650617), tc_HOL_Obool, _1650617), _1650619)), c_Product__Type_OPair(_1650615, _1650617)))))], (7338 ^ _781215) ^ [_905136, _905138, _905140] : [class_Orderings_Olinorder(_905136), 7341 ^ _781215 : [(7342 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905136), _905138), _905140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905136), _905140), _905138))), -(_905138 = _905140)], (7352 ^ _781215) ^ [] : [7353 ^ _781215 : [(7356 ^ _781215) ^ [] : [_905138 = _905140], (7354 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905136), _905140), _905138))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905136), _905138), _905140))]]], (49604 ^ _781215) ^ [_1785569, _1785571] : [-(c_Transitive__Closure_Ortrancl(_1785569, hAPP(c_Relation_Oconverse(_1785569, _1785569), _1785571)) = hAPP(c_Relation_Oconverse(_1785569, _1785569), c_Transitive__Closure_Ortrancl(_1785569, _1785571)))], (10138 ^ _781215) ^ [_953876, _953878] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _953876), _953878)), _953876)))], (49375 ^ _781215) ^ [_1779622, _1779624] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1779622, _1779622), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1779622, _1779624)), c_Relation_OId(_1779622)) = c_Transitive__Closure_Ortrancl(_1779622, _1779624))], (27950 ^ _781215) ^ [_1290690, _1290692, _1290694] : [class_Rings_Odivision__ring(_1290690), -(_1290692 = c_Groups_Ozero__class_Ozero(_1290690)), 27957 ^ _781215 : [(27964 ^ _781215) ^ [] : [_1290694 = _1290692, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290690), _1290694), _1290692) = c_Groups_Oone__class_Oone(_1290690))], (27958 ^ _781215) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290690), _1290694), _1290692) = c_Groups_Oone__class_Oone(_1290690), -(_1290694 = _1290692)]]], (48193 ^ _781215) ^ [_1753152, _1753154, _1753156, _1753158] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1753152, tc_Nat_Onat), _1753154), _1753156) = hAPP(c_Nat_OSuc, _1753158), 48197 ^ _781215 : [(48200 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1753154, 48196 ^ [_1753152, _1753154, _1753156, _1753158]))))], (48198 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753152), 48196 ^ [_1753152, _1753154, _1753156, _1753158]), _1753156)))]]], (50964 ^ _781215) ^ [_1817323, _1817325, _1817327, _1817329] : [-(c_New__Random__Sequence_Oneg__map(_1817323, _1817325, _1817327, _1817329) = c_New__Random__Sequence_Oneg__bind(_1817323, _1817325, _1817329, hAPP(c_Fun_Ocomp(_1817325, 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(_1817325)))))), _1817323, c_New__Random__Sequence_Oneg__single(_1817325)), _1817327)))], (50362 ^ _781215) ^ [_1805209, _1805211, _1805213] : [-(c_Nitpick_Oplus__frac(_1805209, _1805211, _1805213) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1805209), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1805209), _1805211), hAPP(c_Nitpick_Odenom(_1805209), _1805213))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1805209), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1805209), tc_Int_Oint), c_Nitpick_Ofrac(_1805209)), 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(_1805209), _1805211))), 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(_1805209), _1805211))))), 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(_1805209), _1805213))), 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(_1805209), _1805213)))))), c_COMBI(tc_Int_Oint))))], (39669 ^ _781215) ^ [_1552130] : [-(hAPP(c_Option_Omap(_1552130, _1552130), c_COMBI(_1552130)) = c_Fun_Oid(tc_Option_Ooption(_1552130)))], (37846 ^ _781215) ^ [_1500628, _1500630, _1500632] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500628, tc_HOL_Obool)), _1500630), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1500628, tc_HOL_Obool), _1500632)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1500628, tc_HOL_Obool), tc_fun(_1500628, tc_HOL_Obool)), _1500632), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500628, tc_HOL_Obool)), _1500630)))], (15392 ^ _781215) ^ [_1051068, _1051070, _1051072] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1051068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1051070), _1051072)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1051068), _1051070)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1051068), _1051072)))], (43437 ^ _781215) ^ [_1648045, _1648047, _1648049, _1648051] : [class_Groups_Ocomm__monoid__add(_1648045), 43440 ^ _781215 : [(43447 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1648047), _1648049))), -(c_Nitpick_Osetsum_H(_1648047, _1648045, _1648051, _1648049) = c_Groups_Ozero__class_Ozero(_1648045))], (43441 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1648047), _1648049)), -(c_Nitpick_Osetsum_H(_1648047, _1648045, _1648051, _1648049) = hAPP(c_List_Omonoid__add__class_Olistsum(_1648045), hAPP(hAPP(c_List_Omap(_1648047, _1648045), _1648051), c_Hilbert__Choice_OEps(tc_List_Olist(_1648047), hAPP(hAPP(c_COMBS(tc_List_Olist(_1648047), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1648047)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1648047), tc_fun(_1648047, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1648047, tc_HOL_Obool), tc_fun(tc_fun(_1648047, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1648047)), c_fequal), c_List_Oset(_1648047))), _1648049))), c_List_Odistinct(_1648047))))))]]], (3242 ^ _781215) ^ [_830076, _830078, _830080, _830082] : [-(c_Finite__Set_Ofold1(_830082, _830078) = c_Finite__Set_Ofold1(_830080, _830076)), _830082 = _830080, _830078 = _830076], (37157 ^ _781215) ^ [_1484500, _1484502, _1484504, _1484506, _1484508] : [_1484500 = c_Orderings_Obot__class_Obot(tc_fun(_1484502, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484504, tc_HOL_Obool)), _1484506), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484502, tc_fun(_1484504, tc_HOL_Obool)), _1484500), _1484508)) = _1484506)], (25204 ^ _781215) ^ [] : [c_Int_OMin = c_Int_OPls], (7642 ^ _781215) ^ [_909619, _909621, _909623, _909625, _909627] : [hAPP(_909623, _909625) = _909627, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909619, _909621), _909623), _909625), _909627) = _909623)], (28346 ^ _781215) ^ [_1297429, _1297431, _1297433, _1297435] : [class_Fields_Olinordered__field__inverse__zero(_1297429), class_Int_Onumber(_1297429), 28353 ^ _781215 : [(28354 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297429), _1297431), _1297433)), hAPP(c_Int_Onumber__class_Onumber__of(_1297429), _1297435))), 28357 ^ _781215 : [(28364 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), c_Groups_Ozero__class_Ozero(_1297429)), _1297433))), 28367 ^ _781215 : [(28374 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), _1297433), c_Groups_Ozero__class_Ozero(_1297429)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), c_Groups_Ozero__class_Ozero(_1297429)), hAPP(c_Int_Onumber__class_Onumber__of(_1297429), _1297435))))], (28368 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), _1297433), c_Groups_Ozero__class_Ozero(_1297429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297429), hAPP(c_Int_Onumber__class_Onumber__of(_1297429), _1297435)), _1297433)), _1297431)))]]], (28358 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), c_Groups_Ozero__class_Ozero(_1297429)), _1297433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), _1297431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297429), hAPP(c_Int_Onumber__class_Onumber__of(_1297429), _1297435)), _1297433))))]]], (28380 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297429), _1297431), _1297433)), hAPP(c_Int_Onumber__class_Onumber__of(_1297429), _1297435)))), 28383 ^ _781215 : [(28386 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), _1297431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297429), hAPP(c_Int_Onumber__class_Onumber__of(_1297429), _1297435)), _1297433)))], (28384 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), c_Groups_Ozero__class_Ozero(_1297429)), _1297433)))]], 28387 ^ _781215 : [(28390 ^ _781215) ^ [] : [28391 ^ _781215 : [(28394 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297429), hAPP(c_Int_Onumber__class_Onumber__of(_1297429), _1297435)), _1297433)), _1297431))], (28392 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), _1297433), c_Groups_Ozero__class_Ozero(_1297429))))]], 28395 ^ _781215 : [(28398 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), c_Groups_Ozero__class_Ozero(_1297429)), hAPP(c_Int_Onumber__class_Onumber__of(_1297429), _1297435)))], (28396 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), _1297433), c_Groups_Ozero__class_Ozero(_1297429)))]]], (28388 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297429), c_Groups_Ozero__class_Ozero(_1297429)), _1297433))]]]]], (32551 ^ _781215) ^ [_1384027, _1384029, _1384031] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1384027, _1384027)), _1384029), c_Relation_OId__on(_1384027, _1384031))), 32555 ^ _781215 : [(32558 ^ _781215) ^ [] : [-(_1384029 = hAPP(hAPP(c_Product__Type_OPair(_1384027, _1384027), 32554 ^ [_1384027, _1384029, _1384031]), 32554 ^ [_1384027, _1384029, _1384031]))], (32556 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1384027), 32554 ^ [_1384027, _1384029, _1384031]), _1384031)))]]], (38668 ^ _781215) ^ [_1521113, _1521115, _1521117, _1521119] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521113), _1521115)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521113, _1521113), tc_HOL_Obool)), _1521117), hAPP(hAPP(c_Product__Type_OSigma(_1521113, _1521113), _1521115), hAPP(c_COMBK(tc_fun(_1521113, tc_HOL_Obool), _1521113), _1521115)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1521113, tc_HOL_Obool)), _1521119), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1521113), _1521115), _1521117))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521113), _1521119)))], (17711 ^ _781215) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (43211 ^ _781215) ^ [_1642123, _1642125, _1642127, _1642129, _1642131] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1642123, _1642123)), hAPP(hAPP(c_Product__Type_OPair(_1642123, _1642123), _1642125), _1642127)), _1642129)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642123), tc_List_Olist(_1642123))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642123), tc_List_Olist(_1642123)), hAPP(hAPP(c_List_Olist_OCons(_1642123), _1642125), _1642131)), hAPP(hAPP(c_List_Olist_OCons(_1642123), _1642127), _1642131))), c_List_Olistrel1(_1642123, _1642129))))], (10218 ^ _781215) ^ [_955298, _955300] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955298), _955300)), _955298 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _955300 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (49263 ^ _781215) ^ [_1776828, _1776830, _1776832, _1776834, _1776836] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776828, _1776828)), hAPP(hAPP(c_Product__Type_OPair(_1776828, _1776828), _1776830), _1776832)), _1776834)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1776828, _1776828)), hAPP(hAPP(c_Product__Type_OPair(_1776828, _1776828), _1776832), _1776836)), c_Transitive__Closure_Ortrancl(_1776828, _1776834))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776828, _1776828)), hAPP(hAPP(c_Product__Type_OPair(_1776828, _1776828), _1776830), _1776836)), c_Transitive__Closure_Otrancl(_1776828, _1776834))))], (20018 ^ _781215) ^ [_1140228, _1140230] : [class_Orderings_Olinorder(_1140228), hBOOL(hAPP(c_Finite__Set_Ofinite(_1140228), _1140230)), -(_1140230 = c_Orderings_Obot__class_Obot(tc_fun(_1140228, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1140228), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1140228), 20031 ^ [_1140228, _1140230]), 20032 ^ [_1140228, _1140230])), hAPP(hAPP(c_Set_Oinsert(_1140228), 20031 ^ [_1140228, _1140230]), hAPP(hAPP(c_Set_Oinsert(_1140228), 20032 ^ [_1140228, _1140230]), c_Orderings_Obot__class_Obot(tc_fun(_1140228, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1140228), c_Big__Operators_Olattice_OSup__fin(_1140228, c_Orderings_Oord__class_Omax(_1140228), _1140230)), _1140230)))], (46514 ^ _781215) ^ [_1716601, _1716603, _1716605] : [class_Orderings_Olinorder(_1716601), c_List_Olinorder__class_Osorted(_1716601, _1716603), -(c_List_Olinorder__class_Osorted(_1716601, c_List_OtakeWhile(_1716601, _1716605, _1716603)))], (51132 ^ _781215) ^ [_1820221, _1820223] : [class_Orderings_Obot(_1820221), -(class_Orderings_Obot(tc_fun(_1820223, _1820221)))], (51644 ^ _781215) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (24178 ^ _781215) ^ [_1217348, _1217350] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1217348, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1217350)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1217348, 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)))), _1217350)))], (48074 ^ _781215) ^ [_1750220, _1750222, _1750224, _1750226] : [hAPP(c_List_Oset(_1750220), hAPP(hAPP(c_List_Omap(tc_prod(_1750220, _1750222), _1750220), c_Product__Type_Ofst(_1750220, _1750222)), _1750224)) = hAPP(c_List_Oset(_1750220), hAPP(hAPP(c_List_Omap(tc_prod(_1750220, _1750222), _1750220), c_Product__Type_Ofst(_1750220, _1750222)), _1750226)), 48080 ^ _781215 : [(48083 ^ _781215) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1750220, _1750222), _1750224), 48079 ^ [_1750220, _1750222, _1750224, _1750226]) = hAPP(hAPP(c_Map_Omap__of(_1750220, _1750222), _1750226), 48079 ^ [_1750220, _1750222, _1750224, _1750226])], (48081 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750220), 48079 ^ [_1750220, _1750222, _1750224, _1750226]), hAPP(c_List_Oset(_1750220), hAPP(hAPP(c_List_Omap(tc_prod(_1750220, _1750222), _1750220), c_Product__Type_Ofst(_1750220, _1750222)), _1750224)))))]], -(hAPP(c_Map_Omap__of(_1750220, _1750222), _1750224) = hAPP(c_Map_Omap__of(_1750220, _1750222), _1750226))], (8946 ^ _781215) ^ [_932995, _932997, _932999] : [_932997 = _932999, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_932995, tc_HOL_Obool)), _932997) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_932995, tc_HOL_Obool)), _932999))], (13129 ^ _781215) ^ [_1009826] : [_1009826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009826), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (46994 ^ _781215) ^ [_1726544, _1726546] : [class_Orderings_Olinorder(_1726544), -(c_List_Olinorder__class_Osorted(_1726544, c_List_Olinorder__class_Osort__key(_1726544, _1726544, c_COMBI(_1726544), _1726546)))], (51752 ^ _781215) ^ [_1826722, _1826724] : [hBOOL(_1826722), -(hBOOL(hAPP(hAPP(c_fimplies, _1826724), _1826722)))], (50712 ^ _781215) ^ [_1812347, _1812349, _1812351] : [class_HOL_Oequal(_1812347), 50715 ^ _781215 : [(50722 ^ _781215) ^ [] : [_1812349 = _1812351, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1812347), _1812349), _1812351)))], (50716 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1812347), _1812349), _1812351)), -(_1812349 = _1812351)]]], (20786 ^ _781215) ^ [_1153988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153988)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1153988)) = _1153988)], (36534 ^ _781215) ^ [_1467842, _1467844, _1467846, _1467848] : [-(hBOOL(hAPP(hAPP(c_member(_1467842), hAPP(_1467844, _1467846)), hAPP(c_Set_Oimage(_1467848, _1467842, _1467844), c_Orderings_Otop__class_Otop(tc_fun(_1467848, tc_HOL_Obool))))))], (50986 ^ _781215) ^ [_1818005, _1818007, _1818009, _1818011] : [-(hAPP(c_New__DSequence_Opos__union(_1818005, _1818007, _1818009), _1818011) = c_Lazy__Sequence_Oappend(_1818005, hAPP(_1818007, _1818011), hAPP(_1818009, _1818011)))], (43848 ^ _781215) ^ [_1656630, _1656632] : [-(c_List_Osublist(_1656630, _1656632, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1656630))], (36231 ^ _781215) ^ [_1462275, _1462277] : [class_Rings_Olinordered__idom(_1462275), -(hAPP(c_Groups_Oabs__class_Oabs(_1462275), hAPP(hAPP(c_Power_Opower__class_Opower(_1462275), _1462277), 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(_1462275), _1462277), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (3352 ^ _781215) ^ [_831785, _831787, _831789, _831791, _831793, _831795] : [-(c_List_Osublist(_831795, _831791, _831787) = c_List_Osublist(_831793, _831789, _831785)), _831795 = _831793, _831791 = _831789, _831787 = _831785], (20653 ^ _781215) ^ [_1151862] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1151862))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1151862)))))], (27392 ^ _781215) ^ [_1279583, _1279585, _1279587, _1279589] : [-(hAPP(c_Product__Type_Osnd(_1279583, _1279585), hAPP(hAPP(c_Product__Type_OPair(_1279583, _1279585), _1279587), _1279589)) = _1279589)], (20673 ^ _781215) ^ [_1152123, _1152125] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1152123), _1152125) = 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)), _1152123)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1152125))))], (39895 ^ _781215) ^ [_1560166, _1560168, _1560170, _1560172, _1560174] : [hBOOL(hAPP(hAPP(_1560166, _1560168), _1560170)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1560172, _1560174, _1560166), _1560170)))], (19812 ^ _781215) ^ [_1136703, _1136705, _1136707] : [class_Orderings_Olinorder(_1136703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136703), _1136705)), -(c_Big__Operators_Olattice_OSup__fin(_1136703, c_Orderings_Oord__class_Omax(_1136703), hAPP(hAPP(c_Set_Oinsert(_1136703), _1136707), _1136705)) = hAPP(hAPP(c_Finite__Set_Ofold(_1136703, _1136703, c_Orderings_Oord__class_Omax(_1136703)), _1136707), _1136705))], (33392 ^ _781215) ^ [_1402701, _1402703, _1402705, _1402707] : [class_Orderings_Olinorder(_1402701), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402701, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1402701, _1402703, _1402705)), hAPP(c_SetInterval_Oord__class_OatMost(_1402701), _1402707)) = c_SetInterval_Oord__class_OatLeastAtMost(_1402701, _1402703, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1402701), _1402705), _1402707)))], (33300 ^ _781215) ^ [_1400613, _1400615, _1400617] : [class_Lattices_Olattice(_1400613), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400613), _1400615)), hBOOL(hAPP(hAPP(c_member(_1400613), _1400617), _1400615)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1400613), _1400617), c_Big__Operators_Olattice__class_OSup__fin(_1400613, _1400615)) = _1400617)], (22308 ^ _781215) ^ [_1183820, _1183822, _1183824, _1183826] : [class_Divides_Osemiring__div(_1183820), -(c_Divides_Odiv__class_Omod(_1183820, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183820), _1183822), _1183824), _1183826) = c_Divides_Odiv__class_Omod(_1183820, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183820), _1183822), c_Divides_Odiv__class_Omod(_1183820, _1183824, _1183826)), _1183826))], (40005 ^ _781215) ^ [_1562219] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1562219)))], (47499 ^ _781215) ^ [_1736973, _1736975] : [-(hBOOL(hAPP(c_List_Olistsp(_1736973, _1736975), c_List_Olist_ONil(_1736973))))], (42945 ^ _781215) ^ [_1635592, _1635594, _1635596, _1635598, _1635600] : [-(hAPP(hAPP(c_List_Olist__update(_1635592, hAPP(hAPP(c_List_Olist__update(_1635592, _1635594), _1635596), _1635598)), _1635596), _1635600) = hAPP(hAPP(c_List_Olist__update(_1635592, _1635594), _1635596), _1635600))], (11972 ^ _781215) ^ [_989177, _989179] : [11973 ^ _781215 : [(11976 ^ _781215) ^ [] : [_989179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11974 ^ _781215) ^ [] : [_989177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989177), _989179) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10326 ^ _781215) ^ [_957155, _957157, _957159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957155, tc_HOL_Obool)), _957157), _957159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957155, tc_HOL_Obool)), _957157), _957159)))], (28990 ^ _781215) ^ [_1309723, _1309725, _1309727, _1309729] : [class_Fields_Olinordered__field__inverse__zero(_1309723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309723), _1309725), _1309727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309723), _1309729), c_Groups_Ozero__class_Ozero(_1309723))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309723), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309723), _1309727), _1309729)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309723), _1309725), _1309729))))], (21726 ^ _781215) ^ [_1170951, _1170953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1170951)), c_Int_OBit0(_1170953))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170951), _1170953)))], (6515 ^ _781215) ^ [_887478, _887480, _887482, _887484] : [hBOOL(hAPP(hAPP(c_member(_887478), _887480), _887482)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887478, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_887478), _887480), _887484)), _887482) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887478, tc_HOL_Obool)), _887484), _887482))], (34271 ^ _781215) ^ [_1423241, _1423243, _1423245, _1423247, _1423249] : [class_Groups_Ocomm__monoid__add(_1423241), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423243), _1423245)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423243), _1423247)), 34285 ^ _781215 : [(34288 ^ _781215) ^ [] : [hAPP(_1423249, 34284 ^ [_1423241, _1423243, _1423245, _1423247, _1423249]) = c_Groups_Ozero__class_Ozero(_1423241)], (34286 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1423243), 34284 ^ [_1423241, _1423243, _1423245, _1423247, _1423249]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423243, tc_HOL_Obool)), _1423245), _1423247))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423243, _1423241), _1423249), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1423243, tc_HOL_Obool)), _1423245), _1423247)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1423241), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423243, _1423241), _1423249), _1423245)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423243, _1423241), _1423249), _1423247)))], (47934 ^ _781215) ^ [_1746432, _1746434, _1746436, _1746438] : [-(hAPP(c_List_OremoveAll(_1746432, _1746434), hAPP(hAPP(c_List_Oappend(_1746432), _1746436), _1746438)) = hAPP(hAPP(c_List_Oappend(_1746432), hAPP(c_List_OremoveAll(_1746432, _1746434), _1746436)), hAPP(c_List_OremoveAll(_1746432, _1746434), _1746438)))], (51556 ^ _781215) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (21322 ^ _781215) ^ [_1163480, _1163482, _1163484, _1163486, _1163488, _1163490, _1163492] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1163480, tc_fun(_1163482, tc_fun(_1163484, tc_HOL_Obool))), _1163486), _1163488), _1163490), _1163492)), 21326 ^ _781215 : [(21329 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1163488, 21325 ^ [_1163480, _1163482, _1163484, _1163486, _1163488, _1163490, _1163492]), _1163490), _1163492)))], (21327 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1163480), 21325 ^ [_1163480, _1163482, _1163484, _1163486, _1163488, _1163490, _1163492]), _1163486)))]]], (19482 ^ _781215) ^ [_1130593, _1130595, _1130597] : [class_Orderings_Olinorder(_1130593), hBOOL(hAPP(c_Finite__Set_Ofinite(_1130593), _1130595)), 19489 ^ _781215 : [(19496 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130593, tc_HOL_Obool)), _1130595), hAPP(hAPP(c_Set_Oinsert(_1130593), _1130597), c_Orderings_Obot__class_Obot(tc_fun(_1130593, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1130593, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1130593, hAPP(hAPP(c_Set_Oinsert(_1130593), _1130597), _1130595)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1130593), _1130597), c_Big__Operators_Olinorder__class_OMin(_1130593, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130593, tc_HOL_Obool)), _1130595), hAPP(hAPP(c_Set_Oinsert(_1130593), _1130597), c_Orderings_Obot__class_Obot(tc_fun(_1130593, tc_HOL_Obool)))))))], (19490 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130593, tc_HOL_Obool)), _1130595), hAPP(hAPP(c_Set_Oinsert(_1130593), _1130597), c_Orderings_Obot__class_Obot(tc_fun(_1130593, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1130593, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1130593, hAPP(hAPP(c_Set_Oinsert(_1130593), _1130597), _1130595)) = _1130597)]]], (22478 ^ _781215) ^ [_1187350, _1187352] : [class_Divides_Osemiring__div(_1187350), -(c_Divides_Odiv__class_Omod(_1187350, _1187352, c_Groups_Oone__class_Oone(_1187350)) = c_Groups_Ozero__class_Ozero(_1187350))], (31308 ^ _781215) ^ [_1354705] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1354705)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1354705), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1354705)))], (23991 ^ _781215) ^ [_1213767, _1213769, _1213771] : [hBOOL(hAPP(_1213767, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1213769, _1213771))), 23994 ^ _781215 : [(24001 ^ _781215) ^ [] : [-(_1213771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24004 ^ _781215 : [(24005 ^ _781215) ^ [_1214015, _1214017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1214015), _1213771)), _1213769 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1213771), _1214017)), _1214015), -(hBOOL(hAPP(_1213767, _1214015)))]]], (23995 ^ _781215) ^ [] : [_1213771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1213767, _1213769)))]]], (41006 ^ _781215) ^ [_1585590, _1585592] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1585590), hAPP(c_List_Oset(_1585590), _1585592))))], (11164 ^ _781215) ^ [_974742, _974744, _974746, _974748, _974750] : [class_Rings_Ocomm__semiring__1(_974742), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974742), _974744), _974746)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974742), _974748), _974750)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974742), _974744), _974748)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974742), _974746), _974750)))], (31984 ^ _781215) ^ [_1370808, _1370810, _1370812, _1370814, _1370816] : [class_Groups_Ocomm__monoid__add(_1370808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1370810), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1370812), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370808), _1370814), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1370810, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1370812), _1370816))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1370808), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370808), _1370814), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1370810, _1370812))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370808), _1370814), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1370812), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1370812), _1370816)))))], (27080 ^ _781215) ^ [_1273390, _1273392] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1273390, _1273392), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1273390), _1273392)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1273390, _1273392)))))], (42625 ^ _781215) ^ [_1627370, _1627372, _1627374, _1627376] : [-(c_List_Olist_Olist__size(_1627370, _1627372, hAPP(hAPP(c_List_Olist_OCons(_1627370), _1627374), _1627376)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1627372, _1627374)), c_List_Olist_Olist__size(_1627370, _1627372, _1627376))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37438 ^ _781215) ^ [] : [-(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))], (39112 ^ _781215) ^ [_1532231] : [-(c_Finite__Set_Ofun__left__comm__idem(_1532231, tc_fun(_1532231, tc_HOL_Obool), c_Set_Oinsert(_1532231)))], (13430 ^ _781215) ^ [_1014641, _1014643, _1014645, _1014647] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1014641), _1014643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1014645), hAPP(c_Set_Oimage(_1014641, _1014645, _1014647), _1014643))), hAPP(c_Finite__Set_Ocard(_1014641), _1014643))))], (51404 ^ _781215) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (33104 ^ _781215) ^ [_1395575, _1395577, _1395579, _1395581, _1395583, _1395585, _1395587] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395575, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395577, tc_fun(_1395575, tc_HOL_Obool)), _1395579), _1395581)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395583, tc_fun(_1395575, tc_HOL_Obool)), _1395585), _1395587)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395577, tc_fun(_1395575, tc_HOL_Obool)), _1395579), hAPP(hAPP(c_COMBB(tc_fun(_1395583, tc_fun(_1395575, tc_HOL_Obool)), tc_fun(_1395575, tc_HOL_Obool), _1395577), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395583, tc_fun(_1395575, tc_HOL_Obool)), _1395585)), hAPP(hAPP(c_COMBC(_1395577, tc_fun(_1395583, tc_fun(_1395575, tc_HOL_Obool)), tc_fun(_1395583, tc_fun(_1395575, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1395575, tc_HOL_Obool), tc_fun(_1395575, tc_HOL_Obool)), tc_fun(tc_fun(_1395583, tc_fun(_1395575, tc_HOL_Obool)), tc_fun(_1395583, tc_fun(_1395575, tc_HOL_Obool))), _1395577), c_COMBB(tc_fun(_1395575, tc_HOL_Obool), tc_fun(_1395575, tc_HOL_Obool), _1395583)), hAPP(hAPP(c_COMBB(tc_fun(_1395575, tc_HOL_Obool), tc_fun(tc_fun(_1395575, tc_HOL_Obool), tc_fun(_1395575, tc_HOL_Obool)), _1395577), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395575, tc_HOL_Obool))), _1395581))), _1395587))))], (17687 ^ _781215) ^ [_1097363] : [17688 ^ _781215 : [(17689 ^ _781215) ^ [_1097420] : [hBOOL(hAPP(_1097363, _1097420))]], 17691 ^ _781215 : [(17694 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1097363, hAPP(c_Int_Onat, 17690 ^ [_1097363]))))], (17692 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 17690 ^ [_1097363])))]]], (21914 ^ _781215) ^ [_1175288, _1175290] : [class_Int_Onumber__ring(_1175288), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175288), hAPP(c_Int_Onumber__class_Onumber__of(_1175288), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1175290) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1175288), _1175290), _1175290))], (10426 ^ _781215) ^ [_959036, _959038, _959040, _959042] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_959036, _959038)), c_Sum__Type_OPlus(_959036, _959038, _959040, _959042))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_959038), _959042)))], (7018 ^ _781215) ^ [_897755, _897757, _897759, _897761, _897763, _897765, _897767] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_897755, tc_Option_Ooption(_897757)), _897759), _897761), hAPP(c_Option_Ooption_OSome(_897757), _897763)), _897765) = hAPP(c_Option_Ooption_OSome(_897757), _897767)), 7019 ^ _781215 : [(7026 ^ _781215) ^ [] : [-(_897765 = _897761), hAPP(_897759, _897765) = hAPP(c_Option_Ooption_OSome(_897757), _897767)], (7020 ^ _781215) ^ [] : [_897765 = _897761, _897763 = _897767]]], (41140 ^ _781215) ^ [_1588762, _1588764, _1588766, _1588768] : [-(hBOOL(hAPP(c_List_Odistinct(_1588762), hAPP(hAPP(c_List_Omap(_1588764, _1588762), _1588766), _1588768)))), hBOOL(hAPP(c_List_Odistinct(_1588764), _1588768)), c_Fun_Oinj__on(_1588764, _1588762, _1588766, hAPP(c_List_Oset(_1588764), _1588768))], (22472 ^ _781215) ^ [_1187223, _1187225, _1187227, _1187229] : [class_Divides_Osemiring__div(_1187223), -(c_Divides_Odiv__class_Omod(_1187223, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187223), _1187225), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187223), _1187227), _1187229)), _1187229) = c_Divides_Odiv__class_Omod(_1187223, _1187225, _1187229))], (18908 ^ _781215) ^ [_1120185, _1120187, _1120189, _1120191, _1120193] : [class_Orderings_Olinorder(_1120185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120185), _1120187), _1120189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120185), _1120191), _1120193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120185), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1120185), _1120187), _1120191)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1120185), _1120189), _1120193))))], (20239 ^ _781215) ^ [_1144478, _1144480, _1144482, _1144484, _1144486, _1144488, _1144490, _1144492] : [hBOOL(hAPP(hAPP(c_member(_1144478), _1144480), _1144482)), hBOOL(hAPP(hAPP(hAPP(_1144484, _1144480), _1144486), _1144488)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1144478, tc_fun(_1144490, tc_fun(_1144492, tc_HOL_Obool))), _1144482), _1144484), _1144486), _1144488)))], (36863 ^ _781215) ^ [_1475890, _1475892, _1475894, _1475896, _1475898, _1475900] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1475890, tc_fun(_1475892, tc_HOL_Obool)), _1475894), _1475896), _1475898)), hBOOL(hAPP(hAPP(c_member(_1475890), _1475900), _1475894)), -(hBOOL(hAPP(hAPP(_1475896, _1475900), _1475898)))], (15494 ^ _781215) ^ [_1052976, _1052978, _1052980, _1052982, _1052984, _1052986] : [c_Com_Ocom_OLocal(_1052976, _1052978, _1052980) = c_Com_Ocom_OLocal(_1052982, _1052984, _1052986), 15497 ^ _781215 : [(15502 ^ _781215) ^ [] : [-(_1052980 = _1052986)], (15500 ^ _781215) ^ [] : [-(_1052978 = _1052984)], (15498 ^ _781215) ^ [] : [-(_1052976 = _1052982)]]], (7296 ^ _781215) ^ [_904431, _904433, _904435, _904437, _904439] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_904431, _904433, hAPP(hAPP(c_Set_Oinsert(_904431), _904435), _904437)), _904439))), 7297 ^ _781215 : [(7298 ^ _781215) ^ [_904535, _904537] : [hAPP(hAPP(c_Set_Oinsert(_904431), _904435), _904437) = hAPP(hAPP(c_Set_Oinsert(_904431), _904537), _904535), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_904431, _904431, _904433, _904537, _904535), _904439)), -(hBOOL(hAPP(hAPP(c_member(_904431), _904537), _904535)))]]], (2936 ^ _781215) ^ [_825161, _825163, _825165, _825167, _825169, _825171, _825173, _825175] : [-(c_Fun_Othe__inv__into(_825175, _825171, _825167, _825163) = c_Fun_Othe__inv__into(_825173, _825169, _825165, _825161)), _825175 = _825173, _825171 = _825169, _825167 = _825165, _825163 = _825161], (40807 ^ _781215) ^ [_1581027, _1581029] : [hBOOL(hAPP(c_Com_OWT, _1581029)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_1581027, _1581029))))], (14501 ^ _781215) ^ [_1034833, _1034835] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1034833), _1034835)), 14507 ^ _781215 : [(14510 ^ _781215) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14508 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1034833), 14506 ^ [_1034833, _1034835]), _1034835)))]], -(hAPP(c_Finite__Set_Ocard(_1034833), _1034835) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4660 ^ _781215) ^ [_851871, _851873, _851875, _851877] : [-(c_Nitpick_Ouminus__frac(_851877, _851873) = c_Nitpick_Ouminus__frac(_851875, _851871)), _851877 = _851875, _851873 = _851871], (2142 ^ _781215) ^ [_812594, _812596, _812598, _812600] : [-(c_SMT_Oz3mod(_812600, _812596) = c_SMT_Oz3mod(_812598, _812594)), _812600 = _812598, _812596 = _812594], (42455 ^ _781215) ^ [_1622134, _1622136, _1622138, _1622140, _1622142, _1622144] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622134, _1622134)), hAPP(hAPP(c_Product__Type_OPair(_1622134, _1622134), _1622136), _1622138)), _1622140)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622134), tc_List_Olist(_1622134))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622134), tc_List_Olist(_1622134)), _1622142), _1622144)), c_List_Olistrel(_1622134, _1622140))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622134), tc_List_Olist(_1622134))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622134), tc_List_Olist(_1622134)), hAPP(hAPP(c_List_Olist_OCons(_1622134), _1622136), _1622142)), hAPP(hAPP(c_List_Olist_OCons(_1622134), _1622138), _1622144))), c_List_Olistrel(_1622134, _1622140))))], (22922 ^ _781215) ^ [_1194596, _1194598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194596), _1194598)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1194596), _1194598) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22364 ^ _781215) ^ [_1185072, _1185074, _1185076, _1185078] : [class_Divides_Oring__div(_1185072), -(c_Divides_Odiv__class_Omod(_1185072, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185072), _1185074), _1185076), _1185078) = c_Divides_Odiv__class_Omod(_1185072, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185072), c_Divides_Odiv__class_Omod(_1185072, _1185074, _1185078)), _1185076), _1185078))], (22184 ^ _781215) ^ [_1181259, _1181261, _1181263] : [class_Divides_Osemiring__div(_1181259), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181259), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1181259), _1181261), _1181263)), _1181263)), c_Divides_Odiv__class_Omod(_1181259, _1181261, _1181263)) = _1181261)], (13830 ^ _781215) ^ [_1022156] : [class_Rings_Olinordered__semidom(_1022156), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022156), c_Groups_Ozero__class_Ozero(_1022156)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022156), c_Groups_Oone__class_Oone(_1022156)), c_Groups_Oone__class_Oone(_1022156)))))], (23624 ^ _781215) ^ [_1206941, _1206943] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206941), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1206943), _1206941)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206943), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1206943, _1206941)))], (49648 ^ _781215) ^ [_1786988, _1786990, _1786992] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1786988, _1786990)), hAPP(c_Relation_Oconverse(_1786990, _1786988), _1786992))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1786990, _1786988)), _1786992)))], (40313 ^ _781215) ^ [_1569393, _1569395] : [c_Wellfounded_Owf(_1569393, _1569395), -(c_Wellfounded_Owf(tc_List_Olist(_1569393), c_List_Olex(_1569393, _1569395)))], (39787 ^ _781215) ^ [_1555545, _1555547, _1555549] : [-(hAPP(c_Relation_ORange(_1555545, _1555547), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1555545, _1555547), tc_HOL_Obool), _1555549)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1555545, _1555547), tc_HOL_Obool), tc_fun(_1555547, tc_HOL_Obool)), _1555549), c_Relation_ORange(_1555545, _1555547)))], (15182 ^ _781215) ^ [_1047751] : [_1047751 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1047751) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47236 ^ _781215) ^ [_1731605, _1731607] : [class_Enum_Oenum(_1731605), 47239 ^ _781215 : [(47247 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1731605), _1731607)), 47250 ^ _781215 : [(47251 ^ _781215) ^ [_1731823] : [-(hBOOL(hAPP(_1731607, _1731823)))]]], (47240 ^ _781215) ^ [] : [hBOOL(hAPP(_1731607, 47241 ^ [_1731605, _1731607])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1731605), _1731607)))]]], (49948 ^ _781215) ^ [_1794042, _1794044, _1794046] : [c_Relation_Osingle__valued(_1794042, _1794042, _1794044), -(c_Relation_Osingle__valued(_1794042, _1794042, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794042, _1794042), tc_HOL_Obool), _1794046), _1794044)))], (46461 ^ _781215) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (11870 ^ _781215) ^ [_987814] : [hAPP(c_Nat_OSuc, _987814) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22208 ^ _781215) ^ [_1181839, _1181841, _1181843] : [-(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), _1181839), _1181841)), _1181841)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181839, _1181841))), _1181843) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181839), _1181843))], (21620 ^ _781215) ^ [_1169102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1169102)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1169102), c_Int_OPls)))], (14070 ^ _781215) ^ [_1026570, _1026572] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1026570), _1026572)))), -(_1026572 = c_Orderings_Obot__class_Obot(tc_fun(_1026570, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1026570), _1026572))], (19078 ^ _781215) ^ [_1123300, _1123302, _1123304, _1123306] : [class_Orderings_Olinorder(_1123300), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123300), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1123300), _1123302), _1123304)), _1123306) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1123300), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123300), _1123302), _1123306)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123300), _1123304), _1123306)))], (50890 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43381 ^ _781215) ^ [_1646754, _1646756, _1646758, _1646760] : [class_Groups_Oab__group__add(_1646754), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1646754), hAPP(c_List_Omonoid__add__class_Olistsum(_1646754), hAPP(hAPP(c_List_Omap(_1646756, _1646754), _1646758), _1646760))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1646754), hAPP(hAPP(c_List_Omap(_1646756, _1646754), hAPP(c_Fun_Ocomp(_1646754, _1646754, _1646756, c_Groups_Ouminus__class_Ouminus(_1646754)), _1646758)), _1646760)))], (10896 ^ _781215) ^ [_968532, _968534, _968536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968532), _968534)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968534), _968532))), _968536) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _968534)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _968532), _968536)))], (50760 ^ _781215) ^ [_1813050, _1813052, _1813054, _1813056, _1813058] : [_1813050 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1813052, _1813054, _1813056, _1813058), _1813050) = c_Lazy__Sequence_Oempty(_1813054))], (26366 ^ _781215) ^ [_1259681, _1259683] : [class_Rings_Olinordered__idom(_1259681), 26369 ^ _781215 : [(26376 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1259683), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259681), hAPP(c_Int_Oring__1__class_Oof__int(_1259681), _1259683)), c_Groups_Ozero__class_Ozero(_1259681))))], (26370 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259681), hAPP(c_Int_Oring__1__class_Oof__int(_1259681), _1259683)), c_Groups_Ozero__class_Ozero(_1259681))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1259683), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (10824 ^ _781215) ^ [_966757, _966759, _966761, _966763, _966765, _966767] : [-(hAPP(c_Map_Omap__add(_966757, _966759, _966761, _966763), _966765) = hAPP(c_Option_Ooption_OSome(_966759), _966767)), 10825 ^ _781215 : [(10828 ^ _781215) ^ [] : [hAPP(_966763, _966765) = c_Option_Ooption_ONone(_966759), hAPP(_966761, _966765) = hAPP(c_Option_Ooption_OSome(_966759), _966767)], (10826 ^ _781215) ^ [] : [hAPP(_966763, _966765) = hAPP(c_Option_Ooption_OSome(_966759), _966767)]]], (12170 ^ _781215) ^ [_992600, _992602, _992604] : [class_Rings_Oordered__cancel__semiring(_992600), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992600), _992602), _992604)), c_Groups_Ozero__class_Ozero(_992600)))), 12175 ^ _781215 : [(12182 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992600), _992602), c_Groups_Ozero__class_Ozero(_992600))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992600), c_Groups_Ozero__class_Ozero(_992600)), _992604))], (12176 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992600), c_Groups_Ozero__class_Ozero(_992600)), _992602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992600), _992604), c_Groups_Ozero__class_Ozero(_992600)))]]], (25857 ^ _781215) ^ [_1250134, _1250136, _1250138] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250134, tc_Nat_Onat), _1250136), _1250138) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250134, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1250134), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1250136)), _1250138)))], (11862 ^ _781215) ^ [_987674] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _987674)], (15699 ^ _781215) ^ [_1057375, _1057377, _1057379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057375)), _1057375 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1057377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1057375), _1057379)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1057379), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (46572 ^ _781215) ^ [_1717708, _1717710, _1717712, _1717714, _1717716] : [class_Orderings_Olinorder(_1717708), c_List_Olinorder__class_Osorted(_1717708, hAPP(c_List_Orev(_1717708), hAPP(hAPP(c_List_Omap(_1717710, _1717708), _1717712), _1717714))), -(hAPP(c_List_Ofilter(_1717710, hAPP(hAPP(c_COMBB(_1717708, tc_HOL_Obool, _1717710), hAPP(c_Orderings_Oord__class_Oless(_1717708), _1717716)), _1717712)), _1717714) = c_List_OtakeWhile(_1717710, hAPP(hAPP(c_COMBB(_1717708, tc_HOL_Obool, _1717710), hAPP(c_Orderings_Oord__class_Oless(_1717708), _1717716)), _1717712), _1717714))], (43734 ^ _781215) ^ [_1654624, _1654626] : [-(hAPP(hAPP(c_List_Otake(_1654624), _1654626), c_List_Olist_ONil(_1654624)) = c_List_Olist_ONil(_1654624))], (32371 ^ _781215) ^ [_1379919, _1379921, _1379923, _1379925, _1379927] : [c_Equiv__Relations_Oequiv(_1379919, _1379921, _1379923), hBOOL(hAPP(hAPP(c_member(tc_prod(_1379919, _1379919)), hAPP(hAPP(c_Product__Type_OPair(_1379919, _1379919), _1379925), _1379927)), _1379923)), -(hAPP(c_Relation_OImage(_1379919, _1379919, _1379923), hAPP(hAPP(c_Set_Oinsert(_1379919), _1379925), c_Orderings_Obot__class_Obot(tc_fun(_1379919, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1379919, _1379919, _1379923), hAPP(hAPP(c_Set_Oinsert(_1379919), _1379927), c_Orderings_Obot__class_Obot(tc_fun(_1379919, tc_HOL_Obool)))))], (1248 ^ _781215) ^ [_799785, _799787] : [-(class_Groups_Osgn__if(_799785)), _799787 = _799785, class_Groups_Osgn__if(_799787)], (45414 ^ _781215) ^ [_1692693, _1692695, _1692697, _1692699, _1692701] : [-(c_List_Omap__filter(_1692693, _1692695, _1692697, hAPP(hAPP(c_List_Olist_OCons(_1692693), _1692699), _1692701)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1692695), _1692695, c_List_Omap__filter(_1692693, _1692695, _1692697, _1692701), hAPP(hAPP(c_COMBC(_1692695, tc_List_Olist(_1692695), tc_List_Olist(_1692695)), c_List_Olist_OCons(_1692695)), c_List_Omap__filter(_1692693, _1692695, _1692697, _1692701))), hAPP(_1692697, _1692699)))], (36632 ^ _781215) ^ [_1469932, _1469934, _1469936] : [-(c_Map_Odom(_1469932, _1469934, hAPP(hAPP(c_COMBB(_1469934, tc_Option_Ooption(_1469934), _1469932), c_Option_Ooption_OSome(_1469934)), _1469936)) = c_Orderings_Otop__class_Otop(tc_fun(_1469932, tc_HOL_Obool)))], (3262 ^ _781215) ^ [_830374, _830376, _830378, _830380] : [-(c_Big__Operators_Olattice__class_OInf__fin(_830380, _830376) = c_Big__Operators_Olattice__class_OInf__fin(_830378, _830374)), _830380 = _830378, _830376 = _830374], (38432 ^ _781215) ^ [_1514711, _1514713, _1514715] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514711), _1514713)), 38438 ^ _781215 : [(38441 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1514715, 38437 ^ [_1514711, _1514713, _1514715])))], (38439 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514711), 38437 ^ [_1514711, _1514713, _1514715]), _1514713)))]], -(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(_1514711, tc_Nat_Onat), _1514715), _1514713))))], (39759 ^ _781215) ^ [_1554707, _1554709, _1554711, _1554713, _1554715, _1554717] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1554707, _1554709, _1554711), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554707, _1554709), tc_HOL_Obool)), _1554713), _1554715)), _1554717) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554707, _1554711), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1554707, _1554709, _1554711), _1554713), _1554717)), hAPP(hAPP(c_Relation_Orel__comp(_1554707, _1554709, _1554711), _1554715), _1554717)))], (9161 ^ _781215) ^ [_936645, _936647] : [_936647 = c_Orderings_Obot__class_Obot(tc_fun(_936645, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936645, tc_HOL_Obool)), _936647), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_936645, tc_HOL_Obool)), _936647))))], (46479 ^ _781215) ^ [_1715946, _1715948, _1715950] : [46481 ^ _781215 : [(46484 ^ _781215) ^ [] : [hBOOL(hAPP(_1715948, 46480 ^ [_1715946, _1715948, _1715950]))], (46482 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715946), 46480 ^ [_1715946, _1715948, _1715950]), hAPP(c_List_Oset(_1715946), _1715950))))]], -(c_List_OtakeWhile(_1715946, _1715948, _1715950) = _1715950)], (47012 ^ _781215) ^ [_1726839] : [class_Enum_Oenum(_1726839), -(c_Orderings_Otop__class_Otop(tc_fun(_1726839, tc_HOL_Obool)) = hAPP(c_List_Oset(_1726839), c_Enum_Oenum__class_Oenum(_1726839)))], (28042 ^ _781215) ^ [_1292218, _1292220, _1292222, _1292224] : [class_Fields_Ofield__inverse__zero(_1292218), class_Int_Onumber(_1292218), 28049 ^ _781215 : [(28050 ^ _781215) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292218), _1292220), hAPP(c_Int_Onumber__class_Onumber__of(_1292218), _1292222)) = _1292224, 28053 ^ _781215 : [(28060 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1292218), _1292222) = c_Groups_Ozero__class_Ozero(_1292218), -(_1292224 = c_Groups_Ozero__class_Ozero(_1292218))], (28054 ^ _781215) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1292218), _1292222) = c_Groups_Ozero__class_Ozero(_1292218)), -(_1292220 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292218), _1292224), hAPP(c_Int_Onumber__class_Onumber__of(_1292218), _1292222)))]]], (28066 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292218), _1292220), hAPP(c_Int_Onumber__class_Onumber__of(_1292218), _1292222)) = _1292224), 28069 ^ _781215 : [(28072 ^ _781215) ^ [] : [_1292220 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292218), _1292224), hAPP(c_Int_Onumber__class_Onumber__of(_1292218), _1292222))], (28070 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1292218), _1292222) = c_Groups_Ozero__class_Ozero(_1292218)]], 28073 ^ _781215 : [(28076 ^ _781215) ^ [] : [_1292224 = c_Groups_Ozero__class_Ozero(_1292218)], (28074 ^ _781215) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1292218), _1292222) = c_Groups_Ozero__class_Ozero(_1292218))]]]]], (8181 ^ _781215) ^ [_919181, _919183, _919185, _919187] : [class_Groups_Oordered__cancel__ab__semigroup__add(_919181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919181), _919183), _919185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919181), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919181), _919183), _919187)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919181), _919185), _919187))))], (43308 ^ _781215) ^ [_1644905] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1644905) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43311 ^ _781215 : [(43312 ^ _781215) ^ [_1644980] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1644980), hAPP(c_List_Oset(tc_Nat_Onat), _1644905))), -(_1644980 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7820 ^ _781215) ^ [_913178, _913180] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913178), _913180)), _913180) = _913178)], (39450 ^ _781215) ^ [_1543014] : [-(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)))), _1543014)) = 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), _1543014), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (29746 ^ _781215) ^ [_1323458, _1323460, _1323462, _1323464] : [class_Fields_Olinordered__field__inverse__zero(_1323458), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323458), _1323460), _1323462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323458), _1323464), c_Groups_Ozero__class_Ozero(_1323458))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323458), c_Groups_Ozero__class_Ozero(_1323458)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1323458), _1323460), _1323462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323458), _1323464), _1323460)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323458), _1323464), _1323462))))], (46750 ^ _781215) ^ [_1721154, _1721156, _1721158] : [c_List_OdropWhile(_1721154, _1721156, _1721158) = c_List_Olist_ONil(_1721154), 46753 ^ _781215 : [(46754 ^ _781215) ^ [_1721245] : [hBOOL(hAPP(hAPP(c_member(_1721154), _1721245), hAPP(c_List_Oset(_1721154), _1721158))), -(hBOOL(hAPP(_1721156, _1721245)))]]], (11124 ^ _781215) ^ [_973796, _973798, _973800] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973796), _973798)), _973800) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973798), _973800)))], (1548 ^ _781215) ^ [_803535, _803537] : [-(class_Rings_Oordered__cancel__semiring(_803535)), _803537 = _803535, class_Rings_Oordered__cancel__semiring(_803537)], (21806 ^ _781215) ^ [] : [-(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)))))], (21478 ^ _781215) ^ [_1166641, _1166643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1166641), _1166643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1166641)), c_Int_OBit0(_1166643))))], (44391 ^ _781215) ^ [_1669566, _1669568, _1669570, _1669572, _1669574] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1669566), tc_List_Olist(_1669566))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1669566), tc_List_Olist(_1669566)), _1669568), _1669570)), c_List_Olexord(_1669566, _1669572))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1669566), tc_List_Olist(_1669566))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1669566), tc_List_Olist(_1669566)), hAPP(hAPP(c_List_Oappend(_1669566), _1669574), _1669568)), hAPP(hAPP(c_List_Oappend(_1669566), _1669574), _1669570))), c_List_Olexord(_1669566, _1669572))))], (9155 ^ _781215) ^ [_936526, _936528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936526, tc_HOL_Obool)), _936528), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_936526, tc_HOL_Obool)), _936528))), -(_936528 = c_Orderings_Obot__class_Obot(tc_fun(_936526, tc_HOL_Obool)))], (37055 ^ _781215) ^ [_1481924, _1481926, _1481928, _1481930] : [-(hAPP(c_Set_OPow(_1481924), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481926, tc_fun(_1481924, tc_HOL_Obool)), _1481928), _1481930)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481926, tc_fun(tc_fun(_1481924, tc_HOL_Obool), tc_HOL_Obool)), _1481928), hAPP(hAPP(c_COMBB(tc_fun(_1481924, tc_HOL_Obool), tc_fun(tc_fun(_1481924, tc_HOL_Obool), tc_HOL_Obool), _1481926), c_Set_OPow(_1481924)), _1481930)))], (6140 ^ _781215) ^ [_879949] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _879949)], (45043 ^ _781215) ^ [_1684779, _1684781, _1684783] : [class_Orderings_Olinorder(_1684779), -(c_Big__Operators_Olinorder__class_OMin(_1684779, hAPP(c_List_Oset(_1684779), hAPP(hAPP(c_List_Olist_OCons(_1684779), _1684781), _1684783))) = hAPP(c_List_Ofoldl(_1684779, _1684779, c_Orderings_Oord__class_Omin(_1684779), _1684781), _1684783))], (13242 ^ _781215) ^ [_1011432, _1011434] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011432), _1011434) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1011432 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011434 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35945 ^ _781215) ^ [_1457021, _1457023, _1457025] : [class_Groups_Oordered__ab__group__add__abs(_1457021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457021), hAPP(c_Groups_Oabs__class_Oabs(_1457021), _1457023)), _1457025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457021), hAPP(c_Groups_Ouminus__class_Ouminus(_1457021), _1457023)), _1457025)))], (51150 ^ _781215) ^ [_1820458, _1820460] : [-(class_HOL_Oequal(tc_fun(_1820458, _1820460))), class_Enum_Oenum(_1820458), class_HOL_Oequal(_1820460)], (3008 ^ _781215) ^ [_826287, _826289, _826291, _826293, _826295, _826297] : [-(c_Hoare__Mirabelle_Opeek__and(_826297, _826293, _826289) = c_Hoare__Mirabelle_Opeek__and(_826295, _826291, _826287)), _826297 = _826295, _826293 = _826291, _826289 = _826287], (27364 ^ _781215) ^ [_1278902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1278902)), 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), _1278902)) = 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), _1278902))))))], (18055 ^ _781215) ^ [_1103788, _1103790] : [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(_1103788))), 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)), _1103790)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103788)), hAPP(c_Nat_OSuc, _1103790))))], (27642 ^ _781215) ^ [_1284364, _1284366] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284364), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 27645 ^ _781215 : [(27654 ^ _781215) ^ [] : [-(c_Nitpick_Onorm__frac(_1284366, _1284364) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1284366), _1284364)), 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), _1284366))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1284364)))), -(_1284366 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1284364 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27646 ^ _781215) ^ [] : [27647 ^ _781215 : [(27650 ^ _781215) ^ [] : [_1284364 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (27648 ^ _781215) ^ [] : [_1284366 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1284366, _1284364) = 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)))]]], (44970 ^ _781215) ^ [_1683347] : [class_Groups_Omonoid__add(_1683347), -(c_List_Omonoid__add__class_Olistsum(_1683347) = c_List_Ofoldl(_1683347, _1683347, c_Groups_Oplus__class_Oplus(_1683347), c_Groups_Ozero__class_Ozero(_1683347)))], (3728 ^ _781215) ^ [_837707, _837709, _837711, _837713] : [-(c_List_Olistsp(_837713, _837709) = c_List_Olistsp(_837711, _837707)), _837713 = _837711, _837709 = _837707], (49638 ^ _781215) ^ [_1786665, _1786667, _1786669, _1786671, _1786673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1786665, _1786667)), hAPP(hAPP(c_Product__Type_OPair(_1786665, _1786667), _1786669), _1786671)), hAPP(c_Relation_Oconverse(_1786667, _1786665), _1786673))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786667, _1786665)), hAPP(hAPP(c_Product__Type_OPair(_1786667, _1786665), _1786671), _1786669)), _1786673)))], (6926 ^ _781215) ^ [_895855, _895857, _895859, _895861] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _895855))), _895857), _895859), _895861)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _895855)), _895857), hAPP(c_Nat_OSuc, _895859)), _895861)))], (21972 ^ _781215) ^ [_1176430, _1176432, _1176434, _1176436, _1176438, _1176440] : [hBOOL(hAPP(hAPP(c_member(_1176430), _1176432), _1176434)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1176430, tc_fun(_1176436, tc_HOL_Obool)), _1176434), hAPP(hAPP(c_COMBB(tc_fun(_1176436, tc_HOL_Obool), tc_fun(_1176436, tc_HOL_Obool), _1176430), hAPP(c_Set_Oinsert(_1176436), _1176438)), _1176440)) = hAPP(hAPP(c_Set_Oinsert(_1176436), _1176438), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1176430, tc_fun(_1176436, tc_HOL_Obool)), _1176434), _1176440)))], (9195 ^ _781215) ^ [_937495, _937497, _937499, _937501, _937503, _937505] : [class_Rings_Oordered__ring(_937495), 9198 ^ _781215 : [(9205 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937495), _937501), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937495), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937495), _937503), _937497)), _937499)), _937505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937495), _937497), _937499)), _937501)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937495), _937503), _937499)), _937505))))], (9199 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937495), _937497), _937499)), _937501)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937495), _937503), _937499)), _937505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937495), _937501), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937495), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937495), _937503), _937497)), _937499)), _937505))))]]], (42935 ^ _781215) ^ [_1635379, _1635381, _1635383, _1635385, _1635387] : [-(hAPP(hAPP(c_List_Otake(_1635379), _1635381), hAPP(hAPP(c_List_Omap(_1635383, _1635379), _1635385), _1635387)) = hAPP(hAPP(c_List_Omap(_1635383, _1635379), _1635385), hAPP(hAPP(c_List_Otake(_1635383), _1635381), _1635387)))], (30507 ^ _781215) ^ [_1339252, _1339254] : [30515 ^ _781215 : [(30518 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1339254, 30514 ^ [_1339252, _1339254])))], (30516 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 30514 ^ [_1339252, _1339254]), _1339252)))]], 30508 ^ _781215 : [(30509 ^ _781215) ^ [_1339321] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1339321), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1339252))), hBOOL(hAPP(_1339254, _1339321))]]], (22264 ^ _781215) ^ [_1182854, _1182856, _1182858, _1182860] : [class_Divides_Osemiring__div(_1182854), -(c_Divides_Odiv__class_Omod(_1182854, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182854), _1182856), _1182858), _1182860) = c_Divides_Odiv__class_Omod(_1182854, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182854), _1182856), c_Divides_Odiv__class_Omod(_1182854, _1182858, _1182860)), _1182860))], (37207 ^ _781215) ^ [_1485835, _1485837, _1485839, _1485841, _1485843] : [_1485835 = c_Orderings_Obot__class_Obot(tc_fun(_1485837, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485839, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1485837, tc_fun(_1485839, tc_HOL_Obool)), _1485835), _1485841)), _1485843) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485839, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1485839, tc_HOL_Obool))), _1485843))], (36604 ^ _781215) ^ [_1469397, _1469399, _1469401, _1469403, _1469405] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1469397), hAPP(c_Set_Oimage(_1469399, _1469397, _1469401), c_Orderings_Otop__class_Otop(tc_fun(_1469399, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1469403), hAPP(c_Set_Oimage(_1469399, _1469403, hAPP(hAPP(c_COMBB(_1469397, _1469403, _1469399), _1469405), _1469401)), c_Orderings_Otop__class_Otop(tc_fun(_1469399, tc_HOL_Obool))))))], (4804 ^ _781215) ^ [_853963, _853965] : [_853965 = _853963, -(c_Int_Onumber__class_Onumber__of(_853965) = c_Int_Onumber__class_Onumber__of(_853963))], (49964 ^ _781215) ^ [_1794413, _1794415, _1794417, _1794419] : [-(hAPP(_1794413, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1794415, _1794415), _1794417), _1794413), _1794419)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1794415, _1794415), _1794417), _1794413), hAPP(_1794413, _1794419)))], (27776 ^ _781215) ^ [_1287254, _1287256, _1287258, _1287260, _1287262, _1287264, _1287266] : [hBOOL(hAPP(_1287254, _1287256)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1287258, _1287258)), hAPP(hAPP(c_Product__Type_OPair(_1287258, _1287258), _1287260), _1287262)), hAPP(_1287264, _1287256))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1287266, _1287258), tc_prod(_1287266, _1287258))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1287266, _1287258), tc_prod(_1287266, _1287258)), hAPP(hAPP(c_Product__Type_OPair(_1287266, _1287258), _1287256), _1287260)), hAPP(hAPP(c_Product__Type_OPair(_1287266, _1287258), _1287256), _1287262))), c_Recdef_Osame__fst(_1287266, _1287258, _1287254, _1287264))))], (27295 ^ _781215) ^ [_1277137, _1277139, _1277141, _1277143] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1277137, _1277139), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1277141), _1277143))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1277137), _1277139), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1277143), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1277141)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1277141)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1277143), 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), _1277139), _1277143))))))], (4400 ^ _781215) ^ [_847955, _847957] : [_847957 = _847955, -(c_Orderings_Otop__class_Otop(_847957) = c_Orderings_Otop__class_Otop(_847955))], (21331 ^ _781215) ^ [_1163698, _1163700, _1163702, _1163704, _1163706, _1163708, _1163710] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1163698, tc_fun(_1163700, tc_fun(_1163702, tc_HOL_Obool))), _1163704), _1163706), _1163708), _1163710))), 21332 ^ _781215 : [(21333 ^ _781215) ^ [_1163783] : [hBOOL(hAPP(hAPP(c_member(_1163698), _1163783), _1163704)), hBOOL(hAPP(hAPP(hAPP(_1163706, _1163783), _1163708), _1163710))]]], (9447 ^ _781215) ^ [_942104, _942106, _942108] : [class_Orderings_Olinorder(_942104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942104), _942106), _942108)), 9454 ^ _781215 : [(9461 ^ _781215) ^ [] : [_942106 = _942108, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942104), _942106), _942108))], (9455 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942104), _942106), _942108))), -(_942106 = _942108)]]], (20567 ^ _781215) ^ [_1150320, _1150322] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150320)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150322)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150320), _1150322)))], (32622 ^ _781215) ^ [_1385402, _1385404, _1385406] : [class_Lattices_Osemilattice__inf(_1385402), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385402), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1385402), _1385404), _1385406)), _1385406)))], (42595 ^ _781215) ^ [_1626451, _1626453, _1626455, _1626457] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1626451), tc_List_Olist(_1626451))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626451), tc_List_Olist(_1626451)), _1626453), _1626455)), c_List_Olex(_1626451, _1626457))), 42598 ^ _781215 : [(42601 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626451)), _1626453) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626451)), _1626455))], (42599 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1626451), tc_List_Olist(_1626451))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626451), tc_List_Olist(_1626451)), _1626453), _1626455)), c_List_Olexord(_1626451, _1626457))))]]], (50449 ^ _781215) ^ [_1807192, _1807194, _1807196] : [c_List_Olist__all(_1807192, _1807196, _1807194), 50452 ^ _781215 : [(50453 ^ _781215) ^ [_1807273] : [hBOOL(hAPP(hAPP(c_member(_1807192), _1807273), hAPP(c_List_Oset(_1807192), _1807194))), -(hBOOL(hAPP(_1807196, _1807273)))]]], (12914 ^ _781215) ^ [_1006216] : [class_Rings_Olinordered__semidom(_1006216), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006216), c_Groups_Ozero__class_Ozero(_1006216)), c_Groups_Oone__class_Oone(_1006216))))], (32926 ^ _781215) ^ [_1391809, _1391811, _1391813, _1391815, _1391817] : [-(c_Map_Orestrict__map(_1391809, _1391811, c_Map_Orestrict__map(_1391809, _1391811, _1391813, _1391815), _1391817) = c_Map_Orestrict__map(_1391809, _1391811, _1391813, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1391809, tc_HOL_Obool)), _1391815), _1391817)))], (23915 ^ _781215) ^ [_1212316, _1212318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212316)), 23918 ^ _781215 : [(23925 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1212318), _1212316))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1212318), _1212316) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212318), _1212316)), _1212316)))], (23919 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1212318), _1212316)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1212318), _1212316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20420 ^ _781215) ^ [_1147652] : [-(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), _1147652))))], (15588 ^ _781215) ^ [_1054966, _1054968, _1054970, _1054972, _1054974] : [hBOOL(hAPP(hAPP(c_member(_1054966), _1054968), _1054970)), -(hAPP(c_Map_Orestrict__map(_1054966, _1054972, _1054974, _1054970), _1054968) = hAPP(_1054974, _1054968))], (31425 ^ _781215) ^ [_1357169, _1357171, _1357173, _1357175, _1357177] : [hBOOL(hAPP(hAPP(c_member(_1357169), _1357171), hAPP(c_Relation_OImage(_1357173, _1357169, _1357175), hAPP(hAPP(c_Set_Oinsert(_1357173), _1357177), c_Orderings_Obot__class_Obot(tc_fun(_1357173, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1357173, _1357169)), hAPP(hAPP(c_Product__Type_OPair(_1357173, _1357169), _1357177), _1357171)), _1357175)))], (49698 ^ _781215) ^ [_1788081, _1788083, _1788085] : [c_Relation_Orefl__on(_1788081, _1788083, hAPP(c_Relation_Oconverse(_1788081, _1788081), _1788085)), -(c_Relation_Orefl__on(_1788081, _1788083, _1788085))], (14000 ^ _781215) ^ [_1025219, _1025221, _1025223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025219), _1025221)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025219), _1025223))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1025219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025221), _1025223)))], (16031 ^ _781215) ^ [_1064267, _1064269, _1064271, _1064273] : [class_Lattices_Osemilattice__sup(_1064267), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064267), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064267), _1064269), _1064271)), _1064273) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064267), _1064269), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064267), _1064271), _1064273)))], (21312 ^ _781215) ^ [_1163226, _1163228, _1163230, _1163232, _1163234] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1163226, tc_fun(_1163228, tc_HOL_Obool)), _1163230), _1163232), _1163234))), 21313 ^ _781215 : [(21314 ^ _781215) ^ [_1163298] : [hBOOL(hAPP(hAPP(c_member(_1163226), _1163298), _1163230)), hBOOL(hAPP(hAPP(_1163232, _1163298), _1163234))]]], (16768 ^ _781215) ^ [_1082290, _1082292, _1082294] : [hBOOL(hAPP(hAPP(c_member(_1082290), _1082292), hAPP(c_fequal, _1082294))), -(_1082292 = _1082294)], (38191 ^ _781215) ^ [_1508594, _1508596, _1508598] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508594, tc_HOL_Obool)), _1508596), hAPP(hAPP(c_Set_Oinsert(_1508594), _1508598), c_Orderings_Obot__class_Obot(tc_fun(_1508594, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1508594, _1508598, _1508596) = c_HOL_OThe(_1508594, hAPP(hAPP(c_COMBC(_1508594, tc_fun(_1508594, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508594)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1508594, tc_HOL_Obool)), _1508596), hAPP(hAPP(c_Set_Oinsert(_1508594), _1508598), c_Orderings_Obot__class_Obot(tc_fun(_1508594, tc_HOL_Obool)))))))], (51424 ^ _781215) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (23568 ^ _781215) ^ [_1205742, _1205744, _1205746] : [class_Int_Onumber__ring(_1205742), 23571 ^ _781215 : [(23578 ^ _781215) ^ [] : [-(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), _1205744)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1205742), hAPP(c_Int_Onumber__class_Onumber__of(_1205742), _1205746)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1205744))) = c_Groups_Oone__class_Oone(_1205742))], (23572 ^ _781215) ^ [] : [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), _1205744))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1205742), hAPP(c_Int_Onumber__class_Onumber__of(_1205742), _1205746)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1205744))) = hAPP(hAPP(c_HOL_OLet(_1205742, _1205742), hAPP(hAPP(c_Power_Opower__class_Opower(_1205742), hAPP(c_Int_Onumber__class_Onumber__of(_1205742), _1205746)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1205744))), hAPP(hAPP(c_COMBS(_1205742, _1205742, _1205742), hAPP(hAPP(c_COMBB(_1205742, tc_fun(_1205742, _1205742), _1205742), c_Groups_Otimes__class_Otimes(_1205742)), hAPP(c_Groups_Otimes__class_Otimes(_1205742), hAPP(c_Int_Onumber__class_Onumber__of(_1205742), _1205746)))), c_COMBI(_1205742))))]]], (46289 ^ _781215) ^ [_1710419, _1710421] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710419)), c_List_Oconcat(_1710419, _1710421)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1710419), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1710419))), _1710421)))], (38826 ^ _781215) ^ [_1525868, _1525870, _1525872, _1525874, _1525876, _1525878, _1525880, _1525882, _1525884, _1525886] : [hAPP(c_Set_Oimage(_1525868, _1525870, _1525872), _1525874) = _1525876, hAPP(c_Set_Oimage(_1525878, _1525880, _1525882), _1525884) = _1525886, -(hAPP(c_Set_Oimage(tc_prod(_1525868, _1525878), tc_prod(_1525870, _1525880), c_Product__Type_Omap__pair(_1525868, _1525870, _1525878, _1525880, _1525872, _1525882)), hAPP(hAPP(c_Product__Type_OSigma(_1525868, _1525878), _1525874), hAPP(c_COMBK(tc_fun(_1525878, tc_HOL_Obool), _1525868), _1525884))) = hAPP(hAPP(c_Product__Type_OSigma(_1525870, _1525880), _1525876), hAPP(c_COMBK(tc_fun(_1525880, tc_HOL_Obool), _1525870), _1525886)))], (11632 ^ _781215) ^ [_984270, _984272] : [class_Rings_Ocomm__semiring__1(_984270), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984270), c_Groups_Ozero__class_Ozero(_984270)), _984272) = _984272)], (18207 ^ _781215) ^ [_1107187, _1107189, _1107191, _1107193] : [class_Orderings_Olinorder(_1107187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107187), _1107189), _1107191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107187), _1107189), _1107193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107187), _1107189), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1107187), _1107191), _1107193))))], (43758 ^ _781215) ^ [_1655098, _1655100, _1655102, _1655104] : [_1655104 = c_List_Olist_ONil(_1655100), -(c_List_Olist_ONil(_1655098) = hAPP(hAPP(c_List_Omap(_1655100, _1655098), _1655102), _1655104))], (9349 ^ _781215) ^ [_940652, _940654, _940656, _940658] : [class_Orderings_Oorder(_940652), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940652), _940654), _940656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940652), _940658), _940654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940652), _940658), _940656)))], (8514 ^ _781215) ^ [_925691, _925693, _925695, _925697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925691, tc_HOL_Obool)), _925693), _925695)), hBOOL(hAPP(hAPP(c_member(_925691), _925697), _925693)), -(hBOOL(hAPP(hAPP(c_member(_925691), _925697), _925695)))], (25827 ^ _781215) ^ [_1248009, _1248011, _1248013, _1248015] : [_1248013 = _1248015, -(hAPP(hAPP(c_COMBC(_1248009, tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_fun(_1248011, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1248011, tc_fun(tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_fun(_1248011, tc_HOL_Obool)), _1248009), c_COMBC(_1248011, tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1248011, tc_prod(_1248009, _1248011)), tc_fun(_1248011, tc_fun(tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_HOL_Obool)), _1248009), hAPP(c_COMBB(tc_prod(_1248009, _1248011), tc_fun(tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_HOL_Obool), _1248011), c_member(tc_prod(_1248009, _1248011)))), c_Product__Type_OPair(_1248009, _1248011)))), _1248013) = hAPP(hAPP(c_COMBC(_1248009, tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_fun(_1248011, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1248011, tc_fun(tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_fun(_1248011, tc_HOL_Obool)), _1248009), c_COMBC(_1248011, tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1248011, tc_prod(_1248009, _1248011)), tc_fun(_1248011, tc_fun(tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_HOL_Obool)), _1248009), hAPP(c_COMBB(tc_prod(_1248009, _1248011), tc_fun(tc_fun(tc_prod(_1248009, _1248011), tc_HOL_Obool), tc_HOL_Obool), _1248011), c_member(tc_prod(_1248009, _1248011)))), c_Product__Type_OPair(_1248009, _1248011)))), _1248015))], (18740 ^ _781215) ^ [_1117139, _1117141, _1117143] : [class_Orderings_Olinorder(_1117139), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117139), _1117141), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117139), _1117141), _1117143)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117139), _1117141), _1117143))], (51640 ^ _781215) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (13540 ^ _781215) ^ [_1016653, _1016655, _1016657, _1016659] : [class_Rings_Olinordered__semiring__strict(_1016653), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016653), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016653), _1016655), _1016657)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016653), _1016659), _1016657))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016653), c_Groups_Ozero__class_Ozero(_1016653)), _1016657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016653), _1016655), _1016659)))], (45895 ^ _781215) ^ [_1701575] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1701575) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1701575)))], (27048 ^ _781215) ^ [_1272836, _1272838, _1272840, _1272842] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1272836, _1272838), _1272840)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1272836, _1272838), _1272842)), -(_1272840 = _1272842)], (12510 ^ _781215) ^ [_998870, _998872] : [class_Groups_Olinordered__ab__group__add(_998870), 12513 ^ _781215 : [(12520 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998870), _998872), c_Groups_Ozero__class_Ozero(_998870))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998870), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998870), _998872), _998872)), c_Groups_Ozero__class_Ozero(_998870))))], (12514 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998870), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998870), _998872), _998872)), c_Groups_Ozero__class_Ozero(_998870))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998870), _998872), c_Groups_Ozero__class_Ozero(_998870))))]]], (7828 ^ _781215) ^ [_913354, _913356, _913358] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913354), _913356)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913358), _913356)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _913354), _913358))], (9835 ^ _781215) ^ [_948357, _948359] : [_948359 = c_Orderings_Obot__class_Obot(tc_fun(_948357, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_948357, tc_HOL_Obool)), _948359), c_Orderings_Obot__class_Obot(tc_fun(_948357, tc_HOL_Obool)))))], (20430 ^ _781215) ^ [_1147840, _1147842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147840), _1147842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147840)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147842))))], (51342 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (12526 ^ _781215) ^ [_999153, _999155] : [class_Groups_Olinordered__ab__group__add(_999153), 12529 ^ _781215 : [(12536 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999153), c_Groups_Ozero__class_Ozero(_999153)), _999155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999153), c_Groups_Ozero__class_Ozero(_999153)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999153), _999155), _999155))))], (12530 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999153), c_Groups_Ozero__class_Ozero(_999153)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999153), _999155), _999155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999153), c_Groups_Ozero__class_Ozero(_999153)), _999155)))]]], (16531 ^ _781215) ^ [_1075983, _1075985, _1075987, _1075989] : [-(c_Map_Odom(_1075983, _1075985, c_Map_Omap__add(_1075983, _1075985, _1075987, _1075989)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1075983, tc_HOL_Obool)), c_Map_Odom(_1075983, _1075985, _1075989)), c_Map_Odom(_1075983, _1075985, _1075987)))], (15292 ^ _781215) ^ [_1049431, _1049433, _1049435, _1049437, _1049439, _1049441] : [-(hAPP(c_Set_Oimage(_1049431, _1049433, _1049435), hAPP(c_Set_Oimage(_1049437, _1049431, _1049439), _1049441)) = hAPP(c_Set_Oimage(_1049437, _1049433, hAPP(hAPP(c_COMBB(_1049431, _1049433, _1049437), _1049435), _1049439)), _1049441))], (18437 ^ _781215) ^ [_1111346, _1111348, _1111350] : [-(c_Nat_Onat_Onat__case(_1111346, _1111348, _1111350, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1111348)], (30980 ^ _781215) ^ [_1348334] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348334), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (35991 ^ _781215) ^ [_1457963, _1457965, _1457967] : [class_Fields_Olinordered__field(_1457963), -(_1457965 = c_Groups_Ozero__class_Ozero(_1457963)), -(hAPP(c_Groups_Oabs__class_Oabs(_1457963), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1457963), _1457967), _1457965)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1457963), hAPP(c_Groups_Oabs__class_Oabs(_1457963), _1457967)), hAPP(c_Groups_Oabs__class_Oabs(_1457963), _1457965)))], (51554 ^ _781215) ^ [_1824520, _1824522] : [-(class_Nat_Osize(tc_prod(_1824520, _1824522)))], (49415 ^ _781215) ^ [_1780522, _1780524, _1780526] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780522, _1780522)), hAPP(hAPP(c_Product__Type_OPair(_1780522, _1780522), _1780524), _1780526)), c_Relation_OId(_1780522))), -(_1780524 = _1780526)], (38270 ^ _781215) ^ [_1510433, _1510435, _1510437, _1510439, _1510441] : [hBOOL(hAPP(_1510439, hAPP(_1510437, _1510441))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1510433, _1510435, _1510437), _1510439), _1510441)))], (49297 ^ _781215) ^ [_1777640, _1777642, _1777644, _1777646, _1777648] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1777640, _1777640)), hAPP(hAPP(c_Product__Type_OPair(_1777640, _1777640), _1777642), _1777644)), _1777646)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1777640, _1777640)), hAPP(hAPP(c_Product__Type_OPair(_1777640, _1777640), _1777644), _1777648)), c_Transitive__Closure_Ortrancl(_1777640, _1777646))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777640, _1777640)), hAPP(hAPP(c_Product__Type_OPair(_1777640, _1777640), _1777642), _1777648)), c_Transitive__Closure_Ortrancl(_1777640, _1777646))))], (33072 ^ _781215) ^ [_1394794, _1394796, _1394798, _1394800] : [class_Lattices_Osemilattice__inf(_1394794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394794), _1394796), _1394798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394794), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1394794), _1394800), _1394796)), _1394798)))], (2370 ^ _781215) ^ [_816244, _816246, _816248, _816250] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_816250, _816246) = c_Code__Numeral_Odiv__mod__code__numeral(_816248, _816244)), _816250 = _816248, _816246 = _816244], (12740 ^ _781215) ^ [_1003050, _1003052, _1003054] : [class_Rings_Olinordered__ring__strict(_1003050), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003050), _1003052), c_Groups_Ozero__class_Ozero(_1003050))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003050), _1003054), c_Groups_Ozero__class_Ozero(_1003050))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003050), c_Groups_Ozero__class_Ozero(_1003050)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003050), _1003052), _1003054))))], (41763 ^ _781215) ^ [_1603686, _1603688, _1603690, _1603692, _1603694, _1603696, _1603698] : [c_Finite__Set_Ofolding__idem(_1603686, _1603688, _1603690, _1603692), -(hAPP(c_Fun_Ocomp(_1603688, _1603688, _1603694, hAPP(_1603690, _1603696)), hAPP(c_Fun_Ocomp(_1603688, _1603688, _1603694, hAPP(_1603690, _1603696)), _1603698)) = hAPP(c_Fun_Ocomp(_1603688, _1603688, _1603694, hAPP(_1603690, _1603696)), _1603698))], (11784 ^ _781215) ^ [_986541] : [class_Rings_Ozero__neq__one(_986541), c_Groups_Ozero__class_Ozero(_986541) = c_Groups_Oone__class_Oone(_986541)], (49273 ^ _781215) ^ [_1777116, _1777118, _1777120, _1777122] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1777116, _1777116)), hAPP(hAPP(c_Product__Type_OPair(_1777116, _1777116), _1777118), _1777120)), c_Transitive__Closure_Ortrancl(_1777116, _1777122))), -(_1777118 = _1777120), 49280 ^ _781215 : [(49283 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777116, _1777116)), hAPP(hAPP(c_Product__Type_OPair(_1777116, _1777116), _1777118), _1777120)), c_Transitive__Closure_Otrancl(_1777116, _1777122))))], (49281 ^ _781215) ^ [] : [_1777118 = _1777120]]], (51452 ^ _781215) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (51312 ^ _781215) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (34157 ^ _781215) ^ [_1420618, _1420620, _1420622, _1420624, _1420626] : [class_Fields_Ofield(_1420618), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420620), _1420622)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420620), _1420624)), 34171 ^ _781215 : [(34174 ^ _781215) ^ [] : [-(hAPP(_1420626, 34170 ^ [_1420618, _1420620, _1420622, _1420624, _1420626]) = c_Groups_Ozero__class_Ozero(_1420618))], (34172 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1420620), 34170 ^ [_1420618, _1420620, _1420622, _1420624, _1420626]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420620, tc_HOL_Obool)), _1420622), _1420624))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1420620, _1420618), _1420626), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420620, tc_HOL_Obool)), _1420622), _1420624)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420618), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1420620, _1420618), _1420626), _1420622)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1420620, _1420618), _1420626), _1420624))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1420620, _1420618), _1420626), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420620, tc_HOL_Obool)), _1420622), _1420624))))], (15640 ^ _781215) ^ [_1056111, _1056113, _1056115] : [c_Com_Ocom_OLocal(_1056111, _1056113, _1056115) = c_Com_Ocom_OSKIP], (46467 ^ _781215) ^ [_1715658, _1715660, _1715662, _1715664, _1715666] : [-(hAPP(hAPP(c_List_Ozip(_1715658, _1715660), c_List_OtakeWhile(_1715658, _1715662, _1715664)), _1715666) = c_List_OtakeWhile(tc_prod(_1715658, _1715660), hAPP(c_Fun_Ocomp(_1715658, tc_HOL_Obool, tc_prod(_1715658, _1715660), _1715662), c_Product__Type_Ofst(_1715658, _1715660)), hAPP(hAPP(c_List_Ozip(_1715658, _1715660), _1715664), _1715666)))], (27568 ^ _781215) ^ [_1283051, _1283053] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1283051, _1283053) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1283051, _1283053)))], (908 ^ _781215) ^ [_795201, _795203, _795205, _795207, _795209, _795211] : [-(c_Relation_Osingle__valued(_795209, _795205, _795201)), c_Relation_Osingle__valued(_795211, _795207, _795203), _795211 = _795209, _795207 = _795205, _795203 = _795201], (23769 ^ _781215) ^ [_1209746, _1209748] : [23770 ^ _781215 : [(23771 ^ _781215) ^ [_1209795] : [_1209746 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1209748), _1209795)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1209746, _1209748) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30401 ^ _781215) ^ [_1337236, _1337238] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1337236, _1337238)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1337238), _1337236)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35411 ^ _781215) ^ [_1446572, _1446574] : [class_Orderings_Olinorder(_1446572), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1446572, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1446572), _1446574)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1446572), _1446574))], (50744 ^ _781215) ^ [_1812795, _1812797] : [-(c_FunDef_Ois__measure(_1812795, _1812797))], (4772 ^ _781215) ^ [_853495, _853497, _853499, _853501] : [-(c_Product__Type_Osnd(_853501, _853497) = c_Product__Type_Osnd(_853499, _853495)), _853501 = _853499, _853497 = _853495], (50804 ^ _781215) ^ [_1813754] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1813754)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1813754), c_Int_OPls)))], (50378 ^ _781215) ^ [_1805650, _1805652] : [-(c_Nitpick_Ouminus__frac(_1805650, _1805652) = c_Nitpick_OAbs__Frac(_1805650, 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(_1805650), _1805652))), hAPP(c_Nitpick_Odenom(_1805650), _1805652))))], (45019 ^ _781215) ^ [_1684291, _1684293] : [class_Complete__Lattice_Ocomplete__lattice(_1684291), -(c_Complete__Lattice_OSup__class_OSup(_1684291, hAPP(c_List_Oset(_1684291), _1684293)) = hAPP(c_List_Ofoldl(_1684291, _1684291, c_Lattices_Osemilattice__sup__class_Osup(_1684291), c_Orderings_Obot__class_Obot(_1684291)), _1684293))], (30101 ^ _781215) ^ [_1331644, _1331646] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1331644, _1331646))))], (45379 ^ _781215) ^ [_1691878, _1691880, _1691882] : [-(c_List_Omap__filter(_1691878, _1691880, _1691882, c_List_Olist_ONil(_1691878)) = c_List_Olist_ONil(_1691880))], (24234 ^ _781215) ^ [_1218327, _1218329] : [class_Rings_Olinordered__idom(_1218327), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218327), c_Groups_Ozero__class_Ozero(_1218327)), hAPP(hAPP(c_Power_Opower__class_Opower(_1218327), _1218329), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (51378 ^ _781215) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (39448 ^ _781215) ^ [_1542773, _1542775, _1542777, _1542779] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1542773, _1542775), _1542777), _1542779) = hAPP(c_Set_OCollect(tc_prod(_1542775, _1542775)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542775, _1542775, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1542775, tc_fun(tc_prod(_1542773, _1542773), tc_HOL_Obool), tc_fun(_1542775, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542775, tc_fun(tc_fun(tc_prod(_1542773, _1542773), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1542773, _1542773), tc_HOL_Obool), tc_fun(_1542775, tc_HOL_Obool)), _1542775), c_COMBC(_1542775, tc_fun(tc_prod(_1542773, _1542773), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542775, tc_prod(_1542773, _1542773)), tc_fun(_1542775, tc_fun(tc_fun(tc_prod(_1542773, _1542773), tc_HOL_Obool), tc_HOL_Obool)), _1542775), hAPP(c_COMBB(tc_prod(_1542773, _1542773), tc_fun(tc_fun(tc_prod(_1542773, _1542773), tc_HOL_Obool), tc_HOL_Obool), _1542775), c_member(tc_prod(_1542773, _1542773)))), hAPP(hAPP(c_COMBC(_1542775, tc_fun(_1542775, _1542773), tc_fun(_1542775, tc_prod(_1542773, _1542773))), hAPP(hAPP(c_COMBB(tc_fun(_1542773, tc_prod(_1542773, _1542773)), tc_fun(tc_fun(_1542775, _1542773), tc_fun(_1542775, tc_prod(_1542773, _1542773))), _1542775), c_COMBB(_1542773, tc_prod(_1542773, _1542773), _1542775)), hAPP(hAPP(c_COMBB(_1542773, tc_fun(_1542773, tc_prod(_1542773, _1542773)), _1542775), c_Product__Type_OPair(_1542773, _1542773)), _1542779))), _1542779)))), _1542777))))], (15576 ^ _781215) ^ [_1054716, _1054718, _1054720] : [c_Map_Odom(_1054716, _1054718, _1054720) = c_Orderings_Obot__class_Obot(tc_fun(_1054716, tc_HOL_Obool)), -(_1054720 = hAPP(c_COMBK(tc_Option_Ooption(_1054718), _1054716), c_Option_Ooption_ONone(_1054718)))], (43351 ^ _781215) ^ [_1645835, _1645837, _1645839, _1645841, _1645843] : [class_Rings_Osemiring__0(_1645835), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1645835), hAPP(hAPP(c_List_Omap(_1645837, _1645835), hAPP(hAPP(c_COMBC(_1645837, _1645835, _1645835), hAPP(hAPP(c_COMBB(_1645835, tc_fun(_1645835, _1645835), _1645837), c_Groups_Otimes__class_Otimes(_1645835)), _1645839)), _1645841)), _1645843)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1645835), hAPP(c_List_Omonoid__add__class_Olistsum(_1645835), hAPP(hAPP(c_List_Omap(_1645837, _1645835), _1645839), _1645843))), _1645841))], (38260 ^ _781215) ^ [_1510224, _1510226, _1510228] : [-(hAPP(c_Set_Ovimage(_1510224, _1510226, _1510228), c_Orderings_Obot__class_Obot(tc_fun(_1510226, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1510224, tc_HOL_Obool)))], (4246 ^ _781215) ^ [_845670, _845672, _845674, _845676] : [-(c_Code__Numeral_Onat__of__aux(_845676, _845672) = c_Code__Numeral_Onat__of__aux(_845674, _845670)), _845676 = _845674, _845672 = _845670], (5242 ^ _781215) ^ [_861208, _861210] : [_861210 = _861208, -(c_List_Olist_OCons(_861210) = c_List_Olist_OCons(_861208))], (48884 ^ _781215) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (34 ^ _781215) ^ [_781668, _781670, _781672, _781674, _781676, _781678, _781680, _781682, _781684, _781686, _781688, _781690] : [-(c_Nitpick_Ofold__graph_H(_781688, _781684, _781680, _781676, _781672, _781668)), c_Nitpick_Ofold__graph_H(_781690, _781686, _781682, _781678, _781674, _781670), _781690 = _781688, _781686 = _781684, _781682 = _781680, _781678 = _781676, _781674 = _781672, _781670 = _781668], (38800 ^ _781215) ^ [_1525067, _1525069, _1525071, _1525073, _1525075, _1525077, _1525079, _1525081] : [c_Fun_Oinj__on(_1525067, _1525069, _1525071, _1525073), c_Fun_Oinj__on(_1525075, _1525077, _1525079, _1525081), -(c_Fun_Oinj__on(tc_prod(_1525067, _1525075), tc_prod(_1525069, _1525077), c_Product__Type_Omap__pair(_1525067, _1525069, _1525075, _1525077, _1525071, _1525079), hAPP(hAPP(c_Product__Type_OSigma(_1525067, _1525075), _1525073), hAPP(c_COMBK(tc_fun(_1525075, tc_HOL_Obool), _1525067), _1525081))))], (46107 ^ _781215) ^ [_1706482, _1706484] : [-(c_List_Oconcat(_1706482, _1706484) = hAPP(c_List_Ofoldl(tc_List_Olist(_1706482), tc_List_Olist(_1706482), c_List_Oappend(_1706482), c_List_Olist_ONil(_1706482)), _1706484))], (12548 ^ _781215) ^ [_999546, _999548, _999550, _999552] : [class_Rings_Olinordered__ring__strict(_999546), 12551 ^ _781215 : [(12566 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999546), _999548), _999550)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999546), _999552), _999550)))), 12567 ^ _781215 : [(12574 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999546), _999550), c_Groups_Ozero__class_Ozero(_999546))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999546), _999552), _999548))], (12568 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999546), c_Groups_Ozero__class_Ozero(_999546)), _999550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999546), _999548), _999552))]]], (12552 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999546), _999548), _999550)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999546), _999552), _999550))), 12557 ^ _781215 : [(12560 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999546), _999548), _999552)))], (12558 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999546), c_Groups_Ozero__class_Ozero(_999546)), _999550)))]], 12561 ^ _781215 : [(12564 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999546), _999552), _999548)))], (12562 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999546), _999550), c_Groups_Ozero__class_Ozero(_999546))))]]]]], (40405 ^ _781215) ^ [_1571466, _1571468] : [c_Wellfounded_Owf(_1571466, _1571468), -(c_Wellfounded_OwfP(_1571466, c_FunDef_Oin__rel(_1571466, _1571466, _1571468)))], (10210 ^ _781215) ^ [_955187, _955189] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955187), _955189), 10213 ^ _781215 : [(10216 ^ _781215) ^ [] : [-(_955189 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10214 ^ _781215) ^ [] : [-(_955187 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (45123 ^ _781215) ^ [_1686846, _1686848, _1686850] : [-(_1686846 = c_List_Olist_ONil(_1686848)), -(c_List_Olast(_1686848, hAPP(hAPP(c_List_Oappend(_1686848), _1686850), _1686846)) = c_List_Olast(_1686848, _1686846))], (11388 ^ _781215) ^ [_979582, _979584, _979586, _979588, _979590, _979592] : [class_Rings_Olinordered__semiring__1__strict(_979582), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979582), _979584), _979586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979582), _979588), _979586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979582), c_Groups_Ozero__class_Ozero(_979582)), _979590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979582), c_Groups_Ozero__class_Ozero(_979582)), _979592)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979582), _979590), _979592) = c_Groups_Oone__class_Oone(_979582), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979582), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979582), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979582), _979590), _979584)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979582), _979592), _979588))), _979586)))], (41897 ^ _781215) ^ [_1606747, _1606749, _1606751, _1606753, _1606755, _1606757] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606747, _1606749)), hAPP(hAPP(c_Product__Type_OPair(_1606747, _1606749), _1606751), _1606753)), hAPP(c_List_Oset(tc_prod(_1606747, _1606749)), hAPP(hAPP(c_List_Ozip(_1606747, _1606749), _1606755), _1606757)))), -(hBOOL(hAPP(hAPP(c_member(_1606749), _1606753), hAPP(c_List_Oset(_1606749), _1606757))))], (15296 ^ _781215) ^ [_1049522] : [-(c_Int_Opred(_1049522) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1049522), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9115 ^ _781215) ^ [_935871, _935873, _935875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935871), _935873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935873), _935875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935871), _935875)))], (46243 ^ _781215) ^ [_1709310, _1709312] : [46245 ^ _781215 : [(46248 ^ _781215) ^ [] : [46244 ^ [_1709310, _1709312] = c_List_Olist_ONil(_1709310)], (46246 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709310)), 46244 ^ [_1709310, _1709312]), hAPP(c_List_Oset(tc_List_Olist(_1709310)), _1709312))))]], -(c_List_Oconcat(_1709310, _1709312) = c_List_Olist_ONil(_1709310))], (49982 ^ _781215) ^ [_1794890, _1794892, _1794894, _1794896] : [-(hAPP(hAPP(c_Nat_Ocompow(_1794890, _1794890), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1794892), _1794894)), _1794896) = hAPP(c_Fun_Ocomp(_1794890, _1794890, _1794890, hAPP(hAPP(c_Nat_Ocompow(_1794890, _1794890), _1794892), _1794896)), hAPP(hAPP(c_Nat_Ocompow(_1794890, _1794890), _1794894), _1794896)))], (15438 ^ _781215) ^ [_1051928, _1051930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1051928), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1051930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051928), _1051930)))], (17571 ^ _781215) ^ [_1095678, _1095680, _1095682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095678), _1095680)), -(c_Smallcheck_Osmall_H(_1095682, _1095678, _1095680) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (47643 ^ _781215) ^ [_1740189, _1740191, _1740193, _1740195, _1740197, _1740199, _1740201] : [-(c_List_Olist__all2(_1740189, _1740191, _1740193, hAPP(hAPP(c_List_Olist_OCons(_1740189), _1740195), _1740197), hAPP(hAPP(c_List_Olist_OCons(_1740191), _1740199), _1740201))), hBOOL(hAPP(hAPP(_1740193, _1740195), _1740199)), c_List_Olist__all2(_1740189, _1740191, _1740193, _1740197, _1740201)], (45314 ^ _781215) ^ [_1690214, _1690216, _1690218, _1690220, _1690222] : [-(hAPP(c_List_Ofilter(_1690214, _1690216), hAPP(hAPP(c_List_Omap(_1690218, _1690214), _1690220), _1690222)) = hAPP(hAPP(c_List_Omap(_1690218, _1690214), _1690220), hAPP(c_List_Ofilter(_1690218, hAPP(c_Fun_Ocomp(_1690214, tc_HOL_Obool, _1690218, _1690216), _1690220)), _1690222)))], (11940 ^ _781215) ^ [_988747] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _988747)))], (24876 ^ _781215) ^ [_1230057, _1230059, _1230061] : [class_Groups_Omonoid__mult(_1230057), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1230057), _1230059), hAPP(c_Nat_OSuc, _1230061)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230057), hAPP(hAPP(c_Power_Opower__class_Opower(_1230057), _1230059), _1230061)), _1230059))], (37296 ^ _781215) ^ [_1488155, _1488157, _1488159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488155, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1488155, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37297 ^ [_1488155, _1488157, _1488159])), _1488157)), _1488159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488155, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1488155, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1488157)), _1488159)))], (36824 ^ _781215) ^ [_1474875, _1474877, _1474879, _1474881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474875, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1474875, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36825 ^ [_1474875, _1474877, _1474879, _1474881])), _1474877)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1474875, 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), 36825 ^ [_1474875, _1474877, _1474879, _1474881]), _1474879))), _1474881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474875, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1474875, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1474877)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1474875, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1474881))))], (25224 ^ _781215) ^ [_1236326] : [c_Int_OMin = _1236326, -(c_Int_OMin = c_Int_OBit1(_1236326))], (27402 ^ _781215) ^ [_1279788, _1279790, _1279792, _1279794, _1279796] : [hAPP(c_Product__Type_Osnd(_1279788, _1279790), hAPP(hAPP(c_Product__Type_OPair(_1279788, _1279790), _1279792), _1279794)) = _1279796, -(_1279794 = _1279796)], (43852 ^ _781215) ^ [_1656719, _1656721] : [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(_1656719)), _1656721))), _1656721 = c_List_Olist_ONil(_1656719)], (42042 ^ _781215) ^ [_1610583, _1610585, _1610587, _1610589] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1610583, _1610585))), hAPP(hAPP(c_List_Ozip(_1610583, _1610585), _1610587), _1610589)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610583)), _1610587)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610585)), _1610589)))], (49413 ^ _781215) ^ [_1780448, _1780450] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1780448), tc_List_Olist(_1780448)), tc_HOL_Obool)), c_List_Olistrel1(_1780448, c_Transitive__Closure_Ortrancl(_1780448, _1780450))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1780448), c_List_Olistrel1(_1780448, _1780450)))))], (37456 ^ _781215) ^ [_1492289, _1492291, _1492293] : [hBOOL(hAPP(hAPP(c_member(_1492289), _1492293), c_Wellfounded_Oacc(_1492289, _1492291))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1492289, hAPP(hAPP(c_COMBC(_1492289, tc_fun(tc_prod(_1492289, _1492289), tc_HOL_Obool), tc_fun(_1492289, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1492289, tc_fun(tc_fun(tc_prod(_1492289, _1492289), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1492289, _1492289), tc_HOL_Obool), tc_fun(_1492289, tc_HOL_Obool)), _1492289), c_COMBC(_1492289, tc_fun(tc_prod(_1492289, _1492289), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1492289, tc_prod(_1492289, _1492289)), tc_fun(_1492289, tc_fun(tc_fun(tc_prod(_1492289, _1492289), tc_HOL_Obool), tc_HOL_Obool)), _1492289), hAPP(c_COMBB(tc_prod(_1492289, _1492289), tc_fun(tc_fun(tc_prod(_1492289, _1492289), tc_HOL_Obool), tc_HOL_Obool), _1492289), c_member(tc_prod(_1492289, _1492289)))), c_Product__Type_OPair(_1492289, _1492289)))), _1492291)), _1492293)))], (7859 ^ _781215) ^ [_913986, _913988, _913990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913986), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _913988), _913990))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913986), _913990)), _913988)))], (4294 ^ _781215) ^ [_846372, _846374, _846376, _846378] : [-(c_Product__Type_OSigma(_846378, _846374) = c_Product__Type_OSigma(_846376, _846372)), _846378 = _846376, _846374 = _846372], (6826 ^ _781215) ^ [_893503, _893505, _893507, _893509, _893511] : [hAPP(_893503, _893505) = hAPP(c_Option_Ooption_OSome(_893507), _893509), -(hBOOL(hAPP(hAPP(c_member(_893511), _893505), c_Map_Odom(_893511, _893507, _893503))))], (49197 ^ _781215) ^ [_1775185, _1775187, _1775189] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775185, _1775185)), hAPP(hAPP(c_Product__Type_OPair(_1775185, _1775185), _1775187), _1775187)), c_Transitive__Closure_Ortrancl(_1775185, _1775189))))], (44638 ^ _781215) ^ [_1676069, _1676071, _1676073, _1676075] : [hAPP(hAPP(c_List_Oappend(_1676069), _1676071), _1676073) = _1676075, 44641 ^ _781215 : [(44644 ^ _781215) ^ [] : [-(_1676073 = hAPP(hAPP(c_List_Odrop(_1676069), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676069)), _1676071)), _1676075))], (44642 ^ _781215) ^ [] : [-(_1676071 = hAPP(hAPP(c_List_Otake(_1676069), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676069)), _1676071)), _1676075))]]], (7047 ^ _781215) ^ [_898345, _898347, _898349, _898351] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _898345), _898347), _898349), _898351)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898345), _898347), _898351)))], (4846 ^ _781215) ^ [_854722, _854724, _854726, _854728, _854730, _854732, _854734, _854736] : [-(c_New__DSequence_Opos__decr__bind(_854736, _854732, _854728, _854724) = c_New__DSequence_Opos__decr__bind(_854734, _854730, _854726, _854722)), _854736 = _854734, _854732 = _854730, _854728 = _854726, _854724 = _854722], (47374 ^ _781215) ^ [_1734108, _1734110, _1734112] : [class_Enum_Oenum(_1734108), class_Enum_Oenum(_1734110), class_HOL_Oequal(_1734110), 47385 ^ _781215 : [(47392 ^ _781215) ^ [] : [c_Enum_Oall__n__lists(_1734108, hAPP(hAPP(c_COMBB(tc_fun(_1734110, _1734108), tc_HOL_Obool, tc_List_Olist(_1734108)), _1734112), hAPP(hAPP(c_COMBB(tc_fun(_1734110, tc_Option_Ooption(_1734108)), tc_fun(_1734110, _1734108), tc_List_Olist(_1734108)), c_Fun_Ocomp(tc_Option_Ooption(_1734108), _1734108, _1734110, c_Option_Othe(_1734108))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1734110, _1734108)), tc_fun(_1734110, tc_Option_Ooption(_1734108)), tc_List_Olist(_1734108)), c_Map_Omap__of(_1734110, _1734108)), hAPP(c_List_Ozip(_1734110, _1734108), c_Enum_Oenum__class_Oenum(_1734110))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734110)), c_Enum_Oenum__class_Oenum(_1734110))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1734110, _1734108)), _1734112)))], (47386 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1734110, _1734108)), _1734112)), -(c_Enum_Oall__n__lists(_1734108, hAPP(hAPP(c_COMBB(tc_fun(_1734110, _1734108), tc_HOL_Obool, tc_List_Olist(_1734108)), _1734112), hAPP(hAPP(c_COMBB(tc_fun(_1734110, tc_Option_Ooption(_1734108)), tc_fun(_1734110, _1734108), tc_List_Olist(_1734108)), c_Fun_Ocomp(tc_Option_Ooption(_1734108), _1734108, _1734110, c_Option_Othe(_1734108))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1734110, _1734108)), tc_fun(_1734110, tc_Option_Ooption(_1734108)), tc_List_Olist(_1734108)), c_Map_Omap__of(_1734110, _1734108)), hAPP(c_List_Ozip(_1734110, _1734108), c_Enum_Oenum__class_Oenum(_1734110))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734110)), c_Enum_Oenum__class_Oenum(_1734110))))]]], (51680 ^ _781215) ^ [_1825859, _1825861] : [_1825859 = _1825861, -(hBOOL(hAPP(hAPP(c_fequal, _1825859), _1825861)))], (41050 ^ _781215) ^ [_1586486, _1586488, _1586490, _1586492, _1586494] : [c_Fun_Oinj__on(_1586486, _1586488, _1586490, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1586486, tc_HOL_Obool)), hAPP(c_List_Oset(_1586486), _1586492)), hAPP(c_List_Oset(_1586486), _1586494))), 41053 ^ _781215 : [(41060 ^ _781215) ^ [] : [_1586492 = _1586494, -(hAPP(hAPP(c_List_Omap(_1586486, _1586488), _1586490), _1586492) = hAPP(hAPP(c_List_Omap(_1586486, _1586488), _1586490), _1586494))], (41054 ^ _781215) ^ [] : [hAPP(hAPP(c_List_Omap(_1586486, _1586488), _1586490), _1586492) = hAPP(hAPP(c_List_Omap(_1586486, _1586488), _1586490), _1586494), -(_1586492 = _1586494)]]], (39838 ^ _781215) ^ [_1556901, _1556903, _1556905, _1556907] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1556901, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1556903, _1556901), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1556903, _1556901), tc_HOL_Obool)), _1556905), _1556907))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1556901, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1556903, _1556901), _1556905)), hAPP(c_Relation_ORange(_1556903, _1556901), _1556907)))))], (30403 ^ _781215) ^ [_1337283, _1337285, _1337287] : [class_Orderings_Olinorder(_1337283), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337283), _1337285), _1337287)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337283, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1337283), _1337285), c_Orderings_Obot__class_Obot(tc_fun(_1337283, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1337283, _1337285, _1337287)) = c_SetInterval_Oord__class_OatLeastAtMost(_1337283, _1337285, _1337287))], (8592 ^ _781215) ^ [_927025, _927027, _927029] : [class_Groups_Ogroup__add(_927025), 8595 ^ _781215 : [(8602 ^ _781215) ^ [] : [_927027 = _927029, -(hAPP(c_Groups_Ouminus__class_Ouminus(_927025), _927027) = hAPP(c_Groups_Ouminus__class_Ouminus(_927025), _927029))], (8596 ^ _781215) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_927025), _927027) = hAPP(c_Groups_Ouminus__class_Ouminus(_927025), _927029), -(_927027 = _927029)]]], (10270 ^ _781215) ^ [_956131, _956133, _956135, _956137, _956139] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _956131), _956133), _956135), _956137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956135), _956139)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _956131), _956133), _956139), _956137)))], (24478 ^ _781215) ^ [_1222724, _1222726, _1222728] : [class_Rings_Olinordered__idom(_1222724), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222724), c_Groups_Ozero__class_Ozero(_1222724)), hAPP(hAPP(c_Power_Opower__class_Opower(_1222724), _1222726), 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)))), _1222728)))))], (46672 ^ _781215) ^ [_1719510, _1719512, _1719514] : [-(c_List_Oremdups(_1719510, hAPP(c_List_Ofilter(_1719510, _1719512), _1719514)) = hAPP(c_List_Ofilter(_1719510, _1719512), c_List_Oremdups(_1719510, _1719514)))], (21019 ^ _781215) ^ [_1157731, _1157733] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157731) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1157733), 21022 ^ _781215 : [(21025 ^ _781215) ^ [] : [-(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), _1157733))))], (21023 ^ _781215) ^ [] : [-(_1157731 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1157733)))]]], (9377 ^ _781215) ^ [_941118, _941120, _941122, _941124] : [class_Orderings_Oorder(_941118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941118), _941120), _941122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941118), _941124), _941120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941118), _941124), _941122)))], (37229 ^ _781215) ^ [_1486572, _1486574, _1486576, _1486578] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1486572, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486574, tc_fun(_1486572, tc_HOL_Obool)), _1486576), _1486578)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486574, tc_fun(_1486572, tc_HOL_Obool)), _1486576), hAPP(hAPP(c_COMBB(tc_fun(_1486572, tc_HOL_Obool), tc_fun(_1486572, tc_HOL_Obool), _1486574), c_Groups_Ouminus__class_Ouminus(tc_fun(_1486572, tc_HOL_Obool))), _1486578)))], (36283 ^ _781215) ^ [_1463462, _1463464, _1463466, _1463468, _1463470, _1463472, _1463474] : [-(hAPP(c_Product__Type_Oapsnd(_1463462, _1463464, _1463466, _1463468), hAPP(c_Product__Type_Oapfst(_1463470, _1463466, _1463462, _1463472), _1463474)) = hAPP(c_Product__Type_Oapfst(_1463470, _1463466, _1463464, _1463472), hAPP(c_Product__Type_Oapsnd(_1463462, _1463464, _1463470, _1463468), _1463474)))], (32878 ^ _781215) ^ [_1390700, _1390702] : [class_Lattices_Obounded__lattice__bot(_1390700), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1390700), _1390702), c_Orderings_Obot__class_Obot(_1390700)) = c_Orderings_Obot__class_Obot(_1390700))], (41685 ^ _781215) ^ [_1601525, _1601527, _1601529, _1601531, _1601533] : [c_Hoare__Mirabelle_Ohoare__valids(_1601525, _1601527, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1601525)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1601525), c_Hoare__Mirabelle_Opeek__and(_1601525, _1601529, _1601531)), _1601533), _1601529)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1601525), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__valids(_1601525, _1601527, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1601525)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1601525), _1601529), c_Com_Ocom_OWhile(_1601531, _1601533)), c_Hoare__Mirabelle_Opeek__and(_1601525, _1601529, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1601531)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1601525), tc_HOL_Obool)))))], (43752 ^ _781215) ^ [_1654995, _1654997, _1654999, _1655001] : [c_List_Olist_ONil(_1654995) = hAPP(hAPP(c_List_Omap(_1654997, _1654995), _1654999), _1655001), -(_1655001 = c_List_Olist_ONil(_1654997))], (28870 ^ _781215) ^ [_1307458, _1307460, _1307462, _1307464] : [class_Fields_Olinordered__field(_1307458), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307458), c_Groups_Ozero__class_Ozero(_1307458)), _1307460)), 28877 ^ _781215 : [(28884 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307458), _1307462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307458), _1307464), _1307460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307458), _1307462), _1307460)), _1307464)))], (28878 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307458), _1307462), _1307460)), _1307464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307458), _1307462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307458), _1307464), _1307460))))]]], (43736 ^ _781215) ^ [_1654661, _1654663, _1654665] : [-(hAPP(hAPP(c_List_Olist__update(_1654661, c_List_Olist_ONil(_1654661)), _1654663), _1654665) = c_List_Olist_ONil(_1654661))], (43427 ^ _781215) ^ [_1647796, _1647798, _1647800, _1647802, _1647804] : [class_Groups_Ocomm__monoid__add(_1647796), hBOOL(hAPP(hAPP(c_member(_1647798), _1647800), hAPP(c_List_Oset(_1647798), _1647802))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1647796), hAPP(hAPP(c_List_Omap(_1647798, _1647796), _1647804), _1647802)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1647796), hAPP(_1647804, _1647800)), hAPP(c_List_Omonoid__add__class_Olistsum(_1647796), hAPP(hAPP(c_List_Omap(_1647798, _1647796), _1647804), c_List_Oremove1(_1647798, _1647800, _1647802)))))], (5036 ^ _781215) ^ [_857797, _857799, _857801, _857803, _857805, _857807, _857809, _857811, _857813, _857815, _857817, _857819, _857821, _857823] : [-(c_New__Random__Sequence_Oneg__decr__bind(_857823, _857819, _857815, _857811, _857807, _857803, _857799) = c_New__Random__Sequence_Oneg__decr__bind(_857821, _857817, _857813, _857809, _857805, _857801, _857797)), _857823 = _857821, _857819 = _857817, _857815 = _857813, _857811 = _857809, _857807 = _857805, _857803 = _857801, _857799 = _857797], (39188 ^ _781215) ^ [_1533862, _1533864] : [-(hAPP(c_Set_OCollect(_1533862), hAPP(hAPP(c_COMBC(_1533862, _1533862, tc_HOL_Obool), c_fequal), _1533864)) = hAPP(hAPP(c_Set_Oinsert(_1533862), _1533864), c_Orderings_Obot__class_Obot(tc_fun(_1533862, tc_HOL_Obool))))], (48790 ^ _781215) ^ [_1766419, _1766421, _1766423] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1766419), _1766421))), -(c_Random_Ominus__shift(_1766423, _1766419, _1766421) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1766419), _1766421))], (44718 ^ _781215) ^ [_1678051, _1678053, _1678055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678051), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678053)), _1678055))), -(hAPP(hAPP(c_List_Olist_OCons(_1678053), hAPP(hAPP(c_List_Onth(_1678053), _1678055), _1678051)), hAPP(hAPP(c_List_Odrop(_1678053), hAPP(c_Nat_OSuc, _1678051)), _1678055)) = hAPP(hAPP(c_List_Odrop(_1678053), _1678051), _1678055))], (38306 ^ _781215) ^ [_1511269, _1511271, _1511273, _1511275, _1511277, _1511279] : [-(hAPP(c_Set_Ovimage(_1511269, _1511271, _1511273), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1511275, tc_fun(_1511271, tc_HOL_Obool)), _1511277), _1511279)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1511275, tc_fun(_1511269, tc_HOL_Obool)), _1511277), hAPP(hAPP(c_COMBB(tc_fun(_1511271, tc_HOL_Obool), tc_fun(_1511269, tc_HOL_Obool), _1511275), c_Set_Ovimage(_1511269, _1511271, _1511273)), _1511279)))], (28656 ^ _781215) ^ [_1303466, _1303468, _1303470, _1303472] : [class_Fields_Olinordered__field__inverse__zero(_1303466), class_Int_Onumber(_1303466), 28663 ^ _781215 : [(28664 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303466), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303466), _1303468), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470))), _1303472)), 28667 ^ _781215 : [(28674 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303466), c_Groups_Ozero__class_Ozero(_1303466)), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470)))), 28677 ^ _781215 : [(28684 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303466), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470)), c_Groups_Ozero__class_Ozero(_1303466)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303466), c_Groups_Ozero__class_Ozero(_1303466)), _1303472)))], (28678 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303466), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470)), c_Groups_Ozero__class_Ozero(_1303466))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303466), _1303472), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470))), _1303468)))]]], (28668 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303466), c_Groups_Ozero__class_Ozero(_1303466)), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303466), _1303468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303466), _1303472), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470)))))]]], (28690 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303466), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303466), _1303468), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470))), _1303472))), 28693 ^ _781215 : [(28696 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303466), _1303468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303466), _1303472), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470))))], (28694 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303466), c_Groups_Ozero__class_Ozero(_1303466)), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470))))]], 28697 ^ _781215 : [(28700 ^ _781215) ^ [] : [28701 ^ _781215 : [(28704 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303466), _1303472), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470))), _1303468))], (28702 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303466), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470)), c_Groups_Ozero__class_Ozero(_1303466))))]], 28705 ^ _781215 : [(28708 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303466), c_Groups_Ozero__class_Ozero(_1303466)), _1303472))], (28706 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303466), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470)), c_Groups_Ozero__class_Ozero(_1303466)))]]], (28698 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303466), c_Groups_Ozero__class_Ozero(_1303466)), hAPP(c_Int_Onumber__class_Onumber__of(_1303466), _1303470)))]]]]], (19154 ^ _781215) ^ [_1125008, _1125010] : [class_Orderings_Olinorder(_1125008), -(c_Big__Operators_Olinorder__class_OMin(_1125008, hAPP(hAPP(c_Set_Oinsert(_1125008), _1125010), c_Orderings_Obot__class_Obot(tc_fun(_1125008, tc_HOL_Obool)))) = _1125010)], (32854 ^ _781215) ^ [_1390224, _1390226, _1390228, _1390230] : [class_Lattices_Odistrib__lattice(_1390224), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1390224), _1390226), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1390224), _1390228), _1390230)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1390224), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1390224), _1390226), _1390228)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1390224), _1390226), _1390230)))], (22252 ^ _781215) ^ [_1182636, _1182638, _1182640] : [class_Divides_Osemiring__div(_1182636), -(c_Divides_Odiv__class_Omod(_1182636, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182636), _1182638), _1182640), _1182640) = c_Divides_Odiv__class_Omod(_1182636, _1182638, _1182640))], (31900 ^ _781215) ^ [_1368899, _1368901, _1368903, _1368905] : [class_Groups_Ocomm__monoid__add(_1368899), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1368901), _1368903)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1368899), _1368905), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1368901), _1368903)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1368899), hAPP(_1368905, _1368901)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1368899), _1368905), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1368901)), _1368903))))], (16655 ^ _781215) ^ [] : [-(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))))], (27066 ^ _781215) ^ [_1273121, _1273123, _1273125, _1273127] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1273121, _1273123), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1273125), _1273127))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1273121, _1273123) = _1273127)], (51512 ^ _781215) ^ [_1823977, _1823979] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1823977, _1823979))), class_Lazy__Sequence_Osmall__lazy(_1823977), class_Lazy__Sequence_Osmall__lazy(_1823979)], (38061 ^ _781215) ^ [_1505205, _1505207] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1505205, tc_HOL_Obool), _1505207) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1505205, tc_HOL_Obool), tc_fun(_1505205, tc_HOL_Obool)), _1505207), c_COMBI(tc_fun(_1505205, tc_HOL_Obool))))], (5202 ^ _781215) ^ [_860596, _860598] : [_860598 = _860596, -(c_Groups_Ozero__class_Ozero(_860598) = c_Groups_Ozero__class_Ozero(_860596))], (46536 ^ _781215) ^ [_1716940] : [-(c_List_Oreturn__list(_1716940) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1716940))], (6788 ^ _781215) ^ [_892801, _892803, _892805] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_892801, _892803, c_Orderings_Obot__class_Obot(tc_fun(_892801, tc_HOL_Obool))), _892805))], (10146 ^ _781215) ^ [_954035, _954037, _954039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954035), _954037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954035), _954039)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954037), _954039))))], (25036 ^ _781215) ^ [_1233056, _1233058, _1233060, _1233062] : [class_Rings_Olinordered__semidom(_1233056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1233058), _1233060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1233056), c_Groups_Oone__class_Oone(_1233056)), _1233062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1233056), hAPP(hAPP(c_Power_Opower__class_Opower(_1233056), _1233062), _1233058)), hAPP(hAPP(c_Power_Opower__class_Opower(_1233056), _1233062), _1233060))))], (12380 ^ _781215) ^ [_996563, _996565, _996567] : [class_Rings_Oordered__cancel__semiring(_996563), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996563), c_Groups_Ozero__class_Ozero(_996563)), _996565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996563), c_Groups_Ozero__class_Ozero(_996563)), _996567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996563), c_Groups_Ozero__class_Ozero(_996563)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996563), _996565), _996567))))], (36766 ^ _781215) ^ [_1472773, _1472775, _1472777, _1472779, _1472781] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1472773)), hAPP(c_Set_Oimage(_1472775, tc_Option_Ooption(_1472773), _1472777), c_Orderings_Otop__class_Otop(tc_fun(_1472775, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1472773)), hAPP(c_Set_Oimage(_1472775, tc_Option_Ooption(_1472773), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1472775, tc_Option_Ooption(_1472773)), _1472777), _1472779), hAPP(c_Option_Ooption_OSome(_1472773), _1472781))), c_Orderings_Otop__class_Otop(tc_fun(_1472775, tc_HOL_Obool))))))], (15106 ^ _781215) ^ [_1046458, _1046460, _1046462] : [class_Groups_Oab__semigroup__mult(_1046458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046458), _1046460)), -(hBOOL(hAPP(hAPP(c_member(_1046458), _1046462), _1046460))), -(hAPP(c_Finite__Set_Ofold1(_1046458, c_Groups_Otimes__class_Otimes(_1046458)), hAPP(hAPP(c_Set_Oinsert(_1046458), _1046462), _1046460)) = hAPP(hAPP(c_Finite__Set_Ofold(_1046458, _1046458, c_Groups_Otimes__class_Otimes(_1046458)), _1046462), _1046460))], (43952 ^ _781215) ^ [_1659235, _1659237] : [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), _1659235), _1659237))), 43955 ^ _781215 : [(43962 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1659235), _1659237))), -(c_List_Oupto(_1659235, _1659237) = c_List_Olist_ONil(tc_Int_Oint))], (43956 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1659235), _1659237)), -(c_List_Oupto(_1659235, _1659237) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1659235), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1659235), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1659237)))]]], (13866 ^ _781215) ^ [_1022781, _1022783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1022781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1022781), hAPP(c_Nat_OSuc, _1022783))), _1022781)))], (45079 ^ _781215) ^ [_1685649, _1685651, _1685653, _1685655, _1685657] : [-(c_Map_Omap__upds(_1685649, _1685651, _1685653, _1685655, _1685657) = hAPP(c_List_Ofoldl(tc_fun(_1685649, tc_Option_Ooption(_1685651)), tc_prod(_1685649, _1685651), hAPP(hAPP(c_COMBB(tc_fun(_1685649, tc_fun(_1685651, tc_fun(_1685649, tc_Option_Ooption(_1685651)))), tc_fun(tc_prod(_1685649, _1685651), tc_fun(_1685649, tc_Option_Ooption(_1685651))), tc_fun(_1685649, tc_Option_Ooption(_1685651))), c_Product__Type_Oprod_Oprod__case(_1685649, _1685651, tc_fun(_1685649, tc_Option_Ooption(_1685651)))), hAPP(hAPP(c_COMBC(tc_fun(_1685649, tc_Option_Ooption(_1685651)), tc_fun(_1685651, tc_Option_Ooption(_1685651)), tc_fun(_1685649, tc_fun(_1685651, tc_fun(_1685649, tc_Option_Ooption(_1685651))))), hAPP(hAPP(c_COMBB(tc_fun(_1685649, tc_fun(tc_fun(_1685651, tc_Option_Ooption(_1685651)), tc_fun(_1685651, tc_fun(_1685649, tc_Option_Ooption(_1685651))))), tc_fun(tc_fun(_1685651, tc_Option_Ooption(_1685651)), tc_fun(_1685649, tc_fun(_1685651, tc_fun(_1685649, tc_Option_Ooption(_1685651))))), tc_fun(_1685649, tc_Option_Ooption(_1685651))), c_COMBC(_1685649, tc_fun(_1685651, tc_Option_Ooption(_1685651)), tc_fun(_1685651, tc_fun(_1685649, tc_Option_Ooption(_1685651))))), hAPP(hAPP(c_COMBB(tc_fun(_1685649, tc_fun(tc_Option_Ooption(_1685651), tc_fun(_1685649, tc_Option_Ooption(_1685651)))), tc_fun(_1685649, tc_fun(tc_fun(_1685651, tc_Option_Ooption(_1685651)), tc_fun(_1685651, tc_fun(_1685649, tc_Option_Ooption(_1685651))))), tc_fun(_1685649, tc_Option_Ooption(_1685651))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1685651), tc_fun(_1685649, tc_Option_Ooption(_1685651))), tc_fun(tc_fun(_1685651, tc_Option_Ooption(_1685651)), tc_fun(_1685651, tc_fun(_1685649, tc_Option_Ooption(_1685651)))), _1685649), c_COMBB(tc_Option_Ooption(_1685651), tc_fun(_1685649, tc_Option_Ooption(_1685651)), _1685651))), c_Fun_Ofun__upd(_1685649, tc_Option_Ooption(_1685651))))), c_Option_Ooption_OSome(_1685651))), _1685653), hAPP(hAPP(c_List_Ozip(_1685649, _1685651), _1685655), _1685657)))], (33206 ^ _781215) ^ [_1398225, _1398227, _1398229, _1398231, _1398233] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398225, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1398227, _1398225, _1398229), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398227, tc_HOL_Obool)), _1398231), _1398233))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398225, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1398227, _1398225, _1398229), _1398231)), hAPP(c_Set_Oimage(_1398227, _1398225, _1398229), _1398233)))))], (37221 ^ _781215) ^ [_1486216, _1486218, _1486220, _1486222, _1486224] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486216, tc_fun(_1486218, tc_HOL_Obool)), _1486220), hAPP(hAPP(c_COMBB(tc_fun(_1486218, tc_HOL_Obool), tc_fun(_1486218, tc_HOL_Obool), _1486216), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486218, tc_HOL_Obool)), _1486222)), _1486224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486218, tc_HOL_Obool)), _1486222), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486216, tc_fun(_1486218, tc_HOL_Obool)), _1486220), _1486224)))], (26290 ^ _781215) ^ [_1258072, _1258074, _1258076, _1258078, _1258080] : [class_Groups_Ocomm__monoid__mult(_1258072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1258074), _1258076)), 26297 ^ _781215 : [(26304 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1258074), _1258078), _1258076))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1258074, _1258072), hAPP(hAPP(c_COMBC(_1258074, _1258072, _1258072), hAPP(hAPP(c_COMBS(_1258074, _1258072, tc_fun(_1258072, _1258072)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1258072, tc_fun(_1258072, _1258072)), _1258074), c_If(_1258072)), hAPP(c_fequal, _1258078))), _1258080)), c_Groups_Oone__class_Oone(_1258072))), _1258076) = c_Groups_Oone__class_Oone(_1258072))], (26298 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1258074), _1258078), _1258076)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1258074, _1258072), hAPP(hAPP(c_COMBC(_1258074, _1258072, _1258072), hAPP(hAPP(c_COMBS(_1258074, _1258072, tc_fun(_1258072, _1258072)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1258072, tc_fun(_1258072, _1258072)), _1258074), c_If(_1258072)), hAPP(c_fequal, _1258078))), _1258080)), c_Groups_Oone__class_Oone(_1258072))), _1258076) = hAPP(_1258080, _1258078))]]], (23686 ^ _781215) ^ [_1208260, _1208262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1208260)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1208260), _1208262)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1208260)), _1208262))], (11036 ^ _781215) ^ [_971656, _971658, _971660, _971662, _971664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971656), _971658)), 11039 ^ _781215 : [(11046 ^ _781215) ^ [] : [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), _971658), _971656)), _971660)), _971662)), _971664)), -(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), _971658), _971660)), _971662)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971656), _971660)), _971664))))], (11040 ^ _781215) ^ [] : [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), _971658), _971660)), _971662)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971656), _971660)), _971664))), -(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), _971658), _971656)), _971660)), _971662)), _971664)))]]], (31559 ^ _781215) ^ [_1361442, _1361444, _1361446, _1361448, _1361450] : [class_Groups_Ocomm__monoid__add(_1361442), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361444, _1361442), hAPP(hAPP(c_COMBS(_1361444, _1361442, _1361442), hAPP(hAPP(c_COMBB(_1361442, tc_fun(_1361442, _1361442), _1361444), c_Groups_Oplus__class_Oplus(_1361442)), _1361446)), _1361448)), _1361450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361442), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361444, _1361442), _1361446), _1361450)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361444, _1361442), _1361448), _1361450)))], (31072 ^ _781215) ^ [_1349899, _1349901, _1349903] : [-(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)), _1349899)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1349901), _1349903)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1349901), _1349899)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1349903), _1349899)))], (45566 ^ _781215) ^ [_1695878, _1695880] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1695878, _1695880)))], (49895 ^ _781215) ^ [_1792608, _1792610, _1792612] : [49897 ^ _781215 : [(49898 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1792608), 49896 ^ [_1792608, _1792610, _1792612]), _1792610)))], (49903 ^ _781215) ^ [] : [49896 ^ [_1792608, _1792610, _1792612] = 49899 ^ [_1792608, _1792610, _1792612]], (49907 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1792608, _1792608)), hAPP(hAPP(c_Product__Type_OPair(_1792608, _1792608), 49899 ^ [_1792608, _1792610, _1792612]), 49896 ^ [_1792608, _1792610, _1792612])), _1792612))], (49905 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1792608, _1792608)), hAPP(hAPP(c_Product__Type_OPair(_1792608, _1792608), 49896 ^ [_1792608, _1792610, _1792612]), 49899 ^ [_1792608, _1792610, _1792612])), _1792612))], (49901 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1792608), 49899 ^ [_1792608, _1792610, _1792612]), _1792610)))]], -(c_Relation_Ototal__on(_1792608, _1792610, _1792612))], (20747 ^ _781215) ^ [] : [-(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))], (8025 ^ _781215) ^ [_916553, _916555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _916553)), hAPP(c_Nat_OSuc, _916555))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916553), _916555)))], (51768 ^ _781215) ^ [] : [-(c_Hoare__Mirabelle_Ostate__not__singleton)], (31469 ^ _781215) ^ [_1358425, _1358427, _1358429, _1358431] : [-(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), _1358425), _1358427)), 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), _1358429), _1358431)), 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), _1358425), _1358429)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1358427), _1358431))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (15636 ^ _781215) ^ [_1055990, _1055992, _1055994, _1055996, _1055998, _1056000] : [c_Com_Ocom_OLocal(_1055990, _1055992, _1055994) = c_Com_Ocom_OCall(_1055996, _1055998, _1056000)], (37997 ^ _781215) ^ [_1503874, _1503876, _1503878] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1503874, tc_HOL_Obool)), _1503876), _1503878) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1503874, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1503874, tc_HOL_Obool)), _1503876), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1503874, tc_HOL_Obool)), _1503878), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1503874, tc_HOL_Obool), tc_HOL_Obool))))))], (3418 ^ _781215) ^ [_832850, _832852, _832854, _832856, _832858, _832860] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_832860, _832856, _832852) = c_SetInterval_Oord__class_OgreaterThanAtMost(_832858, _832854, _832850)), _832860 = _832858, _832856 = _832854, _832852 = _832850], (15256 ^ _781215) ^ [] : [-(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))], (23781 ^ _781215) ^ [_1209951, _1209953] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209951), _1209953))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1209951, _1209953) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1209951), _1209953), _1209953))], (40609 ^ _781215) ^ [_1576956, _1576958, _1576960, _1576962, _1576964] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1576956, _1576958, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1576956)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1576956), hAPP(hAPP(c_COMBC(_1576956, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1576956), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1576956), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _1576960))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _1576962))), c_Com_Ocom_OWhile(_1576962, _1576964)), _1576960)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1576956), tc_HOL_Obool)))))], (24846 ^ _781215) ^ [_1229563, _1229565] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1229563), c_Groups_Ozero__class_Ozero(_1229563)), hAPP(c_Nat_OSuc, _1229565)) = c_Groups_Ozero__class_Ozero(_1229563)), class_Power_Opower(_1229563), class_Rings_Osemiring__0(_1229563)], (894 ^ _781215) ^ [_795008, _795010, _795012, _795014] : [-(c_Wellfounded_Oacyclic(_795012, _795008)), c_Wellfounded_Oacyclic(_795014, _795010), _795014 = _795012, _795010 = _795008], (44210 ^ _781215) ^ [_1664997, _1664999, _1665001] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664997)), hAPP(hAPP(c_List_Oappend(_1664997), _1664999), _1665001)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664997)), _1664999)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664997)), _1665001)))], (17387 ^ _781215) ^ [_1092611, _1092613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092611), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092611)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092613)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48694 ^ _781215) ^ [_1764333, _1764335, _1764337, _1764339, _1764341, _1764343, _1764345, _1764347] : [class_Groups_Ocomm__monoid__add(_1764333), c_Fun_Oinj__on(_1764335, _1764337, _1764339, _1764341), _1764343 = hAPP(c_Set_Oimage(_1764335, _1764337, _1764339), _1764341), 48708 ^ _781215 : [(48711 ^ _781215) ^ [] : [hAPP(_1764345, 48707 ^ [_1764333, _1764335, _1764337, _1764339, _1764341, _1764343, _1764345, _1764347]) = hAPP(_1764347, hAPP(_1764339, 48707 ^ [_1764333, _1764335, _1764337, _1764339, _1764341, _1764343, _1764345, _1764347]))], (48709 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1764335), 48707 ^ [_1764333, _1764335, _1764337, _1764339, _1764341, _1764343, _1764345, _1764347]), _1764341)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1764337, _1764333), _1764347), _1764343) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1764335, _1764333), _1764345), _1764341))], (41485 ^ _781215) ^ [_1596799, _1596801, _1596803, _1596805, _1596807] : [-(hAPP(c_Map_Omap__of(_1596799, _1596801), hAPP(hAPP(c_List_Omap(tc_prod(_1596799, _1596803), tc_prod(_1596799, _1596801)), hAPP(c_Product__Type_Oprod_Oprod__case(_1596799, _1596803, tc_prod(_1596799, _1596801)), hAPP(hAPP(c_COMBC(_1596799, tc_fun(_1596803, _1596801), tc_fun(_1596803, tc_prod(_1596799, _1596801))), hAPP(hAPP(c_COMBB(tc_fun(_1596801, tc_prod(_1596799, _1596801)), tc_fun(tc_fun(_1596803, _1596801), tc_fun(_1596803, tc_prod(_1596799, _1596801))), _1596799), c_COMBB(_1596801, tc_prod(_1596799, _1596801), _1596803)), c_Product__Type_OPair(_1596799, _1596801))), _1596805))), _1596807)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1596803), tc_Option_Ooption(_1596801), _1596799, hAPP(c_Option_Omap(_1596803, _1596801), _1596805)), hAPP(c_Map_Omap__of(_1596799, _1596803), _1596807)))], (23584 ^ _781215) ^ [_1206152] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1206152)), 23588 ^ _781215 : [(23589 ^ _781215) ^ [_1206232] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1206232), _1206152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1206232), 23587 ^ [_1206152])))]]], (5798 ^ _781215) ^ [_873367, _873369, _873371, _873373, _873375] : [-(hAPP(c_Option_Ooption_Ooption__case(_873367, _873369, _873371, _873373), hAPP(c_Option_Ooption_OSome(_873369), _873375)) = hAPP(_873373, _873375))], (51522 ^ _781215) ^ [_1824106, _1824108] : [-(class_Finite__Set_Ofinite(tc_prod(_1824106, _1824108))), class_Finite__Set_Ofinite(_1824106), class_Finite__Set_Ofinite(_1824108)], (47555 ^ _781215) ^ [_1738153, _1738155, _1738157] : [hBOOL(hAPP(c_List_Olistsp(_1738153, hAPP(hAPP(c_COMBC(_1738153, tc_fun(_1738153, tc_HOL_Obool), tc_HOL_Obool), c_member(_1738153)), _1738155)), _1738157)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1738153)), _1738157), c_List_Olists(_1738153, _1738155))))], (35457 ^ _781215) ^ [_1447537, _1447539] : [class_Groups_Oordered__ab__group__add(_1447537), -(hAPP(c_Set_Oimage(_1447537, _1447537, c_Groups_Ouminus__class_Ouminus(_1447537)), hAPP(c_SetInterval_Oord__class_OatMost(_1447537), _1447539)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1447537), hAPP(c_Groups_Ouminus__class_Ouminus(_1447537), _1447539)))], (38356 ^ _781215) ^ [_1512606, _1512608, _1512610, _1512612] : [-(hAPP(c_Set_Oimage(_1512606, _1512608, _1512610), hAPP(c_Set_Ovimage(_1512606, _1512608, _1512610), _1512612)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1512608, tc_HOL_Obool)), _1512612), hAPP(c_Set_Oimage(_1512606, _1512608, _1512610), c_Orderings_Otop__class_Otop(tc_fun(_1512606, tc_HOL_Obool)))))], (19140 ^ _781215) ^ [_1124687, _1124689, _1124691] : [class_Groups_Olinordered__ab__group__add(_1124687), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1124687), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1124687), _1124689), _1124691)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1124687), hAPP(c_Groups_Ouminus__class_Ouminus(_1124687), _1124689)), hAPP(c_Groups_Ouminus__class_Ouminus(_1124687), _1124691)))], (8818 ^ _781215) ^ [_930719, _930721, _930723, _930725] : [class_Orderings_Oord(_930719), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930719), _930721), _930723)), _930723 = _930725, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930719), _930721), _930725)))], (16469 ^ _781215) ^ [_1072651, _1072653, _1072655, _1072657, _1072659] : [-(hAPP(c_Set_Oimage(_1072651, _1072653, _1072655), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072651, tc_HOL_Obool)), _1072657), _1072659)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072653, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1072651, _1072653, _1072655), _1072657)), hAPP(c_Set_Oimage(_1072651, _1072653, _1072655), _1072659)))], (38181 ^ _781215) ^ [_1508334, _1508336, _1508338] : [-(hAPP(c_Finite__Set_Ofold1(_1508334, _1508336), _1508338) = c_HOL_OThe(_1508334, c_Finite__Set_Ofold1Set(_1508334, _1508336, _1508338)))], (50958 ^ _781215) ^ [_1817018, _1817020, _1817022, _1817024, _1817026] : [-(hAPP(c_New__DSequence_Oneg__bind(_1817018, _1817020, _1817022, _1817024), _1817026) = c_Lazy__Sequence_Ohb__bind(_1817018, _1817020, hAPP(_1817022, _1817026), hAPP(hAPP(c_COMBC(_1817018, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1817020))), _1817024), _1817026)))], (51280 ^ _781215) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (31820 ^ _781215) ^ [_1367183, _1367185, _1367187, _1367189] : [class_Rings_Osemiring__1(_1367183), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1367185, _1367183), hAPP(c_COMBK(_1367183, _1367185), _1367187)), _1367189) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1367183), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1367183), hAPP(c_Finite__Set_Ocard(_1367185), _1367189))), _1367187))], (6874 ^ _781215) ^ [_894615, _894617, _894619, _894621] : [c_Finite__Set_Ofolding__one(_894615, _894617, _894619), hBOOL(hAPP(c_Finite__Set_Ofinite(_894615), _894621)), -(_894621 = c_Orderings_Obot__class_Obot(tc_fun(_894615, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_894615), hAPP(hAPP(_894617, 6887 ^ [_894615, _894617, _894619, _894621]), 6888 ^ [_894615, _894617, _894619, _894621])), hAPP(hAPP(c_Set_Oinsert(_894615), 6887 ^ [_894615, _894617, _894619, _894621]), hAPP(hAPP(c_Set_Oinsert(_894615), 6888 ^ [_894615, _894617, _894619, _894621]), c_Orderings_Obot__class_Obot(tc_fun(_894615, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_894615), hAPP(_894619, _894621)), _894621)))], (33350 ^ _781215) ^ [_1401740, _1401742, _1401744] : [class_Orderings_Oorder(_1401740), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401740, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1401740), _1401742)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1401740, _1401742), _1401744)) = c_Orderings_Obot__class_Obot(tc_fun(_1401740, tc_HOL_Obool)))], (28458 ^ _781215) ^ [_1299612, _1299614, _1299616, _1299618] : [class_Fields_Ofield(_1299612), -(_1299614 = c_Groups_Ozero__class_Ozero(_1299612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1299616), _1299618)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1299612), _1299614), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1299618), _1299616)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299612), hAPP(hAPP(c_Power_Opower__class_Opower(_1299612), _1299614), _1299618)), hAPP(hAPP(c_Power_Opower__class_Opower(_1299612), _1299614), _1299616)))], (30461 ^ _781215) ^ [_1338475, _1338477] : [c_Relation_Oirrefl(_1338475, _1338477), 30464 ^ _781215 : [(30465 ^ _781215) ^ [_1338557] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1338475, _1338475)), hAPP(hAPP(c_Product__Type_OPair(_1338475, _1338475), _1338557), _1338557)), _1338477))]]], (8952 ^ _781215) ^ [_933108, _933110, _933112] : [class_Orderings_Oorder(_933108), 8955 ^ _781215 : [(8964 ^ _781215) ^ [] : [-(_933110 = _933112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933108), _933110), _933112)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933108), _933112), _933110))], (8956 ^ _781215) ^ [] : [_933110 = _933112, 8959 ^ _781215 : [(8962 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933108), _933112), _933110)))], (8960 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933108), _933110), _933112)))]]]]], (48087 ^ _781215) ^ [_1750658, _1750660] : [48089 ^ _781215 : [(48092 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1750660), 48088 ^ [_1750658, _1750660]))], (48090 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 48088 ^ [_1750658, _1750660]), _1750658)))]], -(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)), _1750660), _1750658))], (46173 ^ _781215) ^ [_1707853, _1707855] : [hBOOL(hAPP(c_List_Odistinct(_1707853), _1707855)), -(hBOOL(hAPP(c_List_Odistinct(_1707853), hAPP(c_List_Orev(_1707853), _1707855))))], (23162 ^ _781215) ^ [_1198413, _1198415] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198413, _1198415) = 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), _1198413), _1198415) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (3132 ^ _781215) ^ [_828343, _828345, _828347, _828349] : [-(c_Hilbert__Choice_OEps(_828349, _828345) = c_Hilbert__Choice_OEps(_828347, _828343)), _828349 = _828347, _828345 = _828343], (11644 ^ _781215) ^ [_984460, _984462, _984464] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_984460), 11647 ^ _781215 : [(11654 ^ _781215) ^ [] : [_984464 = c_Groups_Ozero__class_Ozero(_984460), -(_984462 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984460), _984462), _984464))], (11648 ^ _781215) ^ [] : [_984462 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984460), _984462), _984464), -(_984464 = c_Groups_Ozero__class_Ozero(_984460))]]], (36360 ^ _781215) ^ [_1464755] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1464755), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1464755)), c_Option_Ooption_ONone(_1464755)), hAPP(c_Set_Oimage(_1464755, tc_Option_Ooption(_1464755), c_Option_Ooption_OSome(_1464755)), c_Orderings_Otop__class_Otop(tc_fun(_1464755, tc_HOL_Obool)))))], (17381 ^ _781215) ^ [_1092497, _1092499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092497), _1092499)), -(c_Nat__Transfer_Otsub(_1092499, _1092497) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1092499), _1092497))], (1718 ^ _781215) ^ [_805660, _805662] : [-(class_Orderings_Opreorder(_805660)), _805662 = _805660, class_Orderings_Opreorder(_805662)], (23620 ^ _781215) ^ [_1206811, _1206813, _1206815] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206811), _1206813)), _1206815) = 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), _1206811), _1206815)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1206813), _1206815))), 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, _1206811, _1206815)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1206813, _1206815))), _1206815)))], (6493 ^ _781215) ^ [_887054, _887056, _887058, _887060] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_887054), _887056), _887058)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_887054), _887056), _887060)), -(_887060 = _887058)], (35705 ^ _781215) ^ [_1452606] : [class_Rings_Olinordered__idom(_1452606), -(hAPP(c_Groups_Oabs__class_Oabs(_1452606), c_Groups_Oone__class_Oone(_1452606)) = c_Groups_Oone__class_Oone(_1452606))], (24744 ^ _781215) ^ [_1227799, _1227801] : [class_Groups_Omonoid__mult(_1227799), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1227799), c_Groups_Oone__class_Oone(_1227799)), _1227801) = c_Groups_Oone__class_Oone(_1227799))], (28006 ^ _781215) ^ [_1291476, _1291478, _1291480] : [class_Rings_Odivision__ring(_1291476), -(_1291478 = c_Groups_Ozero__class_Ozero(_1291476)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1291476), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291476), _1291480), _1291478)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291476), _1291480), hAPP(c_Groups_Ouminus__class_Ouminus(_1291476), _1291478)))], (18073 ^ _781215) ^ [_1104247, _1104249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104247)), hAPP(c_Nat_OSuc, _1104249))), -(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(_1104247))), 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)), _1104249)))))], (8586 ^ _781215) ^ [_926896, _926898, _926900] : [class_Rings_Oring(_926896), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926896), hAPP(c_Groups_Ouminus__class_Ouminus(_926896), _926898)), hAPP(c_Groups_Ouminus__class_Ouminus(_926896), _926900)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926896), _926898), _926900))], (10316 ^ _781215) ^ [_956958, _956960, _956962, _956964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_956958, tc_HOL_Obool)), _956960), _956962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_956958, tc_HOL_Obool)), _956962), _956964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_956958, tc_HOL_Obool)), _956960), _956964)))], (47948 ^ _781215) ^ [_1746654, _1746656, _1746658] : [hBOOL(hAPP(hAPP(c_member(_1746654), _1746656), hAPP(c_List_Oset(_1746654), _1746658))), -(c_List_Oinsert(_1746654, _1746656, _1746658) = _1746658)], (22982 ^ _781215) ^ [_1195578, _1195580, _1195582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195578), _1195580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195578), _1195582)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195580), _1195582))))], (38616 ^ _781215) ^ [_1519951, _1519953, _1519955, _1519957, _1519959, _1519961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519951, _1519953), tc_HOL_Obool)), _1519955), hAPP(hAPP(c_Product__Type_OSigma(_1519951, _1519953), _1519957), hAPP(c_COMBK(tc_fun(_1519953, tc_HOL_Obool), _1519951), _1519959)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519953, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1519951, _1519953, _1519955), _1519961)), _1519959)))], (47683 ^ _781215) ^ [_1741237, _1741239, _1741241] : [c_List_Olist__all2(_1741241, _1741241, c_fequal, _1741237, _1741239), -(_1741237 = _1741239)], (10114 ^ _781215) ^ [_953305, _953307, _953309] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _953305), _953307)), _953309) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953305), _953309)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953307), _953309)))], (27096 ^ _781215) ^ [_1273797, _1273799, _1273801, _1273803, _1273805] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1273797, _1273799), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1273801), _1273803))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1273799)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1273805), _1273797), _1273799), 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), _1273805), _1273801)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1273805), _1273803)), _1273799))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1273805), _1273803), _1273799)))))], (46167 ^ _781215) ^ [_1707754, _1707756] : [hBOOL(hAPP(c_List_Odistinct(_1707754), hAPP(c_List_Orev(_1707754), _1707756))), -(hBOOL(hAPP(c_List_Odistinct(_1707754), _1707756)))], (31662 ^ _781215) ^ [_1363698, _1363700, _1363702] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1363698), _1363700)), 31665 ^ _781215 : [(31685 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363698, tc_Nat_Onat), _1363702), _1363700) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 31686 ^ _781215 : [(31687 ^ _781215) ^ [_1364179] : [hBOOL(hAPP(hAPP(c_member(_1363698), _1364179), _1363700)), hAPP(_1363702, _1364179) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31695 ^ _781215 : [(31700 ^ _781215) ^ [] : [hAPP(_1363702, 31694 ^ [_1363698, _1363700, _1363702, _1364179]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31698 ^ _781215) ^ [] : [_1364179 = 31694 ^ [_1363698, _1363700, _1363702, _1364179]], (31696 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1363698), 31694 ^ [_1363698, _1363700, _1363702, _1364179]), _1363700)))]]]]], (31666 ^ _781215) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363698, tc_Nat_Onat), _1363702), _1363700) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31670 ^ _781215 : [(31675 ^ _781215) ^ [_1364018] : [hBOOL(hAPP(hAPP(c_member(_1363698), _1364018), _1363700)), -(31669 ^ [_1363698, _1363700, _1363702] = _1364018), -(hAPP(_1363702, _1364018) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31673 ^ _781215) ^ [] : [-(hAPP(_1363702, 31669 ^ [_1363698, _1363700, _1363702]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31671 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1363698), 31669 ^ [_1363698, _1363700, _1363702]), _1363700)))]]]]], (23270 ^ _781215) ^ [_1200402, _1200404, _1200406] : [-(hBOOL(hAPP(_1200402, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1200404), _1200406)))), 23273 ^ _781215 : [(23276 ^ _781215) ^ [] : [hBOOL(hAPP(_1200402, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23274 ^ _781215) ^ [] : [-(_1200406 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 23279 ^ _781215 : [(23280 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200406)))], (23286 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23282 ^ [_1200402, _1200404, _1200406]), _1200406)))], (23290 ^ _781215) ^ [] : [hBOOL(hAPP(_1200402, 23281 ^ [_1200402, _1200404, _1200406]))], (23288 ^ _781215) ^ [] : [-(_1200404 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200406), 23281 ^ [_1200402, _1200404, _1200406])), 23282 ^ [_1200402, _1200404, _1200406]))], (23284 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23282 ^ [_1200402, _1200404, _1200406])))]], 23291 ^ _781215 : [(23292 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200406), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23298 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23294 ^ [_1200402, _1200404, _1200406]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23302 ^ _781215) ^ [] : [hBOOL(hAPP(_1200402, 23293 ^ [_1200402, _1200404, _1200406]))], (23300 ^ _781215) ^ [] : [-(_1200404 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200406), 23293 ^ [_1200402, _1200404, _1200406])), 23294 ^ [_1200402, _1200404, _1200406]))], (23296 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200406), 23294 ^ [_1200402, _1200404, _1200406])))]]], (44224 ^ _781215) ^ [_1665429, _1665431, _1665433, _1665435, _1665437] : [-(hAPP(hAPP(c_List_Omap(_1665429, _1665431), _1665433), hAPP(hAPP(c_List_Oappend(_1665429), _1665435), _1665437)) = hAPP(hAPP(c_List_Oappend(_1665431), hAPP(hAPP(c_List_Omap(_1665429, _1665431), _1665433), _1665435)), hAPP(hAPP(c_List_Omap(_1665429, _1665431), _1665433), _1665437)))], (26000 ^ _781215) ^ [_1252765, _1252767, _1252769, _1252771] : [class_Groups_Ocomm__monoid__mult(_1252765), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1252767), _1252769))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1252767, _1252765), _1252771), _1252769) = c_Groups_Oone__class_Oone(_1252765))], (39414 ^ _781215) ^ [_1541942, _1541944, _1541946, _1541948, _1541950, _1541952] : [-(hBOOL(hAPP(hAPP(c_member(_1541942), _1541944), _1541946))), -(hAPP(c_Fun_Ooverride__on(_1541942, _1541948, _1541950, _1541952, _1541946), _1541944) = hAPP(_1541950, _1541944))], (48025 ^ _781215) ^ [_1748545, _1748547] : [-(c_List_Omeasures(_1748545, _1748547) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1748545), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1748545, tc_List_Olist(tc_fun(_1748545, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1748545, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1748545, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1748545), c_List_Omap(tc_fun(_1748545, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1748545, tc_Nat_Onat), _1748545, tc_Nat_Onat), c_COMBI(tc_fun(_1748545, tc_Nat_Onat))))), _1748547)))], (12352 ^ _781215) ^ [_996053, _996055, _996057] : [class_Rings_Oordered__cancel__semiring(_996053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996053), c_Groups_Ozero__class_Ozero(_996053)), _996055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996053), _996057), c_Groups_Ozero__class_Ozero(_996053))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996053), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996053), _996057), _996055)), c_Groups_Ozero__class_Ozero(_996053))))], (43181 ^ _781215) ^ [_1641282, _1641284, _1641286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1641282, _1641282), tc_HOL_Obool)), _1641284), _1641286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1641282), tc_List_Olist(_1641282)), tc_HOL_Obool)), c_List_Olistrel1(_1641282, _1641284)), c_List_Olistrel1(_1641282, _1641286))))], (41337 ^ _781215) ^ [_1593485, _1593487, _1593489, _1593491, _1593493, _1593495] : [c_Fun_Oinj__on(_1593485, _1593487, hAPP(c_Fun_Ocomp(_1593489, _1593487, _1593485, _1593491), _1593493), _1593495), -(c_Fun_Oinj__on(_1593489, _1593487, _1593491, hAPP(c_Set_Oimage(_1593485, _1593489, _1593493), _1593495)))], (21952 ^ _781215) ^ [_1176211] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176211), 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), _1176211), _1176211))], (7915 ^ _781215) ^ [_914927, _914929] : [-(_914927 = _914929), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914927), _914929))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914929), _914927)))], (25322 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (15426 ^ _781215) ^ [_1051697, _1051699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051697), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1051699), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051697), _1051699)))], (47549 ^ _781215) ^ [_1738000, _1738002, _1738004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1738000, tc_HOL_Obool)), _1738002), _1738004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1738000), tc_HOL_Obool)), c_List_Olistsp(_1738000, _1738002)), c_List_Olistsp(_1738000, _1738004))))], (43387 ^ _781215) ^ [_1646919, _1646921, _1646923] : [-(c_List_Olist_Olist__size(_1646919, _1646921, _1646923) = 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(_1646919, tc_Nat_Onat), _1646921), _1646923))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646919)), _1646923)))], (13111 ^ _781215) ^ [_1009511, _1009513] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009511), hAPP(c_Nat_OSuc, _1009513)))), 13112 ^ _781215 : [(13115 ^ _781215) ^ [_1009599] : [_1009511 = hAPP(c_Nat_OSuc, _1009599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009599), _1009513))], (13113 ^ _781215) ^ [] : [_1009511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (50238 ^ _781215) ^ [_1801995, _1801997, _1801999] : [hBOOL(hAPP(hAPP(c_member(_1801995), _1801997), hAPP(c_List_Oset(_1801995), _1801999))), 50243 ^ _781215 : [(50246 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1801995), _1801997), hAPP(c_List_Oset(_1801995), 50242 ^ [_1801995, _1801997, _1801999])))], (50244 ^ _781215) ^ [] : [-(_1801999 = hAPP(hAPP(c_List_Oappend(_1801995), 50241 ^ [_1801995, _1801997, _1801999]), hAPP(hAPP(c_List_Olist_OCons(_1801995), _1801997), 50242 ^ [_1801995, _1801997, _1801999])))]]], (840 ^ _781215) ^ [_794201, _794203, _794205, _794207, _794209, _794211] : [-(c_Relation_Orefl__on(_794209, _794205, _794201)), c_Relation_Orefl__on(_794211, _794207, _794203), _794211 = _794209, _794207 = _794205, _794203 = _794201], (12034 ^ _781215) ^ [_990125, _990127, _990129, _990131, _990133] : [hBOOL(hAPP(hAPP(c_member(_990125), _990127), _990129)), -(hAPP(hAPP(c_Set_Oinsert(_990131), hAPP(_990133, _990127)), hAPP(c_Set_Oimage(_990125, _990131, _990133), _990129)) = hAPP(c_Set_Oimage(_990125, _990131, _990133), _990129))], (5136 ^ _781215) ^ [_859523, _859525, _859527, _859529, _859531, _859533, _859535, _859537] : [-(c_New__Random__Sequence_Oneg__map(_859537, _859533, _859529, _859525) = c_New__Random__Sequence_Oneg__map(_859535, _859531, _859527, _859523)), _859537 = _859535, _859533 = _859531, _859529 = _859527, _859525 = _859523], (49395 ^ _781215) ^ [_1780124] : [-(c_Transitive__Closure_Ortrancl(_1780124, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1780124, _1780124), tc_HOL_Obool))) = c_Relation_OId(_1780124))], (42453 ^ _781215) ^ [_1622079, _1622081, _1622083] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622079)), hAPP(hAPP(c_List_Olist_OCons(_1622079), _1622081), _1622083)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622079)), _1622083)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50204 ^ _781215) ^ [_1801102, _1801104, _1801106] : [hBOOL(hAPP(hAPP(c_member(_1801102), _1801104), hAPP(c_List_Oset(_1801102), _1801106))), -(_1801106 = hAPP(hAPP(c_List_Oappend(_1801102), 50207 ^ [_1801102, _1801104, _1801106]), hAPP(hAPP(c_List_Olist_OCons(_1801102), _1801104), 50208 ^ [_1801102, _1801104, _1801106])))], (20695 ^ _781215) ^ [_1152459, _1152461] : [class_Rings_Osemiring__1(_1152459), -(hBOOL(hAPP(hAPP(c_member(_1152459), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1152459), _1152461)), c_Nat_Osemiring__1__class_ONats(_1152459))))], (37482 ^ _781215) ^ [_1493041, _1493043, _1493045, _1493047] : [hBOOL(hAPP(hAPP(c_member(_1493041), _1493043), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1493041, tc_HOL_Obool), _1493045))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1493041, tc_HOL_Obool)), _1493047), _1493045)), -(hBOOL(hAPP(hAPP(c_member(_1493041), _1493043), _1493047)))], (33597 ^ _781215) ^ [_1407363, _1407365, _1407367, _1407369, _1407371, _1407373, _1407375, _1407377] : [c_Finite__Set_Ofolding__image__simple(_1407363, _1407365, _1407367, _1407369, _1407371, _1407373), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407365), _1407375)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407365), _1407377)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407365, tc_HOL_Obool)), _1407375), _1407377) = c_Orderings_Obot__class_Obot(tc_fun(_1407365, tc_HOL_Obool)), -(hAPP(_1407373, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407365, tc_HOL_Obool)), _1407375), _1407377)) = hAPP(hAPP(_1407367, hAPP(_1407373, _1407375)), hAPP(_1407373, _1407377)))], (42993 ^ _781215) ^ [_1636885, _1636887, _1636889, _1636891] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636885, tc_HOL_Obool)), hAPP(c_List_Oset(_1636885), hAPP(hAPP(c_List_Olist__update(_1636885, _1636887), _1636889), _1636891))), hAPP(hAPP(c_Set_Oinsert(_1636885), _1636891), hAPP(c_List_Oset(_1636885), _1636887)))))], (18699 ^ _781215) ^ [_1116346, _1116348] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1116346)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1116348)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1116348))), 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, _1116346))), 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), _1116346)), c_Int_Onat)))))], (22454 ^ _781215) ^ [_1186836, _1186838, _1186840] : [class_Divides_Osemiring__div(_1186836), -(c_Divides_Odiv__class_Omod(_1186836, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186836), _1186838), _1186840), _1186838) = c_Groups_Ozero__class_Ozero(_1186836))], (51226 ^ _781215) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (28902 ^ _781215) ^ [_1308145, _1308147, _1308149] : [class_Fields_Ofield__inverse__zero(_1308145), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308145), hAPP(c_Groups_Ouminus__class_Ouminus(_1308145), _1308147)), hAPP(c_Groups_Ouminus__class_Ouminus(_1308145), _1308149)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308145), _1308147), _1308149))], (31529 ^ _781215) ^ [_1360335, _1360337, _1360339, _1360341, _1360343, _1360345] : [class_Groups_Ocomm__monoid__add(_1360335), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360337, _1360335), hAPP(hAPP(c_COMBC(_1360337, tc_fun(_1360339, tc_HOL_Obool), _1360335), hAPP(hAPP(c_COMBB(tc_fun(_1360339, _1360335), tc_fun(tc_fun(_1360339, tc_HOL_Obool), _1360335), _1360337), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360339, _1360335)), _1360341)), _1360343)), _1360345) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360339, _1360335), hAPP(hAPP(c_COMBC(_1360339, tc_fun(_1360337, tc_HOL_Obool), _1360335), hAPP(hAPP(c_COMBB(tc_fun(_1360337, _1360335), tc_fun(tc_fun(_1360337, tc_HOL_Obool), _1360335), _1360339), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360337, _1360335)), hAPP(c_COMBC(_1360337, _1360339, _1360335), _1360341))), _1360345)), _1360343))], (31158 ^ _781215) ^ [_1351692, _1351694] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1351692), _1351694))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1351692), hAPP(c_Nat_OSuc, _1351694)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (46407 ^ _781215) ^ [_1713581, _1713583, _1713585, _1713587] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1713581)), c_List_Otranspose__rel(_1713581)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1713581)), hAPP(hAPP(c_List_Olist_OCons(_1713581), _1713583), _1713585)), _1713587))), -(c_List_Otranspose(_1713581, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1713581)), hAPP(hAPP(c_List_Olist_OCons(_1713581), _1713583), _1713585)), _1713587)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1713581)), hAPP(hAPP(c_List_Olist_OCons(_1713581), _1713583), c_List_Oconcat(_1713581, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1713581), tc_List_Olist(_1713581)), c_List_Olist_Olist__case(tc_List_Olist(_1713581), _1713581, c_List_Olist_ONil(_1713581), hAPP(hAPP(c_COMBB(tc_List_Olist(_1713581), tc_fun(tc_List_Olist(_1713581), tc_List_Olist(_1713581)), _1713581), c_COMBK(tc_List_Olist(_1713581), tc_List_Olist(_1713581))), hAPP(hAPP(c_COMBC(_1713581, tc_List_Olist(_1713581), tc_List_Olist(_1713581)), c_List_Olist_OCons(_1713581)), c_List_Olist_ONil(_1713581))))), _1713587)))), c_List_Otranspose(_1713581, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1713581)), _1713585), c_List_Oconcat(tc_List_Olist(_1713581), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1713581), tc_List_Olist(tc_List_Olist(_1713581))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1713581)), _1713581, c_List_Olist_ONil(tc_List_Olist(_1713581)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1713581), tc_List_Olist(tc_List_Olist(_1713581))), _1713581), hAPP(hAPP(c_COMBC(tc_List_Olist(_1713581), tc_List_Olist(tc_List_Olist(_1713581)), tc_List_Olist(tc_List_Olist(_1713581))), c_List_Olist_OCons(tc_List_Olist(_1713581))), c_List_Olist_ONil(tc_List_Olist(_1713581)))))), _1713587))))))], (11370 ^ _781215) ^ [_979283, _979285, _979287] : [class_Groups_Oab__semigroup__mult(_979283), -(_979285 = c_Orderings_Obot__class_Obot(tc_fun(_979283, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_979283), _979285)), -(hBOOL(hAPP(hAPP(c_member(_979283), _979287), _979285))), -(hAPP(c_Finite__Set_Ofold1(_979283, c_Groups_Otimes__class_Otimes(_979283)), hAPP(hAPP(c_Set_Oinsert(_979283), _979287), _979285)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979283), _979287), hAPP(c_Finite__Set_Ofold1(_979283, c_Groups_Otimes__class_Otimes(_979283)), _979285)))], (46498 ^ _781215) ^ [_1716351, _1716353, _1716355] : [-(c_List_OtakeWhile(_1716351, _1716353, _1716355) = hAPP(hAPP(c_List_Otake(_1716351), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716351)), c_List_OtakeWhile(_1716351, _1716353, _1716355))), _1716355))], (31626 ^ _781215) ^ [_1362678, _1362680, _1362682, _1362684, _1362686] : [class_Groups_Ocomm__monoid__add(_1362678), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362680), _1362682)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362680, _1362678), hAPP(hAPP(c_COMBS(_1362680, _1362678, _1362678), hAPP(hAPP(c_COMBB(_1362678, tc_fun(_1362678, _1362678), _1362680), c_Groups_Oplus__class_Oplus(_1362678)), _1362684)), _1362686)), _1362682) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362678), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362680, _1362678), _1362684), _1362682)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362680, _1362678), _1362686), _1362682)))], (25218 ^ _781215) ^ [_1236251] : [c_Int_OMin = c_Int_OBit1(_1236251), -(c_Int_OMin = _1236251)], (31407 ^ _781215) ^ [_1356746, _1356748] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1356746), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1356748) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1356746, _1356748))], (44274 ^ _781215) ^ [_1666646, _1666648, _1666650, _1666652] : [_1666648 = _1666652, -(hAPP(hAPP(c_List_Oappend(_1666646), _1666648), _1666650) = hAPP(hAPP(c_List_Oappend(_1666646), _1666652), _1666650))], (40085 ^ _781215) ^ [_1563667, _1563669, _1563671] : [c_Wellfounded_Owf(_1563667, _1563669), -(hBOOL(hAPP(hAPP(c_member(_1563667), _1563671), c_Wellfounded_Oacc(_1563667, _1563669))))], (6427 ^ _781215) ^ [_885838, _885840, _885842, _885844] : [-(hBOOL(hAPP(hAPP(c_member(_885838), _885840), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_885838, tc_HOL_Obool)), _885842), _885844)))), hBOOL(hAPP(hAPP(c_member(_885838), _885840), _885842)), -(hBOOL(hAPP(hAPP(c_member(_885838), _885840), _885844)))], (43732 ^ _781215) ^ [_1654589, _1654591] : [-(hAPP(hAPP(c_List_Otake(_1654589), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1654591) = c_List_Olist_ONil(_1654589))], (16495 ^ _781215) ^ [_1075122, _1075124, _1075126] : [-(hAPP(hAPP(c_Set_Oinsert(_1075122), _1075124), _1075126) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1075122, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1075122), _1075124), c_Orderings_Obot__class_Obot(tc_fun(_1075122, tc_HOL_Obool)))), _1075126))], (20804 ^ _781215) ^ [_1154237, _1154239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1154237)), _1154239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1154237), hAPP(c_Int_Onat, _1154239))))], (25324 ^ _781215) ^ [_1237699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1237699)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237699), c_Int_OMin)))], (50766 ^ _781215) ^ [_1813147, _1813149, _1813151, _1813153, _1813155] : [-(_1813147 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1813149, _1813151, _1813153, _1813155), _1813147) = hAPP(c_Lazy__Sequence_Obind(_1813149, _1813151, hAPP(_1813153, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1813147), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1813149, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1813151)), _1813155), _1813147)))], (13330 ^ _781215) ^ [_1013030, _1013032] : [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), _1013030), _1013032))), 13333 ^ _781215 : [(13336 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1013032)))], (13334 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1013030)))]]], (36712 ^ _781215) ^ [_1471481, _1471483] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1471481), c_Orderings_Otop__class_Otop(tc_fun(_1471481, tc_HOL_Obool)))), c_Fun_Oinj__on(_1471481, _1471481, _1471483, c_Orderings_Otop__class_Otop(tc_fun(_1471481, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1471481, _1471481, _1471483), c_Orderings_Otop__class_Otop(tc_fun(_1471481, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1471481, tc_HOL_Obool)))], (30185 ^ _781215) ^ [_1333572, _1333574] : [c_Nat__Transfer_Ois__nat(_1333572), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1333572, _1333574)))], (42319 ^ _781215) ^ [_1619258, _1619260, _1619262, _1619264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619258)), _1619260)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619258)), _1619262))), _1619260 = hAPP(hAPP(c_List_Olist_OCons(_1619258), _1619264), _1619262)], (49139 ^ _781215) ^ [_1772921, _1772923, _1772925, _1772927, _1772929] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1772921, _1772921)), hAPP(hAPP(c_Product__Type_OPair(_1772921, _1772921), _1772923), _1772925)), c_Transitive__Closure_Otrancl(_1772921, _1772927))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772921, _1772921)), hAPP(hAPP(c_Product__Type_OPair(_1772921, _1772921), _1772925), _1772929)), c_Transitive__Closure_Otrancl(_1772921, _1772927))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1772921, _1772921)), hAPP(hAPP(c_Product__Type_OPair(_1772921, _1772921), _1772923), _1772929)), c_Transitive__Closure_Otrancl(_1772921, _1772927))))], (45221 ^ _781215) ^ [_1688273, _1688275, _1688277] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688273)), _1688275), c_List_Olists(_1688273, _1688277))), -(_1688275 = c_List_Olist_ONil(_1688273)), 45230 ^ _781215 : [(45235 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688273)), 45229 ^ [_1688273, _1688275, _1688277]), c_List_Olists(_1688273, _1688277))))], (45233 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1688273), 45228 ^ [_1688273, _1688275, _1688277]), _1688277)))], (45231 ^ _781215) ^ [] : [-(_1688275 = hAPP(hAPP(c_List_Olist_OCons(_1688273), 45228 ^ [_1688273, _1688275, _1688277]), 45229 ^ [_1688273, _1688275, _1688277]))]]], (24906 ^ _781215) ^ [_1230666, _1230668, _1230670, _1230672] : [class_Rings_Olinordered__semidom(_1230666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230666), hAPP(hAPP(c_Power_Opower__class_Opower(_1230666), _1230668), _1230670)), hAPP(hAPP(c_Power_Opower__class_Opower(_1230666), _1230672), _1230670))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230666), c_Groups_Ozero__class_Ozero(_1230666)), _1230672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230666), _1230668), _1230672)))], (27390 ^ _781215) ^ [_1279539, _1279541, _1279543, _1279545] : [-(hAPP(c_Product__Type_Ofst(_1279539, _1279541), hAPP(hAPP(c_Product__Type_OPair(_1279539, _1279541), _1279543), _1279545)) = _1279543)], (50019 ^ _781215) ^ [_1795983, _1795985, _1795987, _1795989] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1795983, _1795983)), _1795985), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1795983, _1795983), tc_HOL_Obool), _1795987), _1795989))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1795983, _1795983)), _1795985), c_Transitive__Closure_Ortrancl(_1795983, _1795989))))], (39949 ^ _781215) ^ [_1561279] : [-(c_Wellfounded_Owf(_1561279, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1561279, _1561279), tc_HOL_Obool))))], (30558 ^ _781215) ^ [_1340331, _1340333, _1340335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340331)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1340333), _1340335)), 30565 ^ _781215 : [(30566 ^ _781215) ^ [_1340521] : [30568 ^ _781215 : [(30574 ^ _781215) ^ [] : [-(_1340521 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30570 ^ [_1340331, _1340333, _1340335, _1340521]), 30567 ^ [_1340331, _1340333, _1340335, _1340521]))], (30572 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30570 ^ [_1340331, _1340333, _1340335, _1340521]), _1340335)))], (30569 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30567 ^ [_1340331, _1340333, _1340335, _1340521]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1340331))))]], -(_1340521 = _1340333), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1340521), _1340331) = _1340333]]], (44988 ^ _781215) ^ [_1683709, _1683711] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1683709), _1683711) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44991 ^ _781215 : [(44994 ^ _781215) ^ [_1683823] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1683823), hAPP(c_List_Oset(tc_Nat_Onat), _1683711))), -(_1683823 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44992 ^ _781215) ^ [] : [-(_1683709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (41202 ^ _781215) ^ [_1590156, _1590158, _1590160, _1590162, _1590164] : [hBOOL(hAPP(c_List_Odistinct(_1590156), hAPP(hAPP(c_List_Omap(tc_prod(_1590156, _1590158), _1590156), c_Product__Type_Ofst(_1590156, _1590158)), _1590160))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590156, _1590158)), hAPP(hAPP(c_Product__Type_OPair(_1590156, _1590158), _1590162), _1590164)), hAPP(c_List_Oset(tc_prod(_1590156, _1590158)), _1590160))), -(hAPP(hAPP(c_Map_Omap__of(_1590156, _1590158), _1590160), _1590162) = hAPP(c_Option_Ooption_OSome(_1590158), _1590164))], (50108 ^ _781215) ^ [_1798305, _1798307, _1798309, _1798311, _1798313] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1798305, _1798305)), hAPP(hAPP(c_Product__Type_OPair(_1798305, _1798305), _1798307), _1798309)), c_Transitive__Closure_Ortrancl(_1798305, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1798305, _1798305), tc_HOL_Obool)), _1798311), _1798313)))), 50114 ^ _781215 : [(50120 ^ _781215) ^ [] : [50113 ^ [_1798305, _1798307, _1798309, _1798311, _1798313] = 50116 ^ [_1798305, _1798307, _1798309, _1798311, _1798313]], (50118 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1798305, _1798305)), hAPP(hAPP(c_Product__Type_OPair(_1798305, _1798305), 50113 ^ [_1798305, _1798307, _1798309, _1798311, _1798313]), 50116 ^ [_1798305, _1798307, _1798309, _1798311, _1798313])), _1798313)))], (50115 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1798305, _1798305)), hAPP(hAPP(c_Product__Type_OPair(_1798305, _1798305), _1798307), 50113 ^ [_1798305, _1798307, _1798309, _1798311, _1798313])), c_Transitive__Closure_Ortrancl(_1798305, _1798311))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1798305, _1798305)), hAPP(hAPP(c_Product__Type_OPair(_1798305, _1798305), _1798307), _1798309)), c_Transitive__Closure_Ortrancl(_1798305, _1798311))))], (15080 ^ _781215) ^ [_1045998, _1046000] : [class_Rings_Olinordered__idom(_1045998), 15083 ^ _781215 : [(15090 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045998), c_Groups_Ozero__class_Ozero(_1045998)), _1046000)), -(c_Groups_Osgn__class_Osgn(_1045998, _1046000) = c_Groups_Oone__class_Oone(_1045998))], (15084 ^ _781215) ^ [] : [c_Groups_Osgn__class_Osgn(_1045998, _1046000) = c_Groups_Oone__class_Oone(_1045998), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045998), c_Groups_Ozero__class_Ozero(_1045998)), _1046000)))]]], (41020 ^ _781215) ^ [_1585947, _1585949, _1585951, _1585953, _1585955] : [41022 ^ _781215 : [(41025 ^ _781215) ^ [] : [hAPP(_1585951, 41021 ^ [_1585947, _1585949, _1585951, _1585953, _1585955]) = hAPP(_1585955, 41021 ^ [_1585947, _1585949, _1585951, _1585953, _1585955])], (41023 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1585947), 41021 ^ [_1585947, _1585949, _1585951, _1585953, _1585955]), hAPP(c_List_Oset(_1585947), _1585953))))]], -(hAPP(hAPP(c_List_Omap(_1585947, _1585949), _1585951), _1585953) = hAPP(hAPP(c_List_Omap(_1585947, _1585949), _1585955), _1585953))], (43333 ^ _781215) ^ [_1645358, _1645360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645358), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1645360))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1645360), _1645358)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1645360))))], (24856 ^ _781215) ^ [_1229718, _1229720, _1229722, _1229724] : [class_Rings_Olinordered__semidom(_1229718), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229718), c_Groups_Oone__class_Oone(_1229718)), _1229720)), 24863 ^ _781215 : [(24870 ^ _781215) ^ [] : [_1229722 = _1229724, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1229718), _1229720), _1229722) = hAPP(hAPP(c_Power_Opower__class_Opower(_1229718), _1229720), _1229724))], (24864 ^ _781215) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1229718), _1229720), _1229722) = hAPP(hAPP(c_Power_Opower__class_Opower(_1229718), _1229720), _1229724), -(_1229722 = _1229724)]]], (46562 ^ _781215) ^ [_1717511, _1717513] : [-(_1717511 = c_List_Olist_ONil(_1717513)), hBOOL(hAPP(c_List_Odistinct(_1717513), _1717511)), -(c_List_OtakeWhile(_1717513, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1717513), c_fNot), hAPP(hAPP(c_COMBC(_1717513, _1717513, tc_HOL_Obool), c_fequal), c_List_Olast(_1717513, _1717511))), _1717511) = c_List_Obutlast(_1717513, _1717511))], (14744 ^ _781215) ^ [_1039296, _1039298, _1039300] : [class_Int_Onumber__ring(_1039296), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039296), hAPP(c_Int_Onumber__class_Onumber__of(_1039296), _1039298)), hAPP(c_Int_Onumber__class_Onumber__of(_1039296), _1039300)) = hAPP(c_Int_Onumber__class_Onumber__of(_1039296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1039298), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1039300))))], (48938 ^ _781215) ^ [_1769029, _1769031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1769029)), -(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(_1769029), _1769031))), _1769029)))], (6998 ^ _781215) ^ [_897310, _897312, _897314, _897316, _897318] : [hAPP(_897310, _897312) = hAPP(c_Option_Ooption_OSome(_897314), _897316), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_897318, tc_Option_Ooption(_897314)), _897310), _897312), hAPP(c_Option_Ooption_OSome(_897314), _897316)) = _897310)], (12796 ^ _781215) ^ [_1004112, _1004114, _1004116, _1004118] : [class_Rings_Olinordered__ring__strict(_1004112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004112), _1004114), _1004116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004112), _1004118), c_Groups_Ozero__class_Ozero(_1004112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004112), _1004116), _1004118)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004112), _1004114), _1004118))))], (49409 ^ _781215) ^ [_1780370, _1780372, _1780374] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1780370, _1780370, _1780372), c_Relation_OId(_1780370)), _1780374) = _1780374)], (29466 ^ _781215) ^ [_1318260, _1318262, _1318264, _1318266] : [class_Fields_Olinordered__field(_1318260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318260), c_Groups_Ozero__class_Ozero(_1318260)), _1318262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318260), _1318264), _1318262)), _1318266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318260), _1318264), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318260), _1318266), _1318262))))], (44610 ^ _781215) ^ [_1675362, _1675364, _1675366, _1675368] : [-(hAPP(hAPP(c_List_Odrop(_1675362), hAPP(c_Nat_OSuc, _1675364)), hAPP(hAPP(c_List_Olist_OCons(_1675362), _1675366), _1675368)) = hAPP(hAPP(c_List_Odrop(_1675362), _1675364), _1675368))], (42873 ^ _781215) ^ [_1633788, _1633790, _1633792, _1633794] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633788), tc_List_Olist(_1633788))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633788), tc_List_Olist(_1633788)), _1633790), _1633792)), c_List_Olexord(_1633788, _1633794)))), 42874 ^ _781215 : [(42881 ^ _781215) ^ [_1634095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634095), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633788)), _1633790)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633788)), _1633792)))), hAPP(hAPP(c_List_Otake(_1633788), _1634095), _1633790) = hAPP(hAPP(c_List_Otake(_1633788), _1634095), _1633792), hBOOL(hAPP(hAPP(c_member(tc_prod(_1633788, _1633788)), hAPP(hAPP(c_Product__Type_OPair(_1633788, _1633788), hAPP(hAPP(c_List_Onth(_1633788), _1633790), _1634095)), hAPP(hAPP(c_List_Onth(_1633788), _1633792), _1634095))), _1633794))], (42875 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633788)), _1633790)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633788)), _1633792))), hAPP(hAPP(c_List_Otake(_1633788), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633788)), _1633790)), _1633792) = _1633790]]], (14702 ^ _781215) ^ [_1038283, _1038285, _1038287] : [class_Int_Onumber__ring(_1038283), -(hAPP(c_Int_Onumber__class_Onumber__of(_1038283), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1038285), _1038287)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038283), hAPP(c_Int_Onumber__class_Onumber__of(_1038283), _1038285)), hAPP(c_Int_Onumber__class_Onumber__of(_1038283), _1038287)))], (24722 ^ _781215) ^ [_1227318, _1227320, _1227322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1227318), _1227320)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1227318), _1227322))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227320), _1227322)))], (30145 ^ _781215) ^ [_1332692, _1332694, _1332696, _1332698, _1332700] : [hAPP(c_Set_Oimage(_1332692, _1332694, _1332696), _1332698) = _1332700, -(hAPP(c_Set_Oimage(tc_fun(_1332692, tc_HOL_Obool), tc_fun(_1332694, tc_HOL_Obool), c_Set_Oimage(_1332692, _1332694, _1332696)), hAPP(c_Set_OPow(_1332692), _1332698)) = hAPP(c_Set_OPow(_1332694), _1332700))], (15713 ^ _781215) ^ [_1057604, _1057606, _1057608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057604)), _1057604 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1057606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1057604), _1057608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057606), _1057604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1057608)))], (21009 ^ _781215) ^ [] : [-(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)))], (18245 ^ _781215) ^ [_1107846, _1107848, _1107850] : [class_Orderings_Olinorder(_1107846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107846), _1107848), _1107850)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1107846), _1107848), _1107850) = _1107848)], (20579 ^ _781215) ^ [_1150545, _1150547, _1150549] : [class_Rings_Olinordered__semidom(_1150545), 20582 ^ _781215 : [(20589 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150547), _1150549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150545), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150545), _1150547)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150545), _1150549))))], (20583 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150545), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150545), _1150547)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150545), _1150549))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150547), _1150549)))]]], (11549 ^ _781215) ^ [_982657, _982659, _982661, _982663] : [c_Orderings_Obot__class_Obot(tc_fun(_982657, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_982659, _982657, _982661), _982663), -(_982663 = c_Orderings_Obot__class_Obot(tc_fun(_982659, tc_HOL_Obool)))], (45349 ^ _781215) ^ [_1691011, _1691013, _1691015, _1691017, _1691019] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691011)), hAPP(c_List_Ofilter(_1691011, _1691013), hAPP(hAPP(c_List_Omap(_1691015, _1691011), _1691017), _1691019))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691015)), hAPP(c_List_Ofilter(_1691015, hAPP(c_Fun_Ocomp(_1691011, tc_HOL_Obool, _1691015, _1691013), _1691017)), _1691019)))], (44226 ^ _781215) ^ [_1665503, _1665505, _1665507, _1665509, _1665511, _1665513] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665503)), _1665505) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665507)), _1665509), -(c_Map_Omap__upds(_1665503, _1665507, _1665511, _1665505, hAPP(hAPP(c_List_Oappend(_1665507), _1665509), _1665513)) = c_Map_Omap__upds(_1665503, _1665507, _1665511, _1665505, _1665509))], (50070 ^ _781215) ^ [_1797216, _1797218] : [-(c_List_Orotate(_1797216, _1797218) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1797216), tc_List_Olist(_1797216)), _1797218), c_List_Orotate1(_1797216)))], (22332 ^ _781215) ^ [_1184376, _1184378, _1184380, _1184382] : [class_Divides_Osemiring__div(_1184376), -(c_Divides_Odiv__class_Omod(_1184376, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184376), _1184378), _1184380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184376), _1184382), _1184380)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184376), c_Divides_Odiv__class_Omod(_1184376, _1184378, _1184382)), _1184380))], (39610 ^ _781215) ^ [_1549586, _1549588] : [c_Predicate_Oreflp(_1549586, _1549588), -(c_Relation_Orefl__on(_1549586, c_Orderings_Otop__class_Otop(tc_fun(_1549586, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1549586, _1549586)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549586, _1549586, tc_HOL_Obool), _1549588))))], (26968 ^ _781215) ^ [_1271436, _1271438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1271436)), 26971 ^ _781215 : [(26978 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1271438))), 26981 ^ _781215 : [(26988 ^ _781215) ^ [] : [-(_1271436 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1271436, _1271438) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1271436), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1271438))))], (26982 ^ _781215) ^ [] : [_1271436 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1271436, _1271438) = 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)))]]], (26972 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1271438)), -(c_Divides_Odivmod__int(_1271436, _1271438) = c_Divides_OposDivAlg(_1271436, _1271438))]]], (16475 ^ _781215) ^ [_1072869, _1072871, _1072873] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072869, tc_HOL_Obool)), _1072871), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1072869, tc_HOL_Obool)), _1072873), _1072871)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072869, tc_HOL_Obool)), _1072871), _1072873))], (34642 ^ _781215) ^ [_1430190, _1430192, _1430194, _1430196, _1430198, _1430200] : [c_Fun_Oinj__on(_1430190, _1430192, _1430194, _1430196), -(_1430198 = _1430200), hBOOL(hAPP(hAPP(c_member(_1430190), _1430198), _1430196)), hBOOL(hAPP(hAPP(c_member(_1430190), _1430200), _1430196)), hAPP(_1430194, _1430198) = hAPP(_1430194, _1430200)], (45095 ^ _781215) ^ [_1686266, _1686268, _1686270] : [45096 ^ _781215 : [(45097 ^ _781215) ^ [_1686355, _1686357] : [_1686268 = hAPP(hAPP(c_List_Olist_OCons(_1686266), _1686357), _1686355)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1686266), tc_List_Olist(_1686266))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1686266), tc_List_Olist(_1686266)), c_List_Olist_ONil(_1686266)), _1686268)), c_List_Olexord(_1686266, _1686270))))], (38632 ^ _781215) ^ [_1520296, _1520298, _1520300, _1520302] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1520296, _1520298)), hAPP(hAPP(c_Product__Type_OSigma(_1520296, _1520298), _1520300), hAPP(c_COMBK(tc_fun(_1520298, tc_HOL_Obool), _1520296), _1520302)))), -(_1520302 = c_Orderings_Obot__class_Obot(tc_fun(_1520298, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1520296), _1520300)))], (2088 ^ _781215) ^ [_811761, _811763, _811765, _811767] : [-(c_Orderings_Oord_Omax(_811767, _811763) = c_Orderings_Oord_Omax(_811765, _811761)), _811767 = _811765, _811763 = _811761], (49682 ^ _781215) ^ [_1787676, _1787678, _1787680, _1787682, _1787684] : [-(hAPP(c_Relation_Oconverse(_1787676, _1787678), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1787680, tc_fun(tc_prod(_1787676, _1787678), tc_HOL_Obool)), _1787682), _1787684)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1787680, tc_fun(tc_prod(_1787678, _1787676), tc_HOL_Obool)), _1787682), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1787676, _1787678), tc_HOL_Obool), tc_fun(tc_prod(_1787678, _1787676), tc_HOL_Obool), _1787680), c_Relation_Oconverse(_1787676, _1787678)), _1787684)))], (17081 ^ _781215) ^ [_1087515, _1087517, _1087519] : [class_Lattices_Olattice(_1087515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087515), _1087517)), hBOOL(hAPP(hAPP(c_member(_1087515), _1087519), _1087517)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1087515), _1087519), c_Big__Operators_Olattice__class_OSup__fin(_1087515, _1087517)) = c_Big__Operators_Olattice__class_OSup__fin(_1087515, _1087517))], (15284 ^ _781215) ^ [_1049310] : [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)), _1049310)), _1049310) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (6539 ^ _781215) ^ [_887916, _887918, _887920, _887922, _887924] : [c_Finite__Set_Ofolding__one__idem(_887916, _887918, _887920), hBOOL(hAPP(c_Finite__Set_Ofinite(_887916), _887922)), hBOOL(hAPP(hAPP(c_member(_887916), _887924), _887922)), -(hAPP(hAPP(_887918, _887924), hAPP(_887920, _887922)) = hAPP(_887920, _887922))], (50315 ^ _781215) ^ [_1803986, _1803988, _1803990, _1803992, _1803994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803986, tc_HOL_Obool)), _1803988), _1803990)), 50321 ^ _781215 : [(50326 ^ _781215) ^ [] : [hBOOL(hAPP(_1803994, 50320 ^ [_1803986, _1803988, _1803990, _1803992, _1803994]))], (50324 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1803992, 50320 ^ [_1803986, _1803988, _1803990, _1803992, _1803994])))], (50322 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803986), 50320 ^ [_1803986, _1803988, _1803990, _1803992, _1803994]), _1803988)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803986, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803986, tc_HOL_Obool)), _1803988), hAPP(c_Set_OCollect(_1803986), _1803992))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803986, tc_HOL_Obool)), _1803990), hAPP(c_Set_OCollect(_1803986), _1803994)))))], (42670 ^ _781215) ^ [_1628557, _1628559, _1628561] : [42672 ^ _781215 : [(42675 ^ _781215) ^ [] : [hBOOL(hAPP(_1628561, 42671 ^ [_1628557, _1628559, _1628561]))], (42673 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1628557), 42671 ^ [_1628557, _1628559, _1628561]), hAPP(c_List_Oset(_1628557), _1628559))))]], 42676 ^ _781215 : [(42677 ^ _781215) ^ [_1628741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628741), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628557)), _1628559))), -(hBOOL(hAPP(_1628561, hAPP(hAPP(c_List_Onth(_1628557), _1628559), _1628741))))]]], (39070 ^ _781215) ^ [_1531283, _1531285, _1531287] : [hBOOL(hAPP(hAPP(c_member(_1531283), _1531285), hAPP(c_Set_OCollect(_1531283), _1531287))), -(hBOOL(hAPP(_1531287, _1531285)))], (10496 ^ _781215) ^ [_960555, _960557, _960559, _960561, _960563] : [class_Groups_Oordered__cancel__ab__semigroup__add(_960555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960555), _960557), _960559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960555), _960561), _960563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960555), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960555), _960557), _960561)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960555), _960559), _960563))))], (5676 ^ _781215) ^ [_870869, _870871, _870873, _870875, _870877] : [-(hAPP(hAPP(c_Set_Oinsert(_870869), _870871), hAPP(hAPP(c_Set_Oinsert(_870869), _870873), c_Orderings_Obot__class_Obot(tc_fun(_870869, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_870869), _870875), hAPP(hAPP(c_Set_Oinsert(_870869), _870877), c_Orderings_Obot__class_Obot(tc_fun(_870869, tc_HOL_Obool))))), 5677 ^ _781215 : [(5684 ^ _781215) ^ [] : [_870871 = _870877, _870873 = _870875], (5678 ^ _781215) ^ [] : [_870871 = _870875, _870873 = _870877]]], (39649 ^ _781215) ^ [_1551809, _1551811] : [-(c_Fun_Oinj__on(_1551809, _1551809, c_Fun_Oid(_1551809), _1551811))], (37643 ^ _781215) ^ [_1496533, _1496535, _1496537] : [class_Complete__Lattice_Ocomplete__lattice(_1496533), -(c_Complete__Lattice_OInf__class_OInf(_1496533, hAPP(hAPP(c_Set_Oinsert(_1496533), _1496535), hAPP(hAPP(c_Set_Oinsert(_1496533), _1496537), c_Orderings_Obot__class_Obot(tc_fun(_1496533, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1496533), _1496535), _1496537))], (36566 ^ _781215) ^ [_1468425] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468425, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1468425, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1468425, tc_HOL_Obool)))], (7881 ^ _781215) ^ [_914340, _914342, _914344] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_914340), _914342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_914340, tc_HOL_Obool)), _914344), _914342)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_914340), _914344)), hAPP(c_Finite__Set_Ocard(_914340), _914342))))], (38488 ^ _781215) ^ [_1516112, _1516114, _1516116, _1516118] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1516112, _1516114)), hAPP(hAPP(c_Product__Type_OSigma(_1516112, _1516114), _1516116), hAPP(c_COMBK(tc_fun(_1516114, tc_HOL_Obool), _1516112), _1516118))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1516112), _1516116)), hAPP(c_Finite__Set_Ocard(_1516114), _1516118)))], (14954 ^ _781215) ^ [_1043416, _1043418, _1043420] : [class_Int_Onumber(_1043416), class_Orderings_Olinorder(_1043416), 14961 ^ _781215 : [(14968 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043416), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043420)), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043418)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043416), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043418)), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043420))))], (14962 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043416), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043418)), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043420))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1043416), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043420)), hAPP(c_Int_Onumber__class_Onumber__of(_1043416), _1043418)))]]], (15396 ^ _781215) ^ [_1051186, _1051188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051186), _1051188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1051186)), _1051188)))], (37562 ^ _781215) ^ [_1494624, _1494626, _1494628] : [class_Complete__Lattice_Ocomplete__lattice(_1494624), hBOOL(hAPP(hAPP(c_member(_1494624), _1494626), _1494628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1494624), c_Complete__Lattice_OInf__class_OInf(_1494624, _1494628)), _1494626)))], (45728 ^ _781215) ^ [_1698480, _1698482] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1698480), _1698482))), -(c_List_Oupt(_1698480, hAPP(c_Nat_OSuc, _1698482)) = c_List_Olist_ONil(tc_Nat_Onat))], (51284 ^ _781215) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (43676 ^ _781215) ^ [_1653641, _1653643] : [-(c_List_Osublist(_1653641, c_List_Olist_ONil(_1653641), _1653643) = c_List_Olist_ONil(_1653641))], (49217 ^ _781215) ^ [_1775685, _1775687] : [-(c_Transitive__Closure_Ortrancl(_1775685, c_Transitive__Closure_Otrancl(_1775685, _1775687)) = c_Transitive__Closure_Ortrancl(_1775685, _1775687))], (25404 ^ _781215) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (46598 ^ _781215) ^ [_1718275, _1718277, _1718279] : [hBOOL(hAPP(c_List_Odistinct(_1718275), _1718277)), -(c_List_Oremove1(_1718275, _1718279, c_List_Oremdups(_1718275, _1718277)) = c_List_Oremdups(_1718275, c_List_Oremove1(_1718275, _1718279, _1718277)))], (5280 ^ _781215) ^ [_861815, _861817] : [_861817 = _861815, -(c_New__Random__Sequence_Oneg__single(_861817) = c_New__Random__Sequence_Oneg__single(_861815))], (40661 ^ _781215) ^ [_1577921, _1577923, _1577925, _1577927] : [c_Com_Ocom_OSemi(_1577921, _1577923) = c_Com_Ocom_OWhile(_1577925, _1577927)], (6692 ^ _781215) ^ [_890750, _890752, _890754, _890756] : [6693 ^ _781215 : [(6696 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890750), _890752), _890756))], (6694 ^ _781215) ^ [] : [_890752 = _890754]], -(hBOOL(hAPP(hAPP(c_member(_890750), _890752), hAPP(hAPP(c_Set_Oinsert(_890750), _890754), _890756))))], (16511 ^ _781215) ^ [_1075426, _1075428, _1075430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1075426, tc_HOL_Obool)), _1075428), _1075430)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1075426, tc_HOL_Obool)), _1075428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075426, tc_HOL_Obool)), _1075430), _1075428)) = _1075430)], (46465 ^ _781215) ^ [_1715584, _1715586, _1715588, _1715590, _1715592] : [-(hAPP(hAPP(c_List_Ozip(_1715584, _1715586), _1715588), c_List_OtakeWhile(_1715586, _1715590, _1715592)) = c_List_OtakeWhile(tc_prod(_1715584, _1715586), hAPP(c_Fun_Ocomp(_1715586, tc_HOL_Obool, tc_prod(_1715584, _1715586), _1715590), c_Product__Type_Osnd(_1715584, _1715586)), hAPP(hAPP(c_List_Ozip(_1715584, _1715586), _1715588), _1715592)))], (13380 ^ _781215) ^ [_1013844, _1013846] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1013844), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013844), _1013846)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26010 ^ _781215) ^ [_1252889, _1252891, _1252893] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1252889), _1252891)), 26013 ^ _781215 : [(26014 ^ _781215) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1252889, tc_Nat_Onat), _1252893), _1252891) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 26017 ^ _781215 : [(26018 ^ _781215) ^ [_1253051] : [hBOOL(hAPP(hAPP(c_member(_1252889), _1253051), _1252891)), -(hAPP(_1252893, _1253051) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (26024 ^ _781215) ^ [] : [26026 ^ _781215 : [(26029 ^ _781215) ^ [] : [hAPP(_1252893, 26025 ^ [_1252889, _1252891, _1252893]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (26027 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1252889), 26025 ^ [_1252889, _1252891, _1252893]), _1252891)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1252889, tc_Nat_Onat), _1252893), _1252891) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (2188 ^ _781215) ^ [_813283, _813285, _813287, _813289, _813291, _813293] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_813293, _813289, _813285) = c_Smallcheck_Ofull__small__class_Ofull__small(_813291, _813287, _813283)), _813293 = _813291, _813289 = _813287, _813285 = _813283], (38388 ^ _781215) ^ [_1513274, _1513276, _1513278, _1513280, _1513282] : [c_Fun_Oinj__on(_1513274, _1513276, _1513278, c_Orderings_Otop__class_Otop(tc_fun(_1513274, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1513276, tc_HOL_Obool)), _1513280), hAPP(c_Set_Oimage(_1513274, _1513276, _1513278), _1513282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1513274, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1513274, _1513276, _1513278), _1513280)), _1513282)))], (49525 ^ _781215) ^ [_1783362, _1783364, _1783366, _1783368] : [-(c_Wellfounded_Oacyclic(_1783362, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1783362, _1783362)), hAPP(hAPP(c_Product__Type_OPair(_1783362, _1783362), _1783364), _1783366)), _1783368))), c_Wellfounded_Oacyclic(_1783362, _1783368), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783362, _1783362)), hAPP(hAPP(c_Product__Type_OPair(_1783362, _1783362), _1783366), _1783364)), c_Transitive__Closure_Ortrancl(_1783362, _1783368))))], (43694 ^ _781215) ^ [_1653957, _1653959, _1653961] : [-(hAPP(hAPP(c_List_Ozip(_1653957, _1653959), _1653961), c_List_Olist_ONil(_1653959)) = c_List_Olist_ONil(tc_prod(_1653957, _1653959)))], (36279 ^ _781215) ^ [_1463357, _1463359, _1463361, _1463363, _1463365] : [-(hAPP(c_Product__Type_Ofst(_1463357, _1463359), hAPP(c_Product__Type_Oapfst(_1463361, _1463357, _1463359, _1463363), _1463365)) = hAPP(_1463363, hAPP(c_Product__Type_Ofst(_1463361, _1463359), _1463365)))], (34414 ^ _781215) ^ [_1425841, _1425843] : [class_Lattices_Olattice(_1425841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425841), _1425843)), -(_1425843 = c_Orderings_Obot__class_Obot(tc_fun(_1425841, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425841), c_Big__Operators_Olattice__class_OInf__fin(_1425841, _1425843)), c_Big__Operators_Olattice__class_OSup__fin(_1425841, _1425843))))], (23712 ^ _781215) ^ [_1208690, _1208692, _1208694] : [class_Rings_Ocomm__semiring__1(_1208690), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1208690), _1208692), hAPP(c_Nat_OSuc, _1208694)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208690), _1208692), hAPP(hAPP(c_Power_Opower__class_Opower(_1208690), _1208692), _1208694)))], (22898 ^ _781215) ^ [_1194192, _1194194, _1194196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194194), _1194196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1194192), _1194196)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1194192), _1194194))))], (50124 ^ _781215) ^ [_1798864, _1798866, _1798868, _1798870, _1798872] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1798864, _1798864)), hAPP(hAPP(c_Product__Type_OPair(_1798864, _1798864), _1798866), _1798868)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1798864, _1798864), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1798870)), _1798872))), 50128 ^ _781215 : [(50131 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1798864, _1798864)), hAPP(hAPP(c_Product__Type_OPair(_1798864, _1798864), 50127 ^ [_1798864, _1798866, _1798868, _1798870, _1798872]), _1798868)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1798864, _1798864), tc_HOL_Obool), _1798870), _1798872))))], (50129 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1798864, _1798864)), hAPP(hAPP(c_Product__Type_OPair(_1798864, _1798864), _1798866), 50127 ^ [_1798864, _1798866, _1798868, _1798870, _1798872])), _1798872)))]]], (35166 ^ _781215) ^ [_1441458, _1441460, _1441462, _1441464] : [c_Fun_Oinj__on(_1441458, tc_Option_Ooption(_1441460), _1441464, c_Map_Odom(_1441458, _1441460, _1441464)), -(c_Fun_Oinj__on(_1441458, tc_Option_Ooption(_1441460), c_Map_Omap__add(_1441458, _1441460, _1441462, _1441464), c_Map_Odom(_1441458, _1441460, _1441464)))], (35593 ^ _781215) ^ [_1450110] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1450110)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1450110)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1450110)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (6150 ^ _781215) ^ [_880103, _880105, _880107, _880109, _880111, _880113] : [hAPP(_880103, _880105) = c_Option_Ooption_ONone(_880107), -(c_Map_Omap__comp(_880107, _880109, _880111, _880113, _880103, _880105) = c_Option_Ooption_ONone(_880109))], (23056 ^ _781215) ^ [_1196871, _1196873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1196871), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196873), _1196871)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1196871, _1196873) = _1196871)], (15606 ^ _781215) ^ [_1055337, _1055339, _1055341, _1055343] : [hAPP(c_Com_Ocom_OBODY, _1055337) = c_Com_Ocom_OLocal(_1055339, _1055341, _1055343)], (6047 ^ _781215) ^ [_878280, _878282, _878284, _878286, _878288, _878290] : [c_Map_Omap__comp(_878280, _878282, _878284, _878286, _878288, _878290) = c_Option_Ooption_ONone(_878282), -(hAPP(_878288, _878290) = c_Option_Ooption_ONone(_878280)), 6055 ^ _781215 : [(6058 ^ _781215) ^ [] : [-(hAPP(_878286, 6054 ^ [_878280, _878282, _878284, _878286, _878288, _878290]) = c_Option_Ooption_ONone(_878282))], (6056 ^ _781215) ^ [] : [-(hAPP(_878288, _878290) = hAPP(c_Option_Ooption_OSome(_878280), 6054 ^ [_878280, _878282, _878284, _878286, _878288, _878290]))]]], (33899 ^ _781215) ^ [_1413436, _1413438, _1413440] : [class_Orderings_Olinorder(_1413436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413436), _1413438)), -(_1413438 = c_Orderings_Obot__class_Obot(tc_fun(_1413436, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413436), _1413440)), -(_1413440 = c_Orderings_Obot__class_Obot(tc_fun(_1413436, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413436, tc_HOL_Obool)), _1413438), _1413440) = c_Orderings_Obot__class_Obot(tc_fun(_1413436, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1413436, c_Orderings_Oord__class_Omin(_1413436), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413436, tc_HOL_Obool)), _1413438), _1413440)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1413436), c_Big__Operators_Olattice_OInf__fin(_1413436, c_Orderings_Oord__class_Omin(_1413436), _1413438)), c_Big__Operators_Olattice_OInf__fin(_1413436, c_Orderings_Oord__class_Omin(_1413436), _1413440)))], (24540 ^ _781215) ^ [_1224030, _1224032] : [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), _1224030))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1224032), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1224030))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1224032), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1224030))), 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), _1224032))), c_COMBI(tc_Int_Oint))))], (39665 ^ _781215) ^ [_1552061] : [-(hAPP(c_Option_Omap(_1552061, _1552061), c_Fun_Oid(_1552061)) = c_Fun_Oid(tc_Option_Ooption(_1552061)))], (47435 ^ _781215) ^ [_1735463, _1735465, _1735467, _1735469] : [47437 ^ _781215 : [(47440 ^ _781215) ^ [] : [hBOOL(hAPP(_1735465, hAPP(hAPP(c_List_Onth(_1735467), _1735469), 47436 ^ [_1735463, _1735465, _1735467, _1735469])))], (47438 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47436 ^ [_1735463, _1735465, _1735467, _1735469]), _1735463)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735463), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735467)), _1735469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735463), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735467)), c_List_OtakeWhile(_1735467, _1735465, _1735469)))))], (40545 ^ _781215) ^ [_1575647, _1575649, _1575651, _1575653] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1575647, tc_fun(_1575649, tc_HOL_Obool)), _1575651), _1575653) = hAPP(c_Set_OCollect(_1575649), hAPP(hAPP(c_COMBB(tc_fun(_1575647, tc_HOL_Obool), tc_HOL_Obool, _1575649), c_HOL_OAll(_1575647)), hAPP(hAPP(c_COMBB(tc_fun(_1575647, tc_HOL_Obool), tc_fun(_1575647, tc_HOL_Obool), _1575649), hAPP(c_COMBS(_1575647, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1575647), c_fimplies), hAPP(hAPP(c_COMBC(_1575647, tc_fun(_1575647, tc_HOL_Obool), tc_HOL_Obool), c_member(_1575647)), _1575651)))), hAPP(hAPP(c_COMBC(_1575649, tc_fun(_1575647, tc_fun(_1575649, tc_HOL_Obool)), tc_fun(_1575647, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1575649, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1575647, tc_fun(_1575649, tc_HOL_Obool)), tc_fun(_1575647, tc_HOL_Obool)), _1575649), c_COMBB(tc_fun(_1575649, tc_HOL_Obool), tc_HOL_Obool, _1575647)), c_member(_1575649))), _1575653)))))], (41283 ^ _781215) ^ [_1591999, _1592001, _1592003, _1592005, _1592007, _1592009] : [-(hAPP(c_Set_Ovimage(_1591999, _1592001, hAPP(c_Fun_Ocomp(_1592003, _1592001, _1591999, _1592005), _1592007)), _1592009) = hAPP(c_Set_Ovimage(_1591999, _1592003, _1592007), hAPP(c_Set_Ovimage(_1592003, _1592001, _1592005), _1592009)))], (14415 ^ _781215) ^ [_1033287, _1033289] : [class_Int_Oring__char__0(_1033287), hBOOL(hAPP(hAPP(c_member(_1033287), _1033289), c_Int_Oring__1__class_OInts(_1033287))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033287), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033287), c_Groups_Oone__class_Oone(_1033287)), _1033289)), _1033289) = c_Groups_Ozero__class_Ozero(_1033287)], (49941 ^ _781215) ^ [_1793970, _1793972] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1793970, _1793970)), hAPP(hAPP(c_Product__Type_OPair(_1793970, _1793970), 49942 ^ [_1793970, _1793972]), 49942 ^ [_1793970, _1793972])), c_Transitive__Closure_Otrancl(_1793970, _1793972)))), -(c_Wellfounded_Oacyclic(_1793970, _1793972))], (37233 ^ _781215) ^ [_1486672, _1486674, _1486676, _1486678, _1486680] : [class_Complete__Lattice_Ocomplete__lattice(_1486672), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1486674, tc_HOL_Obool)), _1486676), _1486678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486672), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486674, _1486672), _1486678), _1486680)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486674, _1486672), _1486676), _1486680))))], (48480 ^ _781215) ^ [_1760149, _1760151, _1760153] : [class_Orderings_Olinorder(_1760149), 48486 ^ _781215 : [(48489 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760149), _1760153), 48485 ^ [_1760149, _1760151, _1760153]))], (48487 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760149), 48485 ^ [_1760149, _1760151, _1760153]), hAPP(c_List_Oset(_1760149), _1760151))))]], c_List_Olinorder__class_Osorted(_1760149, _1760151), -(c_List_Olinorder__class_Osorted(_1760149, hAPP(hAPP(c_List_Olist_OCons(_1760149), _1760153), _1760151)))], (6124 ^ _781215) ^ [_879638, _879640] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_879638, _879640)))), hBOOL(hAPP(c_Com_OWT, _879638)), hBOOL(hAPP(c_Com_OWT, _879640))], (45857 ^ _781215) ^ [_1700847, _1700849, _1700851, _1700853] : [-(c_List_Oupt(_1700847, _1700849) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1700851), _1700853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1700847), _1700849)), _1700847 = _1700851, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1700847), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1700849) = _1700853], (2400 ^ _781215) ^ [_816699, _816701, _816703, _816705] : [-(c_Divides_Odivmod__int__rel(_816705, _816701) = c_Divides_Odivmod__int__rel(_816703, _816699)), _816705 = _816703, _816701 = _816699], (10510 ^ _781215) ^ [_960826, _960828, _960830, _960832, _960834] : [class_Groups_Oordered__cancel__ab__semigroup__add(_960826), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960826), _960828), _960830)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960826), _960832), _960834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960826), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960826), _960828), _960832)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960826), _960830), _960834))))], (12080 ^ _781215) ^ [_991055, _991057, _991059, _991061] : [class_Groups_Oordered__comm__monoid__add(_991055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991055), c_Groups_Ozero__class_Ozero(_991055)), _991057)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991055), _991059), _991061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991055), _991059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_991055), _991057), _991061))))], (23156 ^ _781215) ^ [_1198345, _1198347] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198345, _1198347) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198345, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198347)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198345, _1198347)), _1198347))], (18255 ^ _781215) ^ [_1108007, _1108009, _1108011, _1108013] : [class_Orderings_Olinorder(_1108007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108007), _1108009), _1108011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108007), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1108007), _1108013), _1108009)), _1108011)))], (43930 ^ _781215) ^ [_1658777, _1658779, _1658781, _1658783] : [-(_1658777 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1658779), _1658777), hAPP(hAPP(c_List_Olist_OCons(_1658779), _1658781), _1658783)) = hAPP(hAPP(c_List_Olist_OCons(_1658779), _1658781), hAPP(hAPP(c_List_Otake(_1658779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1658777), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1658783)))], (21960 ^ _781215) ^ [_1176314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1176314), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1176314 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1176314 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20098 ^ _781215) ^ [_1141940, _1141942, _1141944] : [class_Orderings_Olinorder(_1141940), hAPP(_1141942, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1141940), 20103 ^ [_1141940, _1141942, _1141944]), 20104 ^ [_1141940, _1141942, _1141944])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1141940), hAPP(_1141942, 20103 ^ [_1141940, _1141942, _1141944])), hAPP(_1141942, 20104 ^ [_1141940, _1141942, _1141944])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1141940), _1141944)), -(_1141944 = c_Orderings_Obot__class_Obot(tc_fun(_1141940, tc_HOL_Obool))), -(hAPP(_1141942, c_Big__Operators_Olinorder__class_OMin(_1141940, _1141944)) = c_Big__Operators_Olinorder__class_OMin(_1141940, hAPP(c_Set_Oimage(_1141940, _1141940, _1141942), _1141944)))], (41427 ^ _781215) ^ [_1595463, _1595465, _1595467, _1595469, _1595471, _1595473, _1595475] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1595463), tc_Option_Ooption(_1595465), _1595467, hAPP(c_Option_Omap(_1595463, _1595465), _1595469)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1595467, tc_Option_Ooption(_1595463)), _1595471), _1595473), hAPP(c_Option_Ooption_OSome(_1595463), _1595475))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1595467, tc_Option_Ooption(_1595465)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1595463), tc_Option_Ooption(_1595465), _1595467, hAPP(c_Option_Omap(_1595463, _1595465), _1595469)), _1595471)), _1595473), hAPP(c_Option_Ooption_OSome(_1595465), hAPP(_1595469, _1595475))))], (31746 ^ _781215) ^ [_1365366, _1365368, _1365370, _1365372, _1365374] : [class_Groups_Ocomm__monoid__add(_1365366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1365368), _1365370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1365370), _1365372)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1365366), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1365366), _1365374), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1365368), _1365370))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1365366), _1365374), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1365370), _1365372))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1365366), _1365374), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1365368), _1365372)))], (39997 ^ _781215) ^ [_1562105, _1562107] : [c_Wellfounded_Owf(_1562105, _1562107), -(c_Wellfounded_Owf(tc_fun(_1562105, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1562105, _1562107)))], (50258 ^ _781215) ^ [_1802522, _1802524, _1802526] : [class_Divides_Osemiring__div(_1802522), -(_1802524 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1802522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1802522), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1802522), _1802524), _1802526)), _1802526)), c_Divides_Odiv__class_Omod(_1802522, _1802524, _1802526)))], (38858 ^ _781215) ^ [_1526837, _1526839, _1526841] : [-(c_Relation_Orefl__on(_1526837, _1526839, _1526841)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526837, _1526837), tc_HOL_Obool)), _1526841), hAPP(hAPP(c_Product__Type_OSigma(_1526837, _1526837), _1526839), hAPP(c_COMBK(tc_fun(_1526837, tc_HOL_Obool), _1526837), _1526839)))), 38864 ^ _781215 : [(38867 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526837, _1526837)), hAPP(hAPP(c_Product__Type_OPair(_1526837, _1526837), 38863 ^ [_1526837, _1526839, _1526841]), 38863 ^ [_1526837, _1526839, _1526841])), _1526841))], (38865 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526837), 38863 ^ [_1526837, _1526839, _1526841]), _1526839)))]]], (11200 ^ _781215) ^ [_975702, _975704, _975706, _975708] : [class_Rings_Ocomm__semiring__1(_975702), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975702), _975704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975702), _975706), _975708)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975702), _975706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975702), _975704), _975708)))], (35717 ^ _781215) ^ [_1452826, _1452828, _1452830] : [class_Groups_Oordered__ab__group__add__abs(_1452826), -(hAPP(c_Groups_Oabs__class_Oabs(_1452826), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452826), hAPP(c_Groups_Oabs__class_Oabs(_1452826), _1452828)), hAPP(c_Groups_Oabs__class_Oabs(_1452826), _1452830))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452826), hAPP(c_Groups_Oabs__class_Oabs(_1452826), _1452828)), hAPP(c_Groups_Oabs__class_Oabs(_1452826), _1452830)))], (44560 ^ _781215) ^ [_1674207, _1674209, _1674211, _1674213] : [hBOOL(hAPP(hAPP(c_member(_1674207), _1674209), hAPP(c_List_Oset(_1674207), hAPP(hAPP(c_List_Odrop(_1674207), _1674211), _1674213)))), -(hBOOL(hAPP(hAPP(c_member(_1674207), _1674209), hAPP(c_List_Oset(_1674207), _1674213))))], (38701 ^ _781215) ^ [_1522345, _1522347, _1522349, _1522351, _1522353, _1522355] : [class_Groups_Ocomm__monoid__mult(_1522345), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522347), _1522349)), 38711 ^ _781215 : [(38714 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1522351), hAPP(_1522353, 38710 ^ [_1522345, _1522347, _1522349, _1522351, _1522353, _1522355])))], (38712 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1522347), 38710 ^ [_1522345, _1522347, _1522349, _1522351, _1522353, _1522355]), _1522349)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1522345, _1522347, c_Groups_Otimes__class_Otimes(_1522345)), hAPP(hAPP(c_COMBS(_1522347, tc_fun(_1522351, tc_HOL_Obool), _1522345), hAPP(hAPP(c_COMBC(_1522347, _1522345, tc_fun(tc_fun(_1522351, tc_HOL_Obool), _1522345)), hAPP(hAPP(c_COMBB(tc_fun(_1522351, _1522345), tc_fun(_1522345, tc_fun(tc_fun(_1522351, tc_HOL_Obool), _1522345)), _1522347), c_Finite__Set_Ofold__image(_1522345, _1522351, c_Groups_Otimes__class_Otimes(_1522345))), _1522355)), c_Groups_Oone__class_Oone(_1522345))), _1522353)), c_Groups_Oone__class_Oone(_1522345)), _1522349) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1522345, tc_prod(_1522347, _1522351), c_Groups_Otimes__class_Otimes(_1522345)), hAPP(c_Product__Type_Oprod_Oprod__case(_1522347, _1522351, _1522345), _1522355)), c_Groups_Oone__class_Oone(_1522345)), hAPP(hAPP(c_Product__Type_OSigma(_1522347, _1522351), _1522349), _1522353)))], (49487 ^ _781215) ^ [_1782291, _1782293, _1782295, _1782297] : [c_Wellfounded_Owf(_1782291, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1782291, _1782291)), hAPP(hAPP(c_Product__Type_OPair(_1782291, _1782291), _1782293), _1782295)), _1782297)), 49490 ^ _781215 : [(49493 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1782291, _1782291)), hAPP(hAPP(c_Product__Type_OPair(_1782291, _1782291), _1782295), _1782293)), c_Transitive__Closure_Ortrancl(_1782291, _1782297)))], (49491 ^ _781215) ^ [] : [-(c_Wellfounded_Owf(_1782291, _1782297))]]], (30319 ^ _781215) ^ [_1335826, _1335828] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1335826, _1335828)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1335828)), _1335826))], (15138 ^ _781215) ^ [_1046893, _1046895] : [class_Int_Onumber__ring(_1046893), -(hAPP(c_Int_Onumber__class_Onumber__of(_1046893), c_Int_Osucc(_1046895)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046893), c_Groups_Oone__class_Oone(_1046893)), hAPP(c_Int_Onumber__class_Onumber__of(_1046893), _1046895)))], (20557 ^ _781215) ^ [_1150131, _1150133] : [class_Rings_Olinordered__semidom(_1150131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150131), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150131), _1150133)), c_Groups_Ozero__class_Ozero(_1150131)))], (37193 ^ _781215) ^ [_1485388, _1485390, _1485392, _1485394, _1485396] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1485388, tc_fun(_1485390, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1485388), _1485392), _1485394)), _1485396) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485390, tc_HOL_Obool)), hAPP(_1485396, _1485392)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1485388, tc_fun(_1485390, tc_HOL_Obool)), _1485394), _1485396)))], (44574 ^ _781215) ^ [_1674556, _1674558, _1674560, _1674562] : [-(hAPP(hAPP(c_List_Otake(_1674556), _1674558), hAPP(hAPP(c_List_Odrop(_1674556), _1674560), _1674562)) = hAPP(hAPP(c_List_Odrop(_1674556), _1674560), hAPP(hAPP(c_List_Otake(_1674556), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1674558), _1674560)), _1674562)))], (49397 ^ _781215) ^ [_1780160, _1780162] : [-(c_Relation_Orefl__on(_1780160, c_Orderings_Otop__class_Otop(tc_fun(_1780160, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1780160, _1780162)))], (36682 ^ _781215) ^ [_1470850, _1470852, _1470854, _1470856] : [c_Fun_Oinj__on(_1470850, _1470852, _1470854, c_Orderings_Otop__class_Otop(tc_fun(_1470850, tc_HOL_Obool))), 36685 ^ _781215 : [(36699 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1470852), _1470856), hAPP(c_Set_Oimage(_1470850, _1470852, _1470854), c_Orderings_Otop__class_Otop(tc_fun(_1470850, tc_HOL_Obool)))))), 36700 ^ _781215 : [(36701 ^ _781215) ^ [_1471253] : [_1470856 = hAPP(_1470854, _1471253), 36705 ^ _781215 : [(36708 ^ _781215) ^ [] : [36704 ^ [_1470850, _1470852, _1470854, _1470856, _1471253] = _1471253], (36706 ^ _781215) ^ [] : [-(_1470856 = hAPP(_1470854, 36704 ^ [_1470850, _1470852, _1470854, _1470856, _1471253]))]]]]], (36686 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1470852), _1470856), hAPP(c_Set_Oimage(_1470850, _1470852, _1470854), c_Orderings_Otop__class_Otop(tc_fun(_1470850, tc_HOL_Obool))))), 36690 ^ _781215 : [(36693 ^ _781215) ^ [_1471115] : [_1470856 = hAPP(_1470854, _1471115), -(_1471115 = 36689 ^ [_1470850, _1470852, _1470854, _1470856])], (36691 ^ _781215) ^ [] : [-(_1470856 = hAPP(_1470854, 36689 ^ [_1470850, _1470852, _1470854, _1470856]))]]]]], (41108 ^ _781215) ^ [_1587863, _1587865, _1587867, _1587869] : [hAPP(hAPP(c_Map_Omap__of(_1587863, _1587865), _1587867), _1587869) = c_Option_Ooption_ONone(_1587865), hBOOL(hAPP(hAPP(c_member(_1587863), _1587869), hAPP(c_Set_Oimage(tc_prod(_1587863, _1587865), _1587863, c_Product__Type_Ofst(_1587863, _1587865)), hAPP(c_List_Oset(tc_prod(_1587863, _1587865)), _1587867))))], (19536 ^ _781215) ^ [_1131727, _1131729] : [class_Orderings_Olinorder(_1131727), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131727), _1131729)), -(_1131729 = c_Orderings_Obot__class_Obot(tc_fun(_1131727, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1131727), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1131727), 19549 ^ [_1131727, _1131729]), 19550 ^ [_1131727, _1131729])), hAPP(hAPP(c_Set_Oinsert(_1131727), 19549 ^ [_1131727, _1131729]), hAPP(hAPP(c_Set_Oinsert(_1131727), 19550 ^ [_1131727, _1131729]), c_Orderings_Obot__class_Obot(tc_fun(_1131727, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1131727), c_Big__Operators_Olinorder__class_OMin(_1131727, _1131729)), _1131729)))], (2308 ^ _781215) ^ [_815251, _815253, _815255, _815257, _815259, _815261, _815263, _815265] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_815265, _815261, _815257, _815253) = c_SetInterval_Oord_OgreaterThanLessThan(_815263, _815259, _815255, _815251)), _815265 = _815263, _815261 = _815259, _815257 = _815255, _815253 = _815251], (7520 ^ _781215) ^ [_907650, _907652, _907654, _907656] : [class_Orderings_Oorder(_907650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907650), _907652), _907654)), _907652 = _907656, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907650), _907656), _907654)))], (36965 ^ _781215) ^ [_1478989, _1478991, _1478993, _1478995] : [_1478989 = c_Orderings_Obot__class_Obot(tc_fun(_1478991, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1478991, tc_fun(_1478993, tc_HOL_Obool)), _1478989), hAPP(c_COMBK(tc_fun(_1478993, tc_HOL_Obool), _1478991), _1478995)) = c_Orderings_Otop__class_Otop(tc_fun(_1478993, tc_HOL_Obool)))], (45049 ^ _781215) ^ [_1684908, _1684910, _1684912] : [class_Orderings_Olinorder(_1684908), -(c_Big__Operators_Olinorder__class_OMax(_1684908, hAPP(c_List_Oset(_1684908), hAPP(hAPP(c_List_Olist_OCons(_1684908), _1684910), _1684912))) = hAPP(c_List_Ofoldl(_1684908, _1684908, c_Orderings_Oord__class_Omax(_1684908), _1684910), _1684912))], (41964 ^ _781215) ^ [_1608696, _1608698, _1608700] : [class_Orderings_Olinorder(_1608696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608696), _1608698)), -(c_List_Olinorder__class_Osorted__list__of__set(_1608696, hAPP(hAPP(c_Set_Oinsert(_1608696), _1608700), _1608698)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1608696, _1608696, c_COMBI(_1608696)), _1608700), c_List_Olinorder__class_Osorted__list__of__set(_1608696, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1608696, tc_HOL_Obool)), _1608698), hAPP(hAPP(c_Set_Oinsert(_1608696), _1608700), c_Orderings_Obot__class_Obot(tc_fun(_1608696, tc_HOL_Obool)))))))], (4478 ^ _781215) ^ [_849128, _849130, _849132, _849134] : [-(c_Transitive__Closure_Ortrancl(_849134, _849130) = c_Transitive__Closure_Ortrancl(_849132, _849128)), _849134 = _849132, _849130 = _849128], (29966 ^ _781215) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (44558 ^ _781215) ^ [_1674152, _1674154, _1674156] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1674152, tc_HOL_Obool)), hAPP(c_List_Oset(_1674152), hAPP(hAPP(c_List_Odrop(_1674152), _1674154), _1674156))), hAPP(c_List_Oset(_1674152), _1674156))))], (29764 ^ _781215) ^ [_1323817, _1323819, _1323821, _1323823] : [class_Fields_Olinordered__field(_1323817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323817), _1323819), _1323821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323817), c_Groups_Ozero__class_Ozero(_1323817)), _1323823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323817), c_Groups_Ozero__class_Ozero(_1323817)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1323817), _1323821), _1323819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323817), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323817), _1323823), _1323821)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323817), _1323823), _1323819))))], (2238 ^ _781215) ^ [_814114, _814116] : [_814116 = _814114, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_814116) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_814114))], (48582 ^ _781215) ^ [_1762194, _1762196, _1762198, _1762200] : [class_Lattices_Osemilattice__sup(_1762194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1762194), _1762196)), 48592 ^ _781215 : [(48595 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1762194), 48591 ^ [_1762194, _1762196, _1762198, _1762200]), _1762198))], (48593 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1762194), 48591 ^ [_1762194, _1762196, _1762198, _1762200]), _1762196)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1762194), hAPP(hAPP(c_Finite__Set_Ofold(_1762194, _1762194, c_Lattices_Osemilattice__sup__class_Osup(_1762194)), _1762200), _1762196)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1762194), _1762198), _1762200))))], (30175 ^ _781215) ^ [_1333413, _1333415] : [c_Nat__Transfer_Ois__nat(_1333413), c_Nat__Transfer_Ois__nat(_1333415), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1333413, _1333415) = 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, _1333413), hAPP(c_Int_Onat, _1333415))))], (21870 ^ _781215) ^ [_1173948, _1173950, _1173952, _1173954] : [21872 ^ _781215 : [(21875 ^ _781215) ^ [] : [hAPP(_1173954, 21871 ^ [_1173948, _1173950, _1173952, _1173954]) = c_Orderings_Obot__class_Obot(tc_fun(_1173950, tc_HOL_Obool))], (21873 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1173948), 21871 ^ [_1173948, _1173950, _1173952, _1173954]), _1173952)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1173948, tc_fun(_1173950, tc_HOL_Obool)), _1173952), _1173954) = c_Orderings_Obot__class_Obot(tc_fun(_1173950, tc_HOL_Obool)))], (36079 ^ _781215) ^ [_1459749, _1459751] : [class_Groups_Oordered__ab__group__add__abs(_1459749), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459749), hAPP(c_Groups_Ouminus__class_Ouminus(_1459749), hAPP(c_Groups_Oabs__class_Oabs(_1459749), _1459751))), c_Groups_Ozero__class_Ozero(_1459749))))], (7222 ^ _781215) ^ [_902535, _902537, _902539, _902541, _902543, _902545] : [hBOOL(hAPP(hAPP(c_member(_902535), _902537), _902539)), -(c_Map_Orestrict__map(_902535, _902541, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_902535, tc_Option_Ooption(_902541)), _902543), _902537), _902545), _902539) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_902535, tc_Option_Ooption(_902541)), c_Map_Orestrict__map(_902535, _902541, _902543, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902535, tc_HOL_Obool)), _902539), hAPP(hAPP(c_Set_Oinsert(_902535), _902537), c_Orderings_Obot__class_Obot(tc_fun(_902535, tc_HOL_Obool)))))), _902537), _902545))], (32886 ^ _781215) ^ [_1390845, _1390847] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1390845, tc_HOL_Obool)), _1390847), c_Orderings_Obot__class_Obot(tc_fun(_1390845, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1390845, tc_HOL_Obool)))], (8105 ^ _781215) ^ [_917772, _917774, _917776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917772), _917774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917772), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _917774), _917776))))], (20641 ^ _781215) ^ [_1151620, _1151622, _1151624] : [class_Rings_Osemiring__1(_1151620), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151622), _1151624)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151620), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151620), _1151622)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151620), _1151624)))], (14682 ^ _781215) ^ [_1037952, _1037954, _1037956] : [class_Int_Onumber__ring(_1037952), class_Rings_Olinordered__idom(_1037952), 14689 ^ _781215 : [(14696 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1037954), _1037956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037952), hAPP(c_Int_Onumber__class_Onumber__of(_1037952), _1037954)), hAPP(c_Int_Onumber__class_Onumber__of(_1037952), _1037956))))], (14690 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037952), hAPP(c_Int_Onumber__class_Onumber__of(_1037952), _1037954)), hAPP(c_Int_Onumber__class_Onumber__of(_1037952), _1037956))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1037954), _1037956)))]]], (15845 ^ _781215) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (33615 ^ _781215) ^ [_1407752, _1407754, _1407756, _1407758, _1407760] : [c_Finite__Set_Ofolding__one(_1407752, _1407754, _1407756), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407752), _1407758)), -(_1407758 = c_Orderings_Obot__class_Obot(tc_fun(_1407752, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407752), _1407760)), -(_1407760 = c_Orderings_Obot__class_Obot(tc_fun(_1407752, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407752, tc_HOL_Obool)), _1407758), _1407760) = c_Orderings_Obot__class_Obot(tc_fun(_1407752, tc_HOL_Obool)), -(hAPP(_1407756, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407752, tc_HOL_Obool)), _1407758), _1407760)) = hAPP(hAPP(_1407754, hAPP(_1407756, _1407758)), hAPP(_1407756, _1407760)))], (24089 ^ _781215) ^ [_1215540, _1215542, _1215544] : [class_Int_Onumber__ring(_1215540), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1215540), hAPP(c_Int_Onumber__class_Onumber__of(_1215540), _1215542)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1215544))) = hAPP(hAPP(c_HOL_OLet(_1215540, _1215540), hAPP(hAPP(c_Power_Opower__class_Opower(_1215540), hAPP(c_Int_Onumber__class_Onumber__of(_1215540), _1215542)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1215544))), hAPP(hAPP(c_COMBS(_1215540, _1215540, _1215540), c_Groups_Otimes__class_Otimes(_1215540)), c_COMBI(_1215540))))], (46185 ^ _781215) ^ [_1708124] : [-(c_List_Oconcat(_1708124, c_List_Olist_ONil(tc_List_Olist(_1708124))) = c_List_Olist_ONil(_1708124))], (32491 ^ _781215) ^ [_1382509, _1382511, _1382513, _1382515, _1382517] : [hAPP(c_Relation_OImage(_1382509, _1382509, _1382511), hAPP(hAPP(c_Set_Oinsert(_1382509), _1382513), c_Orderings_Obot__class_Obot(tc_fun(_1382509, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1382509, _1382509, _1382511), hAPP(hAPP(c_Set_Oinsert(_1382509), _1382515), c_Orderings_Obot__class_Obot(tc_fun(_1382509, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1382509, _1382517, _1382511), hBOOL(hAPP(hAPP(c_member(_1382509), _1382515), _1382517)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1382509, _1382509)), hAPP(hAPP(c_Product__Type_OPair(_1382509, _1382509), _1382513), _1382515)), _1382511)))], (46137 ^ _781215) ^ [_1707204, _1707206] : [hAPP(c_List_Orev(_1707204), _1707206) = c_List_Olist_ONil(_1707204), -(_1707206 = c_List_Olist_ONil(_1707204))], (20894 ^ _781215) ^ [_1155775] : [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), _1155775))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155775)))], (26256 ^ _781215) ^ [_1257269, _1257271, _1257273, _1257275] : [class_Orderings_Olinorder(_1257269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257269), _1257271), _1257273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257269), _1257273), _1257275)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257269, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1257269, _1257271, _1257273)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1257269, _1257273, _1257275)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1257269, _1257271, _1257275))], (44878 ^ _781215) ^ [_1681275, _1681277, _1681279] : [-(_1681275 = c_List_Olist_ONil(_1681277)), -(hAPP(c_List_Otl(_1681277), hAPP(hAPP(c_List_Oappend(_1681277), _1681275), _1681279)) = hAPP(hAPP(c_List_Oappend(_1681277), hAPP(c_List_Otl(_1681277), _1681275)), _1681279))], (31314 ^ _781215) ^ [_1354803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354803)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354803) = 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, _1354803))))], (144 ^ _781215) ^ [_783489, _783491, _783493, _783495] : [-(c_Nitpick_Orefl_H(_783493, _783489)), c_Nitpick_Orefl_H(_783495, _783491), _783495 = _783493, _783491 = _783489], (24608 ^ _781215) ^ [_1225413, _1225415, _1225417] : [class_Rings_Olinordered__semidom(_1225413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225413), c_Groups_Oone__class_Oone(_1225413)), _1225415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225413), c_Groups_Oone__class_Oone(_1225413)), hAPP(hAPP(c_Power_Opower__class_Opower(_1225413), _1225415), _1225417))))], (10636 ^ _781215) ^ [_963242, _963244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963242), _963244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963242), hAPP(c_Nat_OSuc, _963244))))], (25264 ^ _781215) ^ [_1236842, _1236844] : [c_Nat__Transfer_Ois__nat(_1236842), c_Nat__Transfer_Ois__nat(_1236844), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236842, _1236844)))], (43545 ^ _781215) ^ [_1650498, _1650500, _1650502, _1650504] : [hBOOL(hAPP(_1650498, _1650500)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1650502, c_Hilbert__Choice_OLeastM(_1650504, tc_Nat_Onat, _1650502, _1650498))), hAPP(_1650502, _1650500))))], (45917 ^ _781215) ^ [_1702065, _1702067, _1702069] : [class_Orderings_Olinorder(_1702065), 45920 ^ _781215 : [(45933 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1702065, hAPP(hAPP(c_List_Olist_OCons(_1702065), _1702067), _1702069))), 45937 ^ _781215 : [(45940 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1702065), _1702067), 45936 ^ [_1702065, _1702067, _1702069]))], (45938 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1702065), 45936 ^ [_1702065, _1702067, _1702069]), hAPP(c_List_Oset(_1702065), _1702069))))]], c_List_Olinorder__class_Osorted(_1702065, _1702069)], (45921 ^ _781215) ^ [] : [c_List_Olinorder__class_Osorted(_1702065, hAPP(hAPP(c_List_Olist_OCons(_1702065), _1702067), _1702069)), 45924 ^ _781215 : [(45925 ^ _781215) ^ [_1702233] : [hBOOL(hAPP(hAPP(c_member(_1702065), _1702233), hAPP(c_List_Oset(_1702065), _1702069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1702065), _1702067), _1702233)))], (45931 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1702065, _1702069))]]]]], (15450 ^ _781215) ^ [_1052144, _1052146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052144), _1052146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052144), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1052146)))], (45903 ^ _781215) ^ [_1701750, _1701752, _1701754, _1701756] : [class_Groups_Ocomm__monoid__add(_1701750), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1701750), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1701750), _1701752), c_List_Oupt(_1701754, _1701756))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1701750), _1701752), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701754, _1701756))))], (5987 ^ _781215) ^ [_876568, _876570, _876572, _876574, _876576, _876578] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_876568, _876570, _876572, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_876568), _876574), _876576), _876578)) = hAPP(hAPP(hAPP(_876572, _876574), _876576), _876578))], (34584 ^ _781215) ^ [_1429228, _1429230] : [class_Groups_Oordered__ab__group__add(_1429228), -(c_Fun_Oinj__on(_1429228, _1429228, c_Groups_Ouminus__class_Ouminus(_1429228), _1429230))], (12542 ^ _781215) ^ [_999436, _999438] : [class_Rings_Olinordered__ring(_999436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999436), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999436), _999438), _999438)), c_Groups_Ozero__class_Ozero(_999436)))], (51126 ^ _781215) ^ [_1820142, _1820144] : [class_Orderings_Oord(_1820142), -(class_Orderings_Oord(tc_fun(_1820144, _1820142)))], (15260 ^ _781215) ^ [_1048846] : [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)), _1048846)), _1048846)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1048846), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16991 ^ _781215) ^ [_1086089] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1086089))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1086089)))], (50752 ^ _781215) ^ [_1812897, _1812899, _1812901] : [c_FunDef_Ois__measure(_1812897, _1812899), -(c_FunDef_Ois__measure(tc_prod(_1812897, _1812901), hAPP(hAPP(c_COMBB(_1812897, tc_Nat_Onat, tc_prod(_1812897, _1812901)), _1812899), c_Product__Type_Ofst(_1812897, _1812901))))], (31774 ^ _781215) ^ [_1366012, _1366014] : [hAPP(_1366012, 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), _1366012), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1366014)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1366012), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1366014)))], (15300 ^ _781215) ^ [_1049604, _1049606, _1049608] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049604), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049606), _1049608)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049606), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049604), _1049608)))], (6273 ^ _781215) ^ [_882547, _882549, _882551] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _882547)), _882549), _882551)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _882547))), _882549), _882551)))], (40065 ^ _781215) ^ [_1563316, _1563318] : [-(hAPP(c_Relation_ODomain(_1563316, _1563316), c_Relation_OId__on(_1563316, _1563318)) = _1563318)], (45680 ^ _781215) ^ [_1697649] : [-(c_List_Oupt(_1697649, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (15476 ^ _781215) ^ [_1052644, _1052646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052644), _1052646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052644), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052646), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (19594 ^ _781215) ^ [_1132875, _1132877, _1132879] : [class_Orderings_Olinorder(_1132875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132875), _1132877)), hBOOL(hAPP(hAPP(c_member(_1132875), _1132879), _1132877)), 19605 ^ _781215 : [(19612 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1132875, tc_HOL_Obool)), _1132877), hAPP(hAPP(c_Set_Oinsert(_1132875), _1132879), c_Orderings_Obot__class_Obot(tc_fun(_1132875, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1132875, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1132875, c_Orderings_Oord__class_Omax(_1132875), _1132877) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1132875), _1132879), c_Big__Operators_Olattice_OSup__fin(_1132875, c_Orderings_Oord__class_Omax(_1132875), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1132875, tc_HOL_Obool)), _1132877), hAPP(hAPP(c_Set_Oinsert(_1132875), _1132879), c_Orderings_Obot__class_Obot(tc_fun(_1132875, tc_HOL_Obool)))))))], (19606 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1132875, tc_HOL_Obool)), _1132877), hAPP(hAPP(c_Set_Oinsert(_1132875), _1132879), c_Orderings_Obot__class_Obot(tc_fun(_1132875, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1132875, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1132875, c_Orderings_Oord__class_Omax(_1132875), _1132877) = _1132879)]]], (51564 ^ _781215) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (18922 ^ _781215) ^ [_1120456, _1120458, _1120460, _1120462] : [class_Orderings_Olinorder(_1120456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120456), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1120456), _1120458), _1120460)), _1120462)), 18929 ^ _781215 : [(18932 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120456), _1120460), _1120462)))], (18930 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120456), _1120458), _1120462)))]]], (16325 ^ _781215) ^ [_1069680, _1069682] : [class_Lattices_Obounded__lattice__bot(_1069680), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069680), _1069682), c_Orderings_Obot__class_Obot(_1069680)) = _1069682)], (49579 ^ _781215) ^ [_1784728, _1784730, _1784732] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1784728, _1784728), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1784728, _1784728), _1784730)), c_Transitive__Closure_Ortrancl(_1784728, _1784730)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1784728, _1784728), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1784728, _1784728)), hAPP(hAPP(c_Product__Type_OPair(_1784728, _1784728), _1784732), _1784732)), c_Transitive__Closure_Otrancl(_1784728, _1784730)))], (32097 ^ _781215) ^ [_1373615, _1373617, _1373619, _1373621, _1373623] : [class_Groups_Oordered__comm__monoid__add(_1373615), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373617), _1373619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373617, tc_HOL_Obool)), _1373621), _1373619)), 32111 ^ _781215 : [(32114 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373615), c_Groups_Ozero__class_Ozero(_1373615)), hAPP(_1373623, 32110 ^ [_1373615, _1373617, _1373619, _1373621, _1373623])))], (32112 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373617), 32110 ^ [_1373615, _1373617, _1373619, _1373621, _1373623]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373617, tc_HOL_Obool)), _1373619), _1373621))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373615), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1373617, _1373615), _1373623), _1373621)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1373617, _1373615), _1373623), _1373619))))], (44612 ^ _781215) ^ [_1675418, _1675420, _1675422, _1675424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1675418), _1675420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1675422, tc_HOL_Obool)), hAPP(c_List_Oset(_1675422), hAPP(hAPP(c_List_Odrop(_1675422), _1675420), _1675424))), hAPP(c_List_Oset(_1675422), hAPP(hAPP(c_List_Odrop(_1675422), _1675418), _1675424)))))], (35729 ^ _781215) ^ [_1453112, _1453114, _1453116] : [class_Rings_Olinordered__idom(_1453112), -(hAPP(c_Groups_Oabs__class_Oabs(_1453112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1453112), _1453114), _1453116)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1453112), hAPP(c_Groups_Oabs__class_Oabs(_1453112), _1453114)), hAPP(c_Groups_Oabs__class_Oabs(_1453112), _1453116)))], (35957 ^ _781215) ^ [_1457281, _1457283, _1457285, _1457287, _1457289, _1457291] : [hAPP(c_Product__Type_Oapsnd(_1457281, _1457283, _1457285, _1457287), _1457289) = hAPP(c_Product__Type_Oapsnd(_1457281, _1457283, _1457285, _1457291), _1457289), -(hAPP(_1457287, hAPP(c_Product__Type_Osnd(_1457285, _1457281), _1457289)) = hAPP(_1457291, hAPP(c_Product__Type_Osnd(_1457285, _1457281), _1457289)))], (37637 ^ _781215) ^ [_1496250, _1496252, _1496254] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496250, tc_HOL_Obool)), _1496252), _1496254) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1496250, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1496250, tc_HOL_Obool)), _1496252), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1496250, tc_HOL_Obool)), _1496254), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1496250, tc_HOL_Obool), tc_HOL_Obool))))))], (51394 ^ _781215) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (41839 ^ _781215) ^ [_1605310, _1605312, _1605314] : [hBOOL(hAPP(c_List_Odistinct(_1605310), _1605312)), -(hBOOL(hAPP(c_List_Odistinct(_1605310), c_List_Oremove1(_1605310, _1605314, _1605312))))], (41214 ^ _781215) ^ [_1590464, _1590466, _1590468, _1590470, _1590472] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590464, _1590466)), hAPP(hAPP(c_Product__Type_OPair(_1590464, _1590466), _1590468), _1590470)), hAPP(c_List_Oset(tc_prod(_1590464, _1590466)), _1590472))), -(hAPP(hAPP(c_Map_Omap__of(_1590464, _1590466), _1590472), _1590468) = hAPP(c_Option_Ooption_OSome(_1590466), 41217 ^ [_1590464, _1590466, _1590468, _1590470, _1590472]))], (36989 ^ _781215) ^ [_1479659, _1479661, _1479663, _1479665, _1479667, _1479669] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479659, tc_fun(_1479661, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1479663, _1479659, _1479665), _1479667)), _1479669) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479663, tc_fun(_1479661, tc_HOL_Obool)), _1479667), hAPP(hAPP(c_COMBB(_1479659, tc_fun(_1479661, tc_HOL_Obool), _1479663), _1479669), _1479665)))], (36610 ^ _781215) ^ [_1469564, _1469566, _1469568, _1469570] : [c_Fun_Oinj__on(_1469564, _1469566, _1469568, c_Orderings_Otop__class_Otop(tc_fun(_1469564, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1469564, _1469566, c_Orderings_Otop__class_Otop(tc_fun(_1469564, tc_HOL_Obool)), _1469568), hAPP(_1469568, _1469570)) = _1469570)], (48920 ^ _781215) ^ [_1768798, _1768800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1768798), _1768800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1768798)), hAPP(c_Code__Numeral_Oof__nat, _1768800))))], (1518 ^ _781215) ^ [_803160, _803162] : [-(class_Groups_Oordered__ab__semigroup__add(_803160)), _803162 = _803160, class_Groups_Oordered__ab__semigroup__add(_803162)], (21608 ^ _781215) ^ [_1168882, _1168884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1168882)), c_Int_OBit1(_1168884))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1168882), _1168884)))], (43187 ^ _781215) ^ [_1641433, _1641435, _1641437, _1641439, _1641441] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641433), tc_List_Olist(_1641433))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641433), tc_List_Olist(_1641433)), _1641435), _1641437)), c_List_Olistrel1(_1641433, _1641439))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641433), tc_List_Olist(_1641433))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641433), tc_List_Olist(_1641433)), hAPP(hAPP(c_List_Olist_OCons(_1641433), _1641441), _1641435)), hAPP(hAPP(c_List_Olist_OCons(_1641433), _1641441), _1641437))), c_List_Olistrel1(_1641433, _1641439))))], (27082 ^ _781215) ^ [_1273436, _1273438, _1273440, _1273442, _1273444, _1273446, _1273448] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1273436, _1273438), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1273440), _1273442))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1273444, _1273438), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1273446), _1273448))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1273438)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273436), _1273444), _1273438), 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), _1273440), _1273446)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273442), _1273448)), _1273438))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273442), _1273448), _1273438)))))], (47984 ^ _781215) ^ [_1747398, _1747400, _1747402, _1747404, _1747406] : [-(c_List_Omaps(_1747398, _1747400, _1747402, hAPP(hAPP(c_List_Olist_OCons(_1747398), _1747404), _1747406)) = hAPP(hAPP(c_List_Oappend(_1747400), hAPP(_1747402, _1747404)), c_List_Omaps(_1747398, _1747400, _1747402, _1747406)))], (14499 ^ _781215) ^ [_1034784, _1034786, _1034788] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_1034784, _1034786, _1034788)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1034786)), c_Com_Ocom_Ocom__size(_1034788))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47898 ^ _781215) ^ [_1745861, _1745863, _1745865, _1745867] : [_1745861 = _1745863, -(hAPP(c_List_OremoveAll(_1745865, _1745861), hAPP(hAPP(c_List_Olist_OCons(_1745865), _1745863), _1745867)) = hAPP(c_List_OremoveAll(_1745865, _1745861), _1745867))], (41927 ^ _781215) ^ [_1607564, _1607566, _1607568, _1607570, _1607572, _1607574] : [-(hAPP(hAPP(c_List_Ozip(_1607564, _1607566), _1607568), hAPP(hAPP(c_List_Omap(_1607570, _1607566), _1607572), _1607574)) = hAPP(hAPP(c_List_Omap(tc_prod(_1607564, _1607570), tc_prod(_1607564, _1607566)), hAPP(c_Product__Type_Oprod_Oprod__case(_1607564, _1607570, tc_prod(_1607564, _1607566)), hAPP(hAPP(c_COMBC(_1607564, tc_fun(_1607570, _1607566), tc_fun(_1607570, tc_prod(_1607564, _1607566))), hAPP(hAPP(c_COMBB(tc_fun(_1607566, tc_prod(_1607564, _1607566)), tc_fun(tc_fun(_1607570, _1607566), tc_fun(_1607570, tc_prod(_1607564, _1607566))), _1607564), c_COMBB(_1607566, tc_prod(_1607564, _1607566), _1607570)), c_Product__Type_OPair(_1607564, _1607566))), _1607572))), hAPP(hAPP(c_List_Ozip(_1607564, _1607570), _1607568), _1607574)))], (3224 ^ _781215) ^ [_829775, _829777, _829779, _829781, _829783, _829785, _829787, _829789] : [-(c_Nat_Onat_Onat__case(_829789, _829785, _829781, _829777) = c_Nat_Onat_Onat__case(_829787, _829783, _829779, _829775)), _829789 = _829787, _829785 = _829783, _829781 = _829779, _829777 = _829775], (32760 ^ _781215) ^ [_1387817, _1387819, _1387821] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387817, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1387817, tc_HOL_Obool)), _1387819), _1387821)), _1387819)))], (21287 ^ _781215) ^ [_1162456, _1162458] : [class_Rings_Osemiring__1(_1162456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1162458)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1162456), 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)))), _1162458))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162456), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1162456), hAPP(c_Int_Onat, _1162458))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1162456), hAPP(c_Int_Onat, _1162458))))], (30880 ^ _781215) ^ [_1346574, _1346576, _1346578, _1346580, _1346582] : [class_Orderings_Olinorder(_1346574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346574), _1346576), _1346578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346574), _1346580), _1346582)), 30891 ^ _781215 : [(30900 ^ _781215) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346574, _1346576), _1346578) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346574, _1346580), _1346582)), _1346576 = _1346580, _1346578 = _1346582], (30892 ^ _781215) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346574, _1346576), _1346578) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346574, _1346580), _1346582), 30895 ^ _781215 : [(30898 ^ _781215) ^ [] : [-(_1346578 = _1346582)], (30896 ^ _781215) ^ [] : [-(_1346576 = _1346580)]]]]], (16979 ^ _781215) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (17791 ^ _781215) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2168 ^ _781215) ^ [_812977, _812979] : [_812979 = _812977, -(c_Int_Osucc(_812979) = c_Int_Osucc(_812977))], (29426 ^ _781215) ^ [_1317498, _1317500, _1317502, _1317504] : [class_Fields_Olinordered__field(_1317498), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317498), _1317500), c_Groups_Ozero__class_Ozero(_1317498))), 29433 ^ _781215 : [(29440 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317498), _1317504), _1317500)), _1317502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317498), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317498), _1317502), _1317500)), _1317504)))], (29434 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317498), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317498), _1317502), _1317500)), _1317504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317498), _1317504), _1317500)), _1317502)))]]], (25438 ^ _781215) ^ [_1239400] : [class_Int_Onumber__ring(_1239400), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1239400), c_Groups_Oone__class_Oone(_1239400)) = hAPP(c_Int_Onumber__class_Onumber__of(_1239400), c_Int_OMin))], (43798 ^ _781215) ^ [_1655827, _1655829] : [_1655829 = c_List_Olist_ONil(_1655827), -(hAPP(c_List_Oset(_1655827), _1655829) = c_Orderings_Obot__class_Obot(tc_fun(_1655827, tc_HOL_Obool)))], (15950 ^ _781215) ^ [_1062417, _1062419, _1062421, _1062423] : [15954 ^ _781215 : [(15957 ^ _781215) ^ [] : [hBOOL(hAPP(_1062423, 15953 ^ [_1062417, _1062419, _1062421, _1062423]))], (15955 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062417), 15953 ^ [_1062417, _1062419, _1062421, _1062423]), _1062419)))]], 15959 ^ _781215 : [(15962 ^ _781215) ^ [] : [hBOOL(hAPP(_1062423, 15958 ^ [_1062417, _1062419, _1062421, _1062423]))], (15960 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062417), 15958 ^ [_1062417, _1062419, _1062421, _1062423]), _1062421)))]], 15963 ^ _781215 : [(15964 ^ _781215) ^ [_1062750] : [hBOOL(hAPP(hAPP(c_member(_1062417), _1062750), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062417, tc_HOL_Obool)), _1062419), _1062421))), -(hBOOL(hAPP(_1062423, _1062750)))]]], (9307 ^ _781215) ^ [_939735, _939737, _939739] : [hBOOL(hAPP(hAPP(c_member(_939735), _939737), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_939735, tc_HOL_Obool)), _939739))), hBOOL(hAPP(hAPP(c_member(_939735), _939737), _939739))], (44256 ^ _781215) ^ [_1666248, _1666250, _1666252, _1666254, _1666256, _1666258] : [-(c_List_Ofoldr(_1666248, _1666250, _1666252, hAPP(hAPP(c_List_Oappend(_1666248), _1666254), _1666256), _1666258) = c_List_Ofoldr(_1666248, _1666250, _1666252, _1666254, c_List_Ofoldr(_1666248, _1666250, _1666252, _1666256, _1666258)))], (21552 ^ _781215) ^ [_1167884, _1167886] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1167884)), c_Int_OBit0(_1167886)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1167884), _1167886)))], (44433 ^ _781215) ^ [_1670588, _1670590, _1670592, _1670594, _1670596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670588), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670590)), _1670592))), -(hAPP(hAPP(c_List_Olist__update(_1670590, hAPP(hAPP(c_List_Oappend(_1670590), _1670592), _1670594)), _1670588), _1670596) = hAPP(hAPP(c_List_Oappend(_1670590), hAPP(hAPP(c_List_Olist__update(_1670590, _1670592), _1670588), _1670596)), _1670594))], (36660 ^ _781215) ^ [_1470434, _1470436] : [class_Lattices_Oboolean__algebra(_1470434), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1470434), hAPP(c_Groups_Ouminus__class_Ouminus(_1470434), _1470436)), _1470436) = c_Orderings_Otop__class_Otop(_1470434))], (40003 ^ _781215) ^ [_1562194] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1562194)))], (44982 ^ _781215) ^ [_1683561, _1683563, _1683565] : [class_Groups_Omonoid__add(_1683561), -(hAPP(c_List_Ofoldl(_1683561, _1683561, c_Groups_Oplus__class_Oplus(_1683561), _1683563), _1683565) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1683561), _1683563), c_List_Ofoldr(_1683561, _1683561, c_Groups_Oplus__class_Oplus(_1683561), _1683565, c_Groups_Ozero__class_Ozero(_1683561))))], (21904 ^ _781215) ^ [_1174961, _1174963, _1174965, _1174967, _1174969] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174961, tc_fun(_1174963, tc_HOL_Obool)), _1174965), hAPP(hAPP(c_COMBS(_1174961, tc_fun(_1174963, tc_HOL_Obool), tc_fun(_1174963, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1174963, tc_HOL_Obool), tc_fun(tc_fun(_1174963, tc_HOL_Obool), tc_fun(_1174963, tc_HOL_Obool)), _1174961), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1174963, tc_HOL_Obool))), _1174967)), _1174969)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1174963, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174961, tc_fun(_1174963, tc_HOL_Obool)), _1174965), _1174967)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174961, tc_fun(_1174963, tc_HOL_Obool)), _1174965), _1174969)))], (40104 ^ _781215) ^ [_1564016, _1564018] : [hAPP(hAPP(c_Relation_Orel__comp(_1564016, _1564016, _1564016), _1564018), _1564018) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564016, _1564016), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1564016, _1564018))], (46189 ^ _781215) ^ [_1708200, _1708202] : [-(hAPP(c_List_Orev(_1708200), hAPP(c_List_Orev(_1708200), _1708202)) = _1708202)], (21837 ^ _781215) ^ [_1173190, _1173192, _1173194, _1173196] : [21839 ^ _781215 : [(21842 ^ _781215) ^ [] : [hAPP(_1173196, 21838 ^ [_1173190, _1173192, _1173194, _1173196]) = c_Orderings_Obot__class_Obot(tc_fun(_1173190, tc_HOL_Obool))], (21840 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1173192), 21838 ^ [_1173190, _1173192, _1173194, _1173196]), _1173194)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1173190, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1173192, tc_fun(_1173190, tc_HOL_Obool)), _1173194), _1173196))], (36358 ^ _781215) ^ [] : [-(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)))], (25234 ^ _781215) ^ [_1236468] : [c_Int_OMin = c_Int_OBit0(_1236468)], (8436 ^ _781215) ^ [_924123, _924125, _924127] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_924123), _924125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_924123), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924123, tc_HOL_Obool)), _924125), hAPP(hAPP(c_Set_Oinsert(_924123), _924127), c_Orderings_Obot__class_Obot(tc_fun(_924123, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_924123), _924125))))], (13676 ^ _781215) ^ [_1019267, _1019269, _1019271, _1019273, _1019275] : [class_Rings_Olinordered__semiring__strict(_1019267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019267), _1019269), _1019271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019267), _1019273), _1019275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019267), c_Groups_Ozero__class_Ozero(_1019267)), _1019271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019267), c_Groups_Ozero__class_Ozero(_1019267)), _1019273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019267), _1019269), _1019273)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019267), _1019271), _1019275))))], (39156 ^ _781215) ^ [_1532957] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1532957, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1532957), hAPP(c_COMBK(tc_HOL_Obool, _1532957), c_fFalse)))], (21514 ^ _781215) ^ [_1167310, _1167312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1167310), _1167312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1167310)), c_Int_OBit0(_1167312))))], (40319 ^ _781215) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (4428 ^ _781215) ^ [_848359, _848361, _848363, _848365, _848367, _848369, _848371, _848373] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_848373, _848369, _848365, _848361) = c_New__Random__Sequence_Opos__not__random__dseq(_848371, _848367, _848363, _848359)), _848373 = _848371, _848369 = _848367, _848365 = _848363, _848361 = _848359], (26745 ^ _781215) ^ [_1267070, _1267072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1267070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1267070), _1267072)), -(c_Divides_Odivmod__nat(_1267072, _1267070) = 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), _1267072), _1267070)), _1267070))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1267072), _1267070), _1267070)))], (46830 ^ _781215) ^ [_1722980, _1722982] : [class_Orderings_Olinorder(_1722980), 46837 ^ _781215 : [(46842 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1722980), hAPP(hAPP(c_List_Onth(_1722980), _1722982), 46835 ^ [_1722980, _1722982])), hAPP(hAPP(c_List_Onth(_1722980), _1722982), 46836 ^ [_1722980, _1722982])))], (46840 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46836 ^ [_1722980, _1722982]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722980)), _1722982))))], (46838 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46835 ^ [_1722980, _1722982]), 46836 ^ [_1722980, _1722982])))]], -(c_List_Olinorder__class_Osorted(_1722980, _1722982))], (45706 ^ _781215) ^ [_1698018, _1698020, _1698022, _1698024, _1698026] : [class_Orderings_Olinorder(_1698018), c_List_Olinorder__class_Osorted(_1698018, hAPP(hAPP(c_List_Omap(_1698020, _1698018), _1698022), _1698024)), -(c_List_Olinorder__class_Osorted(_1698018, hAPP(hAPP(c_List_Omap(_1698020, _1698018), _1698022), c_List_Olinorder__class_Oinsort__insert__key(_1698020, _1698018, _1698022, _1698026, _1698024))))], (1138 ^ _781215) ^ [_798410, _798412] : [-(class_Groups_Oordered__ab__group__add(_798410)), _798412 = _798410, class_Groups_Oordered__ab__group__add(_798412)], (25206 ^ _781215) ^ [_1236083] : [c_Int_OBit1(_1236083) = c_Int_OMin, -(_1236083 = c_Int_OMin)], (51042 ^ _781215) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (47822 ^ _781215) ^ [_1744159, _1744161, _1744163, _1744165, _1744167, _1744169] : [c_List_Olist__all2(_1744159, _1744161, _1744163, _1744165, _1744167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744169), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744161)), _1744167))), -(hBOOL(hAPP(hAPP(_1744163, hAPP(hAPP(c_List_Onth(_1744159), _1744165), _1744169)), hAPP(hAPP(c_List_Onth(_1744161), _1744167), _1744169))))], (16079 ^ _781215) ^ [_1065375, _1065377, _1065379] : [class_Lattices_Osemilattice__sup(_1065375), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065375), _1065377), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065375), _1065377), _1065379)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065375), _1065377), _1065379))], (9545 ^ _781215) ^ [_943534, _943536, _943538] : [class_Orderings_Olinorder(_943534), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943534), _943536), _943538))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943534), _943538), _943536)))], (3590 ^ _781215) ^ [_835608, _835610] : [_835610 = _835608, -(c_List_Oembed__list(_835610) = c_List_Oembed__list(_835608))], (31270 ^ _781215) ^ [_1353914, _1353916, _1353918, _1353920, _1353922] : [-(hAPP(c_Relation_OImage(_1353914, _1353916, _1353918), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353914, tc_HOL_Obool)), _1353920), _1353922)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353916, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1353914, _1353916, _1353918), _1353920)), hAPP(c_Relation_OImage(_1353914, _1353916, _1353918), _1353922)))], (33146 ^ _781215) ^ [_1396941, _1396943, _1396945] : [class_Lattices_Oboolean__algebra(_1396941), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1396941), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1396941), _1396943), _1396945)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1396941), hAPP(c_Groups_Ouminus__class_Ouminus(_1396941), _1396943)), hAPP(c_Groups_Ouminus__class_Ouminus(_1396941), _1396945)))], (24202 ^ _781215) ^ [_1217731, _1217733] : [class_Groups_Omonoid__mult(_1217731), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1217731), _1217733), 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(_1217731), _1217733), _1217733))], (39149 ^ _781215) ^ [_1532900, _1532902] : [-(hBOOL(hAPP(_1532902, 39150 ^ [_1532900, _1532902]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1532900, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1532900), _1532902))], (32351 ^ _781215) ^ [_1379431, _1379433, _1379435, _1379437, _1379439] : [c_Equiv__Relations_Oequiv(_1379431, _1379433, _1379435), hBOOL(hAPP(hAPP(c_member(tc_prod(_1379431, _1379431)), hAPP(hAPP(c_Product__Type_OPair(_1379431, _1379431), _1379437), _1379439)), _1379435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379431, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379431, _1379431, _1379435), hAPP(hAPP(c_Set_Oinsert(_1379431), _1379437), c_Orderings_Obot__class_Obot(tc_fun(_1379431, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1379431, _1379431, _1379435), hAPP(hAPP(c_Set_Oinsert(_1379431), _1379439), c_Orderings_Obot__class_Obot(tc_fun(_1379431, tc_HOL_Obool)))))))], (43836 ^ _781215) ^ [_1656463, _1656465, _1656467] : [_1656463 = c_List_Olist_ONil(_1656465), -(c_List_Obutlast(_1656465, hAPP(hAPP(c_List_Olist_OCons(_1656465), _1656467), _1656463)) = c_List_Olist_ONil(_1656465))], (50151 ^ _781215) ^ [_1799796, _1799798, _1799800, _1799802] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1799796, _1799796)), hAPP(hAPP(c_Product__Type_OPair(_1799796, _1799796), _1799798), _1799800)), c_Transitive__Closure_Otrancl(_1799796, _1799802))), 50155 ^ _781215 : [(50158 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1799796, _1799796)), hAPP(hAPP(c_Product__Type_OPair(_1799796, _1799796), 50154 ^ [_1799796, _1799798, _1799800, _1799802]), _1799800)), c_Transitive__Closure_Ortrancl(_1799796, _1799802))))], (50156 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1799796, _1799796)), hAPP(hAPP(c_Product__Type_OPair(_1799796, _1799796), _1799798), 50154 ^ [_1799796, _1799798, _1799800, _1799802])), _1799802)))]]], (16953 ^ _781215) ^ [_1085522] : [class_Int_Onumber__ring(_1085522), -(hAPP(c_Int_Onumber__class_Onumber__of(_1085522), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1085522))], (24228 ^ _781215) ^ [_1218196, _1218198, _1218200] : [class_Groups_Omonoid__mult(_1218196), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1218196), _1218198), 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)))), _1218200)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1218196), hAPP(hAPP(c_Power_Opower__class_Opower(_1218196), _1218198), _1218200)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (43499 ^ _781215) ^ [_1649354, _1649356, _1649358] : [hBOOL(hAPP(_1649354, _1649356)), -(hBOOL(hAPP(_1649354, c_Hilbert__Choice_OEps(_1649358, _1649354))))], (16663 ^ _781215) ^ [_1078848, _1078850, _1078852, _1078854, _1078856] : [c_Hoare__Mirabelle_Ohoare__valids(_1078848, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1078848), tc_HOL_Obool)), _1078850), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1078848), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078848)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078848))), hAPP(hAPP(c_COMBB(tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078848))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1078848)), _1078852)), c_Com_Ocom_OBODY)), _1078854)), _1078856)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1078848), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078848)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078848))), hAPP(hAPP(c_COMBB(tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078848))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1078848)), _1078852)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1078854)), _1078856)), -(c_Hoare__Mirabelle_Ohoare__valids(_1078848, _1078850, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1078848), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078848)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078848))), hAPP(hAPP(c_COMBB(tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1078848, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078848))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1078848)), _1078852)), c_Com_Ocom_OBODY)), _1078854)), _1078856)))], (48111 ^ _781215) ^ [_1751273, _1751275, _1751277, _1751279] : [48113 ^ _781215 : [(48116 ^ _781215) ^ [] : [hBOOL(hAPP(_1751277, 48112 ^ [_1751273, _1751275, _1751277, _1751279]))], (48114 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751273), 48112 ^ [_1751273, _1751275, _1751277, _1751279]), hAPP(c_List_Oset(_1751273), _1751275))))]], -(c_List_OdropWhile(_1751273, _1751277, hAPP(hAPP(c_List_Oappend(_1751273), _1751275), _1751279)) = c_List_OdropWhile(_1751273, _1751277, _1751279))], (38320 ^ _781215) ^ [_1511709, _1511711, _1511713, _1511715] : [-(hAPP(c_Set_Ovimage(_1511709, _1511711, _1511713), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1511711, tc_HOL_Obool), _1511715)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1511711, tc_HOL_Obool), tc_fun(_1511709, tc_HOL_Obool)), _1511715), c_Set_Ovimage(_1511709, _1511711, _1511713)))], (42012 ^ _781215) ^ [_1609964, _1609966, _1609968, _1609970, _1609972, _1609974] : [class_Orderings_Olinorder(_1609964), -(hAPP(_1609966, _1609968) = hAPP(_1609966, _1609970)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1609972, _1609964, _1609966), _1609970), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1609972, _1609964, _1609966), _1609968), _1609974)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1609972, _1609964, _1609966), _1609968), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1609972, _1609964, _1609966), _1609970), _1609974)))], (37057 ^ _781215) ^ [_1482006, _1482008, _1482010, _1482012, _1482014] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482006, tc_fun(_1482008, tc_HOL_Obool)), _1482010), hAPP(hAPP(c_COMBB(tc_fun(_1482008, tc_HOL_Obool), tc_fun(_1482008, tc_HOL_Obool), _1482006), hAPP(c_Set_Oinsert(_1482008), _1482012)), _1482014)) = hAPP(hAPP(c_Set_Oinsert(_1482008), _1482012), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482006, tc_fun(_1482008, tc_HOL_Obool)), _1482010), _1482014)))], (51246 ^ _781215) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (23626 ^ _781215) ^ [_1206988, _1206990] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1206988, _1206990) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1206988), _1206990)), _1206990)))], (51542 ^ _781215) ^ [_1824364, _1824366] : [-(class_HOL_Oequal(tc_prod(_1824364, _1824366)))], (21550 ^ _781215) ^ [_1167853] : [-(c_Int_OBit0(_1167853) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1167853), _1167853))], (7034 ^ _781215) ^ [_898090, _898092, _898094] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898090), _898092), _898094)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _898090), _898092), 7037 ^ [_898090, _898092, _898094]), _898094)))], (40524 ^ _781215) ^ [_1574741, _1574743, _1574745, _1574747] : [-(hAPP(c_Set_OCollect(_1574741), hAPP(hAPP(c_COMBB(tc_fun(_1574743, tc_HOL_Obool), tc_HOL_Obool, _1574741), c_HOL_OAll(_1574743)), hAPP(hAPP(c_COMBB(tc_fun(_1574743, tc_HOL_Obool), tc_fun(_1574743, tc_HOL_Obool), _1574741), hAPP(c_COMBS(_1574743, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574743), c_fimplies), hAPP(hAPP(c_COMBC(_1574743, tc_fun(_1574743, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574743)), _1574745)))), _1574747))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574743, tc_fun(_1574741, tc_HOL_Obool)), _1574745), hAPP(hAPP(c_COMBB(tc_fun(_1574741, tc_HOL_Obool), tc_fun(_1574741, tc_HOL_Obool), _1574743), c_Set_OCollect(_1574741)), hAPP(c_COMBC(_1574741, _1574743, tc_HOL_Obool), _1574747))))], (20798 ^ _781215) ^ [_1154132, _1154134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1154132), hAPP(c_Int_Onat, _1154134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1154132)), _1154134)))], (14252 ^ _781215) ^ [_1030354] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1030354)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1030354)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7893 ^ _781215) ^ [_914575] : [hAPP(c_Nat_OSuc, _914575) = _914575], (4766 ^ _781215) ^ [_853410, _853412] : [_853412 = _853410, -(c_Enum_Oenum__class_Oenum(_853412) = c_Enum_Oenum__class_Oenum(_853410))], (44752 ^ _781215) ^ [_1678870, _1678872, _1678874, _1678876, _1678878] : [-(hAPP(hAPP(c_List_Ozip(_1678870, _1678872), _1678874), hAPP(hAPP(c_List_Oappend(_1678872), _1678876), _1678878)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1678870, _1678872)), hAPP(hAPP(c_List_Ozip(_1678870, _1678872), hAPP(hAPP(c_List_Otake(_1678870), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678872)), _1678876)), _1678874)), _1678876)), hAPP(hAPP(c_List_Ozip(_1678870, _1678872), hAPP(hAPP(c_List_Odrop(_1678870), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678872)), _1678876)), _1678874)), _1678878)))], (624 ^ _781215) ^ [_790909, _790911, _790913, _790915, _790917, _790919] : [-(c_Finite__Set_Ofun__left__comm__idem(_790917, _790913, _790909)), c_Finite__Set_Ofun__left__comm__idem(_790919, _790915, _790911), _790919 = _790917, _790915 = _790913, _790911 = _790909], (5967 ^ _781215) ^ [_876241, _876243, _876245] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _876241))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_876243, _876241, _876245))))], (5012 ^ _781215) ^ [_857411, _857413, _857415, _857417, _857419, _857421, _857423, _857425] : [-(c_New__Random__Sequence_Opos__bind(_857425, _857421, _857417, _857413) = c_New__Random__Sequence_Opos__bind(_857423, _857419, _857415, _857411)), _857425 = _857423, _857421 = _857419, _857417 = _857415, _857413 = _857411], (4122 ^ _781215) ^ [_843786, _843788, _843790, _843792] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_843792, _843788) = c_SetInterval_Oord__class_OatLeastLessThan(_843790, _843786)), _843792 = _843790, _843788 = _843786], (33128 ^ _781215) ^ [_1396612, _1396614] : [class_Lattices_Oboolean__algebra(_1396612), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1396612), _1396614), hAPP(c_Groups_Ouminus__class_Ouminus(_1396612), _1396614)) = c_Orderings_Obot__class_Obot(_1396612))], (45055 ^ _781215) ^ [_1685037, _1685039, _1685041] : [class_Orderings_Olinorder(_1685037), -(c_Big__Operators_Olattice_OInf__fin(_1685037, c_Orderings_Oord__class_Omin(_1685037), hAPP(c_List_Oset(_1685037), hAPP(hAPP(c_List_Olist_OCons(_1685037), _1685039), _1685041))) = hAPP(c_List_Ofoldl(_1685037, _1685037, c_Orderings_Oord__class_Omin(_1685037), _1685039), _1685041))], (38482 ^ _781215) ^ [_1515838, _1515840, _1515842, _1515844, _1515846] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1515838, _1515840), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1515838, tc_HOL_Obool)), _1515842), _1515844)), hAPP(c_COMBK(tc_fun(_1515840, tc_HOL_Obool), _1515838), _1515846)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1515838, _1515840), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1515838, _1515840), _1515842), hAPP(c_COMBK(tc_fun(_1515840, tc_HOL_Obool), _1515838), _1515846))), hAPP(hAPP(c_Product__Type_OSigma(_1515838, _1515840), _1515844), hAPP(c_COMBK(tc_fun(_1515840, tc_HOL_Obool), _1515838), _1515846))))], (31644 ^ _781215) ^ [_1363161, _1363163, _1363165, _1363167, _1363169] : [class_Groups_Ocomm__monoid__add(_1363161), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363161), _1363163), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1363165), _1363167)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1363169), _1363167))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363161), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1363161, tc_Nat_Onat), _1363163), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1363167))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1363165), _1363169)))], (25640 ^ _781215) ^ [_1242647, _1242649, _1242651, _1242653] : [hBOOL(hAPP(hAPP(_1242651, _1242653), _1242649)), -(hBOOL(hAPP(hAPP(c_member(_1242647), _1242649), c_SetInterval_Oord_OatLeast(_1242647, _1242651, _1242653))))], (10812 ^ _781215) ^ [_966552, _966554, _966556, _966558, _966560, _966562] : [hAPP(c_Map_Omap__add(_966552, _966554, _966556, _966558), _966560) = hAPP(c_Option_Ooption_OSome(_966554), _966562), -(hAPP(_966558, _966560) = hAPP(c_Option_Ooption_OSome(_966554), _966562)), 10819 ^ _781215 : [(10822 ^ _781215) ^ [] : [-(hAPP(_966556, _966560) = hAPP(c_Option_Ooption_OSome(_966554), _966562))], (10820 ^ _781215) ^ [] : [-(hAPP(_966558, _966560) = c_Option_Ooption_ONone(_966554))]]], (21908 ^ _781215) ^ [_1175171, _1175173] : [class_Int_Onumber__ring(_1175171), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175171), _1175173), hAPP(c_Int_Onumber__class_Onumber__of(_1175171), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1175171), _1175173), _1175173))], (49666 ^ _781215) ^ [_1787324, _1787326] : [c_Wellfounded_Oacyclic(_1787324, _1787326), -(c_Wellfounded_Oacyclic(_1787324, hAPP(c_Relation_Oconverse(_1787324, _1787324), _1787326)))], (8922 ^ _781215) ^ [_932453, _932455, _932457] : [_932453 = _932455, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932457, tc_HOL_Obool)), _932453), _932455)))], (15120 ^ _781215) ^ [_1046682] : [c_Hoare__Mirabelle_Ostate__not__singleton, c_Com_OWT__bodies, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), _1046682), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), _1046682))], (43217 ^ _781215) ^ [_1642363, _1642365, _1642367, _1642369, _1642371, _1642373] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642363), tc_List_Olist(_1642363))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642363), tc_List_Olist(_1642363)), hAPP(hAPP(c_List_Olist_OCons(_1642363), _1642365), _1642367)), hAPP(hAPP(c_List_Olist_OCons(_1642363), _1642369), _1642371))), c_List_Olistrel1(_1642363, _1642373))), 43222 ^ _781215 : [(43225 ^ _781215) ^ [] : [-(_1642367 = _1642371)], (43223 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1642363, _1642363)), hAPP(hAPP(c_Product__Type_OPair(_1642363, _1642363), _1642365), _1642369)), _1642373)))]], 43226 ^ _781215 : [(43229 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642363), tc_List_Olist(_1642363))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642363), tc_List_Olist(_1642363)), _1642367), _1642371)), c_List_Olistrel1(_1642363, _1642373))))], (43227 ^ _781215) ^ [] : [-(_1642365 = _1642369)]]], (50380 ^ _781215) ^ [_1805718, _1805720, _1805722] : [c_Nitpick_Oless__frac(_1805718, _1805720, _1805722), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1805718), c_Nitpick_Oplus__frac(_1805718, _1805720, c_Nitpick_Ouminus__frac(_1805718, _1805722)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39164 ^ _781215) ^ [_1533239, _1533241, _1533243] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1533239, tc_HOL_Obool)), _1533241), _1533243) = hAPP(c_Set_OCollect(_1533239), hAPP(hAPP(c_COMBS(_1533239, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533239), c_fdisj), hAPP(hAPP(c_COMBC(_1533239, tc_fun(_1533239, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533239)), _1533241))), hAPP(hAPP(c_COMBC(_1533239, tc_fun(_1533239, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533239)), _1533243))))], (24546 ^ _781215) ^ [_1224187, _1224189] : [-(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), _1224187)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1224189), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1224187))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (32842 ^ _781215) ^ [_1389906, _1389908, _1389910, _1389912] : [class_Lattices_Odistrib__lattice(_1389906), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1389906), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1389906), _1389908), _1389910)), _1389912) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1389906), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1389906), _1389908), _1389912)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1389906), _1389910), _1389912)))], (15659 ^ _781215) ^ [_1056577, _1056579, _1056581, _1056583] : [15660 ^ _781215 : [(15661 ^ _781215) ^ [_1056666] : [_1056581 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1056577, tc_Option_Ooption(_1056579)), hAPP(c_COMBK(tc_Option_Ooption(_1056579), _1056577), c_Option_Ooption_ONone(_1056579))), _1056583), hAPP(c_Option_Ooption_OSome(_1056579), _1056666))]], -(c_Map_Odom(_1056577, _1056579, _1056581) = hAPP(hAPP(c_Set_Oinsert(_1056577), _1056583), c_Orderings_Obot__class_Obot(tc_fun(_1056577, tc_HOL_Obool))))], (15204 ^ _781215) ^ [_1048019, _1048021, _1048023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1048019), _1048021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1048023), _1048019)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1048023), _1048021))))], (20409 ^ _781215) ^ [_1147461] : [hBOOL(hAPP(_1147461, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20410 ^ [_1147461]))), 20413 ^ _781215 : [(20414 ^ _781215) ^ [_1147561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147561)), -(hBOOL(hAPP(_1147461, _1147561)))]]], (13000 ^ _781215) ^ [_1007663, _1007665] : [class_Groups_Oordered__ab__group__add(_1007663), 13003 ^ _781215 : [(13010 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007663), c_Groups_Ozero__class_Ozero(_1007663)), _1007665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007663), hAPP(c_Groups_Ouminus__class_Ouminus(_1007663), _1007665)), c_Groups_Ozero__class_Ozero(_1007663))))], (13004 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007663), hAPP(c_Groups_Ouminus__class_Ouminus(_1007663), _1007665)), c_Groups_Ozero__class_Ozero(_1007663))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007663), c_Groups_Ozero__class_Ozero(_1007663)), _1007665)))]]], (14467 ^ _781215) ^ [_1034132, _1034134] : [class_Rings_Olinordered__idom(_1034132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1034132), _1034134), c_Groups_Ozero__class_Ozero(_1034132))), -(c_Groups_Osgn__class_Osgn(_1034132, _1034134) = hAPP(c_Groups_Ouminus__class_Ouminus(_1034132), c_Groups_Oone__class_Oone(_1034132)))], (45201 ^ _781215) ^ [_1687947, _1687949, _1687951, _1687953] : [-(hAPP(hAPP(c_List_Oappend(_1687947), _1687949), hAPP(hAPP(c_List_Olist_OCons(_1687947), _1687951), c_List_Olist_ONil(_1687947))) = _1687953), -(_1687953 = c_List_Olist_ONil(_1687947)), c_List_Obutlast(_1687947, _1687953) = _1687949, c_List_Olast(_1687947, _1687953) = _1687951], (42803 ^ _781215) ^ [_1631731, _1631733, _1631735, _1631737] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1631731) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1631733), hAPP(hAPP(c_List_Olist_OCons(_1631733), _1631735), _1631737)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1631731)) = hAPP(hAPP(c_List_Onth(_1631733), _1631737), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1631731)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (36748 ^ _781215) ^ [_1472212, _1472214, _1472216, _1472218, _1472220] : [c_Fun_Oinj__on(_1472212, _1472214, _1472216, c_Orderings_Otop__class_Otop(tc_fun(_1472212, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1472212, _1472214, _1472216), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472212, tc_HOL_Obool)), _1472218), _1472220)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472214, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1472212, _1472214, _1472216), _1472218)), hAPP(c_Set_Oimage(_1472212, _1472214, _1472216), _1472220)))], (6297 ^ _781215) ^ [_883127, _883129, _883131] : [_883131 = hAPP(c_Option_Ooption_OSome(_883127), _883129), -(hBOOL(hAPP(hAPP(c_member(_883127), _883129), c_Option_Oset(_883127, _883131))))], (570 ^ _781215) ^ [_790078, _790080, _790082, _790084, _790086, _790088, _790090, _790092] : [-(c_Finite__Set_Ofolding__idem(_790090, _790086, _790082, _790078)), c_Finite__Set_Ofolding__idem(_790092, _790088, _790084, _790080), _790092 = _790090, _790088 = _790086, _790084 = _790082, _790080 = _790078], (34021 ^ _781215) ^ [_1415999, _1416001, _1416003, _1416005, _1416007, _1416009, _1416011, _1416013, _1416015] : [c_Equiv__Relations_Oequiv(_1415999, _1416001, _1416003), c_Equiv__Relations_Oequiv(_1416005, _1416007, _1416009), c_Equiv__Relations_Ocongruent2(_1415999, _1416005, tc_fun(_1416011, tc_HOL_Obool), _1416003, _1416009, _1416013), hBOOL(hAPP(hAPP(c_member(_1416005), _1416015), _1416007)), -(c_Equiv__Relations_Ocongruent(_1415999, tc_fun(_1416011, tc_HOL_Obool), _1416003, hAPP(hAPP(c_COMBB(tc_fun(_1416005, tc_fun(_1416011, tc_HOL_Obool)), tc_fun(_1416011, tc_HOL_Obool), _1415999), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416005, tc_fun(_1416011, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1416005, _1416005, _1416009), hAPP(hAPP(c_Set_Oinsert(_1416005), _1416015), c_Orderings_Obot__class_Obot(tc_fun(_1416005, tc_HOL_Obool)))))), _1416013)))], (11442 ^ _781215) ^ [_980751, _980753] : [-(_980751 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980751), _980753) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _980753), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980751), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _980753)))], (43982 ^ _781215) ^ [_1659976, _1659978, _1659980, _1659982, _1659984] : [-(hAPP(hAPP(c_List_Ozip(_1659976, _1659978), _1659980), hAPP(hAPP(c_List_Olist_OCons(_1659978), _1659982), _1659984)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1659976, _1659978)), _1659976, c_List_Olist_ONil(tc_prod(_1659976, _1659978)), hAPP(hAPP(c_COMBC(_1659976, tc_fun(tc_List_Olist(_1659976), tc_List_Olist(tc_prod(_1659976, _1659978))), tc_fun(tc_List_Olist(_1659976), tc_List_Olist(tc_prod(_1659976, _1659978)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1659976, _1659978)), tc_List_Olist(tc_prod(_1659976, _1659978))), tc_fun(tc_fun(tc_List_Olist(_1659976), tc_List_Olist(tc_prod(_1659976, _1659978))), tc_fun(tc_List_Olist(_1659976), tc_List_Olist(tc_prod(_1659976, _1659978)))), _1659976), c_COMBB(tc_List_Olist(tc_prod(_1659976, _1659978)), tc_List_Olist(tc_prod(_1659976, _1659978)), tc_List_Olist(_1659976))), hAPP(hAPP(c_COMBB(tc_prod(_1659976, _1659978), tc_fun(tc_List_Olist(tc_prod(_1659976, _1659978)), tc_List_Olist(tc_prod(_1659976, _1659978))), _1659976), c_List_Olist_OCons(tc_prod(_1659976, _1659978))), hAPP(hAPP(c_COMBC(_1659976, _1659978, tc_prod(_1659976, _1659978)), c_Product__Type_OPair(_1659976, _1659978)), _1659982)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1659976), tc_List_Olist(_1659978), tc_List_Olist(tc_prod(_1659976, _1659978))), c_List_Ozip(_1659976, _1659978)), _1659984))), _1659980))], (18087 ^ _781215) ^ [_1104625, _1104627] : [-(c_Int_Onat__aux(_1104625, _1104627) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1104625)), _1104627))], (28032 ^ _781215) ^ [_1291951, _1291953, _1291955, _1291957, _1291959] : [class_Fields_Ofield__inverse__zero(_1291951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291953), _1291955)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1291953, _1291951), hAPP(hAPP(c_COMBS(_1291953, _1291951, _1291951), hAPP(hAPP(c_COMBB(_1291951, tc_fun(_1291951, _1291951), _1291953), c_Rings_Oinverse__class_Odivide(_1291951)), _1291957)), _1291959)), _1291955) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291951), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1291953, _1291951), _1291957), _1291955)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1291953, _1291951), _1291959), _1291955)))], (18405 ^ _781215) ^ [_1110675, _1110677] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1110675)), hAPP(c_Nat_OSuc, _1110677)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1110675), _1110677)))], (8129 ^ _781215) ^ [_918212, _918214, _918216, _918218, _918220] : [class_Groups_Oordered__ab__group__add(_918212), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918212), _918214), _918216) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918212), _918218), _918220), 8136 ^ _781215 : [(8143 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918212), _918218), _918220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918212), _918214), _918216)))], (8137 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918212), _918214), _918216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918212), _918218), _918220)))]]], (4016 ^ _781215) ^ [_842141, _842143] : [_842143 = _842141, -(c_Orderings_Oord__class_Omin(_842143) = c_Orderings_Oord__class_Omin(_842141))], (25296 ^ _781215) ^ [_1237265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1237265)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237265), c_Int_OMin)))], (33553 ^ _781215) ^ [_1406272, _1406274, _1406276] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1406272), _1406274)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406272), _1406276)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1406272), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406272, tc_HOL_Obool)), _1406274), _1406276))), hAPP(c_Finite__Set_Ocard(_1406272), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406272, tc_HOL_Obool)), _1406274), _1406276))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1406272), _1406274)), hAPP(c_Finite__Set_Ocard(_1406272), _1406276)))], (51458 ^ _781215) ^ [] : [-(class_HOL_Oequal(tc_Com_Ovname))], (26698 ^ _781215) ^ [_1265624, _1265626] : [c_Nitpick_Orefl_H(_1265624, _1265626), 26701 ^ _781215 : [(26702 ^ _781215) ^ [_1265702] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1265624, _1265624)), hAPP(hAPP(c_Product__Type_OPair(_1265624, _1265624), _1265702), _1265702)), _1265626)))]]], (28896 ^ _781215) ^ [_1308016, _1308018, _1308020] : [class_Fields_Ofield__inverse__zero(_1308016), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1308016), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308016), _1308018), _1308020)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308016), _1308018), hAPP(c_Groups_Ouminus__class_Ouminus(_1308016), _1308020)))], (7090 ^ _781215) ^ [_899283, _899285, _899287, _899289, _899291, _899293] : [c_Finite__Set_Ofolding__image__simple(_899283, _899285, _899287, _899289, _899291, _899293), -(hAPP(_899293, c_Orderings_Obot__class_Obot(tc_fun(_899285, tc_HOL_Obool))) = _899289)], (51322 ^ _781215) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (9153 ^ _781215) ^ [_936483] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936483), _936483)))], (4534 ^ _781215) ^ [_849966, _849968, _849970, _849972, _849974, _849976] : [-(c_Relation_Orel__comp(_849976, _849972, _849968) = c_Relation_Orel__comp(_849974, _849970, _849966)), _849976 = _849974, _849972 = _849970, _849968 = _849966], (51724 ^ _781215) ^ [_1826414, _1826416] : [hBOOL(_1826414), -(hBOOL(hAPP(hAPP(c_fdisj, _1826414), _1826416)))], (16830 ^ _781215) ^ [_1083438, _1083440] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1083438, tc_HOL_Obool)), _1083440)), -(hBOOL(hAPP(hAPP(c_member(_1083438), _1083440), c_Orderings_Obot__class_Obot(tc_fun(_1083438, tc_HOL_Obool)))))], (23897 ^ _781215) ^ [_1211946, _1211948, _1211950] : [class_Int_Onumber__ring(_1211946), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1211946), _1211948), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1211950))) = hAPP(hAPP(c_HOL_OLet(_1211946, _1211946), hAPP(hAPP(c_Power_Opower__class_Opower(_1211946), _1211948), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1211950))), hAPP(hAPP(c_COMBS(_1211946, _1211946, _1211946), c_Groups_Otimes__class_Otimes(_1211946)), c_COMBI(_1211946))))], (27245 ^ _781215) ^ [_1276332, _1276334, _1276336, _1276338] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1276332, _1276334), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1276336), _1276338))), -(_1276334 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1276332), _1276334) = _1276336)], (12282 ^ _781215) ^ [_994736, _994738, _994740, _994742] : [class_Rings_Oordered__comm__semiring(_994736), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994736), _994738), _994740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994736), c_Groups_Ozero__class_Ozero(_994736)), _994742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994736), _994742), _994738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994736), _994742), _994740))))], (12296 ^ _781215) ^ [_995005, _995007, _995009, _995011] : [class_Rings_Oordered__semiring(_995005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995005), _995007), _995009)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995005), c_Groups_Ozero__class_Ozero(_995005)), _995011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995005), _995011), _995007)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995005), _995011), _995009))))], (27822 ^ _781215) ^ [_1288341, _1288343, _1288345, _1288347] : [class_Rings_Odivision__ring(_1288341), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288341), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288341), _1288343), _1288345)), _1288347) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288341), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288341), _1288343), _1288347)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288341), _1288345), _1288347)))], (42949 ^ _781215) ^ [_1635709, _1635711, _1635713] : [hBOOL(hAPP(c_List_Odistinct(_1635709), _1635711)), -(hBOOL(hAPP(c_List_Odistinct(_1635709), hAPP(hAPP(c_List_Otake(_1635709), _1635713), _1635711))))], (41813 ^ _781215) ^ [_1604707, _1604709, _1604711] : [hBOOL(hAPP(c_List_Odistinct(_1604707), _1604709)), -(hAPP(c_List_Oset(_1604707), c_List_Oremove1(_1604707, _1604711, _1604709)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1604707, tc_HOL_Obool)), hAPP(c_List_Oset(_1604707), _1604709)), hAPP(hAPP(c_Set_Oinsert(_1604707), _1604711), c_Orderings_Obot__class_Obot(tc_fun(_1604707, tc_HOL_Obool)))))], (48606 ^ _781215) ^ [_1762777, _1762779, _1762781] : [c_List_Olist__ex(_1762777, _1762779, _1762781), 48610 ^ _781215 : [(48613 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1762779, hAPP(hAPP(c_List_Onth(_1762777), _1762781), 48609 ^ [_1762777, _1762779, _1762781]))))], (48611 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48609 ^ [_1762777, _1762779, _1762781]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762777)), _1762781))))]]], (18541 ^ _781215) ^ [_1113273, _1113275, _1113277] : [class_Orderings_Olinorder(_1113273), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113273), _1113275)), -(_1113275 = c_Orderings_Obot__class_Obot(tc_fun(_1113273, tc_HOL_Obool))), 18552 ^ _781215 : [(18553 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113273), _1113277), hAPP(c_Finite__Set_Ofold1(_1113273, c_Orderings_Oord__class_Omin(_1113273)), _1113275))), 18556 ^ _781215 : [(18557 ^ _781215) ^ [_1113566] : [hBOOL(hAPP(hAPP(c_member(_1113273), _1113566), _1113275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113273), _1113277), _1113566)))]]], (18563 ^ _781215) ^ [] : [18565 ^ _781215 : [(18568 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113273), _1113277), 18564 ^ [_1113273, _1113275, _1113277]))], (18566 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1113273), 18564 ^ [_1113273, _1113275, _1113277]), _1113275)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113273), _1113277), hAPP(c_Finite__Set_Ofold1(_1113273, c_Orderings_Oord__class_Omin(_1113273)), _1113275))))]]], (43876 ^ _781215) ^ [_1657285, _1657287, _1657289] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657285), tc_List_Olist(_1657285))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657285), tc_List_Olist(_1657285)), _1657287), c_List_Olist_ONil(_1657285))), c_List_Olex(_1657285, _1657289)))], (44964 ^ _781215) ^ [_1683141, _1683143, _1683145, _1683147, _1683149, _1683151, _1683153] : [-(hAPP(c_List_Ofoldl(_1683141, _1683143, _1683145, _1683147), hAPP(hAPP(c_List_Omap(_1683149, _1683143), _1683151), _1683153)) = hAPP(c_List_Ofoldl(_1683141, _1683149, hAPP(hAPP(c_COMBC(_1683141, tc_fun(_1683149, _1683143), tc_fun(_1683149, _1683141)), hAPP(hAPP(c_COMBB(tc_fun(_1683143, _1683141), tc_fun(tc_fun(_1683149, _1683143), tc_fun(_1683149, _1683141)), _1683141), c_COMBB(_1683143, _1683141, _1683149)), _1683145)), _1683151), _1683147), _1683153))], (15144 ^ _781215) ^ [_1047012, _1047014, _1047016] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1047012, _1047014, _1047016))), -(hBOOL(hAPP(c_Com_OWT, _1047016)))], (34428 ^ _781215) ^ [_1426027, _1426029, _1426031] : [class_Lattices_Olattice(_1426027), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426027), _1426029)), -(c_Big__Operators_Olattice__class_OInf__fin(_1426027, hAPP(hAPP(c_Set_Oinsert(_1426027), _1426031), _1426029)) = hAPP(hAPP(c_Finite__Set_Ofold(_1426027, _1426027, c_Lattices_Osemilattice__inf__class_Oinf(_1426027)), _1426031), _1426029))], (18221 ^ _781215) ^ [_1107436, _1107438, _1107440, _1107442] : [class_Orderings_Olinorder(_1107436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107436), _1107438), _1107440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107436), _1107438), _1107442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107436), _1107438), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1107436), _1107440), _1107442))))], (9235 ^ _781215) ^ [_938370, _938372, _938374] : [class_Groups_Oordered__ab__group__add(_938370), 9238 ^ _781215 : [(9245 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938370), _938374), hAPP(c_Groups_Ouminus__class_Ouminus(_938370), _938372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938370), _938372), hAPP(c_Groups_Ouminus__class_Ouminus(_938370), _938374))))], (9239 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938370), _938372), hAPP(c_Groups_Ouminus__class_Ouminus(_938370), _938374))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938370), _938374), hAPP(c_Groups_Ouminus__class_Ouminus(_938370), _938372))))]]], (51566 ^ _781215) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (12754 ^ _781215) ^ [_1003305, _1003307, _1003309, _1003311] : [class_Rings_Olinordered__semiring__strict(_1003305), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003305), _1003307), _1003309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003305), c_Groups_Ozero__class_Ozero(_1003305)), _1003311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003305), _1003307), _1003311)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003305), _1003309), _1003311))))], (45897 ^ _781215) ^ [_1701607, _1701609, _1701611, _1701613] : [class_Groups_Ocomm__monoid__add(_1701607), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1701607), _1701609), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701611, _1701613))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1701607), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1701607), _1701609), c_List_Oupt(_1701611, _1701613))))], (51658 ^ _781215) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (11436 ^ _781215) ^ [_980668, _980670] : [_980668 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980668), _980670) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15380 ^ _781215) ^ [_1050833] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050833), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1050833)], (178 ^ _781215) ^ [_783932, _783934] : [-(class_Fields_Ofield__inverse__zero(_783932)), _783934 = _783932, class_Fields_Ofield__inverse__zero(_783934)], (27492 ^ _781215) ^ [_1281543] : [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), _1281543))), -(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), _1281543)) = 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), _1281543))))], (36273 ^ _781215) ^ [_1463202, _1463204, _1463206, _1463208, _1463210, _1463212] : [hAPP(_1463208, hAPP(c_Product__Type_Ofst(_1463202, _1463206), _1463210)) = hAPP(_1463212, hAPP(c_Product__Type_Ofst(_1463202, _1463206), _1463210)), -(hAPP(c_Product__Type_Oapfst(_1463202, _1463204, _1463206, _1463208), _1463210) = hAPP(c_Product__Type_Oapfst(_1463202, _1463204, _1463206, _1463212), _1463210))], (33020 ^ _781215) ^ [_1393856, _1393858, _1393860] : [class_Lattices_Olattice(_1393856), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393856), _1393858), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393856), _1393858), _1393860)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393856), _1393858), _1393860))], (21410 ^ _781215) ^ [_1165481] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1165481)), -(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)), _1165481))))], (32467 ^ _781215) ^ [_1381961, _1381963, _1381965, _1381967, _1381969] : [c_Equiv__Relations_Oequiv(_1381961, _1381963, _1381965), hBOOL(hAPP(hAPP(c_member(_1381961), _1381967), _1381963)), hBOOL(hAPP(hAPP(c_member(_1381961), _1381969), _1381963)), 32478 ^ _781215 : [(32485 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1381961, _1381961)), hAPP(hAPP(c_Product__Type_OPair(_1381961, _1381961), _1381967), _1381969)), _1381965)), -(hAPP(c_Relation_OImage(_1381961, _1381961, _1381965), hAPP(hAPP(c_Set_Oinsert(_1381961), _1381967), c_Orderings_Obot__class_Obot(tc_fun(_1381961, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1381961, _1381961, _1381965), hAPP(hAPP(c_Set_Oinsert(_1381961), _1381969), c_Orderings_Obot__class_Obot(tc_fun(_1381961, tc_HOL_Obool)))))], (32479 ^ _781215) ^ [] : [hAPP(c_Relation_OImage(_1381961, _1381961, _1381965), hAPP(hAPP(c_Set_Oinsert(_1381961), _1381967), c_Orderings_Obot__class_Obot(tc_fun(_1381961, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1381961, _1381961, _1381965), hAPP(hAPP(c_Set_Oinsert(_1381961), _1381969), c_Orderings_Obot__class_Obot(tc_fun(_1381961, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1381961, _1381961)), hAPP(hAPP(c_Product__Type_OPair(_1381961, _1381961), _1381967), _1381969)), _1381965)))]]], (47924 ^ _781215) ^ [_1746297, _1746299] : [-(c_List_OremoveAll(_1746297, _1746299) = c_List_Ofilter(_1746297, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1746297), c_fNot), hAPP(c_fequal, _1746299))))], (30984 ^ _781215) ^ [_1348403, _1348405] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348403), _1348405)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1348403)), hAPP(c_Nat_OSuc, _1348405)))], (39707 ^ _781215) ^ [_1552871, _1552873] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1552871), _1552873)), -(_1552873 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1552871, 39711 ^ [_1552871, _1552873]), 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)), 39710 ^ [_1552871, _1552873]))))], (37709 ^ _781215) ^ [_1497670, _1497672] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1497670, tc_HOL_Obool), _1497672) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1497670, tc_HOL_Obool), tc_fun(_1497670, tc_HOL_Obool)), _1497672), c_COMBI(tc_fun(_1497670, tc_HOL_Obool))))], (32816 ^ _781215) ^ [_1389069, _1389071, _1389073, _1389075] : [-(hBOOL(hAPP(hAPP(c_member(_1389069), _1389071), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389069, tc_HOL_Obool)), _1389073), _1389075)))), hBOOL(hAPP(hAPP(c_member(_1389069), _1389071), _1389073)), hBOOL(hAPP(hAPP(c_member(_1389069), _1389071), _1389075))], (51050 ^ _781215) ^ [_1819144, _1819146] : [class_Complete__Lattice_Ocomplete__lattice(_1819144), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1819146, _1819144)))], (39468 ^ _781215) ^ [_1543582, _1543584, _1543586] : [class_Groups_Olinordered__ab__semigroup__add(_1543582), hBOOL(hAPP(c_Finite__Set_Ofinite(_1543582), _1543584)), -(_1543584 = c_Orderings_Obot__class_Obot(tc_fun(_1543582, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1543582), _1543586), c_Big__Operators_Olinorder__class_OMin(_1543582, _1543584)) = c_Big__Operators_Olinorder__class_OMin(_1543582, hAPP(c_Set_OCollect(_1543582), hAPP(hAPP(c_COMBB(tc_fun(_1543582, tc_HOL_Obool), tc_HOL_Obool, _1543582), c_HOL_OEx(_1543582)), hAPP(hAPP(c_COMBC(_1543582, tc_fun(_1543582, tc_HOL_Obool), tc_fun(_1543582, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543582, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1543582, tc_HOL_Obool), tc_fun(_1543582, tc_HOL_Obool)), _1543582), c_COMBS(_1543582, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543582, tc_HOL_Obool), tc_fun(_1543582, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1543582), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543582), c_fconj)), hAPP(hAPP(c_COMBC(_1543582, tc_fun(_1543582, _1543582), tc_fun(_1543582, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543582, tc_HOL_Obool), tc_fun(tc_fun(_1543582, _1543582), tc_fun(_1543582, tc_HOL_Obool)), _1543582), c_COMBB(_1543582, tc_HOL_Obool, _1543582)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1543582), _1543586))))), hAPP(hAPP(c_COMBC(_1543582, tc_fun(_1543582, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543582)), _1543584))))))], (22623 ^ _781215) ^ [_1189682, _1189684] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1189682), _1189684) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189682, _1189684) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (11710 ^ _781215) ^ [_985391, _985393] : [class_Rings_Omult__zero(_985391), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985391), _985393), c_Groups_Ozero__class_Ozero(_985391)) = c_Groups_Ozero__class_Ozero(_985391))], (7742 ^ _781215) ^ [_911659, _911661, _911663] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911659), _911661) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911663), _911661), -(_911659 = _911663)], (25274 ^ _781215) ^ [_1236973, _1236975] : [c_Nat__Transfer_Ois__nat(_1236973), c_Nat__Transfer_Ois__nat(_1236975), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1236973), _1236975)))], (7360 ^ _781215) ^ [_905390, _905392, _905394] : [class_Orderings_Olinorder(_905390), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905390), _905392), _905394))), -(_905392 = _905394), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905390), _905394), _905392)))], (16824 ^ _781215) ^ [_1083282, _1083284, _1083286] : [_1083284 = _1083286, -(hAPP(hAPP(c_COMBC(_1083282, tc_fun(_1083282, tc_HOL_Obool), tc_HOL_Obool), c_member(_1083282)), _1083284) = hAPP(hAPP(c_COMBC(_1083282, tc_fun(_1083282, tc_HOL_Obool), tc_HOL_Obool), c_member(_1083282)), _1083286))], (33232 ^ _781215) ^ [_1399037, _1399039, _1399041, _1399043] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399037, tc_HOL_Obool)), _1399039), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399037, tc_HOL_Obool)), _1399041), _1399043)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399037, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399037, tc_HOL_Obool)), _1399039), _1399041)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399037, tc_HOL_Obool)), _1399039), _1399043)))], (9847 ^ _781215) ^ [_948605, _948607, _948609] : [_948607 = _948609, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _948605)), _948607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _948605)), _948609))], (27996 ^ _781215) ^ [_1291328, _1291330, _1291332] : [class_Rings_Odivision__ring(_1291328), -(_1291330 = c_Groups_Ozero__class_Ozero(_1291328)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291328), hAPP(c_Groups_Ouminus__class_Ouminus(_1291328), _1291332)), hAPP(c_Groups_Ouminus__class_Ouminus(_1291328), _1291330)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291328), _1291332), _1291330))], (10300 ^ _781215) ^ [_956656, _956658, _956660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_956656), tc_HOL_Obool)), _956658), _956660)), -(c_Hoare__Mirabelle_Ohoare__derivs(_956656, _956660, _956658))], (6946 ^ _781215) ^ [_896248, _896250, _896252, _896254, _896256] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_896248, _896248, _896250, _896252, _896254), _896256)), -(hBOOL(hAPP(hAPP(c_member(_896248), _896252), _896254))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_896248, _896250, hAPP(hAPP(c_Set_Oinsert(_896248), _896252), _896254)), _896256)))], (48033 ^ _781215) ^ [_1748837, _1748839, _1748841, _1748843, _1748845] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1748837, _1748837)), hAPP(hAPP(c_Product__Type_OPair(_1748837, _1748837), _1748839), _1748841)), c_List_Omeasures(_1748837, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1748837, tc_Nat_Onat)), _1748843), _1748845)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1748843, _1748839)), hAPP(_1748843, _1748841)))), 48040 ^ _781215 : [(48043 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1748837, _1748837)), hAPP(hAPP(c_Product__Type_OPair(_1748837, _1748837), _1748839), _1748841)), c_List_Omeasures(_1748837, _1748845))))], (48041 ^ _781215) ^ [] : [-(hAPP(_1748843, _1748839) = hAPP(_1748843, _1748841))]]], (51418 ^ _781215) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (16949 ^ _781215) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7216 ^ _781215) ^ [_902291, _902293, _902295, _902297, _902299, _902301] : [hBOOL(hAPP(hAPP(c_member(_902291), _902293), _902295)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_902291, tc_Option_Ooption(_902297)), c_Map_Orestrict__map(_902291, _902297, _902299, _902295)), _902293), _902301) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_902291, tc_Option_Ooption(_902297)), c_Map_Orestrict__map(_902291, _902297, _902299, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902291, tc_HOL_Obool)), _902295), hAPP(hAPP(c_Set_Oinsert(_902291), _902293), c_Orderings_Obot__class_Obot(tc_fun(_902291, tc_HOL_Obool)))))), _902293), _902301))], (46688 ^ _781215) ^ [_1719794, _1719796] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719794)), c_List_Oremdups(_1719794, _1719796)) = hAPP(c_Finite__Set_Ocard(_1719794), hAPP(c_List_Oset(_1719794), _1719796)))], (25172 ^ _781215) ^ [_1235567, _1235569] : [class_Int_Onumber__ring(_1235567), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1235567), hAPP(c_Int_Onumber__class_Onumber__of(_1235567), 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)))), _1235569)) = c_Groups_Oone__class_Oone(_1235567))], (51572 ^ _781215) ^ [_1824691] : [-(class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(_1824691)))], (46846 ^ _781215) ^ [_1723355, _1723357, _1723359] : [-(c_Enum_On__lists(_1723355, hAPP(c_Nat_OSuc, _1723357), _1723359) = c_List_Oconcat(tc_List_Olist(_1723355), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1723355), tc_List_Olist(tc_List_Olist(_1723355))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1723355), tc_List_Olist(_1723355), tc_List_Olist(tc_List_Olist(_1723355))), hAPP(hAPP(c_COMBB(tc_fun(_1723355, tc_List_Olist(_1723355)), tc_fun(tc_List_Olist(_1723355), tc_List_Olist(tc_List_Olist(_1723355))), tc_List_Olist(_1723355)), c_List_Omap(_1723355, tc_List_Olist(_1723355))), hAPP(c_COMBC(_1723355, tc_List_Olist(_1723355), tc_List_Olist(_1723355)), c_List_Olist_OCons(_1723355)))), _1723359)), c_Enum_On__lists(_1723355, _1723357, _1723359))))], (36299 ^ _781215) ^ [_1463706, _1463708, _1463710, _1463712, _1463714, _1463716, _1463718] : [-(hAPP(c_Product__Type_Oapsnd(_1463706, _1463708, _1463710, _1463712), hAPP(c_Product__Type_Oapfst(_1463714, _1463710, _1463706, _1463716), _1463718)) = hAPP(hAPP(c_Product__Type_OPair(_1463710, _1463708), hAPP(_1463716, hAPP(c_Product__Type_Ofst(_1463714, _1463706), _1463718))), hAPP(_1463712, hAPP(c_Product__Type_Osnd(_1463714, _1463706), _1463718))))], (43866 ^ _781215) ^ [_1656930, _1656932, _1656934] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656930), tc_List_Olist(_1656930))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656930), tc_List_Olist(_1656930)), _1656932), c_List_Olist_ONil(_1656930))), c_List_Olistrel1(_1656930, _1656934)))], (44896 ^ _781215) ^ [_1681661, _1681663, _1681665] : [-(c_List_Orotate(_1681661, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1681663), _1681665)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1681661), tc_List_Olist(_1681661), tc_List_Olist(_1681661), c_List_Orotate(_1681661, _1681663)), c_List_Orotate(_1681661, _1681665)))], (49032 ^ _781215) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (19218 ^ _781215) ^ [_1126105, _1126107, _1126109] : [class_Orderings_Olinorder(_1126105), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126105), _1126107)), hBOOL(hAPP(hAPP(c_member(_1126105), _1126109), _1126107)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1126105), _1126109), c_Big__Operators_Olinorder__class_OMin(_1126105, _1126107)) = c_Big__Operators_Olinorder__class_OMin(_1126105, _1126107))], (24920 ^ _781215) ^ [_1230935, _1230937, _1230939, _1230941] : [class_Rings_Olinordered__semidom(_1230935), hAPP(hAPP(c_Power_Opower__class_Opower(_1230935), _1230937), hAPP(c_Nat_OSuc, _1230939)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1230935), _1230941), hAPP(c_Nat_OSuc, _1230939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230935), c_Groups_Ozero__class_Ozero(_1230935)), _1230937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230935), c_Groups_Ozero__class_Ozero(_1230935)), _1230941)), -(_1230937 = _1230941)], (16473 ^ _781215) ^ [_1072809, _1072811, _1072813] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072809, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1072809, tc_HOL_Obool)), _1072811), _1072813)), _1072813) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072809, tc_HOL_Obool)), _1072811), _1072813))], (46676 ^ _781215) ^ [_1719595, _1719597, _1719599] : [hBOOL(hAPP(hAPP(c_member(_1719595), _1719597), hAPP(c_List_Oset(_1719595), _1719599))), -(c_List_Oremdups(_1719595, hAPP(hAPP(c_List_Olist_OCons(_1719595), _1719597), _1719599)) = c_List_Oremdups(_1719595, _1719599))], (33088 ^ _781215) ^ [_1395214, _1395216, _1395218, _1395220] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395214, tc_HOL_Obool)), _1395216), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1395214, tc_HOL_Obool)), _1395218), _1395220)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1395214, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395214, tc_HOL_Obool)), _1395216), _1395218)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395214, tc_HOL_Obool)), _1395216), _1395220)))], (41831 ^ _781215) ^ [_1605144, _1605146, _1605148, _1605150] : [-(c_List_Oremove1(_1605144, _1605146, c_List_Oremove1(_1605144, _1605148, _1605150)) = c_List_Oremove1(_1605144, _1605148, c_List_Oremove1(_1605144, _1605146, _1605150)))], (8526 ^ _781215) ^ [_925912, _925914, _925916] : [-(hBOOL(hAPP(hAPP(c_member(_925912), _925914), _925916))), -(hBOOL(hAPP(hAPP(c_member(_925912), _925914), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_925912, tc_HOL_Obool)), _925916))))], (48144 ^ _781215) ^ [_1752001, _1752003, _1752005, _1752007, _1752009, _1752011] : [48147 ^ _781215 : [(48150 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1752007), _1752009), hAPP(hAPP(_1752011, 48145 ^ [_1752001, _1752003, _1752005, _1752007, _1752009, _1752011]), 48146 ^ [_1752001, _1752003, _1752005, _1752007, _1752009, _1752011])))], (48148 ^ _781215) ^ [] : [-(_1752001 = hAPP(hAPP(c_Product__Type_OPair(_1752003, _1752005), 48145 ^ [_1752001, _1752003, _1752005, _1752007, _1752009, _1752011]), 48146 ^ [_1752001, _1752003, _1752005, _1752007, _1752009, _1752011]))]], -(hBOOL(hAPP(hAPP(c_member(_1752007), _1752009), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1752003, _1752005, tc_fun(_1752007, tc_HOL_Obool)), _1752011), _1752001))))], (1828 ^ _781215) ^ [_807035, _807037] : [-(class_Power_Opower(_807035)), _807037 = _807035, class_Power_Opower(_807037)], (40507 ^ _781215) ^ [_1574414, _1574416] : [hBOOL(hAPP(_1574416, 40508 ^ [_1574414, _1574416])), 40511 ^ _781215 : [(40512 ^ _781215) ^ [_1574521] : [hBOOL(hAPP(hAPP(c_member(_1574414), _1574521), c_Orderings_Otop__class_Otop(tc_fun(_1574414, tc_HOL_Obool)))), -(hBOOL(hAPP(_1574416, _1574521)))]]], (49215 ^ _781215) ^ [_1775638, _1775640] : [-(c_Transitive__Closure_Otrancl(_1775638, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1775638, _1775638), tc_HOL_Obool)), _1775640), c_Relation_OId(_1775638))) = c_Transitive__Closure_Ortrancl(_1775638, _1775640))], (16337 ^ _781215) ^ [_1069870, _1069872, _1069874, _1069876] : [hBOOL(hAPP(hAPP(c_member(_1069870), _1069872), _1069874)), -(hBOOL(hAPP(hAPP(c_member(_1069870), _1069872), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1069870, tc_HOL_Obool)), _1069876), _1069874))))], (33416 ^ _781215) ^ [_1403263, _1403265, _1403267, _1403269] : [class_Orderings_Oorder(_1403263), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1403263, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1403263, _1403265, _1403267)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1403263, _1403267, _1403269)) = c_Orderings_Obot__class_Obot(tc_fun(_1403263, tc_HOL_Obool)))], (24378 ^ _781215) ^ [_1220782, _1220784] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220782)))), 24381 ^ _781215 : [(24388 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220784)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220782), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220784)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220782), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220784))))], (24382 ^ _781215) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220784))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220782), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220784)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220782))]]], (16459 ^ _781215) ^ [_1072432, _1072434, _1072436] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072432, tc_HOL_Obool)), _1072434), _1072436) = _1072436, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072432, tc_HOL_Obool)), _1072434), _1072436)))], (44966 ^ _781215) ^ [_1683243, _1683245, _1683247, _1683249] : [-(hAPP(c_List_Ofoldl(_1683243, _1683245, _1683247, _1683249), c_List_Olist_ONil(_1683245)) = _1683249)], (23845 ^ _781215) ^ [_1211043, _1211045] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1211043)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1211043)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1211045)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1211043)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1211045))))], (48733 ^ _781215) ^ [_1765369, _1765371, _1765373, _1765375, _1765377] : [-(_1765369 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1765371, _1765373, _1765369, _1765375), _1765377) = hAPP(hAPP(c_Product__Type_Oscomp(_1765373, _1765371, _1765373, tc_prod(_1765371, _1765373)), hAPP(_1765375, _1765377)), c_Random_Oiterate(_1765371, _1765373, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1765369), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1765375)))], (4320 ^ _781215) ^ [_846755, _846757, _846759, _846761] : [-(c_Relation_ORange(_846761, _846757) = c_Relation_ORange(_846759, _846755)), _846761 = _846759, _846757 = _846755], (20615 ^ _781215) ^ [] : [-(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)))], (51196 ^ _781215) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (10794 ^ _781215) ^ [_966252, _966254, _966256, _966258, _966260] : [-(hBOOL(hAPP(hAPP(c_member(_966252), _966254), c_Map_Odom(_966252, _966256, _966258)))), -(hAPP(c_Map_Omap__add(_966252, _966256, _966258, _966260), _966254) = hAPP(_966260, _966254))], (21954 ^ _781215) ^ [_1176246] : [-(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)))), _1176246) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1176246), _1176246))], (26940 ^ _781215) ^ [_1270872, _1270874, _1270876, _1270878, _1270880, _1270882] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1270872, _1270874, _1270876), _1270878), hAPP(hAPP(c_Product__Type_OPair(_1270872, _1270874), _1270880), _1270882)) = hAPP(hAPP(_1270878, _1270880), _1270882))], (24714 ^ _781215) ^ [_1227181, _1227183] : [24715 ^ _781215 : [(24718 ^ _781215) ^ [] : [_1227183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24716 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227181))]], -(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), _1227181), _1227183))))], (49676 ^ _781215) ^ [_1787495, _1787497] : [-(hAPP(c_Relation_Oconverse(_1787495, _1787495), c_Relation_OId__on(_1787495, _1787497)) = c_Relation_OId__on(_1787495, _1787497))], (37322 ^ _781215) ^ [_1488876, _1488878, _1488880, _1488882, _1488884, _1488886, _1488888] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1488876, tc_fun(_1488878, tc_fun(_1488880, tc_HOL_Obool))), _1488882), _1488884), _1488886), _1488888)), 37325 ^ _781215 : [(37326 ^ _781215) ^ [_1489004] : [hBOOL(hAPP(hAPP(c_member(_1488876), _1489004), _1488882)), -(hBOOL(hAPP(hAPP(hAPP(_1488884, _1489004), _1488886), _1488888)))]]], (35581 ^ _781215) ^ [_1449860, _1449862] : [class_Groups_Oordered__ab__group__add(_1449860), -(hAPP(c_Set_Oimage(_1449860, _1449860, c_Groups_Ouminus__class_Ouminus(_1449860)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1449860), _1449862)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1449860), hAPP(c_Groups_Ouminus__class_Ouminus(_1449860), _1449862)))], (42297 ^ _781215) ^ [_1617998, _1618000, _1618002, _1618004] : [hBOOL(hAPP(hAPP(c_member(_1617998), _1618000), hAPP(c_List_Oset(_1617998), c_List_Osublist(_1617998, _1618002, _1618004)))), -(hBOOL(hAPP(hAPP(c_member(_1617998), _1618000), hAPP(c_List_Oset(_1617998), _1618002))))], (36432 ^ _781215) ^ [_1465913, _1465915, _1465917] : [class_Orderings_Otop(_1465913), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1465915, _1465913)), _1465917) = c_Orderings_Otop__class_Otop(_1465913))], (15566 ^ _781215) ^ [_1054549, _1054551, _1054553, _1054555] : [-(_1054549 = c_Orderings_Obot__class_Obot(tc_fun(_1054551, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1054551, _1054553, hAPP(c_COMBK(_1054553, _1054551), _1054555)), _1054549) = hAPP(hAPP(c_Set_Oinsert(_1054553), _1054555), c_Orderings_Obot__class_Obot(tc_fun(_1054553, tc_HOL_Obool))))], (40069 ^ _781215) ^ [] : [-(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)))))], (34374 ^ _781215) ^ [_1425178, _1425180, _1425182] : [class_Lattices_Olattice(_1425178), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425178), _1425180)), -(_1425182 = c_Orderings_Obot__class_Obot(tc_fun(_1425178, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1425178, tc_HOL_Obool)), _1425182), _1425180)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1425178), c_Big__Operators_Olattice__class_OInf__fin(_1425178, _1425182)), c_Big__Operators_Olattice__class_OInf__fin(_1425178, _1425180)) = c_Big__Operators_Olattice__class_OInf__fin(_1425178, _1425180))], (3710 ^ _781215) ^ [_837452, _837454] : [_837454 = _837452, -(c_Enum_Oenum__class_Oenum__ex(_837454) = c_Enum_Oenum__class_Oenum__ex(_837452))], (34105 ^ _781215) ^ [_1418398, _1418400, _1418402, _1418404, _1418406, _1418408, _1418410] : [c_Equiv__Relations_Oequiv(_1418398, _1418400, _1418402), c_Equiv__Relations_Ocongruent(_1418398, tc_fun(_1418404, tc_HOL_Obool), _1418402, _1418406), hBOOL(hAPP(hAPP(c_member(tc_fun(_1418398, tc_HOL_Obool)), _1418408), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1418398), _1418400), _1418402))), 34119 ^ _781215 : [(34122 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1418404, tc_HOL_Obool)), hAPP(_1418406, 34118 ^ [_1418398, _1418400, _1418402, _1418404, _1418406, _1418408, _1418410])), _1418410))], (34120 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418398), 34118 ^ [_1418398, _1418400, _1418402, _1418404, _1418406, _1418408, _1418410]), _1418400)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1418404, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418398, tc_fun(_1418404, tc_HOL_Obool)), _1418408), _1418406)), _1418410)))], (19658 ^ _781215) ^ [_1134168, _1134170, _1134172] : [class_Orderings_Olinorder(_1134168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134168), _1134170)), hBOOL(hAPP(hAPP(c_member(_1134168), _1134172), _1134170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134168), _1134172), c_Big__Operators_Olinorder__class_OMax(_1134168, _1134170))))], (25160 ^ _781215) ^ [_1235351] : [class_Power_Opower(_1235351), -(c_Power_Opower__class_Opower(_1235351) = c_Power_Opower_Opower(_1235351, c_Groups_Oone__class_Oone(_1235351), c_Groups_Otimes__class_Otimes(_1235351)))], (14018 ^ _781215) ^ [_1025558, _1025560, _1025562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1025558)), 14021 ^ _781215 : [(14028 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025560), _1025562)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025558), _1025560)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025558), _1025562))))], (14022 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025558), _1025560)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025558), _1025562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025560), _1025562)))]]], (46797 ^ _781215) ^ [_1722138, _1722140, _1722142, _1722144, _1722146] : [-(c_List_OdropWhile(_1722138, _1722140, _1722142) = hAPP(hAPP(c_List_Olist_OCons(_1722138), _1722144), _1722146)), _1722142 = hAPP(hAPP(c_List_Oappend(_1722138), c_List_OtakeWhile(_1722138, _1722140, _1722142)), hAPP(hAPP(c_List_Olist_OCons(_1722138), _1722144), _1722146)), -(hBOOL(hAPP(_1722140, _1722144)))], (2830 ^ _781215) ^ [_823492, _823494] : [_823494 = _823492, -(c_Set_OBall(_823494) = c_Set_OBall(_823492))], (34962 ^ _781215) ^ [_1436614, _1436616, _1436618, _1436620, _1436622] : [c_Fun_Oinj__on(_1436614, _1436616, _1436618, hAPP(hAPP(c_Set_Oinsert(_1436614), _1436620), _1436622)), 34965 ^ _781215 : [(34968 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1436616), hAPP(_1436618, _1436620)), hAPP(c_Set_Oimage(_1436614, _1436616, _1436618), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1436614, tc_HOL_Obool)), _1436622), hAPP(hAPP(c_Set_Oinsert(_1436614), _1436620), c_Orderings_Obot__class_Obot(tc_fun(_1436614, tc_HOL_Obool)))))))], (34966 ^ _781215) ^ [] : [-(c_Fun_Oinj__on(_1436614, _1436616, _1436618, _1436622))]]], (47324 ^ _781215) ^ [_1732987, _1732989, _1732991, _1732993] : [class_Orderings_Oorder(_1732987), class_Enum_Oenum(_1732989), 47331 ^ _781215 : [(47340 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1732989, _1732987)), _1732991), _1732993))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1732989, _1732987)), _1732991), _1732993)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732989), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732989), c_fNot), hAPP(hAPP(c_COMBS(_1732989, _1732987, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1732987, tc_fun(_1732987, tc_HOL_Obool), _1732989), c_fequal), _1732991)), _1732993))))], (47332 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1732989, _1732987)), _1732991), _1732993)), 47335 ^ _781215 : [(47338 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732989), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732989), c_fNot), hAPP(hAPP(c_COMBS(_1732989, _1732987, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1732987, tc_fun(_1732987, tc_HOL_Obool), _1732989), c_fequal), _1732991)), _1732993)))))], (47336 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1732989, _1732987)), _1732991), _1732993)))]]]]], (27922 ^ _781215) ^ [_1290230, _1290232, _1290234, _1290236] : [class_Rings_Odivision__ring(_1290230), -(_1290232 = c_Groups_Ozero__class_Ozero(_1290230)), _1290234 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290230), _1290236), _1290232), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290230), _1290234), _1290232) = _1290236)], (46287 ^ _781215) ^ [_1710356, _1710358, _1710360] : [-(hAPP(c_List_Orev(_1710356), hAPP(hAPP(c_List_Olist_OCons(_1710356), _1710358), _1710360)) = hAPP(hAPP(c_List_Oappend(_1710356), hAPP(c_List_Orev(_1710356), _1710360)), hAPP(hAPP(c_List_Olist_OCons(_1710356), _1710358), c_List_Olist_ONil(_1710356))))], (43171 ^ _781215) ^ [_1641041, _1641043, _1641045, _1641047] : [hBOOL(hAPP(hAPP(c_member(_1641041), _1641043), c_Wellfounded_Oacc(_1641041, _1641045))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1641041)), _1641047), c_Wellfounded_Oacc(tc_List_Olist(_1641041), c_List_Olistrel1(_1641041, _1641045)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1641041)), hAPP(hAPP(c_List_Olist_OCons(_1641041), _1641043), _1641047)), c_Wellfounded_Oacc(tc_List_Olist(_1641041), c_List_Olistrel1(_1641041, _1641045)))))], (23068 ^ _781215) ^ [_1197053] : [c_Nat__Transfer_Onat__set(_1197053), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1197053) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197053)))], (35685 ^ _781215) ^ [_1452083, _1452085, _1452087, _1452089, _1452091, _1452093] : [-(hAPP(c_Product__Type_Oapsnd(_1452083, _1452085, _1452087, _1452089), hAPP(hAPP(c_Product__Type_OPair(_1452087, _1452083), _1452091), _1452093)) = hAPP(hAPP(c_Product__Type_OPair(_1452087, _1452085), _1452091), hAPP(_1452089, _1452093)))], (8684 ^ _781215) ^ [_928572, _928574, _928576] : [class_Rings_Oring(_928572), -(hAPP(c_Groups_Ouminus__class_Ouminus(_928572), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928572), _928574), _928576)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928572), _928574), hAPP(c_Groups_Ouminus__class_Ouminus(_928572), _928576)))], (18181 ^ _781215) ^ [_1106693, _1106695, _1106697, _1106699] : [class_Orderings_Olinorder(_1106693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106693), _1106695), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106693), _1106697), _1106699))), 18188 ^ _781215 : [(18191 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106693), _1106695), _1106699)))], (18189 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106693), _1106695), _1106697)))]]], (40894 ^ _781215) ^ [_1582871] : [-(_1582871 = hAPP(c_Int_OAbs__Integ, 40892 ^ [_1582871]))], (43142 ^ _781215) ^ [_1640295, _1640297, _1640299, _1640301, _1640303, _1640305] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640295)), _1640297) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640299)), _1640301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1640295, tc_HOL_Obool)), hAPP(c_List_Oset(_1640295), _1640297)), _1640303)), -(c_Map_Orestrict__map(_1640295, _1640299, c_Map_Omap__upds(_1640295, _1640299, _1640305, _1640297, _1640301), _1640303) = c_Map_Omap__upds(_1640295, _1640299, c_Map_Orestrict__map(_1640295, _1640299, _1640305, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640295, tc_HOL_Obool)), _1640303), hAPP(c_List_Oset(_1640295), _1640297))), _1640297, _1640301))], (21039 ^ _781215) ^ [_1158047, _1158049] : [class_Rings_Olinordered__semidom(_1158047), 21042 ^ _781215 : [(21049 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1158049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158047), c_Groups_Ozero__class_Ozero(_1158047)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1158047), _1158049))))], (21043 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158047), c_Groups_Ozero__class_Ozero(_1158047)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1158047), _1158049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1158049)))]]], (27394 ^ _781215) ^ [_1279627, _1279629, _1279631] : [-(hAPP(hAPP(c_Product__Type_OPair(_1279627, _1279629), hAPP(c_Product__Type_Ofst(_1279627, _1279629), _1279631)), hAPP(c_Product__Type_Osnd(_1279627, _1279629), _1279631)) = _1279631)], (20150 ^ _781215) ^ [_1142896, _1142898, _1142900, _1142902] : [class_Complete__Lattice_Ocomplete__lattice(_1142896), hBOOL(hAPP(c_Finite__Set_Ofinite(_1142898), _1142900)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1142898, _1142896), _1142900), _1142902) = hAPP(hAPP(c_Finite__Set_Ofold(_1142898, _1142896, hAPP(hAPP(c_COMBB(_1142896, tc_fun(_1142896, _1142896), _1142898), c_Lattices_Osemilattice__sup__class_Osup(_1142896)), _1142902)), c_Orderings_Obot__class_Obot(_1142896)), _1142900))], (6102 ^ _781215) ^ [_879278, _879280, _879282] : [c_Com_Ocom_OSemi(_879278, _879280) = hAPP(c_Com_Ocom_OBODY, _879282)], (18956 ^ _781215) ^ [_1121028, _1121030, _1121032, _1121034] : [class_Orderings_Olinorder(_1121028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121028), _1121030), _1121032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121028), _1121030), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1121028), _1121032), _1121034))))], (5778 ^ _781215) ^ [_872713, _872715, _872717, _872719, _872721] : [hAPP(_872713, _872715) = hAPP(c_Option_Ooption_OSome(_872717), _872719), -(hAPP(hAPP(c_Set_Oinsert(_872721), _872715), c_Map_Odom(_872721, _872717, _872713)) = c_Map_Odom(_872721, _872717, _872713))], (38896 ^ _781215) ^ [_1527631, _1527633, _1527635, _1527637, _1527639] : [c_Relation_Orefl__on(_1527631, _1527633, _1527635), c_Relation_Orefl__on(_1527631, _1527637, _1527639), -(c_Relation_Orefl__on(_1527631, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1527631, tc_HOL_Obool)), _1527633), _1527637), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1527631, _1527631), tc_HOL_Obool)), _1527635), _1527639)))], (37673 ^ _781215) ^ [_1497031, _1497033, _1497035, _1497037, _1497039] : [c_Typedef_Otype__definition(_1497031, _1497033, _1497035, _1497037, _1497039), -(hAPP(c_Set_Oimage(_1497031, _1497033, _1497035), c_Orderings_Otop__class_Otop(tc_fun(_1497031, tc_HOL_Obool))) = _1497039)], (38871 ^ _781215) ^ [_1527186, _1527188] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1527186), c_Int_OInteg)), hBOOL(hAPP(_1527188, hAPP(c_Int_ORep__Integ, 38876 ^ [_1527186, _1527188]))), -(hBOOL(hAPP(_1527188, _1527186)))], (32720 ^ _781215) ^ [_1387074, _1387076, _1387078, _1387080] : [class_Lattices_Osemilattice__inf(_1387074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387074), _1387076), _1387078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387074), _1387076), _1387080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387074), _1387076), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1387074), _1387078), _1387080))))], (36039 ^ _781215) ^ [_1458779, _1458781, _1458783] : [class_Rings_Olinordered__idom(_1458779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458779), c_Groups_Ozero__class_Ozero(_1458779)), _1458781)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1458779), hAPP(c_Groups_Oabs__class_Oabs(_1458779), _1458783)), _1458781) = hAPP(c_Groups_Oabs__class_Oabs(_1458779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1458779), _1458783), _1458781)))], (21790 ^ _781215) ^ [_1172118, _1172120] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1172118)), c_Int_OBit1(_1172120)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1172118), c_Int_Osucc(_1172120))))], (9673 ^ _781215) ^ [_945366, _945368, _945370, _945372] : [hBOOL(hAPP(hAPP(c_member(_945366), _945368), _945370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945366, tc_HOL_Obool)), _945370), _945372)), -(hBOOL(hAPP(hAPP(c_member(_945366), _945368), _945372)))], (43692 ^ _781215) ^ [_1653924, _1653926] : [-(c_List_Oremove1(_1653924, _1653926, c_List_Olist_ONil(_1653924)) = c_List_Olist_ONil(_1653924))], (15931 ^ _781215) ^ [_1061995, _1061997, _1061999, _1062001] : [15933 ^ _781215 : [(15936 ^ _781215) ^ [] : [hBOOL(hAPP(_1062001, 15932 ^ [_1061995, _1061997, _1061999, _1062001]))], (15934 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1061995), 15932 ^ [_1061995, _1061997, _1061999, _1062001]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061995, tc_HOL_Obool)), _1061997), _1061999))))]], 15937 ^ _781215 : [(15944 ^ _781215) ^ [_1062312] : [hBOOL(hAPP(hAPP(c_member(_1061995), _1062312), _1061999)), -(hBOOL(hAPP(_1062001, _1062312)))], (15938 ^ _781215) ^ [_1062215] : [hBOOL(hAPP(hAPP(c_member(_1061995), _1062215), _1061997)), -(hBOOL(hAPP(_1062001, _1062215)))]]], (37374 ^ _781215) ^ [_1490603, _1490605, _1490607, _1490609, _1490611] : [c_Equiv__Relations_Oequivp(_1490603, _1490605), hBOOL(hAPP(hAPP(_1490605, _1490607), _1490609)), hBOOL(hAPP(hAPP(_1490605, _1490609), _1490611)), -(hBOOL(hAPP(hAPP(_1490605, _1490607), _1490611)))], (41883 ^ _781215) ^ [_1606122, _1606124, _1606126] : [-(hAPP(hAPP(c_List_Ozip(_1606122, _1606124), hAPP(hAPP(c_List_Omap(tc_prod(_1606122, _1606124), _1606122), c_Product__Type_Ofst(_1606122, _1606124)), _1606126)), hAPP(hAPP(c_List_Omap(tc_prod(_1606122, _1606124), _1606124), c_Product__Type_Osnd(_1606122, _1606124)), _1606126)) = _1606126)], (3412 ^ _781215) ^ [_832765, _832767] : [_832767 = _832765, -(c_SetInterval_Oord__class_OlessThan(_832767) = c_SetInterval_Oord__class_OlessThan(_832765))], (4094 ^ _781215) ^ [_843336, _843338, _843340, _843342, _843344, _843346, _843348, _843350] : [-(c_Random_Oiterate(_843350, _843346, _843342, _843338) = c_Random_Oiterate(_843348, _843344, _843340, _843336)), _843350 = _843348, _843346 = _843344, _843342 = _843340, _843338 = _843336], (13972 ^ _781215) ^ [_1024689, _1024691] : [-(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), _1024689), _1024691)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1024689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1024691))], (7106 ^ _781215) ^ [_899629, _899631, _899633, _899635, _899637] : [c_Hoare__Mirabelle_Otriple__valid(_899629, _899631, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_899629), _899633), _899635), _899637)), 7109 ^ _781215 : [(7110 ^ _781215) ^ [_899759, _899761] : [hBOOL(hAPP(hAPP(_899633, _899761), _899759)), 7113 ^ _781215 : [(7114 ^ _781215) ^ [_899858] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _899635), _899759), _899631), _899858)), -(hBOOL(hAPP(hAPP(_899637, _899761), _899858)))]]]]], (23524 ^ _781215) ^ [_1205068, _1205070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205068)), -(c_SMT_Oz3div(_1205070, _1205068) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205070), _1205068))], (8790 ^ _781215) ^ [_930287, _930289, _930291] : [class_Orderings_Oorder(_930287), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930287), _930289), _930291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930287), _930291), _930289)), -(_930289 = _930291)], (42337 ^ _781215) ^ [_1619639, _1619641, _1619643] : [-(hAPP(c_List_Oset(_1619639), hAPP(hAPP(c_List_Olist_OCons(_1619639), _1619641), _1619643)) = hAPP(hAPP(c_Set_Oinsert(_1619639), _1619641), hAPP(c_List_Oset(_1619639), _1619643)))], (13982 ^ _781215) ^ [_1024862, _1024864, _1024866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1024862), _1024864)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1024866), _1024864))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1024862), _1024866)))], (26922 ^ _781215) ^ [_1270502, _1270504, _1270506, _1270508, _1270510, _1270512] : [_1270502 = _1270504, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1270506, _1270508, _1270510), _1270512), _1270502) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1270506, _1270508, _1270510), _1270512), _1270504))], (48926 ^ _781215) ^ [_1768915] : [-(_1768915 = 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)), _1768915)))], (22526 ^ _781215) ^ [_1188140, _1188142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188140)), 22529 ^ _781215 : [(22536 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1188142), 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), _1188142), _1188140)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22530 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1188142), _1188140)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1188142), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (12984 ^ _781215) ^ [_1007395, _1007397] : [class_Groups_Olinordered__ab__group__add(_1007395), 12987 ^ _781215 : [(12994 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007395), c_Groups_Ozero__class_Ozero(_1007395)), _1007397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007395), hAPP(c_Groups_Ouminus__class_Ouminus(_1007395), _1007397)), _1007397)))], (12988 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007395), hAPP(c_Groups_Ouminus__class_Ouminus(_1007395), _1007397)), _1007397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007395), c_Groups_Ozero__class_Ozero(_1007395)), _1007397)))]]], (43874 ^ _781215) ^ [_1657211, _1657213, _1657215] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657211), tc_List_Olist(_1657211))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657211), tc_List_Olist(_1657211)), c_List_Olist_ONil(_1657211)), _1657213)), c_List_Olex(_1657211, _1657215)))], (49688 ^ _781215) ^ [_1787858, _1787860, _1787862] : [-(hAPP(c_Relation_ORange(_1787858, _1787860), hAPP(c_Relation_Oconverse(_1787860, _1787858), _1787862)) = hAPP(c_Relation_ODomain(_1787860, _1787858), _1787862))], (43124 ^ _781215) ^ [_1639874, _1639876, _1639878, _1639880, _1639882, _1639884, _1639886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639874)), _1639876)), _1639878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639878), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639880)), _1639882))), -(c_Map_Omap__upds(_1639874, _1639880, _1639884, _1639876, hAPP(hAPP(c_List_Olist__update(_1639880, _1639882), _1639878), _1639886)) = c_Map_Omap__upds(_1639874, _1639880, _1639884, _1639876, _1639882))], (50742 ^ _781215) ^ [_1812770, _1812772] : [-(c_FunDef_Ois__measure(_1812770, _1812772))], (30113 ^ _781215) ^ [_1331892, _1331894] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1331892, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1331892, tc_HOL_Obool))), hAPP(c_Set_OPow(_1331892), _1331894))))], (41933 ^ _781215) ^ [_1607981, _1607983, _1607985] : [class_Orderings_Olinorder(_1607981), hBOOL(hAPP(c_Finite__Set_Ofinite(_1607981), _1607983)), -(c_List_Olinorder__class_Osorted__list__of__set(_1607981, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1607981, tc_HOL_Obool)), _1607983), hAPP(hAPP(c_Set_Oinsert(_1607981), _1607985), c_Orderings_Obot__class_Obot(tc_fun(_1607981, tc_HOL_Obool))))) = c_List_Oremove1(_1607981, _1607985, c_List_Olinorder__class_Osorted__list__of__set(_1607981, _1607983)))], (16818 ^ _781215) ^ [_1083147, _1083149, _1083151] : [hAPP(hAPP(c_COMBC(_1083147, tc_fun(_1083147, tc_HOL_Obool), tc_HOL_Obool), c_member(_1083147)), _1083149) = hAPP(hAPP(c_COMBC(_1083147, tc_fun(_1083147, tc_HOL_Obool), tc_HOL_Obool), c_member(_1083147)), _1083151), -(_1083149 = _1083151)], (19836 ^ _781215) ^ [_1137102, _1137104, _1137106] : [class_Orderings_Olinorder(_1137102), hBOOL(hAPP(c_Finite__Set_Ofinite(_1137102), _1137104)), -(_1137106 = c_Orderings_Obot__class_Obot(tc_fun(_1137102, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1137102, tc_HOL_Obool)), _1137106), _1137104)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1137102), c_Big__Operators_Olinorder__class_OMax(_1137102, _1137106)), c_Big__Operators_Olinorder__class_OMax(_1137102, _1137104)) = c_Big__Operators_Olinorder__class_OMax(_1137102, _1137104))], (15594 ^ _781215) ^ [_1055079, _1055081, _1055083, _1055085, _1055087] : [-(hBOOL(hAPP(hAPP(c_member(_1055079), _1055081), _1055083))), -(hAPP(c_Map_Orestrict__map(_1055079, _1055085, _1055087, _1055083), _1055081) = c_Option_Ooption_ONone(_1055085))], (9343 ^ _781215) ^ [_940459, _940461, _940463, _940465, _940467] : [class_Rings_Osemiring(_940459), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940459), _940461), _940463)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940459), _940465), _940463)), _940467)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940459), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940459), _940461), _940465)), _940463)), _940467))], (35069 ^ _781215) ^ [_1439409, _1439411, _1439413, _1439415] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1439409), _1439411)), -(hAPP(c_Set_Oimage(_1439409, _1439413, _1439415), _1439411) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1439413, tc_HOL_Obool), _1439409, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439413, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1439409, tc_fun(_1439413, tc_HOL_Obool), tc_fun(_1439413, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1439413, tc_fun(tc_fun(_1439413, tc_HOL_Obool), tc_fun(_1439413, tc_HOL_Obool)), _1439409), c_Set_Oinsert(_1439413)), _1439415)), c_Orderings_Obot__class_Obot(tc_fun(_1439413, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1439413, tc_HOL_Obool))), _1439411))], (48523 ^ _781215) ^ [_1761086, _1761088, _1761090] : [class_Orderings_Olinorder(_1761086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1761086), _1761088)), 48533 ^ _781215 : [(48536 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1761086), _1761090), 48532 ^ [_1761086, _1761088, _1761090]))], (48534 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1761086), 48532 ^ [_1761086, _1761088, _1761090]), _1761088)))]], hBOOL(hAPP(hAPP(c_member(_1761086), _1761090), _1761088)), -(c_Big__Operators_Olinorder__class_OMin(_1761086, _1761088) = _1761090)], (48283 ^ _781215) ^ [_1755373, _1755375, _1755377, _1755379, _1755381] : [hAPP(hAPP(c_List_Olist_OCons(_1755373), _1755375), _1755377) = hAPP(c_List_Ofilter(_1755373, _1755379), _1755381), 48288 ^ _781215 : [(48297 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1755379, _1755375)))], (48299 ^ _781215) ^ [] : [-(_1755377 = hAPP(c_List_Ofilter(_1755373, _1755379), 48287 ^ [_1755373, _1755375, _1755377, _1755379, _1755381]))], (48291 ^ _781215) ^ [_1755687] : [hBOOL(hAPP(hAPP(c_member(_1755373), _1755687), hAPP(c_List_Oset(_1755373), 48286 ^ [_1755373, _1755375, _1755377, _1755379, _1755381]))), hBOOL(hAPP(_1755379, _1755687))], (48289 ^ _781215) ^ [] : [-(_1755381 = hAPP(hAPP(c_List_Oappend(_1755373), 48286 ^ [_1755373, _1755375, _1755377, _1755379, _1755381]), hAPP(hAPP(c_List_Olist_OCons(_1755373), _1755375), 48287 ^ [_1755373, _1755375, _1755377, _1755379, _1755381])))]]], (2532 ^ _781215) ^ [_818821, _818823, _818825, _818827] : [-(c_Nitpick_Onat__lcm(_818827, _818823) = c_Nitpick_Onat__lcm(_818825, _818821)), _818827 = _818825, _818823 = _818821], (7979 ^ _781215) ^ [_915773, _915775, _915777] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_915773), _915775)), -(hBOOL(hAPP(hAPP(c_member(_915773), _915777), _915775))), -(hAPP(c_Finite__Set_Ocard(_915773), hAPP(hAPP(c_Set_Oinsert(_915773), _915777), _915775)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_915773), _915775)))], (6992 ^ _781215) ^ [_897147, _897149, _897151, _897153, _897155, _897157, _897159] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_897147, tc_Option_Ooption(_897149)), _897151), _897153), hAPP(c_Option_Ooption_OSome(_897149), _897155)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_897147, tc_Option_Ooption(_897149)), _897157), _897153), hAPP(c_Option_Ooption_OSome(_897149), _897159)), -(_897155 = _897159)], (3986 ^ _781215) ^ [_841686, _841688, _841690, _841692, _841694, _841696] : [-(c_List_Olinorder__class_Oinsort__key(_841696, _841692, _841688) = c_List_Olinorder__class_Oinsort__key(_841694, _841690, _841686)), _841696 = _841694, _841692 = _841690, _841688 = _841686], (34336 ^ _781215) ^ [_1424578, _1424580, _1424582] : [class_Lattices_Olattice(_1424578), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424578), _1424580)), hBOOL(hAPP(hAPP(c_member(_1424578), _1424582), _1424580)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1424578), _1424582), c_Big__Operators_Olattice__class_OInf__fin(_1424578, _1424580)) = c_Big__Operators_Olattice__class_OInf__fin(_1424578, _1424580))], (49547 ^ _781215) ^ [_1784006, _1784008] : [-(c_Relation_Orefl__on(_1784006, c_Orderings_Otop__class_Otop(tc_fun(_1784006, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1784006, _1784006), tc_HOL_Obool)), _1784008), c_Relation_OId(_1784006))))], (47910 ^ _781215) ^ [_1746046, _1746048, _1746050] : [hBOOL(hAPP(c_List_Odistinct(_1746046), _1746048)), -(hBOOL(hAPP(c_List_Odistinct(_1746046), c_List_Oinsert(_1746046, _1746050, _1746048))))], (48335 ^ _781215) ^ [_1756808, _1756810, _1756812] : [48337 ^ _781215 : [(48340 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1756808), 48336 ^ [_1756808, _1756810, _1756812]), c_Wellfounded_Oacc(_1756808, _1756812)))], (48338 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1756808, _1756808)), hAPP(hAPP(c_Product__Type_OPair(_1756808, _1756808), 48336 ^ [_1756808, _1756810, _1756812]), _1756810)), _1756812)))]], -(hBOOL(hAPP(hAPP(c_member(_1756808), _1756810), c_Wellfounded_Oacc(_1756808, _1756812))))], (45740 ^ _781215) ^ [_1698658, _1698660] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1698658), _1698660) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1698658, _1698660)))], (3640 ^ _781215) ^ [_836331, _836333, _836335, _836337] : [-(c_HOL_OThe(_836337, _836333) = c_HOL_OThe(_836335, _836331)), _836337 = _836335, _836333 = _836331], (44786 ^ _781215) ^ [_1679770, _1679772, _1679774] : [-(_1679770 = c_List_Olist_ONil(_1679772)), -(hAPP(c_List_Ohd(_1679772), hAPP(hAPP(c_List_Oappend(_1679772), _1679770), _1679774)) = hAPP(c_List_Ohd(_1679772), _1679770))], (39114 ^ _781215) ^ [_1532260, _1532262, _1532264] : [-(hAPP(c_Set_OCollect(_1532260), hAPP(hAPP(c_COMBS(_1532260, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532260), c_fconj), _1532262)), _1532264)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1532260, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1532260), _1532262)), hAPP(c_Set_OCollect(_1532260), _1532264)))], (42246 ^ _781215) ^ [_1615919, _1615921, _1615923, _1615925] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615919), tc_List_Olist(_1615919))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615919), tc_List_Olist(_1615919)), _1615921), _1615923)), c_List_Olistrel(_1615919, _1615925))), 42249 ^ _781215 : [(42252 ^ _781215) ^ [_1616255] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615919, _1615919)), _1616255), hAPP(c_List_Oset(tc_prod(_1615919, _1615919)), hAPP(hAPP(c_List_Ozip(_1615919, _1615919), _1615921), _1615923)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1615919, _1615919, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1615919, tc_fun(tc_prod(_1615919, _1615919), tc_HOL_Obool), tc_fun(_1615919, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615919, tc_fun(tc_fun(tc_prod(_1615919, _1615919), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1615919, _1615919), tc_HOL_Obool), tc_fun(_1615919, tc_HOL_Obool)), _1615919), c_COMBC(_1615919, tc_fun(tc_prod(_1615919, _1615919), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615919, tc_prod(_1615919, _1615919)), tc_fun(_1615919, tc_fun(tc_fun(tc_prod(_1615919, _1615919), tc_HOL_Obool), tc_HOL_Obool)), _1615919), hAPP(c_COMBB(tc_prod(_1615919, _1615919), tc_fun(tc_fun(tc_prod(_1615919, _1615919), tc_HOL_Obool), tc_HOL_Obool), _1615919), c_member(tc_prod(_1615919, _1615919)))), c_Product__Type_OPair(_1615919, _1615919)))), _1615925)), _1616255)))], (42250 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615919)), _1615921) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615919)), _1615923))]]], (2860 ^ _781215) ^ [_823947, _823949, _823951, _823953, _823955, _823957] : [-(c_Com_Ocom_OLocal(_823957, _823953, _823949) = c_Com_Ocom_OLocal(_823955, _823951, _823947)), _823957 = _823955, _823953 = _823951, _823949 = _823947], (50579 ^ _781215) ^ [_1809668, _1809670] : [c_List_Olist__ex1(_1809668, _1809670, c_List_Olist_ONil(_1809668))], (2006 ^ _781215) ^ [_810384, _810386, _810388, _810390, _810392, _810394, _810396, _810398, _810400, _810402, _810404, _810406] : [-(c_Map_Omap__comp(_810406, _810402, _810398, _810394, _810390, _810386) = c_Map_Omap__comp(_810404, _810400, _810396, _810392, _810388, _810384)), _810406 = _810404, _810402 = _810400, _810398 = _810396, _810394 = _810392, _810390 = _810388, _810386 = _810384], (24694 ^ _781215) ^ [_1226905, _1226907] : [24695 ^ _781215 : [(24698 ^ _781215) ^ [] : [_1226905 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24696 ^ _781215) ^ [] : [_1226907 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1226905), _1226907) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23903 ^ _781215) ^ [_1212117, _1212119] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1212117), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1212119))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1212117), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1212119))), 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))))], (30223 ^ _781215) ^ [_1334091, _1334093, _1334095] : [class_Orderings_Oorder(_1334091), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334091), _1334093), _1334095)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1334091, _1334095, _1334093) = c_Orderings_Obot__class_Obot(tc_fun(_1334091, tc_HOL_Obool)))], (11128 ^ _781215) ^ [_973884, _973886, _973888, _973890, _973892] : [class_Rings_Ocomm__semiring__1(_973884), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973884), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973884), _973886), _973888)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973884), _973890), _973892)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973884), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973884), _973886), _973890)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973884), _973888), _973892)))], (11541 ^ _781215) ^ [_982475, _982477, _982479, _982481] : [_982481 = c_Orderings_Obot__class_Obot(tc_fun(_982475, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_982475, _982477, _982479), _982481) = c_Orderings_Obot__class_Obot(tc_fun(_982477, tc_HOL_Obool)))], (49614 ^ _781215) ^ [_1785895, _1785897, _1785899, _1785901] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1785895), tc_List_Olist(_1785895))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1785895), tc_List_Olist(_1785895)), _1785897), _1785899)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1785895), tc_List_Olist(_1785895)), c_List_Olistrel1(_1785895, _1785901)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1785895), tc_List_Olist(_1785895))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1785895), tc_List_Olist(_1785895)), _1785897), _1785899)), c_List_Olistrel1(_1785895, hAPP(c_Relation_Oconverse(_1785895, _1785895), _1785901)))))], (32944 ^ _781215) ^ [_1392132, _1392134, _1392136, _1392138] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392132, tc_HOL_Obool)), _1392134), _1392136), _1392138)), -(hBOOL(hAPP(_1392136, _1392138)))], (39651 ^ _781215) ^ [_1551838, _1551840] : [-(hAPP(c_Fun_Oid(_1551838), _1551840) = _1551840)], (51264 ^ _781215) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (31942 ^ _781215) ^ [_1369923, _1369925, _1369927, _1369929] : [class_Groups_Ocomm__monoid__add(_1369923), 31945 ^ _781215 : [(31952 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1369925), _1369927))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369923), _1369929), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1369927), hAPP(c_Nat_OSuc, _1369925))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369923), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369923), _1369929), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1369927), _1369925))), hAPP(_1369929, _1369925)))], (31946 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1369925), _1369927)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369923), _1369929), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1369927), hAPP(c_Nat_OSuc, _1369925))) = c_Groups_Ozero__class_Ozero(_1369923))]]], (40411 ^ _781215) ^ [_1571566, _1571568] : [c_Wellfounded_OwfP(_1571566, hAPP(hAPP(c_COMBC(_1571566, tc_fun(tc_prod(_1571566, _1571566), tc_HOL_Obool), tc_fun(_1571566, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571566, tc_fun(tc_fun(tc_prod(_1571566, _1571566), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1571566, _1571566), tc_HOL_Obool), tc_fun(_1571566, tc_HOL_Obool)), _1571566), c_COMBC(_1571566, tc_fun(tc_prod(_1571566, _1571566), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571566, tc_prod(_1571566, _1571566)), tc_fun(_1571566, tc_fun(tc_fun(tc_prod(_1571566, _1571566), tc_HOL_Obool), tc_HOL_Obool)), _1571566), hAPP(c_COMBB(tc_prod(_1571566, _1571566), tc_fun(tc_fun(tc_prod(_1571566, _1571566), tc_HOL_Obool), tc_HOL_Obool), _1571566), c_member(tc_prod(_1571566, _1571566)))), c_Product__Type_OPair(_1571566, _1571566)))), _1571568)), -(c_Wellfounded_Owf(_1571566, _1571568))], (51350 ^ _781215) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (40323 ^ _781215) ^ [_1569548, _1569550, _1569552] : [c_Wellfounded_Owf(_1569548, _1569550), -(c_Wellfounded_Owf(tc_List_Olist(_1569548), hAPP(c_List_Olexn(_1569548, _1569550), _1569552)))], (706 ^ _781215) ^ [_792110, _792112, _792114, _792116] : [-(c_Wellfounded_OwfP(_792114, _792110)), c_Wellfounded_OwfP(_792116, _792112), _792116 = _792114, _792112 = _792110], (5468 ^ _781215) ^ [_864699, _864701] : [_864701 = _864699, -(tc_Lazy__Sequence_Olazy__sequence(_864701) = tc_Lazy__Sequence_Olazy__sequence(_864699))], (23536 ^ _781215) ^ [_1205225, _1205227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205225)), -(c_SMT_Oz3mod(_1205227, _1205225) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1205227, _1205225))], (40063 ^ _781215) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (20472 ^ _781215) ^ [_1148636, _1148638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148636)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148638))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1148636), _1148638)))], (21720 ^ _781215) ^ [_1170791, _1170793] : [class_Int_Onumber__ring(_1170791), -(hAPP(c_Int_Onumber__class_Onumber__of(_1170791), c_Int_OBit0(_1170793)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170791), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170791), c_Groups_Ozero__class_Ozero(_1170791)), hAPP(c_Int_Onumber__class_Onumber__of(_1170791), _1170793))), hAPP(c_Int_Onumber__class_Onumber__of(_1170791), _1170793)))], (40898 ^ _781215) ^ [_1582934, _1582936] : [40900 ^ _781215 : [(40903 ^ _781215) ^ [] : [hBOOL(hAPP(_1582934, hAPP(c_Int_OAbs__Integ, 40899 ^ [_1582934, _1582936])))], (40901 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40899 ^ [_1582934, _1582936]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1582934, _1582936)))], (21684 ^ _781215) ^ [_1170240] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170240))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1170240)))))], (25833 ^ _781215) ^ [_1248585, _1248587, _1248589, _1248591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1248585, tc_fun(_1248587, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1248585, tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_fun(_1248587, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1248587, tc_fun(tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_fun(_1248587, tc_HOL_Obool)), _1248585), c_COMBC(_1248587, tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1248587, tc_prod(_1248585, _1248587)), tc_fun(_1248587, tc_fun(tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_HOL_Obool)), _1248585), hAPP(c_COMBB(tc_prod(_1248585, _1248587), tc_fun(tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_HOL_Obool), _1248587), c_member(tc_prod(_1248585, _1248587)))), c_Product__Type_OPair(_1248585, _1248587)))), _1248589)), hAPP(hAPP(c_COMBC(_1248585, tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_fun(_1248587, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1248587, tc_fun(tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_fun(_1248587, tc_HOL_Obool)), _1248585), c_COMBC(_1248587, tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1248587, tc_prod(_1248585, _1248587)), tc_fun(_1248587, tc_fun(tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_HOL_Obool)), _1248585), hAPP(c_COMBB(tc_prod(_1248585, _1248587), tc_fun(tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool), tc_HOL_Obool), _1248587), c_member(tc_prod(_1248585, _1248587)))), c_Product__Type_OPair(_1248585, _1248587)))), _1248591))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1248585, _1248587), tc_HOL_Obool)), _1248589), _1248591)))], (17399 ^ _781215) ^ [_1092792, _1092794, _1092796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092792), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092792)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092794)), _1092796)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20693 ^ _781215) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (51544 ^ _781215) ^ [_1824391, _1824393] : [-(class_Enum_Oenum(tc_prod(_1824391, _1824393))), class_Enum_Oenum(_1824391), class_Enum_Oenum(_1824393)], (51380 ^ _781215) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (22406 ^ _781215) ^ [_1185941] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185941) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7748 ^ _781215) ^ [_911758, _911760, _911762] : [_911758 = _911762, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911758), _911760) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911762), _911760))], (6171 ^ _781215) ^ [_880573, _880575, _880577, _880579, _880581, _880583, _880585] : [-(c_Map_Omap__comp(_880573, _880575, _880577, _880579, _880581, _880583) = hAPP(c_Option_Ooption_OSome(_880575), _880585)), 6172 ^ _781215 : [(6173 ^ _781215) ^ [_880651] : [hAPP(_880581, _880583) = hAPP(c_Option_Ooption_OSome(_880573), _880651), hAPP(_880579, _880651) = hAPP(c_Option_Ooption_OSome(_880575), _880585)]]], (17755 ^ _781215) ^ [_1098452, _1098454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1098452)), 17758 ^ _781215 : [(17765 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098454), _1098452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1098454)), hAPP(c_Int_Onat, _1098452))))], (17759 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1098454)), hAPP(c_Int_Onat, _1098452))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098454), _1098452)))]]], (2756 ^ _781215) ^ [_822345, _822347] : [_822347 = _822345, -(c_Int_Oint__ge__less__than2(_822347) = c_Int_Oint__ge__less__than2(_822345))], (25376 ^ _781215) ^ [_1238513] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1238513) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1238513))], (17583 ^ _781215) ^ [_1095839, _1095841] : [class_Int_Onumber__ring(_1095839), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1095841)), -(hBOOL(hAPP(hAPP(c_member(_1095839), hAPP(c_Int_Onumber__class_Onumber__of(_1095839), _1095841)), c_Nat_Osemiring__1__class_ONats(_1095839))))], (18319 ^ _781215) ^ [_1109108, _1109110, _1109112] : [class_Orderings_Olinorder(_1109108), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109108), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1109108), _1109110), _1109112)), _1109110)))], (36007 ^ _781215) ^ [_1458260, _1458262] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1458260), _1458262)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458260) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (37953 ^ _781215) ^ [_1502931, _1502933, _1502935] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502931, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1502931, tc_HOL_Obool), tc_HOL_Obool)), _1502933), _1502935)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1502931, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502931, tc_HOL_Obool), _1502933)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502931, tc_HOL_Obool), _1502935)))], (42668 ^ _781215) ^ [_1628484, _1628486, _1628488, _1628490] : [-(hAPP(hAPP(c_List_Onth(_1628484), hAPP(hAPP(c_List_Olist_OCons(_1628484), _1628486), _1628488)), _1628490) = c_Nat_Onat_Onat__case(_1628484, _1628486, hAPP(c_List_Onth(_1628484), _1628488), _1628490))], (35322 ^ _781215) ^ [_1444675, _1444677, _1444679, _1444681, _1444683] : [class_Groups_Ocomm__monoid__add(_1444675), class_Groups_Oordered__cancel__ab__semigroup__add(_1444675), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444677), _1444679)), -(_1444679 = c_Orderings_Obot__class_Obot(tc_fun(_1444677, tc_HOL_Obool))), 35340 ^ _781215 : [(35343 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444675), hAPP(_1444681, 35339 ^ [_1444675, _1444677, _1444679, _1444681, _1444683])), hAPP(_1444683, 35339 ^ [_1444675, _1444677, _1444679, _1444681, _1444683])))], (35341 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444677), 35339 ^ [_1444675, _1444677, _1444679, _1444681, _1444683]), _1444679)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444675), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444677, _1444675), _1444681), _1444679)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444677, _1444675), _1444683), _1444679))))], (23632 ^ _781215) ^ [_1207121, _1207123] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207121)), _1207123) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1207121), _1207123)))], (21301 ^ _781215) ^ [_1162895, _1162897, _1162899, _1162901, _1162903, _1162905] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162895, tc_fun(_1162897, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162899, tc_fun(_1162895, tc_HOL_Obool)), _1162901), _1162903)), _1162905) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162899, tc_fun(_1162897, tc_HOL_Obool)), _1162901), hAPP(hAPP(c_COMBC(_1162899, tc_fun(_1162895, tc_fun(_1162897, tc_HOL_Obool)), tc_fun(_1162897, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1162895, tc_HOL_Obool), tc_fun(tc_fun(_1162895, tc_fun(_1162897, tc_HOL_Obool)), tc_fun(_1162897, tc_HOL_Obool)), _1162899), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162895, tc_fun(_1162897, tc_HOL_Obool))), _1162903)), _1162905)))], (2762 ^ _781215) ^ [_822430, _822432] : [_822432 = _822430, -(c_Int_Oint__ge__less__than(_822432) = c_Int_Oint__ge__less__than(_822430))], (38660 ^ _781215) ^ [_1520882, _1520884, _1520886, _1520888] : [-(_1520882 = c_Orderings_Obot__class_Obot(tc_fun(_1520884, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1520884, _1520886), _1520886, c_Product__Type_Osnd(_1520884, _1520886)), hAPP(hAPP(c_Product__Type_OSigma(_1520884, _1520886), _1520882), hAPP(c_COMBK(tc_fun(_1520886, tc_HOL_Obool), _1520884), _1520888))) = _1520888)], (32928 ^ _781215) ^ [_1391866] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1391866) = c_Orderings_Oord__class_Omin(_1391866)), class_Lattices_Osemilattice__inf(_1391866), class_Orderings_Olinorder(_1391866)], (32962 ^ _781215) ^ [_1392445, _1392447, _1392449, _1392451] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392445, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392445, tc_HOL_Obool)), _1392447), _1392449)), _1392451) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392445, tc_HOL_Obool)), _1392447), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392445, tc_HOL_Obool)), _1392449), _1392451)))], (50746 ^ _781215) ^ [_1812820] : [class_Nat_Osize(_1812820), -(c_FunDef_Ois__measure(_1812820, c_Nat_Osize__class_Osize(_1812820)))], (33084 ^ _781215) ^ [_1395057, _1395059, _1395061, _1395063] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395057, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1395057, tc_HOL_Obool)), _1395059), _1395061)), _1395063) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1395057, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395057, tc_HOL_Obool)), _1395059), _1395063)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395057, tc_HOL_Obool)), _1395061), _1395063)))], (26440 ^ _781215) ^ [_1260868, _1260870] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1260868, _1260870)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1260870), _1260868)))], (47066 ^ _781215) ^ [_1728078, _1728080, _1728082] : [class_Enum_Oenum(_1728078), 47069 ^ _781215 : [(47070 ^ _781215) ^ [] : [c_Enum_Oall__n__lists(_1728078, _1728080, _1728082), 47073 ^ _781215 : [(47074 ^ _781215) ^ [_1728228] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728078)), _1728228), hAPP(c_List_Oset(tc_List_Olist(_1728078)), c_Enum_On__lists(_1728078, _1728082, c_Enum_Oenum__class_Oenum(_1728078))))), -(hBOOL(hAPP(_1728080, _1728228)))]]], (47080 ^ _781215) ^ [] : [47082 ^ _781215 : [(47085 ^ _781215) ^ [] : [hBOOL(hAPP(_1728080, 47081 ^ [_1728078, _1728080, _1728082]))], (47083 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728078)), 47081 ^ [_1728078, _1728080, _1728082]), hAPP(c_List_Oset(tc_List_Olist(_1728078)), c_Enum_On__lists(_1728078, _1728082, c_Enum_Oenum__class_Oenum(_1728078))))))]], -(c_Enum_Oall__n__lists(_1728078, _1728080, _1728082))]]], (42623 ^ _781215) ^ [_1627145, _1627147, _1627149, _1627151] : [-(hAPP(c_List_Oset(tc_prod(_1627145, _1627147)), hAPP(hAPP(c_List_Ozip(_1627145, _1627147), _1627149), _1627151)) = hAPP(c_Set_OCollect(tc_prod(_1627145, _1627147)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1627145, _1627147)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1627145, _1627147), 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(_1627145, _1627147)), 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(_1627145, _1627147)), 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(_1627145, _1627147), tc_fun(tc_Nat_Onat, tc_prod(_1627145, _1627147)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1627145, _1627147), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1627145, _1627147)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1627145, _1627147)), c_COMBB(tc_prod(_1627145, _1627147), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1627147, tc_prod(_1627145, _1627147)), hAPP(hAPP(c_COMBB(_1627145, tc_fun(_1627147, tc_prod(_1627145, _1627147)), tc_Nat_Onat), c_Product__Type_OPair(_1627145, _1627147)), hAPP(c_List_Onth(_1627145), _1627149))), hAPP(c_List_Onth(_1627147), _1627151)))))), 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(_1627145)), _1627149)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627147)), _1627151)))))))], (33246 ^ _781215) ^ [_1399400, _1399402, _1399404, _1399406, _1399408] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1399400, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1399402, _1399400, _1399404), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399402, tc_HOL_Obool)), _1399406), _1399408))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399400, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1399402, _1399400, _1399404), _1399406)), hAPP(c_Relation_OImage(_1399402, _1399400, _1399404), _1399408)))))], (36478 ^ _781215) ^ [_1466824] : [class_Finite__Set_Ofinite(_1466824), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1466824), c_Orderings_Otop__class_Otop(tc_fun(_1466824, tc_HOL_Obool)))))], (41887 ^ _781215) ^ [_1606369, _1606371, _1606373, _1606375, _1606377, _1606379, _1606381, _1606383] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1606369, _1606371), _1606373), _1606375), hAPP(hAPP(c_List_Ozip(_1606369, _1606371), hAPP(hAPP(c_List_Omap(_1606377, _1606369), _1606379), _1606381)), _1606383)) = hAPP(hAPP(c_List_Omap(tc_prod(_1606377, _1606371), _1606373), hAPP(c_Product__Type_Oprod_Oprod__case(_1606377, _1606371, _1606373), hAPP(hAPP(c_COMBB(tc_fun(_1606371, tc_prod(_1606369, _1606371)), tc_fun(_1606371, _1606373), _1606377), hAPP(c_COMBB(tc_prod(_1606369, _1606371), _1606373, _1606371), _1606375)), hAPP(hAPP(c_COMBB(_1606369, tc_fun(_1606371, tc_prod(_1606369, _1606371)), _1606377), c_Product__Type_OPair(_1606369, _1606371)), _1606379)))), hAPP(hAPP(c_List_Ozip(_1606377, _1606371), _1606381), _1606383)))], (43648 ^ _781215) ^ [_1653027, _1653029, _1653031] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653027), tc_List_Olist(_1653027))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653027), tc_List_Olist(_1653027)), _1653029), c_List_Olist_ONil(_1653027))), c_List_Olistrel(_1653027, _1653031))), -(_1653029 = c_List_Olist_ONil(_1653027))], (7084 ^ _781215) ^ [_899174, _899176, _899178, _899180, _899182, _899184] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_899174, _899176, _899178, _899180, _899182), _899184)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_899174), _899182)))], (22072 ^ _781215) ^ [_1178734, _1178736, _1178738, _1178740, _1178742] : [-(_1178734 = c_Orderings_Obot__class_Obot(tc_fun(_1178736, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1178738, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1178736, tc_fun(_1178738, tc_HOL_Obool)), _1178734), _1178740)), _1178742) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1178736, tc_fun(_1178738, tc_HOL_Obool)), _1178734), hAPP(hAPP(c_COMBC(_1178736, tc_fun(_1178738, tc_HOL_Obool), tc_fun(_1178738, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1178738, tc_HOL_Obool), tc_fun(tc_fun(_1178738, tc_HOL_Obool), tc_fun(_1178738, tc_HOL_Obool)), _1178736), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1178738, tc_HOL_Obool))), _1178740)), _1178742)))], (47579 ^ _781215) ^ [_1738786, _1738788, _1738790, _1738792, _1738794] : [-(c_List_Olist__all2(_1738786, _1738788, _1738790, _1738792, _1738794)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738786)), _1738792) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738788)), _1738794), 47585 ^ _781215 : [(47588 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1738786, _1738788, tc_HOL_Obool), _1738790), 47584 ^ [_1738786, _1738788, _1738790, _1738792, _1738794]))], (47586 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1738786, _1738788)), 47584 ^ [_1738786, _1738788, _1738790, _1738792, _1738794]), hAPP(c_List_Oset(tc_prod(_1738786, _1738788)), hAPP(hAPP(c_List_Ozip(_1738786, _1738788), _1738792), _1738794)))))]]], (49333 ^ _781215) ^ [_1778590, _1778592, _1778594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778590, _1778590), tc_HOL_Obool)), _1778592), _1778594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778590, _1778590), tc_HOL_Obool)), _1778594), c_Transitive__Closure_Ortrancl(_1778590, _1778592))), -(c_Transitive__Closure_Ortrancl(_1778590, _1778594) = c_Transitive__Closure_Ortrancl(_1778590, _1778592))], (50392 ^ _781215) ^ [_1805964, _1805966, _1805968] : [c_Nitpick_Oless__eq__frac(_1805964, _1805966, _1805968), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1805964), c_Nitpick_Oplus__frac(_1805964, _1805966, c_Nitpick_Ouminus__frac(_1805964, _1805968)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34143 ^ _781215) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (10248 ^ _781215) ^ [_955739, _955741, _955743, _955745] : [class_Orderings_Oord(_955739), 10251 ^ _781215 : [(10260 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_955741, _955739)), _955743), _955745))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_955741, _955739)), _955743), _955745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_955741, _955739)), _955745), _955743)))], (10252 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_955741, _955739)), _955743), _955745)), 10255 ^ _781215 : [(10258 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_955741, _955739)), _955745), _955743))], (10256 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_955741, _955739)), _955743), _955745)))]]]]], (5784 ^ _781215) ^ [_872844, _872846] : [-(c_Set_Othe__elem(_872844, hAPP(hAPP(c_Set_Oinsert(_872844), _872846), c_Orderings_Obot__class_Obot(tc_fun(_872844, tc_HOL_Obool)))) = _872846)], (50072 ^ _781215) ^ [_1797259, _1797261, _1797263, _1797265, _1797267] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1797259, _1797259)), hAPP(hAPP(c_Product__Type_OPair(_1797259, _1797259), _1797261), _1797263)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1797259, _1797259), tc_HOL_Obool), _1797265), _1797267))), 50077 ^ _781215 : [(50080 ^ _781215) ^ [] : [-(_1797261 = _1797263)], (50078 ^ _781215) ^ [] : [-(_1797265 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 50083 ^ _781215 : [(50088 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1797259, _1797259)), hAPP(hAPP(c_Product__Type_OPair(_1797259, _1797259), 50081 ^ [_1797259, _1797261, _1797263, _1797265, _1797267]), _1797263)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1797259, _1797259), tc_HOL_Obool), 50082 ^ [_1797259, _1797261, _1797263, _1797265, _1797267]), _1797267))))], (50086 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1797259, _1797259)), hAPP(hAPP(c_Product__Type_OPair(_1797259, _1797259), _1797261), 50081 ^ [_1797259, _1797261, _1797263, _1797265, _1797267])), _1797267)))], (50084 ^ _781215) ^ [] : [-(_1797265 = hAPP(c_Nat_OSuc, 50082 ^ [_1797259, _1797261, _1797263, _1797265, _1797267]))]]], (19198 ^ _781215) ^ [_1125812, _1125814] : [class_Orderings_Olinorder(_1125812), -(c_Big__Operators_Olattice_OInf__fin(_1125812, c_Orderings_Oord__class_Omin(_1125812), hAPP(hAPP(c_Set_Oinsert(_1125812), _1125814), c_Orderings_Obot__class_Obot(tc_fun(_1125812, tc_HOL_Obool)))) = _1125814)], (44570 ^ _781215) ^ [_1674451, _1674453] : [-(hAPP(c_List_Oset(_1674451), hAPP(c_List_Orotate1(_1674451), _1674453)) = hAPP(c_List_Oset(_1674451), _1674453))], (10136 ^ _781215) ^ [_953828, _953830, _953832] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953828, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953828, tc_HOL_Obool)), _953830), _953832)), _953830)))], (14882 ^ _781215) ^ [_1042099, _1042101, _1042103, _1042105] : [hAPP(c_Com_Ocom_OBODY, _1042099) = c_Com_Ocom_OCond(_1042101, _1042103, _1042105)], (35565 ^ _781215) ^ [_1449542, _1449544, _1449546] : [class_Orderings_Olinorder(_1449542), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1449542), _1449544), _1449546)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1449542, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1449542, _1449544, _1449546)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1449542), _1449546)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1449542), _1449544))], (12824 ^ _781215) ^ [_1004650, _1004652, _1004654] : [class_Groups_Oordered__ab__group__add(_1004650), 12827 ^ _781215 : [(12834 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004650), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1004650), _1004652), _1004654)), c_Groups_Ozero__class_Ozero(_1004650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004650), _1004652), _1004654)))], (12828 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004650), _1004652), _1004654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004650), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1004650), _1004652), _1004654)), c_Groups_Ozero__class_Ozero(_1004650))))]]], (48222 ^ _781215) ^ [_1753765, _1753767, _1753769, _1753771, _1753773] : [class_Orderings_Olinorder(_1753765), 48228 ^ _781215 : [(48231 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1753765), hAPP(_1753771, _1753773)), hAPP(_1753771, 48227 ^ [_1753765, _1753767, _1753769, _1753771, _1753773])))], (48229 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753767), 48227 ^ [_1753765, _1753767, _1753769, _1753771, _1753773]), hAPP(c_List_Oset(_1753767), _1753769))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1753767, _1753765, _1753771), _1753773), _1753769) = hAPP(hAPP(c_List_Olist_OCons(_1753767), _1753773), _1753769))], (26137 ^ _781215) ^ [_1255199, _1255201, _1255203] : [class_Rings_Oring__1(_1255199), -(hAPP(c_Int_Oring__1__class_Oof__int(_1255199), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1255201), _1255203)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255199), hAPP(c_Int_Oring__1__class_Oof__int(_1255199), _1255201)), hAPP(c_Int_Oring__1__class_Oof__int(_1255199), _1255203)))], (49559 ^ _781215) ^ [_1784343, _1784345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1784343), _1784345)), -(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), _1784343), _1784345)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (38252 ^ _781215) ^ [_1509999, _1510001, _1510003, _1510005, _1510007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509999, tc_HOL_Obool)), _1510001), _1510003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510005, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1510005, _1509999, _1510007), _1510001)), hAPP(c_Set_Ovimage(_1510005, _1509999, _1510007), _1510003))))], (37059 ^ _781215) ^ [_1482090, _1482092, _1482094, _1482096, _1482098] : [-(hAPP(hAPP(c_Set_Oinsert(_1482090), _1482092), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482094, tc_fun(_1482090, tc_HOL_Obool)), _1482096), _1482098)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482094, tc_fun(_1482090, tc_HOL_Obool)), _1482096), hAPP(hAPP(c_COMBB(tc_fun(_1482090, tc_HOL_Obool), tc_fun(_1482090, tc_HOL_Obool), _1482094), hAPP(c_Set_Oinsert(_1482090), _1482092)), _1482098)))], (44556 ^ _781215) ^ [_1674103, _1674105, _1674107] : [-(hAPP(hAPP(c_List_Odrop(_1674103), _1674105), c_List_Obutlast(_1674103, _1674107)) = c_List_Obutlast(_1674103, hAPP(hAPP(c_List_Odrop(_1674103), _1674105), _1674107)))], (21662 ^ _781215) ^ [_1169821, _1169823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1169821), _1169823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1169821)), c_Int_OBit0(_1169823))))], (5621 ^ _781215) ^ [_869781, _869783, _869785, _869787] : [c_Hoare__Mirabelle_Ohoare__derivs(_869781, _869783, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_869781)), _869785), _869787)), 5624 ^ _781215 : [(5627 ^ _781215) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_869781, _869783, _869787))], (5625 ^ _781215) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_869781, _869783, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_869781)), _869785), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_869781), tc_HOL_Obool)))))]]], (15330 ^ _781215) ^ [_1050124, _1050126] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050124), _1050126))), -(_1050124 = _1050126), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050126), _1050124)))], (46183 ^ _781215) ^ [_1708067, _1708069, _1708071, _1708073, _1708075] : [-(c_List_Ofoldr(_1708067, _1708069, _1708071, _1708073, _1708075) = hAPP(c_List_Ofoldl(_1708069, _1708067, hAPP(c_COMBC(_1708067, _1708069, _1708069), _1708071), _1708075), hAPP(c_List_Orev(_1708067), _1708073)))], (51062 ^ _781215) ^ [_1819302, _1819304] : [class_Lattices_Obounded__lattice(_1819302), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1819304, _1819302)))], (51774 ^ _781215) ^ [] : [-(hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))], (21656 ^ _781215) ^ [_1169720, _1169722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1169720)), c_Int_OBit0(_1169722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1169720), _1169722)))], (42809 ^ _781215) ^ [_1631812, _1631814, _1631816, _1631818, _1631820] : [hBOOL(hAPP(hAPP(c_member(_1631812), _1631814), hAPP(c_List_Oset(_1631812), _1631816))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631818), hAPP(_1631820, _1631814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631818), c_List_Olist_Olist__size(_1631812, _1631820, _1631816))))], (43375 ^ _781215) ^ [_1646613, _1646615] : [class_Groups_Oordered__ab__group__add__abs(_1646613), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1646613), hAPP(c_Groups_Oabs__class_Oabs(_1646613), hAPP(c_List_Omonoid__add__class_Olistsum(_1646613), _1646615))), hAPP(c_List_Omonoid__add__class_Olistsum(_1646613), hAPP(hAPP(c_List_Omap(_1646613, _1646613), c_Groups_Oabs__class_Oabs(_1646613)), _1646615)))))], (36466 ^ _781215) ^ [_1466578] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466578), c_Orderings_Otop__class_Otop(tc_fun(_1466578, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1466578)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1466578), tc_HOL_Obool)))))], (21127 ^ _781215) ^ [_1159380, _1159382] : [class_Int_Onumber__ring(_1159380), class_Rings_Olinordered__idom(_1159380), 21134 ^ _781215 : [(21141 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1159382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159380), c_Groups_Oone__class_Oone(_1159380)), hAPP(c_Int_Onumber__class_Onumber__of(_1159380), _1159382))))], (21135 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159380), c_Groups_Oone__class_Oone(_1159380)), hAPP(c_Int_Onumber__class_Onumber__of(_1159380), _1159382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1159382)))]]], (42929 ^ _781215) ^ [_1635155, _1635157, _1635159] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1635155, tc_HOL_Obool)), hAPP(c_List_Oset(_1635155), hAPP(hAPP(c_List_Otake(_1635155), _1635157), _1635159))), hAPP(c_List_Oset(_1635155), _1635159))))], (49598 ^ _781215) ^ [_1785388, _1785390, _1785392, _1785394] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785388, _1785388)), hAPP(hAPP(c_Product__Type_OPair(_1785388, _1785388), _1785390), _1785392)), c_Transitive__Closure_Ortrancl(_1785388, hAPP(c_Relation_Oconverse(_1785388, _1785388), _1785394)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785388, _1785388)), hAPP(hAPP(c_Product__Type_OPair(_1785388, _1785388), _1785392), _1785390)), c_Transitive__Closure_Ortrancl(_1785388, _1785394))))], (35969 ^ _781215) ^ [_1457585, _1457587, _1457589] : [class_Rings_Olinordered__idom(_1457585), 35972 ^ _781215 : [(35981 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457585), hAPP(c_Groups_Oabs__class_Oabs(_1457585), _1457587)), _1457589))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457585), _1457587), _1457589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457585), hAPP(c_Groups_Ouminus__class_Ouminus(_1457585), _1457587)), _1457589))], (35973 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457585), hAPP(c_Groups_Oabs__class_Oabs(_1457585), _1457587)), _1457589)), 35976 ^ _781215 : [(35979 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457585), hAPP(c_Groups_Ouminus__class_Ouminus(_1457585), _1457587)), _1457589)))], (35977 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457585), _1457587), _1457589)))]]]]], (48262 ^ _781215) ^ [_1754823, _1754825, _1754827, _1754829, _1754831] : [-(hAPP(c_List_Ofilter(_1754823, _1754825), _1754827) = hAPP(hAPP(c_List_Olist_OCons(_1754823), _1754829), _1754831)), 48263 ^ _781215 : [(48264 ^ _781215) ^ [_1754951, _1754953] : [_1754827 = hAPP(hAPP(c_List_Oappend(_1754823), _1754953), hAPP(hAPP(c_List_Olist_OCons(_1754823), _1754829), _1754951)), 48270 ^ _781215 : [(48273 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1754825, 48269 ^ [_1754823, _1754825, _1754827, _1754829, _1754831, _1754951, _1754953])))], (48271 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754823), 48269 ^ [_1754823, _1754825, _1754827, _1754829, _1754831, _1754951, _1754953]), hAPP(c_List_Oset(_1754823), _1754953))))]], hBOOL(hAPP(_1754825, _1754829)), _1754831 = hAPP(c_List_Ofilter(_1754823, _1754825), _1754951)]]], (41909 ^ _781215) ^ [_1607130, _1607132, _1607134, _1607136] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607130, _1607130)), hAPP(hAPP(c_Product__Type_OPair(_1607130, _1607130), _1607132), _1607134)), hAPP(c_List_Oset(tc_prod(_1607130, _1607130)), hAPP(hAPP(c_List_Ozip(_1607130, _1607130), _1607136), _1607136)))), 41912 ^ _781215 : [(41915 ^ _781215) ^ [] : [-(_1607132 = _1607134)], (41913 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1607130), _1607132), hAPP(c_List_Oset(_1607130), _1607136))))]]], (21670 ^ _781215) ^ [_1169971, _1169973] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1169971)), c_Int_OBit1(_1169973)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1169971), _1169973)))], (44876 ^ _781215) ^ [_1681230, _1681232, _1681234] : [-(hAPP(c_List_Orotate1(_1681230), hAPP(c_List_Orotate(_1681230, _1681232), _1681234)) = hAPP(c_List_Orotate(_1681230, _1681232), hAPP(c_List_Orotate1(_1681230), _1681234)))], (16441 ^ _781215) ^ [_1072055, _1072057, _1072059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072055, tc_HOL_Obool)), _1072057), _1072059)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072055, tc_HOL_Obool)), _1072059), _1072057) = _1072059)], (41132 ^ _781215) ^ [_1588611, _1588613, _1588615, _1588617] : [hBOOL(hAPP(c_List_Odistinct(_1588611), hAPP(hAPP(c_List_Omap(_1588613, _1588611), _1588615), _1588617))), 41135 ^ _781215 : [(41138 ^ _781215) ^ [] : [-(c_Fun_Oinj__on(_1588613, _1588611, _1588615, hAPP(c_List_Oset(_1588613), _1588617)))], (41136 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1588613), _1588617)))]]], (16983 ^ _781215) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (1878 ^ _781215) ^ [_807660, _807662] : [-(class_Nat_Osize(_807660)), _807662 = _807660, class_Nat_Osize(_807662)], (42579 ^ _781215) ^ [_1626106, _1626108, _1626110] : [class_Orderings_Olinorder(_1626106), -(hAPP(c_List_Oset(_1626106), c_List_Olinorder__class_Oinsort__insert__key(_1626106, _1626106, c_COMBI(_1626106), _1626108, _1626110)) = hAPP(hAPP(c_Set_Oinsert(_1626106), _1626108), hAPP(c_List_Oset(_1626106), _1626110)))], (30143 ^ _781215) ^ [_1332650, _1332652, _1332654] : [hAPP(c_Set_Oimage(_1332652, tc_fun(_1332652, tc_HOL_Obool), _1332650), _1332654) = hAPP(c_Set_OPow(_1332652), _1332654)], (51382 ^ _781215) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (7680 ^ _781215) ^ [_910402, _910404] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _910402), _910404)), hAPP(c_Nat_OSuc, _910402))))], (40329 ^ _781215) ^ [_1569643, _1569645] : [-(hAPP(c_List_Olexn(_1569643, _1569645), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1569643), tc_List_Olist(_1569643)), tc_HOL_Obool)))], (45067 ^ _781215) ^ [_1685307, _1685309, _1685311, _1685313] : [class_Complete__Lattice_Ocomplete__lattice(_1685307), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1685309, _1685307), hAPP(c_List_Oset(_1685309), _1685311)), _1685313) = hAPP(c_List_Ofoldl(_1685307, _1685309, hAPP(c_COMBC(_1685309, _1685307, _1685307), hAPP(hAPP(c_COMBB(_1685307, tc_fun(_1685307, _1685307), _1685309), c_Lattices_Osemilattice__sup__class_Osup(_1685307)), _1685313)), c_Orderings_Obot__class_Obot(_1685307)), _1685311))], (5286 ^ _781215) ^ [_861900, _861902, _861904, _861906] : [-(c_New__DSequence_Oneg__single(_861906, _861902) = c_New__DSequence_Oneg__single(_861904, _861900)), _861906 = _861904, _861902 = _861900], (4304 ^ _781215) ^ [_846521, _846523, _846525, _846527] : [-(c_Relation_Oinv__image(_846527, _846523) = c_Relation_Oinv__image(_846525, _846521)), _846527 = _846525, _846523 = _846521], (47936 ^ _781215) ^ [_1746491, _1746493, _1746495] : [-(hBOOL(hAPP(hAPP(c_member(_1746491), _1746493), hAPP(c_List_Oset(_1746491), _1746495)))), -(hAPP(c_List_OremoveAll(_1746491, _1746493), _1746495) = _1746495)], (21984 ^ _781215) ^ [_1176782, _1176784, _1176786, _1176788, _1176790] : [hBOOL(hAPP(hAPP(c_member(_1176782), _1176784), _1176786)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1176788, tc_HOL_Obool)), hAPP(_1176790, _1176784)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1176782, tc_fun(_1176788, tc_HOL_Obool)), _1176786), _1176790)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1176782, tc_fun(_1176788, tc_HOL_Obool)), _1176786), _1176790))], (14355 ^ _781215) ^ [] : [-(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))], (51770 ^ _781215) ^ [] : [-(c_Com_OWT__bodies)], (7632 ^ _781215) ^ [_909371, _909373, _909375, _909377, _909379] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909371, _909373), _909375), _909377), _909379), _909377) = _909379)], (46728 ^ _781215) ^ [_1720807, _1720809, _1720811] : [class_Orderings_Olinorder(_1720807), c_List_Olinorder__class_Osorted(_1720807, _1720809), -(c_List_Olinorder__class_Osorted(_1720807, c_List_OdropWhile(_1720807, _1720811, _1720809)))], (12936 ^ _781215) ^ [_1006579, _1006581] : [class_Groups_Oordered__ab__group__add(_1006579), 12939 ^ _781215 : [(12946 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006579), c_Groups_Ozero__class_Ozero(_1006579)), _1006581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006579), hAPP(c_Groups_Ouminus__class_Ouminus(_1006579), _1006581)), c_Groups_Ozero__class_Ozero(_1006579))))], (12940 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006579), hAPP(c_Groups_Ouminus__class_Ouminus(_1006579), _1006581)), c_Groups_Ozero__class_Ozero(_1006579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006579), c_Groups_Ozero__class_Ozero(_1006579)), _1006581)))]]], (2576 ^ _781215) ^ [_819505, _819507] : [_819507 = _819505, -(c_SetInterval_Oord__class_OgreaterThan(_819507) = c_SetInterval_Oord__class_OgreaterThan(_819505))], (11170 ^ _781215) ^ [_974919, _974921, _974923, _974925, _974927] : [class_Rings_Ocomm__semiring__1(_974919), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974919), _974921), _974923)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974919), _974925), _974927)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974919), _974925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974919), _974921), _974923)), _974927)))], (46271 ^ _781215) ^ [_1709913, _1709915, _1709917, _1709919] : [-(hAPP(hAPP(c_List_Omap(_1709913, _1709915), _1709917), c_List_Oconcat(_1709913, _1709919)) = c_List_Oconcat(_1709915, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1709913), tc_List_Olist(_1709915)), hAPP(c_List_Omap(_1709913, _1709915), _1709917)), _1709919)))], (42797 ^ _781215) ^ [_1631612, _1631614, _1631616, _1631618] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1631612) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1631614), hAPP(hAPP(c_List_Olist_OCons(_1631614), _1631616), _1631618)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1631612)) = _1631616)], (47743 ^ _781215) ^ [_1742393, _1742395, _1742397, _1742399, _1742401] : [c_List_Olist__all2(_1742393, _1742395, _1742397, hAPP(c_List_Orev(_1742393), _1742399), _1742401), -(c_List_Olist__all2(_1742393, _1742395, _1742397, _1742399, hAPP(c_List_Orev(_1742395), _1742401)))], (30926 ^ _781215) ^ [_1347311, _1347313] : [30934 ^ _781215 : [(30937 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1347313, 30933 ^ [_1347311, _1347313])))], (30935 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30933 ^ [_1347311, _1347313]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1347311))))]], 30927 ^ _781215 : [(30928 ^ _781215) ^ [_1347379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1347379), _1347311)), hBOOL(hAPP(_1347313, _1347379))]]], (31266 ^ _781215) ^ [_1353837, _1353839] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1353837), _1353839))))], (21007 ^ _781215) ^ [] : [-(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)))))], (44756 ^ _781215) ^ [_1679084, _1679086, _1679088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679084), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679086)), _1679088))), -(_1679088 = hAPP(hAPP(c_List_Oappend(_1679086), hAPP(hAPP(c_List_Otake(_1679086), _1679084), _1679088)), hAPP(hAPP(c_List_Olist_OCons(_1679086), hAPP(hAPP(c_List_Onth(_1679086), _1679088), _1679084)), hAPP(hAPP(c_List_Odrop(_1679086), hAPP(c_Nat_OSuc, _1679084)), _1679088))))], (40013 ^ _781215) ^ [_1562362, _1562364, _1562366, _1562368] : [c_Wellfounded_Owf(_1562362, _1562364), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562362, _1562362)), hAPP(hAPP(c_Product__Type_OPair(_1562362, _1562362), _1562366), _1562368)), _1562364)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562362, _1562362)), hAPP(hAPP(c_Product__Type_OPair(_1562362, _1562362), _1562368), _1562366)), _1562364))], (47089 ^ _781215) ^ [_1728519, _1728521, _1728523] : [class_Enum_Oenum(_1728519), 47092 ^ _781215 : [(47102 ^ _781215) ^ [] : [-(c_Enum_Oex__n__lists(_1728519, _1728521, _1728523)), 47103 ^ _781215 : [(47104 ^ _781215) ^ [_1728775] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728519)), _1728775), hAPP(c_List_Oset(tc_List_Olist(_1728519)), c_Enum_On__lists(_1728519, _1728523, c_Enum_Oenum__class_Oenum(_1728519))))), hBOOL(hAPP(_1728521, _1728775))]]], (47093 ^ _781215) ^ [] : [c_Enum_Oex__n__lists(_1728519, _1728521, _1728523), 47097 ^ _781215 : [(47100 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1728521, 47096 ^ [_1728519, _1728521, _1728523])))], (47098 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728519)), 47096 ^ [_1728519, _1728521, _1728523]), hAPP(c_List_Oset(tc_List_Olist(_1728519)), c_Enum_On__lists(_1728519, _1728523, c_Enum_Oenum__class_Oenum(_1728519))))))]]]]], (37828 ^ _781215) ^ [_1500107, _1500109, _1500111, _1500113] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1500107, tc_HOL_Obool)), _1500109), _1500111)), hBOOL(hAPP(hAPP(c_member(_1500107), _1500113), _1500109)), -(hBOOL(hAPP(hAPP(c_member(_1500107), _1500113), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1500107, tc_HOL_Obool), _1500111))))], (33501 ^ _781215) ^ [_1404932, _1404934, _1404936, _1404938, _1404940] : [class_Groups_Ocomm__monoid__add(_1404932), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404934), _1404936)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404934), _1404938)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1404932), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1404934, _1404932), _1404940), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404934, tc_HOL_Obool)), _1404936), _1404938))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1404934, _1404932), _1404940), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404934, tc_HOL_Obool)), _1404936), _1404938))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1404932), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1404934, _1404932), _1404940), _1404936)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1404934, _1404932), _1404940), _1404938)))], (3022 ^ _781215) ^ [_826508, _826510, _826512, _826514] : [-(c_List_Olenlex(_826514, _826510) = c_List_Olenlex(_826512, _826508)), _826514 = _826512, _826510 = _826508], (51300 ^ _781215) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (20866 ^ _781215) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (48544 ^ _781215) ^ [_1761458, _1761460, _1761462] : [class_Orderings_Olinorder(_1761458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1761458), _1761460)), 48554 ^ _781215 : [(48557 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1761458), 48553 ^ [_1761458, _1761460, _1761462]), _1761462))], (48555 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1761458), 48553 ^ [_1761458, _1761460, _1761462]), _1761460)))]], hBOOL(hAPP(hAPP(c_member(_1761458), _1761462), _1761460)), -(c_Big__Operators_Olinorder__class_OMax(_1761458, _1761460) = _1761462)], (25342 ^ _781215) ^ [_1237990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1237990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1237990))))], (9879 ^ _781215) ^ [_949213, _949215, _949217, _949219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949213, tc_HOL_Obool)), _949215), _949217)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949213, tc_HOL_Obool)), _949215), hAPP(hAPP(c_Set_Oinsert(_949213), _949219), _949217))))], (7804 ^ _781215) ^ [_912886, _912888, _912890, _912892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912886), _912888)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912890), _912888) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912886), _912892), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912890), _912892)))], (36903 ^ _781215) ^ [_1476738, _1476740, _1476742, _1476744] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1476742), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1476738, tc_fun(_1476742, tc_HOL_Obool)), _1476740), _1476744)))), 36904 ^ _781215 : [(36905 ^ _781215) ^ [_1476812] : [hBOOL(hAPP(hAPP(c_member(_1476738), _1476812), _1476740)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476742), hAPP(_1476744, _1476812)))]]], (530 ^ _781215) ^ [_789456, _789458, _789460, _789462, _789464, _789466, _789468, _789470] : [-(c_Finite__Set_Ofolding(_789468, _789464, _789460, _789456)), c_Finite__Set_Ofolding(_789470, _789466, _789462, _789458), _789470 = _789468, _789466 = _789464, _789462 = _789460, _789458 = _789456], (41541 ^ _781215) ^ [_1598317, _1598319, _1598321, _1598323, _1598325, _1598327, _1598329, _1598331] : [c_Finite__Set_Ofolding__image(_1598317, _1598319, _1598321, _1598323, _1598325), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598319), _1598327)), -(hAPP(hAPP(_1598325, hAPP(hAPP(c_COMBS(_1598319, _1598317, _1598317), hAPP(hAPP(c_COMBB(_1598317, tc_fun(_1598317, _1598317), _1598319), _1598321), _1598329)), _1598331)), _1598327) = hAPP(hAPP(_1598321, hAPP(hAPP(_1598325, _1598329), _1598327)), hAPP(hAPP(_1598325, _1598331), _1598327)))], (37935 ^ _781215) ^ [_1502559, _1502561, _1502563] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502559, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1502559, tc_HOL_Obool)), _1502561), _1502563)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1502559, tc_HOL_Obool)), _1502561), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502559, tc_HOL_Obool), _1502563)))], (9915 ^ _781215) ^ [_949842, _949844] : [9916 ^ _781215 : [(9919 ^ _781215) ^ [] : [_949842 = hAPP(c_Nat_OSuc, _949844)], (9917 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949842), _949844))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949842), hAPP(c_Nat_OSuc, _949844))))], (43553 ^ _781215) ^ [_1650693, _1650695, _1650697, _1650699] : [-(c_Hilbert__Choice_OEps(tc_prod(_1650693, _1650695), hAPP(c_Product__Type_Oprod_Oprod__case(_1650693, _1650695, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1650693, tc_fun(_1650695, tc_HOL_Obool), tc_fun(_1650695, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1650695, tc_HOL_Obool), tc_fun(_1650695, tc_HOL_Obool)), _1650693), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1650695)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1650693), c_fconj), hAPP(c_fequal, _1650697)))), hAPP(c_fequal, _1650699)))) = hAPP(hAPP(c_Product__Type_OPair(_1650693, _1650695), _1650697), _1650699))], (5879 ^ _781215) ^ [_874724, _874726, _874728, _874730] : [-(c_Option_Ooption_Ooption__rec(_874724, _874726, _874728, _874730, c_Option_Ooption_ONone(_874726)) = _874728)], (39446 ^ _781215) ^ [_1542679, _1542681, _1542683] : [-(c_Map_Oran(_1542679, _1542681, _1542683) = hAPP(c_Set_OCollect(_1542681), hAPP(hAPP(c_COMBB(tc_fun(_1542679, tc_HOL_Obool), tc_HOL_Obool, _1542681), c_HOL_OEx(_1542679)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1542681), tc_fun(_1542679, tc_HOL_Obool), _1542681), hAPP(c_COMBC(_1542679, tc_Option_Ooption(_1542681), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1542681), tc_fun(tc_Option_Ooption(_1542681), tc_HOL_Obool), _1542679), c_fequal), _1542683))), c_Option_Ooption_OSome(_1542681)))))], (50892 ^ _781215) ^ [_1815261, _1815263, _1815265, _1815267, _1815269, _1815271, _1815273] : [-(c_New__Random__Sequence_Opos__decr__bind(_1815261, _1815263, _1815265, _1815267, _1815269, _1815271, _1815273) = c_New__DSequence_Opos__decr__bind(_1815261, _1815263, hAPP(hAPP(hAPP(_1815265, _1815269), _1815271), _1815273), hAPP(hAPP(c_COMBC(_1815261, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1815263))), hAPP(hAPP(c_COMBC(_1815261, 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(_1815263)))), hAPP(hAPP(c_COMBC(_1815261, 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(_1815263))))), _1815267), _1815269)), _1815271)), _1815273)))], (14540 ^ _781215) ^ [_1035545, _1035547, _1035549, _1035551, _1035553, _1035555] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1035545, _1035547, _1035549)), _1035551), _1035553), _1035555)), 14545 ^ _781215 : [(14548 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1035547), _1035551), _1035553), _1035555)))], (14546 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1035545, _1035551)))]], 14549 ^ _781215 : [(14552 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1035549), _1035551), _1035553), _1035555)))], (14550 ^ _781215) ^ [] : [hBOOL(hAPP(_1035545, _1035551))]]], (19618 ^ _781215) ^ [_1133399, _1133401, _1133403] : [class_Orderings_Olinorder(_1133399), hAPP(_1133401, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1133399), 19623 ^ [_1133399, _1133401, _1133403]), 19624 ^ [_1133399, _1133401, _1133403])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1133399), hAPP(_1133401, 19623 ^ [_1133399, _1133401, _1133403])), hAPP(_1133401, 19624 ^ [_1133399, _1133401, _1133403])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133399), _1133403)), -(_1133403 = c_Orderings_Obot__class_Obot(tc_fun(_1133399, tc_HOL_Obool))), -(hAPP(_1133401, c_Big__Operators_Olattice_OInf__fin(_1133399, c_Orderings_Oord__class_Omin(_1133399), _1133403)) = c_Big__Operators_Olattice_OInf__fin(_1133399, c_Orderings_Oord__class_Omin(_1133399), hAPP(c_Set_Oimage(_1133399, _1133399, _1133401), _1133403)))], (49726 ^ _781215) ^ [_1788790, _1788792] : [c_Wellfounded_Owf(_1788790, hAPP(c_Relation_Oconverse(_1788790, _1788790), _1788792)), -(c_Wellfounded_Owf(_1788790, hAPP(c_Relation_Oconverse(_1788790, _1788790), c_Transitive__Closure_Otrancl(_1788790, _1788792))))], (17839 ^ _781215) ^ [_1099839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1099839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1099839)))], (15675 ^ _781215) ^ [_1056958, _1056960, _1056962] : [class_Lattices_Oab__semigroup__idem__mult(_1056958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056958), _1056960)), -(hAPP(c_Finite__Set_Ofold1(_1056958, c_Groups_Otimes__class_Otimes(_1056958)), hAPP(hAPP(c_Set_Oinsert(_1056958), _1056962), _1056960)) = hAPP(hAPP(c_Finite__Set_Ofold(_1056958, _1056958, c_Groups_Otimes__class_Otimes(_1056958)), _1056962), _1056960))], (5084 ^ _781215) ^ [_858687, _858689] : [_858689 = _858687, -(c_New__Random__Sequence_Opos__single(_858689) = c_New__Random__Sequence_Opos__single(_858687))], (50832 ^ _781215) ^ [_1814241, _1814243] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1814241), _1814243)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1814241), _1814243) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4350 ^ _781215) ^ [_847202, _847204, _847206, _847208] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_847208, _847204) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_847206, _847202)), _847208 = _847206, _847204 = _847202], (38936 ^ _781215) ^ [_1528409, _1528411, _1528413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528409, _1528409), tc_HOL_Obool)), _1528411), hAPP(hAPP(c_Product__Type_OSigma(_1528409, _1528409), _1528413), hAPP(c_COMBK(tc_fun(_1528409, tc_HOL_Obool), _1528409), _1528413)))), 38942 ^ _781215 : [(38945 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528409, _1528409)), hAPP(hAPP(c_Product__Type_OPair(_1528409, _1528409), 38941 ^ [_1528409, _1528411, _1528413]), 38941 ^ [_1528409, _1528411, _1528413])), _1528411))], (38943 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1528409), 38941 ^ [_1528409, _1528411, _1528413]), _1528413)))]], -(c_Relation_Orefl__on(_1528409, _1528413, _1528411))], (23184 ^ _781215) ^ [_1198743, _1198745, _1198747, _1198749] : [class_Divides_Osemiring__div(_1198743), -(_1198745 = c_Groups_Ozero__class_Ozero(_1198743)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1198743), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198743), _1198747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1198743), _1198749), _1198745))), _1198745) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198743), _1198749), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1198743), _1198747), _1198745)))], (8111 ^ _781215) ^ [_917883, _917885, _917887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917883), _917885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917883), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _917887), _917885))))], (42720 ^ _781215) ^ [_1629825, _1629827] : [42722 ^ _781215 : [(42726 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42724 ^ [_1629825, _1629827]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629825)), _1629827))))], (42728 ^ _781215) ^ [] : [42721 ^ [_1629825, _1629827] = 42724 ^ [_1629825, _1629827]], (42730 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1629825), _1629827), 42721 ^ [_1629825, _1629827]) = hAPP(hAPP(c_List_Onth(_1629825), _1629827), 42724 ^ [_1629825, _1629827]))], (42723 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42721 ^ [_1629825, _1629827]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629825)), _1629827))))]], -(hBOOL(hAPP(c_List_Odistinct(_1629825), _1629827)))], (19672 ^ _781215) ^ [_1134395, _1134397] : [class_Orderings_Olinorder(_1134395), -(c_Big__Operators_Olattice_OSup__fin(_1134395, c_Orderings_Oord__class_Omax(_1134395), hAPP(hAPP(c_Set_Oinsert(_1134395), _1134397), c_Orderings_Obot__class_Obot(tc_fun(_1134395, tc_HOL_Obool)))) = _1134397)], (32990 ^ _781215) ^ [_1393159, _1393161, _1393163, _1393165] : [class_Lattices_Osemilattice__inf(_1393159), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393159), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393159), _1393161), _1393163)), _1393165) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393159), _1393161), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393159), _1393163), _1393165)))], (11516 ^ _781215) ^ [_981941, _981943, _981945, _981947, _981949] : [hBOOL(hAPP(hAPP(c_member(_981941), _981943), hAPP(c_Set_Oimage(_981945, _981941, _981947), _981949))), 11520 ^ _781215 : [(11523 ^ _781215) ^ [] : [-(_981943 = hAPP(_981947, 11519 ^ [_981941, _981943, _981945, _981947, _981949]))], (11521 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_981945), 11519 ^ [_981941, _981943, _981945, _981947, _981949]), _981949)))]]], (42279 ^ _781215) ^ [_1617621, _1617623, _1617625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1617621, _1617621), tc_HOL_Obool)), _1617623), _1617625)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1617621), tc_List_Olist(_1617621)), tc_HOL_Obool)), c_List_Olistrel(_1617621, _1617623)), c_List_Olistrel(_1617621, _1617625))))], (3850 ^ _781215) ^ [_839578, _839580, _839582, _839584] : [-(c_List_Omeasures(_839584, _839580) = c_List_Omeasures(_839582, _839578)), _839584 = _839582, _839580 = _839578], (6389 ^ _781215) ^ [_885128, _885130, _885132, _885134, _885136] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885128), _885130), _885132)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885134), _885132), _885136)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_885128, _885134)), _885130), _885136)))], (39933 ^ _781215) ^ [_1560941, _1560943, _1560945] : [c_Wellfounded_Owf(_1560941, _1560943), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1560941, _1560941), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1560941, _1560941, _1560941), _1560943), _1560945)), _1560943)), -(c_FunDef_Oreduction__pair(_1560941, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1560941, _1560941), tc_HOL_Obool), tc_fun(tc_prod(_1560941, _1560941), tc_HOL_Obool)), _1560943), _1560945)))], (3398 ^ _781215) ^ [_832544, _832546, _832548, _832550, _832552, _832554] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_832554, _832550, _832546) = c_SetInterval_Oord__class_OatLeastAtMost(_832552, _832548, _832544)), _832554 = _832552, _832550 = _832548, _832546 = _832544], (4912 ^ _781215) ^ [_855795, _855797, _855799, _855801, _855803, _855805, _855807, _855809] : [-(c_Option_Ooption_Ooption__case(_855809, _855805, _855801, _855797) = c_Option_Ooption_Ooption__case(_855807, _855803, _855799, _855795)), _855809 = _855807, _855805 = _855803, _855801 = _855799, _855797 = _855795], (5941 ^ _781215) ^ [_875783] : [-(c_Option_Oset(_875783, c_Option_Ooption_ONone(_875783)) = c_Orderings_Obot__class_Obot(tc_fun(_875783, tc_HOL_Obool)))], (7814 ^ _781215) ^ [_913067, _913069, _913071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913067), _913069)), _913071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913067), _913071)))], (27213 ^ _781215) ^ [_1275933, _1275935, _1275937] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1275933), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1275935)), _1275937)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1275933, _1275935), hAPP(c_Divides_OnegateSnd, _1275937))))], (41537 ^ _781215) ^ [_1598175, _1598177, _1598179, _1598181, _1598183, _1598185] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1598175, tc_fun(_1598177, tc_HOL_Obool)), _1598179), hAPP(c_Fun_Ocomp(_1598181, tc_fun(_1598177, tc_HOL_Obool), _1598175, _1598183), _1598185)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1598181, tc_fun(_1598177, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1598175, _1598181, _1598185), _1598179)), _1598183))], (48066 ^ _781215) ^ [_1749808, _1749810, _1749812, _1749814, _1749816] : [48067 ^ _781215 : [(48070 ^ _781215) ^ [] : [hBOOL(hAPP(_1749816, hAPP(hAPP(c_List_Ozip(_1749808, _1749812), hAPP(hAPP(c_List_Otake(_1749808), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749808)), _1749810)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749812)), _1749814))), _1749810)), hAPP(hAPP(c_List_Otake(_1749812), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749808)), _1749810)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749812)), _1749814))), _1749814))))], (48068 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749808)), hAPP(hAPP(c_List_Otake(_1749808), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749808)), _1749810)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749812)), _1749814))), _1749810)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749812)), hAPP(hAPP(c_List_Otake(_1749812), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749808)), _1749810)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749812)), _1749814))), _1749814)))]], -(hBOOL(hAPP(_1749816, hAPP(hAPP(c_List_Ozip(_1749808, _1749812), _1749810), _1749814))))], (25444 ^ _781215) ^ [_1239509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1239509)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239509), c_Int_OMin)))], (1848 ^ _781215) ^ [_807285, _807287] : [-(class_Int_Onumber(_807285)), _807287 = _807285, class_Int_Onumber(_807287)], (38820 ^ _781215) ^ [_1525633, _1525635, _1525637, _1525639, _1525641, _1525643, _1525645, _1525647] : [-(hAPP(c_Product__Type_Omap__pair(_1525633, _1525635, _1525637, _1525639, _1525641, _1525643), hAPP(hAPP(c_Product__Type_OPair(_1525633, _1525637), _1525645), _1525647)) = hAPP(hAPP(c_Product__Type_OPair(_1525635, _1525639), hAPP(_1525641, _1525645)), hAPP(_1525643, _1525647)))], (16529 ^ _781215) ^ [_1075918, _1075920, _1075922] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1075918, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075918, tc_HOL_Obool)), _1075920), _1075922)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1075918, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1075918, tc_HOL_Obool)), _1075920)), _1075922))], (26442 ^ _781215) ^ [_1260909, _1260911, _1260913, _1260915, _1260917] : [class_Groups_Ocomm__monoid__mult(_1260909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1260911), _1260913)), hBOOL(hAPP(hAPP(c_member(_1260911), _1260915), _1260913)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1260911, _1260909), _1260917), _1260913) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1260909), hAPP(_1260917, _1260915)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1260911, _1260909), _1260917), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260911, tc_HOL_Obool)), _1260913), hAPP(hAPP(c_Set_Oinsert(_1260911), _1260915), c_Orderings_Obot__class_Obot(tc_fun(_1260911, tc_HOL_Obool)))))))], (42160 ^ _781215) ^ [_1613833, _1613835, _1613837] : [_1613833 = _1613835, 42163 ^ _781215 : [(42166 ^ _781215) ^ [_1613989] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613837, _1613837)), _1613989), hAPP(c_List_Oset(tc_prod(_1613837, _1613837)), hAPP(hAPP(c_List_Ozip(_1613837, _1613837), _1613833), _1613835)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1613837, _1613837, tc_HOL_Obool), c_fequal), _1613989)))], (42164 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613837)), _1613833) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613837)), _1613835))]]], (30838 ^ _781215) ^ [_1345863] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1345863) = 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), _1345863))))], (40597 ^ _781215) ^ [_1576779, _1576781] : [-(c_Nitpick_Owf_H(_1576779, _1576781)), c_Wellfounded_Oacyclic(_1576779, _1576781), 40602 ^ _781215 : [(40605 ^ _781215) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (40603 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576779, _1576779)), _1576781))]]], (8564 ^ _781215) ^ [_926470, _926472, _926474, _926476] : [class_Groups_Oab__semigroup__mult(_926470), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926470), _926472), _926474)), _926476) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926470), _926472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926470), _926474), _926476)))], (34564 ^ _781215) ^ [_1428751, _1428753, _1428755, _1428757, _1428759] : [class_Groups_Ocomm__monoid__mult(_1428751), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428753), _1428755)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428753), _1428757)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428753, tc_HOL_Obool)), _1428755), _1428757) = c_Orderings_Obot__class_Obot(tc_fun(_1428753, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1428751, _1428753, c_Groups_Otimes__class_Otimes(_1428751)), _1428759), c_Groups_Oone__class_Oone(_1428751)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1428753, tc_HOL_Obool)), _1428755), _1428757)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1428751), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1428751, _1428753, c_Groups_Otimes__class_Otimes(_1428751)), _1428759), c_Groups_Oone__class_Oone(_1428751)), _1428755)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1428751, _1428753, c_Groups_Otimes__class_Otimes(_1428751)), _1428759), c_Groups_Oone__class_Oone(_1428751)), _1428757)))], (48213 ^ _781215) ^ [_1753531, _1753533, _1753535, _1753537] : [48215 ^ _781215 : [(48218 ^ _781215) ^ [] : [hBOOL(hAPP(_1753535, 48214 ^ [_1753531, _1753533, _1753535, _1753537]))], (48216 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753531), 48214 ^ [_1753531, _1753533, _1753535, _1753537]), hAPP(c_List_Oset(_1753531), _1753533))))]], -(c_List_OtakeWhile(_1753531, _1753535, hAPP(hAPP(c_List_Oappend(_1753531), _1753533), _1753537)) = hAPP(hAPP(c_List_Oappend(_1753531), _1753533), c_List_OtakeWhile(_1753531, _1753535, _1753537)))], (7120 ^ _781215) ^ [_899983, _899985, _899987, _899989, _899991] : [7123 ^ _781215 : [(7129 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_899991, 7121 ^ [_899983, _899985, _899987, _899989, _899991]), 7125 ^ [_899983, _899985, _899987, _899989, _899991]))], (7127 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _899989), 7122 ^ [_899983, _899985, _899987, _899989, _899991]), _899985), 7125 ^ [_899983, _899985, _899987, _899989, _899991])))], (7124 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_899987, 7121 ^ [_899983, _899985, _899987, _899989, _899991]), 7122 ^ [_899983, _899985, _899987, _899989, _899991])))]], -(c_Hoare__Mirabelle_Otriple__valid(_899983, _899985, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_899983), _899987), _899989), _899991)))], (20340 ^ _781215) ^ [_1146365, _1146367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1146365)), c_Int_OBit1(_1146367))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1146365), _1146367)))], (28224 ^ _781215) ^ [_1295085, _1295087] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295085), _1295087), hAPP(c_Int_Onumber__class_Onumber__of(_1295085), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1295085), _1295087)), class_Fields_Ofield__inverse__zero(_1295085), class_Int_Onumber__ring(_1295085)], (32439 ^ _781215) ^ [_1381361, _1381363, _1381365, _1381367, _1381369] : [c_Equiv__Relations_Oequiv(_1381361, _1381363, _1381365), 32442 ^ _781215 : [(32453 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1381361, _1381361)), hAPP(hAPP(c_Product__Type_OPair(_1381361, _1381361), _1381367), _1381369)), _1381365))), hAPP(c_Relation_OImage(_1381361, _1381361, _1381365), hAPP(hAPP(c_Set_Oinsert(_1381361), _1381367), c_Orderings_Obot__class_Obot(tc_fun(_1381361, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1381361, _1381361, _1381365), hAPP(hAPP(c_Set_Oinsert(_1381361), _1381369), c_Orderings_Obot__class_Obot(tc_fun(_1381361, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1381361), _1381367), _1381363)), hBOOL(hAPP(hAPP(c_member(_1381361), _1381369), _1381363))], (32443 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1381361, _1381361)), hAPP(hAPP(c_Product__Type_OPair(_1381361, _1381361), _1381367), _1381369)), _1381365)), 32446 ^ _781215 : [(32451 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381361), _1381369), _1381363)))], (32449 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381361), _1381367), _1381363)))], (32447 ^ _781215) ^ [] : [-(hAPP(c_Relation_OImage(_1381361, _1381361, _1381365), hAPP(hAPP(c_Set_Oinsert(_1381361), _1381367), c_Orderings_Obot__class_Obot(tc_fun(_1381361, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1381361, _1381361, _1381365), hAPP(hAPP(c_Set_Oinsert(_1381361), _1381369), c_Orderings_Obot__class_Obot(tc_fun(_1381361, tc_HOL_Obool)))))]]]]], (49042 ^ _781215) ^ [_1770825, _1770827] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1770825), _1770827) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1770825, 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)))), _1770827))))], (45153 ^ _781215) ^ [_1687236, _1687238, _1687240] : [-(_1687236 = c_List_Olist_ONil(_1687238)), -(c_List_Olast(_1687238, hAPP(hAPP(c_List_Olist_OCons(_1687238), _1687240), _1687236)) = c_List_Olast(_1687238, _1687236))], (50090 ^ _781215) ^ [_1797701, _1797703, _1797705, _1797707] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1797701, _1797703, _1797705, _1797707) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1797701, _1797703), _1797705), _1797707)))], (31445 ^ _781215) ^ [] : [-(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))))))], (44365 ^ _781215) ^ [_1668845, _1668847, _1668849, _1668851] : [44366 ^ _781215 : [(44369 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1668845), _1668847), hAPP(c_List_Oset(_1668845), c_List_Obutlast(_1668845, _1668851))))], (44367 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1668845), _1668847), hAPP(c_List_Oset(_1668845), c_List_Obutlast(_1668845, _1668849))))]], -(hBOOL(hAPP(hAPP(c_member(_1668845), _1668847), hAPP(c_List_Oset(_1668845), c_List_Obutlast(_1668845, hAPP(hAPP(c_List_Oappend(_1668845), _1668849), _1668851))))))], (33244 ^ _781215) ^ [_1399351, _1399353] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399351, tc_HOL_Obool)), _1399353), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1399351, tc_HOL_Obool)), _1399353)) = c_Orderings_Obot__class_Obot(tc_fun(_1399351, tc_HOL_Obool)))], (37879 ^ _781215) ^ [_1501254, _1501256, _1501258] : [class_Complete__Lattice_Ocomplete__lattice(_1501254), 37882 ^ _781215 : [(37883 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501254), c_Complete__Lattice_OSup__class_OSup(_1501254, _1501256)), _1501258)), 37886 ^ _781215 : [(37887 ^ _781215) ^ [_1501412] : [hBOOL(hAPP(hAPP(c_member(_1501254), _1501412), _1501256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501254), _1501412), _1501258)))]]], (37893 ^ _781215) ^ [] : [37895 ^ _781215 : [(37898 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501254), 37894 ^ [_1501254, _1501256, _1501258]), _1501258))], (37896 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501254), 37894 ^ [_1501254, _1501256, _1501258]), _1501256)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501254), c_Complete__Lattice_OSup__class_OSup(_1501254, _1501256)), _1501258)))]]], (40617 ^ _781215) ^ [_1577104, _1577106, _1577108, _1577110, _1577112, _1577114] : [hBOOL(hAPP(_1577104, _1577106)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1577108), _1577106), _1577110), _1577112)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1577104, _1577108)), _1577112), _1577110), _1577114)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1577104, _1577108)), _1577106), _1577110), _1577114)))], (42391 ^ _781215) ^ [_1620759, _1620761, _1620763, _1620765, _1620767] : [-(hAPP(hAPP(c_List_Omap(_1620759, _1620761), _1620763), hAPP(hAPP(c_List_Olist_OCons(_1620759), _1620765), _1620767)) = hAPP(hAPP(c_List_Olist_OCons(_1620761), hAPP(_1620763, _1620765)), hAPP(hAPP(c_List_Omap(_1620759, _1620761), _1620763), _1620767)))], (48886 ^ _781215) ^ [_1768207, _1768209] : [hAPP(c_Code__Numeral_Oof__nat, _1768207) = hAPP(c_Code__Numeral_Oof__nat, _1768209), -(_1768207 = _1768209)], (15312 ^ _781215) ^ [_1049861, _1049863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049861), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049863), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049861), _1049863))), -(_1049861 = _1049863)], (8624 ^ _781215) ^ [_927549, _927551, _927553] : [class_Groups_Ogroup__add(_927549), 8627 ^ _781215 : [(8634 ^ _781215) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_927549), _927553) = _927551, -(hAPP(c_Groups_Ouminus__class_Ouminus(_927549), _927551) = _927553)], (8628 ^ _781215) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_927549), _927551) = _927553, -(hAPP(c_Groups_Ouminus__class_Ouminus(_927549), _927553) = _927551)]]], (44578 ^ _781215) ^ [_1674690, _1674692, _1674694, _1674696, _1674698] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1674690, _1674692)), _1674694), hAPP(hAPP(c_List_Ozip(_1674690, _1674692), _1674696), _1674698)) = hAPP(hAPP(c_List_Ozip(_1674690, _1674692), hAPP(hAPP(c_List_Odrop(_1674690), _1674694), _1674696)), hAPP(hAPP(c_List_Odrop(_1674692), _1674694), _1674698)))], (15504 ^ _781215) ^ [_1053123, _1053125, _1053127, _1053129, _1053131, _1053133] : [-(c_Com_Ocom_OLocal(_1053123, _1053125, _1053127) = c_Com_Ocom_OLocal(_1053129, _1053131, _1053133)), _1053123 = _1053129, _1053125 = _1053131, _1053127 = _1053133], (44198 ^ _781215) ^ [_1664794, _1664796, _1664798] : [-(_1664794 = c_List_Olist_ONil(_1664796)), -(c_List_Obutlast(_1664796, hAPP(hAPP(c_List_Oappend(_1664796), _1664798), _1664794)) = hAPP(hAPP(c_List_Oappend(_1664796), _1664798), c_List_Obutlast(_1664796, _1664794)))], (48027 ^ _781215) ^ [_1748642, _1748644, _1748646, _1748648, _1748650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1748642, _1748644)), hAPP(_1748642, _1748646))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1748648, _1748648)), hAPP(hAPP(c_Product__Type_OPair(_1748648, _1748648), _1748644), _1748646)), c_List_Omeasures(_1748648, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1748648, tc_Nat_Onat)), _1748642), _1748650)))))], (20138 ^ _781215) ^ [_1142752] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1142752))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1142752)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2272 ^ _781215) ^ [_814641, _814643, _814645, _814647, _814649, _814651] : [-(c_SetInterval_Oord_OlessThan(_814651, _814647, _814643) = c_SetInterval_Oord_OlessThan(_814649, _814645, _814641)), _814651 = _814649, _814647 = _814645, _814643 = _814641], (50854 ^ _781215) ^ [_1814589, _1814591] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1814589), _1814591)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1814589)), c_Int_OBit1(_1814591))))], (44670 ^ _781215) ^ [_1676749, _1676751, _1676753, _1676755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1676749), _1676751)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676753)), _1676755))), -(hAPP(hAPP(c_List_Onth(_1676753), hAPP(hAPP(c_List_Odrop(_1676753), _1676749), _1676755)), _1676751) = hAPP(hAPP(c_List_Onth(_1676753), _1676755), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1676749), _1676751)))], (30910 ^ _781215) ^ [_1347055, _1347057, _1347059] : [class_Orderings_Olinorder(_1347055), 30913 ^ _781215 : [(30920 ^ _781215) ^ [] : [_1347057 = _1347059, -(hAPP(c_SetInterval_Oord__class_OatMost(_1347055), _1347057) = hAPP(c_SetInterval_Oord__class_OatMost(_1347055), _1347059))], (30914 ^ _781215) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1347055), _1347057) = hAPP(c_SetInterval_Oord__class_OatMost(_1347055), _1347059), -(_1347057 = _1347059)]]], (12338 ^ _781215) ^ [_995798, _995800, _995802] : [class_Rings_Oordered__cancel__semiring(_995798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995798), _995800), c_Groups_Ozero__class_Ozero(_995798))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995798), c_Groups_Ozero__class_Ozero(_995798)), _995802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995798), _995800), _995802)), c_Groups_Ozero__class_Ozero(_995798))))], (29534 ^ _781215) ^ [_1319560, _1319562, _1319564, _1319566] : [class_Fields_Olinordered__field__inverse__zero(_1319560), 29537 ^ _781215 : [(29538 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319560), _1319562), _1319564)), _1319566)), 29541 ^ _781215 : [(29548 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), c_Groups_Ozero__class_Ozero(_1319560)), _1319564))), 29551 ^ _781215 : [(29558 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), _1319564), c_Groups_Ozero__class_Ozero(_1319560)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), c_Groups_Ozero__class_Ozero(_1319560)), _1319566)))], (29552 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), _1319564), c_Groups_Ozero__class_Ozero(_1319560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319560), _1319566), _1319564)), _1319562)))]]], (29542 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), c_Groups_Ozero__class_Ozero(_1319560)), _1319564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), _1319562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319560), _1319566), _1319564))))]]], (29564 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319560), _1319562), _1319564)), _1319566))), 29567 ^ _781215 : [(29570 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), _1319562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319560), _1319566), _1319564)))], (29568 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), c_Groups_Ozero__class_Ozero(_1319560)), _1319564)))]], 29571 ^ _781215 : [(29574 ^ _781215) ^ [] : [29575 ^ _781215 : [(29578 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319560), _1319566), _1319564)), _1319562))], (29576 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), _1319564), c_Groups_Ozero__class_Ozero(_1319560))))]], 29579 ^ _781215 : [(29582 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), c_Groups_Ozero__class_Ozero(_1319560)), _1319566))], (29580 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), _1319564), c_Groups_Ozero__class_Ozero(_1319560)))]]], (29572 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319560), c_Groups_Ozero__class_Ozero(_1319560)), _1319564))]]]]], (2634 ^ _781215) ^ [_820356, _820358, _820360, _820362] : [-(c_Divides_Odivmod__nat__rel(_820362, _820358) = c_Divides_Odivmod__nat__rel(_820360, _820356)), _820362 = _820360, _820358 = _820356], (50212 ^ _781215) ^ [_1801261, _1801263, _1801265] : [50213 ^ _781215 : [(50214 ^ _781215) ^ [_1801338, _1801340] : [_1801265 = hAPP(hAPP(c_List_Oappend(_1801261), _1801340), hAPP(hAPP(c_List_Olist_OCons(_1801261), _1801263), _1801338))]], -(hBOOL(hAPP(hAPP(c_member(_1801261), _1801263), hAPP(c_List_Oset(_1801261), _1801265))))], (36400 ^ _781215) ^ [_1465432, _1465434] : [class_Lattices_Obounded__lattice__top(_1465432), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465432), _1465434), c_Orderings_Otop__class_Otop(_1465432)) = _1465434)], (42777 ^ _781215) ^ [_1631134, _1631136, _1631138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631134), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631136)), _1631138))), -(hBOOL(hAPP(hAPP(c_member(_1631136), hAPP(hAPP(c_List_Onth(_1631136), _1631138), _1631134)), hAPP(c_List_Oset(_1631136), _1631138))))], (36540 ^ _781215) ^ [_1467957, _1467959] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467957), c_Orderings_Otop__class_Otop(tc_fun(_1467957, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1467957), _1467959) = hAPP(c_Finite__Set_Ocard(_1467957), c_Orderings_Otop__class_Otop(tc_fun(_1467957, tc_HOL_Obool))), -(_1467959 = c_Orderings_Otop__class_Otop(tc_fun(_1467957, tc_HOL_Obool)))], (39920 ^ _781215) ^ [_1560708, _1560710, _1560712, _1560714] : [hBOOL(hAPP(c_Predicate_ORangeP(_1560708, _1560710, _1560712), _1560714)), -(hBOOL(hAPP(hAPP(_1560712, 39923 ^ [_1560708, _1560710, _1560712, _1560714]), _1560714)))], (10752 ^ _781215) ^ [_965436, _965438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965436), _965438)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965436), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965438), _965436)) = _965438)], (25546 ^ _781215) ^ [_1240965, _1240967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1240965), _1240967)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1240965), _1240967) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36550 ^ _781215) ^ [_1468144, _1468146, _1468148, _1468150, _1468152] : [c_Fun_Oinj__on(_1468144, _1468146, _1468148, c_Orderings_Otop__class_Otop(tc_fun(_1468144, tc_HOL_Obool))), 36553 ^ _781215 : [(36560 ^ _781215) ^ [] : [_1468150 = _1468152, -(hAPP(c_Set_Oimage(_1468144, _1468146, _1468148), _1468150) = hAPP(c_Set_Oimage(_1468144, _1468146, _1468148), _1468152))], (36554 ^ _781215) ^ [] : [hAPP(c_Set_Oimage(_1468144, _1468146, _1468148), _1468150) = hAPP(c_Set_Oimage(_1468144, _1468146, _1468148), _1468152), -(_1468150 = _1468152)]]], (43936 ^ _781215) ^ [_1658866, _1658868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1658866)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1658868))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1658866), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1658868)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1658866)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1658866)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1658868))))], (12190 ^ _781215) ^ [_992976, _992978, _992980] : [class_Rings_Oordered__ring(_992976), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992976), c_Groups_Ozero__class_Ozero(_992976)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992976), _992978), _992980)))), 12195 ^ _781215 : [(12202 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992976), _992978), c_Groups_Ozero__class_Ozero(_992976))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992976), _992980), c_Groups_Ozero__class_Ozero(_992976)))], (12196 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992976), c_Groups_Ozero__class_Ozero(_992976)), _992978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992976), c_Groups_Ozero__class_Ozero(_992976)), _992980))]]], (38231 ^ _781215) ^ [_1509532, _1509534, _1509536, _1509538] : [-(hAPP(hAPP(c_Option_Omap(_1509532, _1509534), _1509536), hAPP(c_Option_Ooption_OSome(_1509532), _1509538)) = hAPP(c_Option_Ooption_OSome(_1509534), hAPP(_1509536, _1509538)))], (36165 ^ _781215) ^ [_1461188] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1461188), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1461188) = _1461188)], (51638 ^ _781215) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (15286 ^ _781215) ^ [_1049342] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1049342) = _1049342)], (11324 ^ _781215) ^ [_978313, _978315, _978317, _978319] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_978313, _978317)), c_Sum__Type_OPlus(_978313, _978317, _978315, _978319)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_978313), _978315)), hAPP(c_Finite__Set_Ocard(_978317), _978319))), hBOOL(hAPP(c_Finite__Set_Ofinite(_978313), _978315)), hBOOL(hAPP(c_Finite__Set_Ofinite(_978317), _978319))], (49367 ^ _781215) ^ [_1779427, _1779429] : [-(c_Transitive__Closure_Ortrancl(_1779427, c_Transitive__Closure_Ortrancl(_1779427, _1779429)) = c_Transitive__Closure_Ortrancl(_1779427, _1779429))], (37981 ^ _781215) ^ [_1503480, _1503482, _1503484] : [class_Complete__Lattice_Ocomplete__lattice(_1503480), -(c_Complete__Lattice_OSup__class_OSup(_1503480, hAPP(hAPP(c_Set_Oinsert(_1503480), _1503482), _1503484)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1503480), _1503482), c_Complete__Lattice_OSup__class_OSup(_1503480, _1503484)))], (15741 ^ _781215) ^ [_1058066, _1058068, _1058070] : [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), _1058066), _1058068)), _1058070)), 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)), _1058070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1058068), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16421 ^ _781215) ^ [_1071591, _1071593, _1071595, _1071597, _1071599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1071591, tc_HOL_Obool)), _1071593), _1071595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1071591, tc_HOL_Obool)), _1071597), _1071599)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1071591, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071591, tc_HOL_Obool)), _1071593), _1071597)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071591, tc_HOL_Obool)), _1071595), _1071599))))], (44144 ^ _781215) ^ [_1663858, _1663860, _1663862] : [hAPP(hAPP(c_List_Oappend(_1663858), _1663860), _1663862) = c_List_Olist_ONil(_1663858), 44147 ^ _781215 : [(44150 ^ _781215) ^ [] : [-(_1663862 = c_List_Olist_ONil(_1663858))], (44148 ^ _781215) ^ [] : [-(_1663860 = c_List_Olist_ONil(_1663858))]]], (10584 ^ _781215) ^ [_962359, _962361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962359)), _962361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962359), _962361)))], (13854 ^ _781215) ^ [_1022585, _1022587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1022585), _1022587))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1022585), _1022587)))], (15278 ^ _781215) ^ [_1049190, _1049192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1049190), _1049192)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049190), _1049192)))], (38175 ^ _781215) ^ [_1508150, _1508152, _1508154, _1508156, _1508158] : [-(hAPP(c_Fun_Othe__inv__into(_1508150, _1508152, _1508154, _1508156), _1508158) = c_HOL_OThe(_1508150, hAPP(hAPP(c_COMBS(_1508150, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508150), c_fconj), hAPP(hAPP(c_COMBC(_1508150, tc_fun(_1508150, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508150)), _1508154))), hAPP(hAPP(c_COMBC(_1508150, _1508152, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1508152, tc_fun(_1508152, tc_HOL_Obool), _1508150), c_fequal), _1508156)), _1508158))))], (31070 ^ _781215) ^ [_1349869] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1349869) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1349869))], (43992 ^ _781215) ^ [_1660546, _1660548, _1660550] : [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), _1660546), _1660548))), -(hBOOL(hAPP(hAPP(_1660550, _1660546), _1660548))), 43999 ^ _781215 : [(44002 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 43997 ^ [_1660546, _1660548, _1660550]), 43998 ^ [_1660546, _1660548, _1660550])), -(hBOOL(hAPP(hAPP(_1660550, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43997 ^ [_1660546, _1660548, _1660550]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 43998 ^ [_1660546, _1660548, _1660550])))], (44008 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1660550, 43997 ^ [_1660546, _1660548, _1660550]), 43998 ^ [_1660546, _1660548, _1660550]))], (44000 ^ _781215) ^ [] : [-(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), 43997 ^ [_1660546, _1660548, _1660550]), 43998 ^ [_1660546, _1660548, _1660550]))))]]], (41126 ^ _781215) ^ [_1588277, _1588279, _1588281] : [hBOOL(hAPP(c_List_Odistinct(_1588277), hAPP(hAPP(c_List_Omap(tc_prod(_1588277, _1588279), _1588277), c_Product__Type_Ofst(_1588277, _1588279)), _1588281))), -(hAPP(c_List_Oset(tc_prod(_1588277, _1588279)), _1588281) = hAPP(c_Set_OCollect(tc_prod(_1588277, _1588279)), hAPP(c_Product__Type_Oprod_Oprod__case(_1588277, _1588279, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1588277, tc_fun(_1588279, tc_Option_Ooption(_1588279)), tc_fun(_1588279, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1588279), tc_HOL_Obool), tc_fun(tc_fun(_1588279, tc_Option_Ooption(_1588279)), tc_fun(_1588279, tc_HOL_Obool)), _1588277), c_COMBB(tc_Option_Ooption(_1588279), tc_HOL_Obool, _1588279)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1588279), tc_fun(tc_Option_Ooption(_1588279), tc_HOL_Obool), _1588277), c_fequal), hAPP(c_Map_Omap__of(_1588277, _1588279), _1588281)))), c_Option_Ooption_OSome(_1588279)))))], (16523 ^ _781215) ^ [_1075751, _1075753, _1075755, _1075757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1075751, tc_HOL_Obool)), _1075753), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1075751, tc_HOL_Obool)), _1075755), _1075757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1075751, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075751, tc_HOL_Obool)), _1075753), _1075755)), _1075757)))], (12268 ^ _781215) ^ [_994467, _994469, _994471, _994473] : [class_Rings_Oordered__ring(_994467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994467), _994469), _994471)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994467), _994473), c_Groups_Ozero__class_Ozero(_994467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994467), _994471), _994473)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_994467), _994469), _994473))))], (32238 ^ _781215) ^ [_1376769, _1376771] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1376769), c_Orderings_Obot__class_Obot(tc_fun(_1376769, tc_HOL_Obool))), _1376771) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1376769, tc_HOL_Obool), tc_HOL_Obool)))], (50936 ^ _781215) ^ [_1816506, _1816508, _1816510] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1816506)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1816506, _1816508, _1816510)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1816506)), _1816510)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20310 ^ _781215) ^ [_1145797, _1145799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145797), _1145799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1145797)), c_Int_OBit1(_1145799))))], (47270 ^ _781215) ^ [_1732101, _1732103] : [class_Enum_Oenum(_1732101), 47273 ^ _781215 : [(47280 ^ _781215) ^ [] : [hBOOL(hAPP(_1732103, 47281 ^ [_1732101, _1732103])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1732101), _1732103)))], (47274 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1732101), _1732103)), 47277 ^ _781215 : [(47278 ^ _781215) ^ [_1732227] : [-(hBOOL(hAPP(_1732103, _1732227)))]]]]], (130 ^ _781215) ^ [_783296, _783298, _783300, _783302] : [-(c_Int_Oiszero(_783300, _783296)), c_Int_Oiszero(_783302, _783298), _783302 = _783300, _783298 = _783296], (40477 ^ _781215) ^ [_1573829, _1573831, _1573833] : [hBOOL(hAPP(c_Predicate_OPowp(_1573829, _1573831), _1573833)), 40480 ^ _781215 : [(40481 ^ _781215) ^ [_1573913] : [hBOOL(hAPP(hAPP(c_member(_1573829), _1573913), _1573833)), -(hBOOL(hAPP(_1573831, _1573913)))]]], (17015 ^ _781215) ^ [_1086409] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086409), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086409), c_Int_OPls)))], (51610 ^ _781215) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (46588 ^ _781215) ^ [_1718036, _1718038] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718036)), c_List_Oremdups(_1718036, c_List_Oconcat(_1718036, _1718038))) = hAPP(c_Finite__Set_Ocard(_1718036), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1718036), tc_fun(_1718036, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1718036)), _1718038)), c_List_Oset(_1718036))))], (51270 ^ _781215) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (33811 ^ _781215) ^ [_1411786, _1411788, _1411790] : [class_Orderings_Olinorder(_1411786), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411786), _1411788)), -(_1411788 = c_Orderings_Obot__class_Obot(tc_fun(_1411786, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411786), _1411790)), -(_1411790 = c_Orderings_Obot__class_Obot(tc_fun(_1411786, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411786, tc_HOL_Obool)), _1411788), _1411790) = c_Orderings_Obot__class_Obot(tc_fun(_1411786, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1411786, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411786, tc_HOL_Obool)), _1411788), _1411790)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1411786), c_Big__Operators_Olinorder__class_OMin(_1411786, _1411788)), c_Big__Operators_Olinorder__class_OMin(_1411786, _1411790)))], (41249 ^ _781215) ^ [_1591154, _1591156, _1591158, _1591160, _1591162, _1591164, _1591166] : [hAPP(c_Fun_Ocomp(_1591154, _1591156, _1591158, _1591160), _1591162) = hAPP(c_Fun_Ocomp(_1591156, _1591156, _1591158, c_Fun_Oid(_1591156)), _1591164), -(hAPP(_1591160, hAPP(_1591162, _1591166)) = hAPP(_1591164, _1591166))], (40249 ^ _781215) ^ [_1567608, _1567610, _1567612, _1567614] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567608, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567608, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1567608, _1567610), _1567612)), hAPP(c_Relation_ODomain(_1567608, _1567610), _1567614))), hAPP(c_Relation_ODomain(_1567608, _1567610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1567608, _1567610), tc_HOL_Obool)), _1567612), _1567614)))))], (38480 ^ _781215) ^ [_1515755, _1515757, _1515759, _1515761, _1515763] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1515755, _1515757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1515755, tc_HOL_Obool)), _1515759), _1515761)), _1515763) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1515755, _1515757), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1515755, _1515757), _1515759), _1515763)), hAPP(hAPP(c_Product__Type_OSigma(_1515755, _1515757), _1515761), _1515763)))], (27834 ^ _781215) ^ [_1288595, _1288597, _1288599, _1288601] : [class_Fields_Ofield__inverse__zero(_1288595), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1288595), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288595), _1288597), _1288599)), _1288601) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288595), hAPP(hAPP(c_Power_Opower__class_Opower(_1288595), _1288597), _1288601)), hAPP(hAPP(c_Power_Opower__class_Opower(_1288595), _1288599), _1288601)))], (2644 ^ _781215) ^ [_820505, _820507, _820509, _820511, _820513, _820515] : [-(c_Finite__Set_Ofold1Set(_820515, _820511, _820507) = c_Finite__Set_Ofold1Set(_820513, _820509, _820505)), _820515 = _820513, _820511 = _820509, _820507 = _820505], (19050 ^ _781215) ^ [_1122689] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1122689), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1122689)], (41225 ^ _781215) ^ [_1590717, _1590719] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1590717, _1590719))))], (27301 ^ _781215) ^ [_1277364, _1277366] : [-(c_Divides_Odivmod__int__rel(_1277364, _1277366) = 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, _1277364))), 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), _1277366)))))), 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)), _1277366))), 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)), _1277366))))), 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)), _1277366)))), 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), _1277366))), 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))))))))], (27225 ^ _781215) ^ [_1276090, _1276092, _1276094] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1276090, _1276090), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1276092), _1276094))), -(_1276090 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1276092 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (48497 ^ _781215) ^ [_1760465, _1760467, _1760469] : [48499 ^ _781215 : [(48502 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1760465), _1760469), 48498 ^ [_1760465, _1760467, _1760469]))], (48500 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1760465, tc_HOL_Obool)), 48498 ^ [_1760465, _1760467, _1760469]), _1760467)))]], -(hBOOL(hAPP(hAPP(c_member(_1760465), _1760469), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1760465, tc_HOL_Obool), _1760467))))], (44888 ^ _781215) ^ [_1681447, _1681449, _1681451] : [-(hAPP(hAPP(c_List_Odrop(_1681447), hAPP(c_Nat_OSuc, _1681449)), _1681451) = hAPP(hAPP(c_List_Odrop(_1681447), _1681449), hAPP(c_List_Otl(_1681447), _1681451)))], (23658 ^ _781215) ^ [_1207671, _1207673] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1207671, _1207673)), _1207671)))], (15488 ^ _781215) ^ [_1052885, _1052887, _1052889, _1052891, _1052893, _1052895] : [-(_1052885 = _1052887), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1052889, _1052891), _1052893), _1052887), _1052895), _1052885) = hAPP(_1052893, _1052885))], (34534 ^ _781215) ^ [_1427958, _1427960] : [class_Lattices_Olattice(_1427958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427958), _1427960)), -(_1427960 = c_Orderings_Obot__class_Obot(tc_fun(_1427958, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1427958), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1427958), 34547 ^ [_1427958, _1427960]), 34548 ^ [_1427958, _1427960])), hAPP(hAPP(c_Set_Oinsert(_1427958), 34547 ^ [_1427958, _1427960]), hAPP(hAPP(c_Set_Oinsert(_1427958), 34548 ^ [_1427958, _1427960]), c_Orderings_Obot__class_Obot(tc_fun(_1427958, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1427958), c_Big__Operators_Olattice__class_OInf__fin(_1427958, _1427960)), _1427960)))], (18147 ^ _781215) ^ [_1106144, _1106146, _1106148] : [class_Orderings_Olinorder(_1106144), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106144), _1106146), _1106148) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106144), _1106148), _1106146))], (23630 ^ _781215) ^ [_1207078, _1207080] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1207078), _1207080)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207078)), _1207080))], (16271 ^ _781215) ^ [_1068781, _1068783, _1068785] : [class_Lattices_Osemilattice__sup(_1068781), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068781), _1068783), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068781), _1068783), _1068785))))], (49873 ^ _781215) ^ [_1792119, _1792121, _1792123] : [c_Relation_Ototal__on(_1792119, _1792121, _1792123), 49876 ^ _781215 : [(49877 ^ _781215) ^ [_1792263] : [hBOOL(hAPP(hAPP(c_member(_1792119), _1792263), _1792121)), 49880 ^ _781215 : [(49881 ^ _781215) ^ [_1792403] : [hBOOL(hAPP(hAPP(c_member(_1792119), _1792403), _1792121)), -(_1792263 = _1792403), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1792119, _1792119)), hAPP(hAPP(c_Product__Type_OPair(_1792119, _1792119), _1792263), _1792403)), _1792123))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1792119, _1792119)), hAPP(hAPP(c_Product__Type_OPair(_1792119, _1792119), _1792403), _1792263)), _1792123)))]]]]], (50828 ^ _781215) ^ [_1814146, _1814148] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1814146)), c_Int_OBit0(_1814148)))], (5458 ^ _781215) ^ [_864550, _864552, _864554, _864556] : [-(tc_prod(_864556, _864552) = tc_prod(_864554, _864550)), _864556 = _864554, _864552 = _864550], (8900 ^ _781215) ^ [_932058, _932060, _932062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932058, tc_HOL_Obool)), _932060), _932062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932058, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_932058, tc_HOL_Obool)), _932062)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_932058, tc_HOL_Obool)), _932060))))], (11734 ^ _781215) ^ [_985787, _985789] : [class_Groups_Ogroup__add(_985787), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_985787), _985789), c_Groups_Ozero__class_Ozero(_985787)) = _985789)], (17973 ^ _781215) ^ [_1102098] : [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, _1102098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1102098)))], (22326 ^ _781215) ^ [_1184233, _1184235, _1184237, _1184239] : [class_Divides_Osemiring__div(_1184233), -(c_Divides_Odiv__class_Omod(_1184233, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184233), _1184235), _1184237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184233), _1184235), _1184239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184233), _1184235), c_Divides_Odiv__class_Omod(_1184233, _1184237, _1184239)))], (13264 ^ _781215) ^ [_1011794, _1011796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1011796), _1011794)), _1011796)))], (43872 ^ _781215) ^ [_1657137, _1657139, _1657141] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657137), tc_List_Olist(_1657137))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657137), tc_List_Olist(_1657137)), _1657139), c_List_Olist_ONil(_1657137))), c_List_Olexord(_1657137, _1657141)))], (8856 ^ _781215) ^ [_931354, _931356, _931358, _931360] : [class_Orderings_Oord(_931354), _931356 = _931358, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931354), _931358), _931360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931354), _931356), _931360)))], (5979 ^ _781215) ^ [_876425, _876427, _876429] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_876425), _876427)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_876425), hAPP(hAPP(c_Set_Oinsert(_876425), _876429), _876427))))], (15298 ^ _781215) ^ [_1049553, _1049555, _1049557] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049553), _1049555)), _1049557) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049553), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049555), _1049557)))], (6023 ^ _781215) ^ [_877495, _877497, _877499, _877501, _877503, _877505] : [c_Hoare__Mirabelle_Ohoare__derivs(_877495, _877497, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877495)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877495), _877499), _877501), _877503)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877495), tc_HOL_Obool)))), 6030 ^ _781215 : [(6033 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_877499, 6028 ^ [_877495, _877497, _877499, _877501, _877503, _877505]), 6029 ^ [_877495, _877497, _877499, _877501, _877503, _877505]))], (6031 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_877505, 6028 ^ [_877495, _877497, _877499, _877501, _877503, _877505]), 6029 ^ [_877495, _877497, _877499, _877501, _877503, _877505])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_877495, _877497, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877495)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877495), _877505), _877501), _877503)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877495), tc_HOL_Obool)))))], (50822 ^ _781215) ^ [_1814045] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1814045)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1814045))))], (30520 ^ _781215) ^ [_1339507, _1339509] : [30522 ^ _781215 : [(30525 ^ _781215) ^ [] : [hBOOL(hAPP(_1339509, 30521 ^ [_1339507, _1339509]))], (30523 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 30521 ^ [_1339507, _1339509]), _1339507)))]], 30526 ^ _781215 : [(30527 ^ _781215) ^ [_1339658] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1339658), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1339507))), -(hBOOL(hAPP(_1339509, _1339658)))]]], (43345 ^ _781215) ^ [_1645604, _1645606, _1645608, _1645610, _1645612] : [class_Groups_Ocomm__monoid__add(_1645604), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1645604), hAPP(hAPP(c_List_Omap(_1645606, _1645604), hAPP(hAPP(c_COMBS(_1645606, _1645604, _1645604), hAPP(hAPP(c_COMBB(_1645604, tc_fun(_1645604, _1645604), _1645606), c_Groups_Oplus__class_Oplus(_1645604)), _1645608)), _1645610)), _1645612)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1645604), hAPP(c_List_Omonoid__add__class_Olistsum(_1645604), hAPP(hAPP(c_List_Omap(_1645606, _1645604), _1645608), _1645612))), hAPP(c_List_Omonoid__add__class_Olistsum(_1645604), hAPP(hAPP(c_List_Omap(_1645606, _1645604), _1645610), _1645612))))], (38790 ^ _781215) ^ [_1524782, _1524784, _1524786, _1524788, _1524790, _1524792] : [hAPP(c_Set_Oimage(_1524782, _1524784, _1524786), c_Orderings_Otop__class_Otop(tc_fun(_1524782, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1524784, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1524788, _1524790, _1524792), c_Orderings_Otop__class_Otop(tc_fun(_1524788, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1524790, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1524782, _1524788), tc_prod(_1524784, _1524790), c_Product__Type_Omap__pair(_1524782, _1524784, _1524788, _1524790, _1524786, _1524792)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1524782, _1524788), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1524784, _1524790), tc_HOL_Obool)))], (50988 ^ _781215) ^ [_1818051, _1818053, _1818055] : [-(hAPP(c_New__DSequence_Oneg__single(_1818051, _1818053), _1818055) = c_Lazy__Sequence_Ohb__single(_1818051, _1818053))], (44572 ^ _781215) ^ [_1674491, _1674493, _1674495, _1674497, _1674499] : [-(hAPP(hAPP(c_List_Odrop(_1674491), _1674493), hAPP(hAPP(c_List_Omap(_1674495, _1674491), _1674497), _1674499)) = hAPP(hAPP(c_List_Omap(_1674495, _1674491), _1674497), hAPP(hAPP(c_List_Odrop(_1674495), _1674493), _1674499)))], (20595 ^ _781215) ^ [_1150822, _1150824, _1150826] : [class_Rings_Olinordered__semidom(_1150822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150824), _1150826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150822), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150822), _1150824)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150822), _1150826))))], (32996 ^ _781215) ^ [_1393302, _1393304, _1393306, _1393308] : [class_Lattices_Osemilattice__inf(_1393302), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393302), _1393304), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393302), _1393306), _1393308)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393302), _1393306), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393302), _1393304), _1393308)))], (21978 ^ _781215) ^ [_1176635, _1176637, _1176639, _1176641, _1176643] : [hBOOL(hAPP(hAPP(c_member(_1176635), _1176637), _1176639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1176641, tc_HOL_Obool)), hAPP(_1176643, _1176637)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1176635, tc_fun(_1176641, tc_HOL_Obool)), _1176639), _1176643))))], (11414 ^ _781215) ^ [_980111, _980113, _980115, _980117, _980119, _980121, _980123] : [hBOOL(hAPP(hAPP(c_member(_980111), _980113), _980115)), c_Nitpick_Ofold__graph_H(_980111, _980117, _980119, _980121, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980111, tc_HOL_Obool)), _980115), hAPP(hAPP(c_Set_Oinsert(_980111), _980113), c_Orderings_Obot__class_Obot(tc_fun(_980111, tc_HOL_Obool)))), _980123), -(c_Nitpick_Ofold__graph_H(_980111, _980117, _980119, _980121, _980115, hAPP(hAPP(_980119, _980113), _980123)))], (13070 ^ _781215) ^ [_1008850, _1008852, _1008854] : [class_Groups_Ogroup__add(_1008850), 13073 ^ _781215 : [(13080 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008850), _1008852), _1008854) = c_Groups_Ozero__class_Ozero(_1008850), -(_1008852 = hAPP(c_Groups_Ouminus__class_Ouminus(_1008850), _1008854))], (13074 ^ _781215) ^ [] : [_1008852 = hAPP(c_Groups_Ouminus__class_Ouminus(_1008850), _1008854), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008850), _1008852), _1008854) = c_Groups_Ozero__class_Ozero(_1008850))]]], (50507 ^ _781215) ^ [_1808226, _1808228, _1808230] : [c_List_Olist__all(_1808226, _1808228, _1808230), 50510 ^ _781215 : [(50511 ^ _781215) ^ [_1808307] : [hBOOL(hAPP(hAPP(c_member(_1808226), _1808307), hAPP(c_List_Oset(_1808226), _1808230))), -(hBOOL(hAPP(_1808228, _1808307)))]]], (9631 ^ _781215) ^ [_944763, _944765, _944767] : [class_Orderings_Olinorder(_944763), 9634 ^ _781215 : [(9641 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944763), _944767), _944765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944763), _944765), _944767))], (9635 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944763), _944765), _944767))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944763), _944767), _944765)))]]], (51198 ^ _781215) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (18976 ^ _781215) ^ [_1121386, _1121388, _1121390, _1121392] : [class_Orderings_Olinorder(_1121386), 18979 ^ _781215 : [(18980 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121386), _1121388), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1121386), _1121390), _1121392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121386), _1121388), _1121390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121386), _1121388), _1121392)))], (18990 ^ _781215) ^ [] : [18991 ^ _781215 : [(18994 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121386), _1121388), _1121392))], (18992 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121386), _1121388), _1121390))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121386), _1121388), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1121386), _1121390), _1121392))))]]], (33677 ^ _781215) ^ [_1409004, _1409006, _1409008, _1409010, _1409012] : [class_Groups_Oab__group__add(_1409004), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409006), _1409008)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409006), _1409010)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409006, _1409004), _1409012), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409006, tc_HOL_Obool)), _1409008), _1409010)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409004), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409004), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409006, _1409004), _1409012), _1409008)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409006, _1409004), _1409012), _1409010))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409006, _1409004), _1409012), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409006, tc_HOL_Obool)), _1409008), _1409010))))], (25556 ^ _781215) ^ [_1241132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241132)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1241132) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1241132), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38288 ^ _781215) ^ [_1510874, _1510876, _1510878, _1510880, _1510882] : [hBOOL(hAPP(hAPP(c_member(_1510878), hAPP(_1510880, _1510876)), _1510882)), -(hBOOL(hAPP(hAPP(c_member(_1510874), _1510876), hAPP(c_Set_Ovimage(_1510874, _1510878, _1510880), _1510882))))], (35787 ^ _781215) ^ [_1454090, _1454092] : [class_Groups_Oordered__ab__group__add__abs(_1454090), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454090), _1454092), hAPP(c_Groups_Oabs__class_Oabs(_1454090), _1454092))))], (26634 ^ _781215) ^ [_1264488, _1264490] : [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), _1264488))), 26637 ^ _781215 : [(26644 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264490)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264488)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264490), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264488)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264488)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264490), 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), _1264488)))))], (26638 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264490)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264488))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264490), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264488)) = 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), _1264490)))]]], (29408 ^ _781215) ^ [_1317139, _1317141, _1317143, _1317145] : [class_Fields_Olinordered__field(_1317139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317139), _1317141), _1317143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317139), c_Groups_Ozero__class_Ozero(_1317139)), _1317145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317139), c_Groups_Ozero__class_Ozero(_1317139)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1317139), _1317143), _1317141))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317139), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317139), _1317145), _1317143)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317139), _1317145), _1317141))))], (30157 ^ _781215) ^ [_1333003, _1333005] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1333003, tc_HOL_Obool)), hAPP(c_Set_OPow(_1333003), _1333005))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1333003), _1333005)))], (6527 ^ _781215) ^ [_887714, _887716, _887718, _887720] : [c_Finite__Set_Ofolding__one__idem(_887714, _887716, _887718), -(hAPP(hAPP(_887716, _887720), _887720) = _887720)], (39496 ^ _781215) ^ [_1544554, _1544556, _1544558] : [class_Lattices_Odistrib__lattice(_1544554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544554), _1544556)), -(_1544556 = c_Orderings_Obot__class_Obot(tc_fun(_1544554, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544554), _1544558)), -(_1544558 = c_Orderings_Obot__class_Obot(tc_fun(_1544554, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1544554), c_Big__Operators_Olattice__class_OInf__fin(_1544554, _1544556)), c_Big__Operators_Olattice__class_OInf__fin(_1544554, _1544558)) = c_Big__Operators_Olattice__class_OInf__fin(_1544554, hAPP(c_Set_OCollect(_1544554), hAPP(hAPP(c_COMBB(tc_fun(_1544554, tc_HOL_Obool), tc_HOL_Obool, _1544554), c_HOL_OEx(_1544554)), hAPP(hAPP(c_COMBB(tc_fun(_1544554, tc_fun(_1544554, tc_HOL_Obool)), tc_fun(_1544554, tc_HOL_Obool), _1544554), hAPP(c_COMBB(tc_fun(_1544554, tc_HOL_Obool), tc_HOL_Obool, _1544554), c_HOL_OEx(_1544554))), hAPP(hAPP(c_COMBC(_1544554, tc_fun(_1544554, tc_fun(_1544554, tc_HOL_Obool)), tc_fun(_1544554, tc_fun(_1544554, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1544554, tc_fun(tc_fun(_1544554, tc_HOL_Obool), tc_fun(_1544554, tc_HOL_Obool))), tc_fun(tc_fun(_1544554, tc_fun(_1544554, tc_HOL_Obool)), tc_fun(_1544554, tc_fun(_1544554, tc_HOL_Obool))), _1544554), c_COMBS(_1544554, tc_fun(_1544554, tc_HOL_Obool), tc_fun(_1544554, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1544554, tc_fun(_1544554, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1544554, tc_fun(tc_fun(_1544554, tc_HOL_Obool), tc_fun(_1544554, tc_HOL_Obool))), _1544554), hAPP(c_COMBB(tc_fun(_1544554, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1544554, tc_HOL_Obool), tc_fun(_1544554, tc_HOL_Obool)), _1544554), c_COMBS(_1544554, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1544554, tc_fun(_1544554, tc_HOL_Obool)), tc_fun(_1544554, tc_fun(_1544554, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1544554), hAPP(c_COMBB(tc_fun(_1544554, tc_HOL_Obool), tc_fun(_1544554, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1544554), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1544554), c_fconj))), hAPP(hAPP(c_COMBC(_1544554, tc_fun(_1544554, tc_fun(_1544554, _1544554)), tc_fun(_1544554, tc_fun(_1544554, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1544554, _1544554), tc_fun(_1544554, tc_HOL_Obool)), tc_fun(tc_fun(_1544554, tc_fun(_1544554, _1544554)), tc_fun(_1544554, tc_fun(_1544554, tc_HOL_Obool))), _1544554), c_COMBB(tc_fun(_1544554, _1544554), tc_fun(_1544554, tc_HOL_Obool), _1544554)), hAPP(hAPP(c_COMBB(tc_fun(_1544554, tc_HOL_Obool), tc_fun(tc_fun(_1544554, _1544554), tc_fun(_1544554, tc_HOL_Obool)), _1544554), c_COMBB(_1544554, tc_HOL_Obool, _1544554)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1544554)))))), hAPP(hAPP(c_COMBC(_1544554, tc_fun(_1544554, tc_HOL_Obool), tc_fun(_1544554, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1544554, tc_HOL_Obool), tc_fun(_1544554, tc_HOL_Obool)), _1544554), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1544554)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1544554), c_fconj), hAPP(hAPP(c_COMBC(_1544554, tc_fun(_1544554, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544554)), _1544556)))), hAPP(hAPP(c_COMBC(_1544554, tc_fun(_1544554, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544554)), _1544558))))))))], (11294 ^ _781215) ^ [_977653, _977655, _977657] : [class_Rings_Ocomm__semiring__1(_977653), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977653), _977655), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977653), _977657), _977655)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977653), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977653), _977657), c_Groups_Oone__class_Oone(_977653))), _977655))], (35347 ^ _781215) ^ [_1445206, _1445208] : [class_Orderings_Oorder(_1445206), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445206, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1445206), _1445208)), hAPP(c_SetInterval_Oord__class_OatLeast(_1445206), _1445208)) = hAPP(hAPP(c_Set_Oinsert(_1445206), _1445208), c_Orderings_Obot__class_Obot(tc_fun(_1445206, tc_HOL_Obool))))], (42218 ^ _781215) ^ [_1615159, _1615161, _1615163] : [hBOOL(hAPP(hAPP(c_member(_1615159), _1615161), hAPP(c_List_Oset(_1615159), _1615163))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615159)), c_List_Oremove1(_1615159, _1615161, _1615163)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615159)), _1615163)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (36957 ^ _781215) ^ [_1478436, _1478438, _1478440, _1478442, _1478444, _1478446] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1478438, _1478440)), hAPP(hAPP(c_Product__Type_OPair(_1478438, _1478440), _1478444), _1478446)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1478436, tc_fun(tc_prod(_1478438, _1478440), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1478436, tc_HOL_Obool))), _1478442))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1478436, tc_fun(_1478438, tc_fun(_1478440, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1478436, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1478438, _1478440), tc_HOL_Obool), tc_fun(_1478438, tc_fun(_1478440, tc_HOL_Obool)), _1478436), hAPP(c_COMBC(_1478438, tc_fun(tc_prod(_1478438, _1478440), tc_HOL_Obool), tc_fun(_1478440, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478440, tc_fun(tc_fun(tc_prod(_1478438, _1478440), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1478438, _1478440), tc_HOL_Obool), tc_fun(_1478440, tc_HOL_Obool)), _1478438), c_COMBC(_1478440, tc_fun(tc_prod(_1478438, _1478440), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478440, tc_prod(_1478438, _1478440)), tc_fun(_1478440, tc_fun(tc_fun(tc_prod(_1478438, _1478440), tc_HOL_Obool), tc_HOL_Obool)), _1478438), hAPP(c_COMBB(tc_prod(_1478438, _1478440), tc_fun(tc_fun(tc_prod(_1478438, _1478440), tc_HOL_Obool), tc_HOL_Obool), _1478440), c_member(tc_prod(_1478438, _1478440)))), c_Product__Type_OPair(_1478438, _1478440))))), _1478442)), _1478444), _1478446)))], (38642 ^ _781215) ^ [_1520475, _1520477, _1520479, _1520481] : [_1520475 = c_Orderings_Obot__class_Obot(tc_fun(_1520477, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1520479, _1520477), _1520479, c_Product__Type_Ofst(_1520479, _1520477)), hAPP(hAPP(c_Product__Type_OSigma(_1520479, _1520477), _1520481), hAPP(c_COMBK(tc_fun(_1520477, tc_HOL_Obool), _1520479), _1520475))) = c_Orderings_Obot__class_Obot(tc_fun(_1520479, tc_HOL_Obool)))], (18043 ^ _781215) ^ [_1103495, _1103497] : [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(_1103497))), 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), _1103495)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1103495)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103497))))], (48096 ^ _781215) ^ [_1750833, _1750835, _1750837] : [c_Wellfounded_OwfP(_1750833, hAPP(_1750835, 48097 ^ [_1750833, _1750835, _1750837])), 48104 ^ _781215 : [(48107 ^ _781215) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1750833, tc_HOL_Obool)), c_Predicate_ODomainP(_1750833, _1750833, hAPP(_1750835, 48102 ^ [_1750833, _1750835, _1750837]))), c_Predicate_ORangeP(_1750833, _1750833, hAPP(_1750835, 48103 ^ [_1750833, _1750835, _1750837]))) = c_Orderings_Obot__class_Obot(tc_fun(_1750833, tc_HOL_Obool))], (48105 ^ _781215) ^ [] : [hAPP(_1750835, 48102 ^ [_1750833, _1750835, _1750837]) = hAPP(_1750835, 48103 ^ [_1750833, _1750835, _1750837])]], -(c_Wellfounded_OwfP(_1750833, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1750837, tc_fun(_1750833, tc_fun(_1750833, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1750837, tc_HOL_Obool))), _1750835)))], (43824 ^ _781215) ^ [_1656271] : [-(c_List_Obutlast(_1656271, c_List_Olist_ONil(_1656271)) = c_List_Olist_ONil(_1656271))], (45275 ^ _781215) ^ [_1689475, _1689477, _1689479, _1689481] : [-(hBOOL(hAPP(_1689475, _1689477))), -(c_List_Oremove1(_1689479, _1689477, hAPP(c_List_Ofilter(_1689479, _1689475), _1689481)) = hAPP(c_List_Ofilter(_1689479, _1689475), _1689481))], (35087 ^ _781215) ^ [_1439917, _1439919] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1439917), _1439919))), -(hAPP(c_Finite__Set_Ocard(_1439917), _1439919) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43057 ^ _781215) ^ [_1638418, _1638420, _1638422, _1638424, _1638426, _1638428] : [-(c_Map_Omap__add(_1638418, _1638420, _1638422, c_Map_Omap__upds(_1638418, _1638420, _1638424, _1638426, _1638428)) = c_Map_Omap__upds(_1638418, _1638420, c_Map_Omap__add(_1638418, _1638420, _1638422, _1638424), _1638426, _1638428))], (40292 ^ _781215) ^ [_1569016, _1569018, _1569020, _1569022, _1569024] : [hBOOL(hAPP(hAPP(_1569016, _1569018), _1569020)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1569022, _1569024, _1569016), _1569018)))], (16121 ^ _781215) ^ [_1066146, _1066148, _1066150, _1066152, _1066154] : [c_Finite__Set_Ofun__left__comm(_1066146, _1066148, _1066150), -(c_Finite__Set_Ofun__left__comm(_1066152, _1066148, hAPP(hAPP(c_COMBB(_1066146, tc_fun(_1066148, _1066148), _1066152), _1066150), _1066154)))], (49976 ^ _781215) ^ [_1794708, _1794710, _1794712] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794708, _1794708), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1794710)), _1794712) = hAPP(hAPP(c_Relation_Orel__comp(_1794708, _1794708, _1794708), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794708, _1794708), tc_HOL_Obool), _1794710), _1794712)), _1794712))], (27712 ^ _781215) ^ [_1285552, _1285554, _1285556] : [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), _1285552), _1285554))), -(hBOOL(hAPP(hAPP(_1285556, _1285552), _1285554))), 27719 ^ _781215 : [(27722 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 27718 ^ [_1285552, _1285554, _1285556]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1285556, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 27717 ^ [_1285552, _1285554, _1285556])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 27718 ^ [_1285552, _1285554, _1285556]))))], (27728 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1285556, 27717 ^ [_1285552, _1285554, _1285556]), 27718 ^ [_1285552, _1285554, _1285556]))], (27720 ^ _781215) ^ [] : [-(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), 27717 ^ [_1285552, _1285554, _1285556]), 27718 ^ [_1285552, _1285554, _1285556]))))]]], (13302 ^ _781215) ^ [_1012482, _1012484, _1012486] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012482), _1012484)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012486), _1012484)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1012484)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012482), _1012486))], (47812 ^ _781215) ^ [_1743942, _1743944, _1743946, _1743948, _1743950, _1743952] : [c_List_Olist__all2(_1743942, _1743944, _1743946, _1743948, _1743950), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743952), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743942)), _1743948))), -(hBOOL(hAPP(hAPP(_1743946, hAPP(hAPP(c_List_Onth(_1743942), _1743948), _1743952)), hAPP(hAPP(c_List_Onth(_1743944), _1743950), _1743952))))], (49307 ^ _781215) ^ [_1777907, _1777909, _1777911, _1777913, _1777915] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1777907, _1777907)), hAPP(hAPP(c_Product__Type_OPair(_1777907, _1777907), _1777909), _1777911)), c_Transitive__Closure_Ortrancl(_1777907, _1777913))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1777907, _1777907)), hAPP(hAPP(c_Product__Type_OPair(_1777907, _1777907), _1777911), _1777915)), _1777913)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777907, _1777907)), hAPP(hAPP(c_Product__Type_OPair(_1777907, _1777907), _1777909), _1777915)), c_Transitive__Closure_Ortrancl(_1777907, _1777913))))], (6630 ^ _781215) ^ [_889765, _889767, _889769] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_889765), _889767)), 6633 ^ _781215 : [(6640 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_889765), _889769)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_889765), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889765, tc_HOL_Obool)), _889769), _889767))))], (6634 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_889765), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889765, tc_HOL_Obool)), _889769), _889767))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_889765), _889769)))]]], (22240 ^ _781215) ^ [_1182458, _1182460] : [class_Divides_Osemiring__div(_1182458), -(c_Divides_Odiv__class_Omod(_1182458, _1182460, c_Groups_Ozero__class_Ozero(_1182458)) = _1182460)], (21277 ^ _781215) ^ [_1162247, _1162249, _1162251, _1162253, _1162255] : [class_Complete__Lattice_Ocomplete__lattice(_1162247), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1162249, tc_HOL_Obool)), _1162251), _1162253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162247), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162249, _1162247), _1162251), _1162255)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162249, _1162247), _1162253), _1162255))))], (13135 ^ _781215) ^ [_1009925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1009925)), -(_1009925 = hAPP(c_Nat_OSuc, 13138 ^ [_1009925]))], (42947 ^ _781215) ^ [_1635650, _1635652, _1635654, _1635656] : [-(hAPP(hAPP(c_List_Otake(_1635650), _1635652), hAPP(hAPP(c_List_Otake(_1635650), _1635654), _1635656)) = hAPP(hAPP(c_List_Otake(_1635650), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1635652), _1635654)), _1635656))], (42303 ^ _781215) ^ [_1618135, _1618137, _1618139] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1618135, tc_HOL_Obool)), hAPP(c_List_Oset(_1618135), c_List_Osublist(_1618135, _1618137, _1618139))), hAPP(c_List_Oset(_1618135), _1618137))))], (16211 ^ _781215) ^ [_1067752, _1067754, _1067756, _1067758] : [class_Lattices_Osemilattice__sup(_1067752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067752), _1067754), _1067756)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067752), _1067754), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067752), _1067756), _1067758))))], (5585 ^ _781215) ^ [_869221, _869223] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_869221, _869223, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_869221), tc_HOL_Obool))))], (7096 ^ _781215) ^ [_899391, _899393, _899395, _899397, _899399, _899401, _899403] : [-(hBOOL(hAPP(hAPP(c_member(_899391), _899393), _899395))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_899391, _899397, _899399, _899401, _899395), _899403)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_899391, _899397, _899399, _899401, hAPP(hAPP(c_Set_Oinsert(_899391), _899393), _899395)), hAPP(hAPP(_899399, _899393), _899403))))], (36027 ^ _781215) ^ [_1458640, _1458642] : [_1458640 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1458642, _1458640) = 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), _1458642)))], (15560 ^ _781215) ^ [_1054428, _1054430, _1054432, _1054434] : [_1054428 = c_Orderings_Obot__class_Obot(tc_fun(_1054430, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1054430, _1054432, hAPP(c_COMBK(_1054432, _1054430), _1054434)), _1054428) = c_Orderings_Obot__class_Obot(tc_fun(_1054432, tc_HOL_Obool)))], (10009 ^ _781215) ^ [_951315, _951317] : [10010 ^ _781215 : [(10013 ^ _781215) ^ [] : [_951315 = _951317], (10011 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _951315), _951317))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951315), _951317)))], (50934 ^ _781215) ^ [_1816449, _1816451, _1816453] : [-(hAPP(c_Lazy__Sequence_Oyield(_1816449), c_Lazy__Sequence_Olazy__sequence_OInsert(_1816449, _1816451, _1816453)) = hAPP(c_Option_Ooption_OSome(tc_prod(_1816449, tc_Lazy__Sequence_Olazy__sequence(_1816449))), hAPP(hAPP(c_Product__Type_OPair(_1816449, tc_Lazy__Sequence_Olazy__sequence(_1816449)), _1816451), _1816453)))], (39202 ^ _781215) ^ [_1534173, _1534175, _1534177] : [hBOOL(hAPP(_1534173, _1534175)), -(hAPP(c_Set_OCollect(_1534177), hAPP(hAPP(c_COMBS(_1534177, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534177), c_fconj), hAPP(hAPP(c_COMBC(_1534177, _1534177, tc_HOL_Obool), c_fequal), _1534175))), _1534173)) = hAPP(hAPP(c_Set_Oinsert(_1534177), _1534175), c_Orderings_Obot__class_Obot(tc_fun(_1534177, tc_HOL_Obool))))], (6249 ^ _781215) ^ [_881999, _882001] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_881999), _882001))), 6250 ^ _781215 : [(6253 ^ _781215) ^ [_882102] : [6254 ^ _781215 : [(6255 ^ _781215) ^ [_882155] : [_882001 = hAPP(hAPP(c_Set_Oinsert(_881999), _882155), _882102)]], hBOOL(hAPP(c_Finite__Set_Ofinite(_881999), _882102))], (6251 ^ _781215) ^ [] : [_882001 = c_Orderings_Obot__class_Obot(tc_fun(_881999, tc_HOL_Obool))]]], (45061 ^ _781215) ^ [_1685172, _1685174, _1685176] : [class_Orderings_Olinorder(_1685172), -(c_Big__Operators_Olattice_OSup__fin(_1685172, c_Orderings_Oord__class_Omax(_1685172), hAPP(c_List_Oset(_1685172), hAPP(hAPP(c_List_Olist_OCons(_1685172), _1685174), _1685176))) = hAPP(c_List_Ofoldl(_1685172, _1685172, c_Orderings_Oord__class_Omax(_1685172), _1685174), _1685176))], (11535 ^ _781215) ^ [_982364, _982366, _982368, _982370] : [hAPP(c_Set_Oimage(_982364, _982366, _982368), _982370) = c_Orderings_Obot__class_Obot(tc_fun(_982366, tc_HOL_Obool)), -(_982370 = c_Orderings_Obot__class_Obot(tc_fun(_982364, tc_HOL_Obool)))], (34990 ^ _781215) ^ [_1437376, _1437378, _1437380, _1437382, _1437384] : [-(c_Fun_Oinj__on(_1437376, _1437378, _1437380, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437376, tc_HOL_Obool)), _1437382), _1437384))), c_Fun_Oinj__on(_1437376, _1437378, _1437380, _1437382), c_Fun_Oinj__on(_1437376, _1437378, _1437380, _1437384), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437378, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1437376, _1437378, _1437380), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1437376, tc_HOL_Obool)), _1437382), _1437384))), hAPP(c_Set_Oimage(_1437376, _1437378, _1437380), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1437376, tc_HOL_Obool)), _1437384), _1437382))) = c_Orderings_Obot__class_Obot(tc_fun(_1437378, tc_HOL_Obool))], (3932 ^ _781215) ^ [_840853, _840855, _840857, _840859, _840861, _840863] : [-(c_List_OdropWhile(_840863, _840859, _840855) = c_List_OdropWhile(_840861, _840857, _840853)), _840863 = _840861, _840859 = _840857, _840855 = _840853], (430 ^ _781215) ^ [_787946, _787948, _787950, _787952, _787954, _787956, _787958, _787960] : [-(c_Equiv__Relations_Ocongruent(_787958, _787954, _787950, _787946)), c_Equiv__Relations_Ocongruent(_787960, _787956, _787952, _787948), _787960 = _787958, _787956 = _787954, _787952 = _787950, _787948 = _787946], (30058 ^ _781215) ^ [_1330684] : [-(c_Wellfounded_Omeasure(_1330684) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1330684), c_Wellfounded_Oless__than))], (51218 ^ _781215) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (39028 ^ _781215) ^ [_1530547, _1530549, _1530551, _1530553] : [-(hAPP(c_Set_OCollect(tc_prod(_1530547, _1530549)), hAPP(c_Product__Type_Oprod_Oprod__case(_1530547, _1530549, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1530547, tc_fun(_1530549, tc_HOL_Obool), tc_fun(_1530549, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1530549, tc_HOL_Obool), tc_fun(_1530549, tc_HOL_Obool)), _1530547), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1530549)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1530547), c_fconj), _1530551))), _1530553))) = hAPP(hAPP(c_Product__Type_OSigma(_1530547, _1530549), hAPP(c_Set_OCollect(_1530547), _1530551)), hAPP(hAPP(c_COMBB(tc_fun(_1530549, tc_HOL_Obool), tc_fun(_1530549, tc_HOL_Obool), _1530547), c_Set_OCollect(_1530549)), _1530553)))], (30060 ^ _781215) ^ [_1330742, _1330744, _1330746, _1330748, _1330750, _1330752] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1330742, _1330742)), hAPP(hAPP(c_Product__Type_OPair(_1330742, _1330742), _1330744), _1330746)), hAPP(hAPP(c_Relation_Oinv__image(_1330748, _1330742), _1330750), _1330752))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1330748, _1330748)), hAPP(hAPP(c_Product__Type_OPair(_1330748, _1330748), hAPP(_1330752, _1330744)), hAPP(_1330752, _1330746))), _1330750)))], (49213 ^ _781215) ^ [_1775591, _1775593] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1775591, _1775591), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1775591, _1775593)), c_Relation_OId(_1775591)) = c_Transitive__Closure_Ortrancl(_1775591, _1775593))], (27438 ^ _781215) ^ [_1280504, _1280506, _1280508, _1280510, _1280512, _1280514] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1280504, _1280506), _1280506, _1280508), hAPP(hAPP(c_COMBB(_1280510, tc_fun(_1280506, _1280508), tc_prod(_1280504, _1280506)), _1280512), hAPP(hAPP(c_COMBB(_1280504, _1280510, tc_prod(_1280504, _1280506)), _1280514), c_Product__Type_Ofst(_1280504, _1280506)))), c_Product__Type_Osnd(_1280504, _1280506)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1280504, _1280506, _1280508), hAPP(hAPP(c_COMBB(_1280510, tc_fun(_1280506, _1280508), _1280504), _1280512), _1280514)))], (44126 ^ _781215) ^ [_1663525, _1663527, _1663529] : [_1663529 = c_List_Olist_ONil(_1663527), -(_1663525 = hAPP(hAPP(c_List_Oappend(_1663527), _1663525), _1663529))], (12920 ^ _781215) ^ [_1006311, _1006313] : [class_Groups_Olinordered__ab__group__add(_1006311), 12923 ^ _781215 : [(12930 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006311), c_Groups_Ozero__class_Ozero(_1006311)), _1006313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006311), hAPP(c_Groups_Ouminus__class_Ouminus(_1006311), _1006313)), _1006313)))], (12924 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006311), hAPP(c_Groups_Ouminus__class_Ouminus(_1006311), _1006313)), _1006313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006311), c_Groups_Ozero__class_Ozero(_1006311)), _1006313)))]]], (7284 ^ _781215) ^ [_904040, _904042, _904044, _904046, _904048] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_904040, _904042, hAPP(hAPP(c_Set_Oinsert(_904040), _904044), _904046)), _904048)), 7289 ^ _781215 : [(7294 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_904040), 7287 ^ [_904040, _904042, _904044, _904046, _904048]), 7288 ^ [_904040, _904042, _904044, _904046, _904048]))], (7292 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_904040, _904040, _904042, 7287 ^ [_904040, _904042, _904044, _904046, _904048], 7288 ^ [_904040, _904042, _904044, _904046, _904048]), _904048)))], (7290 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_904040), _904044), _904046) = hAPP(hAPP(c_Set_Oinsert(_904040), 7287 ^ [_904040, _904042, _904044, _904046, _904048]), 7288 ^ [_904040, _904042, _904044, _904046, _904048]))]]], (10724 ^ _781215) ^ [_964899, _964901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964899), _964901)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964901), _964899)), _964899) = _964901)], (46708 ^ _781215) ^ [_1720324, _1720326, _1720328] : [hBOOL(hAPP(c_List_Odistinct(_1720324), _1720326)), hBOOL(hAPP(hAPP(c_member(_1720324), _1720328), hAPP(c_List_Oset(_1720324), _1720326))), -(c_List_OdropWhile(_1720324, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1720324), c_fNot), hAPP(hAPP(c_COMBC(_1720324, _1720324, tc_HOL_Obool), c_fequal), _1720328)), hAPP(c_List_Orev(_1720324), _1720326)) = hAPP(hAPP(c_List_Olist_OCons(_1720324), _1720328), hAPP(c_List_Orev(_1720324), c_List_OtakeWhile(_1720324, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1720324), c_fNot), hAPP(hAPP(c_COMBC(_1720324, _1720324, tc_HOL_Obool), c_fequal), _1720328)), _1720326))))], (44976 ^ _781215) ^ [_1683442, _1683444] : [class_Groups_Omonoid__add(_1683442), -(hAPP(c_List_Ofoldl(_1683442, _1683442, c_Groups_Oplus__class_Oplus(_1683442), c_Groups_Ozero__class_Ozero(_1683442)), _1683444) = c_List_Ofoldr(_1683442, _1683442, c_Groups_Oplus__class_Oplus(_1683442), _1683444, c_Groups_Ozero__class_Ozero(_1683442)))], (3840 ^ _781215) ^ [_839429, _839431, _839433, _839435] : [-(c_List_Olex(_839435, _839431) = c_List_Olex(_839433, _839429)), _839435 = _839433, _839431 = _839429], (48902 ^ _781215) ^ [_1768462, _1768464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1768462)), hAPP(c_Code__Numeral_Oof__nat, _1768464))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1768462), _1768464)))], (36293 ^ _781215) ^ [_1463658, _1463660] : [-(_1463658 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1463660, _1463658) = c_Nitpick_Onat__gcd(_1463658, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1463660, _1463658)))], (16359 ^ _781215) ^ [_1070307, _1070309, _1070311, _1070313] : [16360 ^ _781215 : [(16363 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1070307), _1070309), _1070313))], (16361 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1070307), _1070309), _1070311))]], -(hBOOL(hAPP(hAPP(c_member(_1070307), _1070309), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1070307, tc_HOL_Obool)), _1070311), _1070313))))], (50984 ^ _781215) ^ [_1817957, _1817959, _1817961, _1817963, _1817965] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1817957), _1817959), _1817961), _1817963), _1817965) = c_New__DSequence_Oneg__single(_1817957, _1817959))], (21650 ^ _781215) ^ [_1169598, _1169600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1169598), _1169600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1169598)), c_Int_OBit0(_1169600))))], (38686 ^ _781215) ^ [_1521974, _1521976, _1521978] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521974), _1521976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521974, _1521974), tc_HOL_Obool)), _1521978), hAPP(hAPP(c_Product__Type_OSigma(_1521974, _1521974), _1521976), hAPP(c_COMBK(tc_fun(_1521974, tc_HOL_Obool), _1521974), _1521976)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1521974, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1521974), _1521976), _1521978))))], (44850 ^ _781215) ^ [_1680686, _1680688, _1680690, _1680692, _1680694] : [-(hAPP(c_List_Orotate(_1680686, _1680688), hAPP(hAPP(c_List_Omap(_1680690, _1680686), _1680692), _1680694)) = hAPP(hAPP(c_List_Omap(_1680690, _1680686), _1680692), hAPP(c_List_Orotate(_1680690, _1680688), _1680694)))], (51450 ^ _781215) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (8762 ^ _781215) ^ [_929841, _929843, _929845] : [class_Orderings_Oorder(_929841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929841), _929843), _929845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929841), _929845), _929843)), -(_929845 = _929843)], (45081 ^ _781215) ^ [_1685956, _1685958] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1685956), hAPP(c_List_Oset(tc_Nat_Onat), _1685958))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1685956), 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)), _1685958))))], (43810 ^ _781215) ^ [_1656042, _1656044] : [_1656044 = c_List_Olist_ONil(_1656042), -(c_Orderings_Obot__class_Obot(tc_fun(_1656042, tc_HOL_Obool)) = hAPP(c_List_Oset(_1656042), _1656044))], (27482 ^ _781215) ^ [_1281386, _1281388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281388)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1281386, _1281388) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1281386, _1281388)))], (31603 ^ _781215) ^ [_1362258, _1362260, _1362262] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362258), _1362260)), 31606 ^ _781215 : [(31607 ^ _781215) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362258, tc_Nat_Onat), _1362262), _1362260) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 31610 ^ _781215 : [(31611 ^ _781215) ^ [_1362420] : [hBOOL(hAPP(hAPP(c_member(_1362258), _1362420), _1362260)), -(hAPP(_1362262, _1362420) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31617 ^ _781215) ^ [] : [31619 ^ _781215 : [(31622 ^ _781215) ^ [] : [hAPP(_1362262, 31618 ^ [_1362258, _1362260, _1362262]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31620 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1362258), 31618 ^ [_1362258, _1362260, _1362262]), _1362260)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362258, tc_Nat_Onat), _1362262), _1362260) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9647 ^ _781215) ^ [_944972, _944974, _944976] : [class_Orderings_Olinorder(_944972), 9650 ^ _781215 : [(9657 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944972), _944976), _944974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944972), _944974), _944976))], (9651 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944972), _944974), _944976))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944972), _944976), _944974)))]]], (16349 ^ _781215) ^ [_1070153, _1070155, _1070157, _1070159] : [hBOOL(hAPP(hAPP(c_member(_1070153), _1070155), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1070153, tc_HOL_Obool)), _1070157), _1070159))), -(hBOOL(hAPP(hAPP(c_member(_1070153), _1070155), _1070157))), -(hBOOL(hAPP(hAPP(c_member(_1070153), _1070155), _1070159)))], (9785 ^ _781215) ^ [_947496, _947498] : [class_Groups_Ocomm__monoid__mult(_947496), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947496), c_Groups_Oone__class_Oone(_947496)), _947498) = _947498)], (16985 ^ _781215) ^ [_1085976, _1085978] : [class_Lattices_Olattice(_1085976), -(c_Big__Operators_Olattice__class_OSup__fin(_1085976, hAPP(hAPP(c_Set_Oinsert(_1085976), _1085978), c_Orderings_Obot__class_Obot(tc_fun(_1085976, tc_HOL_Obool)))) = _1085978)], (6148 ^ _781215) ^ [_880072, _880074, _880076] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCall(_880072, _880074, _880076)], (30720 ^ _781215) ^ [_1343467, _1343469, _1343471, _1343473] : [-(hAPP(c_Relation_OField(_1343467), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1343467, _1343467)), hAPP(hAPP(c_Product__Type_OPair(_1343467, _1343467), _1343469), _1343471)), _1343473)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1343467, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1343467), _1343469), hAPP(hAPP(c_Set_Oinsert(_1343467), _1343471), c_Orderings_Obot__class_Obot(tc_fun(_1343467, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1343467), _1343473)))], (15376 ^ _781215) ^ [_1050719, _1050721, _1050723] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050719), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050721), _1050723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050719), _1050721)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050719), _1050723)))], (32302 ^ _781215) ^ [_1378209, _1378211, _1378213] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378209), hAPP(hAPP(c_Set_Oinsert(_1378209), _1378211), c_Orderings_Obot__class_Obot(tc_fun(_1378209, tc_HOL_Obool)))), _1378213) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1378209, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1378209, _1378209, _1378213), hAPP(hAPP(c_Set_Oinsert(_1378209), _1378211), c_Orderings_Obot__class_Obot(tc_fun(_1378209, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1378209, tc_HOL_Obool), tc_HOL_Obool))))], (47592 ^ _781215) ^ [_1739127, _1739129] : [class_Orderings_Olinorder(_1739127), 47595 ^ _781215 : [(47616 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1739127, _1739129)), 47617 ^ _781215 : [(47620 ^ _781215) ^ [_1739687, _1739689] : [_1739129 = hAPP(hAPP(c_List_Olist_OCons(_1739127), _1739687), _1739689), 47626 ^ _781215 : [(47629 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1739127), _1739687), 47625 ^ [_1739127, _1739129, _1739687, _1739689]))], (47627 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739127), 47625 ^ [_1739127, _1739129, _1739687, _1739689]), hAPP(c_List_Oset(_1739127), _1739689))))]], c_List_Olinorder__class_Osorted(_1739127, _1739689)], (47618 ^ _781215) ^ [] : [_1739129 = c_List_Olist_ONil(_1739127)]]], (47596 ^ _781215) ^ [] : [c_List_Olinorder__class_Osorted(_1739127, _1739129), -(_1739129 = c_List_Olist_ONil(_1739127)), 47605 ^ _781215 : [(47608 ^ _781215) ^ [_1739461] : [hBOOL(hAPP(hAPP(c_member(_1739127), _1739461), hAPP(c_List_Oset(_1739127), 47603 ^ [_1739127, _1739129]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1739127), 47604 ^ [_1739127, _1739129]), _1739461)))], (47614 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1739127, 47603 ^ [_1739127, _1739129]))], (47606 ^ _781215) ^ [] : [-(_1739129 = hAPP(hAPP(c_List_Olist_OCons(_1739127), 47604 ^ [_1739127, _1739129]), 47603 ^ [_1739127, _1739129]))]]]]], (4614 ^ _781215) ^ [_851182, _851184] : [_851184 = _851182, -(c_Int_Oring__1__class_Oof__int(_851184) = c_Int_Oring__1__class_Oof__int(_851182))], (37049 ^ _781215) ^ [_1481715, _1481717, _1481719, _1481721, _1481723, _1481725] : [class_Complete__Lattice_Ocomplete__lattice(_1481715), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481717, _1481715), _1481719), hAPP(hAPP(c_COMBB(tc_fun(_1481721, _1481715), _1481715, _1481717), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481721, _1481715), _1481723)), _1481725)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481721, _1481715), _1481723), hAPP(hAPP(c_COMBB(tc_fun(_1481717, _1481715), _1481715, _1481721), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481717, _1481715), _1481719)), hAPP(c_COMBC(_1481717, _1481721, _1481715), _1481725))))], (36841 ^ _781215) ^ [_1475420, _1475422] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1475420, tc_HOL_Obool)), _1475422)))], (6007 ^ _781215) ^ [_877010, _877012, _877014] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_877010, _877012, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877010)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877010), _877014), c_Com_Ocom_OSKIP), _877014)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877010), tc_HOL_Obool)))))], (8259 ^ _781215) ^ [_920508, _920510, _920512, _920514] : [class_Groups_Ocancel__semigroup__add(_920508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920508), _920510), _920512) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920508), _920510), _920514), -(_920512 = _920514)], (1528 ^ _781215) ^ [_803285, _803287] : [-(class_Groups_Oordered__comm__monoid__add(_803285)), _803287 = _803285, class_Groups_Oordered__comm__monoid__add(_803287)], (19716 ^ _781215) ^ [_1135086, _1135088] : [class_Orderings_Olinorder(_1135086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135086), _1135088)), -(c_Big__Operators_Olinorder__class_OMax(_1135086, _1135088) = hAPP(c_Finite__Set_Ofold1(_1135086, c_Orderings_Oord__class_Omax(_1135086)), _1135088))], (9599 ^ _781215) ^ [_944309, _944311, _944313] : [class_Orderings_Oorder(_944309), 9602 ^ _781215 : [(9611 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944309), _944311), _944313))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944309), _944311), _944313)), -(_944311 = _944313)], (9603 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944309), _944311), _944313)), 9606 ^ _781215 : [(9609 ^ _781215) ^ [] : [_944311 = _944313], (9607 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944309), _944311), _944313)))]]]]], (33470 ^ _781215) ^ [_1404354, _1404356, _1404358] : [class_Lattices_Osemilattice__inf(_1404354), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404354), _1404356)), -(_1404356 = c_Orderings_Obot__class_Obot(tc_fun(_1404354, tc_HOL_Obool))), 33481 ^ _781215 : [(33482 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404354), _1404358), hAPP(c_Finite__Set_Ofold1(_1404354, c_Lattices_Osemilattice__inf__class_Oinf(_1404354)), _1404356))), 33485 ^ _781215 : [(33486 ^ _781215) ^ [_1404647] : [hBOOL(hAPP(hAPP(c_member(_1404354), _1404647), _1404356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404354), _1404358), _1404647)))]]], (33492 ^ _781215) ^ [] : [33494 ^ _781215 : [(33497 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404354), _1404358), 33493 ^ [_1404354, _1404356, _1404358]))], (33495 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404354), 33493 ^ [_1404354, _1404356, _1404358]), _1404356)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404354), _1404358), hAPP(c_Finite__Set_Ofold1(_1404354, c_Lattices_Osemilattice__inf__class_Oinf(_1404354)), _1404356))))]]], (38314 ^ _781215) ^ [_1511566, _1511568, _1511570, _1511572] : [hAPP(c_Set_Oimage(_1511566, _1511568, _1511570), c_Orderings_Otop__class_Otop(tc_fun(_1511566, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1511568, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1511566, _1511568, _1511570), hAPP(c_Set_Ovimage(_1511566, _1511568, _1511570), _1511572)) = _1511572)], (47519 ^ _781215) ^ [_1737408, _1737410, _1737412] : [-(c_List_Olistsp(_1737408, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1737408, tc_HOL_Obool)), _1737410), _1737412)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1737408), tc_HOL_Obool)), c_List_Olistsp(_1737408, _1737410)), c_List_Olistsp(_1737408, _1737412)))], (16939 ^ _781215) ^ [_1085346] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085346), c_Int_OPls) = _1085346)], (7600 ^ _781215) ^ [_908850, _908852, _908854, _908856, _908858] : [-(c_Map_Orestrict__map(_908850, _908852, _908854, hAPP(hAPP(c_Set_Oinsert(_908850), _908856), _908858)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_908850, tc_Option_Ooption(_908852)), c_Map_Orestrict__map(_908850, _908852, _908854, _908858)), _908856), hAPP(_908854, _908856)))], (40152 ^ _781215) ^ [_1565242, _1565244] : [c_Wellfounded_Owf(_1565242, _1565244), 40156 ^ _781215 : [(40157 ^ _781215) ^ [_1565378] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565242, _1565242)), hAPP(hAPP(c_Product__Type_OPair(_1565242, _1565242), hAPP(_1565378, hAPP(c_Nat_OSuc, 40155 ^ [_1565242, _1565244, _1565378]))), hAPP(_1565378, 40155 ^ [_1565242, _1565244, _1565378]))), _1565244))]]], (13048 ^ _781215) ^ [_1008479, _1008481, _1008483] : [class_Groups_Ogroup__add(_1008479), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008479), _1008481), _1008483) = c_Groups_Ozero__class_Ozero(_1008479), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1008479), _1008481) = _1008483)], (45877 ^ _781215) ^ [_1701199, _1701201, _1701203, _1701205, _1701207, _1701209] : [class_Orderings_Olinorder(_1701199), c_List_Olinorder__class_Osorted(_1701199, hAPP(hAPP(c_List_Omap(_1701201, _1701199), _1701203), _1701205)), hBOOL(hAPP(_1701207, _1701209)), -(hAPP(c_List_Ofilter(_1701201, _1701207), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701201, _1701199, _1701203), _1701209), _1701205)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1701201, _1701199, _1701203), _1701209), hAPP(c_List_Ofilter(_1701201, _1701207), _1701205)))], (36722 ^ _781215) ^ [_1471676, _1471678] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1471676), c_Orderings_Otop__class_Otop(tc_fun(_1471676, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1471676, _1471676, _1471678), c_Orderings_Otop__class_Otop(tc_fun(_1471676, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1471676, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1471676, _1471676, _1471678, c_Orderings_Otop__class_Otop(tc_fun(_1471676, tc_HOL_Obool))))], (51406 ^ _781215) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (13364 ^ _781215) ^ [_1013591, _1013593, _1013595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1013591)), 13367 ^ _781215 : [(13374 ^ _781215) ^ [] : [_1013593 = _1013595, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013591), _1013593) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013591), _1013595))], (13368 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013591), _1013593) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013591), _1013595), -(_1013593 = _1013595)]]], (5248 ^ _781215) ^ [_861293, _861295, _861297, _861299, _861301, _861303, _861305, _861307] : [-(c_Lazy__Sequence_Oproduct(_861307, _861303, _861299, _861295) = c_Lazy__Sequence_Oproduct(_861305, _861301, _861297, _861293)), _861307 = _861305, _861303 = _861301, _861299 = _861297, _861295 = _861293], (29802 ^ _781215) ^ [_1324557, _1324559, _1324561, _1324563] : [class_Fields_Olinordered__field(_1324557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324557), _1324559), c_Groups_Ozero__class_Ozero(_1324557))), 29809 ^ _781215 : [(29816 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324557), _1324563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324557), _1324561), _1324559))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324557), _1324561), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324557), _1324563), _1324559))))], (29810 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324557), _1324561), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324557), _1324563), _1324559))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324557), _1324563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324557), _1324561), _1324559))))]]], (11822 ^ _781215) ^ [_987081, _987083] : [class_Groups_Olinordered__ab__group__add(_987081), 11825 ^ _781215 : [(11832 ^ _781215) ^ [] : [_987083 = c_Groups_Ozero__class_Ozero(_987081), -(_987083 = hAPP(c_Groups_Ouminus__class_Ouminus(_987081), _987083))], (11826 ^ _781215) ^ [] : [_987083 = hAPP(c_Groups_Ouminus__class_Ouminus(_987081), _987083), -(_987083 = c_Groups_Ozero__class_Ozero(_987081))]]], (34151 ^ _781215) ^ [_1419955, _1419957, _1419959, _1419961, _1419963, _1419965] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1419955, _1419957)), hAPP(hAPP(c_Product__Type_OPair(_1419955, _1419957), _1419963), _1419965)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool)), _1419959), _1419961))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419955, tc_fun(_1419957, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1419955, tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_fun(_1419957, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419957, tc_fun(tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_fun(_1419957, tc_HOL_Obool)), _1419955), c_COMBC(_1419957, tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419957, tc_prod(_1419955, _1419957)), tc_fun(_1419957, tc_fun(tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_HOL_Obool)), _1419955), hAPP(c_COMBB(tc_prod(_1419955, _1419957), tc_fun(tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_HOL_Obool), _1419957), c_member(tc_prod(_1419955, _1419957)))), c_Product__Type_OPair(_1419955, _1419957)))), _1419959)), hAPP(hAPP(c_COMBC(_1419955, tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_fun(_1419957, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419957, tc_fun(tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_fun(_1419957, tc_HOL_Obool)), _1419955), c_COMBC(_1419957, tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419957, tc_prod(_1419955, _1419957)), tc_fun(_1419957, tc_fun(tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_HOL_Obool)), _1419955), hAPP(c_COMBB(tc_prod(_1419955, _1419957), tc_fun(tc_fun(tc_prod(_1419955, _1419957), tc_HOL_Obool), tc_HOL_Obool), _1419957), c_member(tc_prod(_1419955, _1419957)))), c_Product__Type_OPair(_1419955, _1419957)))), _1419961)), _1419963), _1419965)))], (50376 ^ _781215) ^ [_1805604, _1805606] : [-(c_Nitpick_Oinverse__frac(_1805604, _1805606) = hAPP(hAPP(c_Nitpick_Ofrac(_1805604), hAPP(c_Nitpick_Odenom(_1805604), _1805606)), hAPP(c_Nitpick_Onum(_1805604), _1805606)))], (26185 ^ _781215) ^ [_1256107, _1256109, _1256111] : [class_Rings_Oring__1(_1256107), -(hAPP(c_Int_Oring__1__class_Oof__int(_1256107), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1256109), _1256111)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1256107), hAPP(c_Int_Oring__1__class_Oof__int(_1256107), _1256109)), _1256111))], (51614 ^ _781215) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (25518 ^ _781215) ^ [_1240560, _1240562, _1240564, _1240566] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1240560, _1240562, _1240564), _1240566), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1240562)], (16419 ^ _781215) ^ [_1071524, _1071526, _1071528, _1071530] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071524, tc_HOL_Obool)), _1071526), hAPP(hAPP(c_Set_Oinsert(_1071524), _1071528), _1071530)) = hAPP(hAPP(c_Set_Oinsert(_1071524), _1071528), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071524, tc_HOL_Obool)), _1071526), _1071530)))], (17417 ^ _781215) ^ [_1093122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093122), 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), _1093122)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (44100 ^ _781215) ^ [_1663085, _1663087, _1663089] : [c_List_Olist_ONil(_1663085) = hAPP(hAPP(c_List_Oappend(_1663085), _1663087), _1663089), 44103 ^ _781215 : [(44106 ^ _781215) ^ [] : [-(_1663089 = c_List_Olist_ONil(_1663085))], (44104 ^ _781215) ^ [] : [-(_1663087 = c_List_Olist_ONil(_1663085))]]], (20842 ^ _781215) ^ [_1154882, _1154884] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1154882)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1154884))))), _1154882 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1154884 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29390 ^ _781215) ^ [_1316780, _1316782, _1316784, _1316786] : [class_Fields_Olinordered__field(_1316780), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316780), _1316782), _1316784)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316780), _1316786), c_Groups_Ozero__class_Ozero(_1316780))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316780), c_Groups_Ozero__class_Ozero(_1316780)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1316780), _1316782), _1316784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316780), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1316780), _1316786), _1316782)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1316780), _1316786), _1316784))))], (45185 ^ _781215) ^ [_1687675, _1687677] : [-(_1687675 = c_List_Olist_ONil(_1687677)), -(hAPP(hAPP(c_List_Oappend(_1687677), c_List_Obutlast(_1687677, _1687675)), hAPP(hAPP(c_List_Olist_OCons(_1687677), c_List_Olast(_1687677, _1687675)), c_List_Olist_ONil(_1687677))) = _1687675)], (47480 ^ _781215) ^ [_1736585, _1736587, _1736589] : [hBOOL(hAPP(c_List_Olistsp(_1736585, _1736587), _1736589)), 47483 ^ _781215 : [(47484 ^ _781215) ^ [_1736674] : [hBOOL(hAPP(hAPP(c_member(_1736585), _1736674), hAPP(c_List_Oset(_1736585), _1736589))), -(hBOOL(hAPP(_1736587, _1736674)))]]], (31192 ^ _781215) ^ [_1352298, _1352300, _1352302] : [class_Orderings_Olinorder(_1352298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1352298), _1352300), _1352302)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352298, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1352298, _1352300), _1352302)), hAPP(hAPP(c_Set_Oinsert(_1352298), _1352302), c_Orderings_Obot__class_Obot(tc_fun(_1352298, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1352298, _1352300, _1352302))], (5849 ^ _781215) ^ [_874244, _874246] : [_874246 = c_Option_Ooption_ONone(_874244), -(c_Option_Ois__none(_874244, _874246))], (11074 ^ _781215) ^ [_972609, _972611, _972613, _972615, _972617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972609), _972611)), 11077 ^ _781215 : [(11084 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972615), 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), _972611), _972609)), _972613)), _972617))), -(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), _972609), _972613)), _972615)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972611), _972613)), _972617))))], (11078 ^ _781215) ^ [] : [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), _972609), _972613)), _972615)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972611), _972613)), _972617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972615), 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), _972611), _972609)), _972613)), _972617))))]]], (43678 ^ _781215) ^ [_1653674, _1653676] : [-(c_List_Opartition(_1653674, _1653676, c_List_Olist_ONil(_1653674)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653674), tc_List_Olist(_1653674)), c_List_Olist_ONil(_1653674)), c_List_Olist_ONil(_1653674)))], (26572 ^ _781215) ^ [_1263302, _1263304, _1263306, _1263308, _1263310, _1263312] : [hBOOL(hAPP(hAPP(_1263302, _1263304), _1263306)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263308, tc_fun(_1263310, tc_HOL_Obool))), _1263302), _1263312), _1263304), _1263306)))], (33110 ^ _781215) ^ [_1395977, _1395979, _1395981, _1395983, _1395985] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395977, tc_HOL_Obool)), _1395979), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395981, tc_fun(_1395977, tc_HOL_Obool)), _1395983), _1395985)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395981, tc_fun(_1395977, tc_HOL_Obool)), _1395983), hAPP(hAPP(c_COMBB(tc_fun(_1395977, tc_HOL_Obool), tc_fun(_1395977, tc_HOL_Obool), _1395981), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395977, tc_HOL_Obool)), _1395979)), _1395985)))], (37201 ^ _781215) ^ [_1485690, _1485692, _1485694, _1485696, _1485698] : [-(_1485690 = c_Orderings_Obot__class_Obot(tc_fun(_1485692, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1485692, tc_fun(_1485694, tc_HOL_Obool)), _1485690), hAPP(hAPP(c_COMBC(_1485692, tc_fun(_1485694, tc_HOL_Obool), tc_fun(_1485694, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485694, tc_HOL_Obool), tc_fun(tc_fun(_1485694, tc_HOL_Obool), tc_fun(_1485694, tc_HOL_Obool)), _1485692), c_Groups_Ominus__class_Ominus(tc_fun(_1485694, tc_HOL_Obool))), _1485696)), _1485698)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485694, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1485692, tc_fun(_1485694, tc_HOL_Obool)), _1485690), _1485696)), _1485698))], (21153 ^ _781215) ^ [_1159806, _1159808] : [class_Int_Onumber__ring(_1159806), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1159806), hAPP(c_Int_Onumber__class_Onumber__of(_1159806), _1159808)), c_Groups_Oone__class_Oone(_1159806)) = hAPP(c_Int_Onumber__class_Onumber__of(_1159806), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1159808), c_Int_OBit1(c_Int_OPls))))], (48882 ^ _781215) ^ [_1768128, _1768130] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1768128)), hAPP(c_Code__Numeral_Oof__nat, _1768130)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1768128), _1768130)))], (12040 ^ _781215) ^ [_990272, _990274, _990276, _990278, _990280] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_990272), _990274)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990276, tc_HOL_Obool)), _990278), hAPP(c_Set_Oimage(_990272, _990276, _990280), _990274))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_990276), _990278)))], (50528 ^ _781215) ^ [_1808644, _1808646, _1808648] : [c_List_Olist__all(_1808644, _1808646, _1808648), 50531 ^ _781215 : [(50532 ^ _781215) ^ [_1808725] : [hBOOL(hAPP(hAPP(c_member(_1808644), _1808725), hAPP(c_List_Oset(_1808644), _1808648))), -(hBOOL(hAPP(_1808646, _1808725)))]]], (4056 ^ _781215) ^ [_842745, _842747, _842749, _842751] : [-(c_Big__Operators_Olinorder__class_OMax(_842751, _842747) = c_Big__Operators_Olinorder__class_OMax(_842749, _842745)), _842751 = _842749, _842747 = _842745], (50398 ^ _781215) ^ [_1806075, _1806077, _1806079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1806075), c_Nitpick_Oplus__frac(_1806075, _1806077, c_Nitpick_Ouminus__frac(_1806075, _1806079)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1806075, _1806077, _1806079))], (9331 ^ _781215) ^ [_940181, _940183, _940185] : [class_Groups_Oab__group__add(_940181), -(hAPP(c_Groups_Ouminus__class_Ouminus(_940181), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_940181), _940183), _940185)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_940181), _940185), _940183))], (26350 ^ _781215) ^ [_1259319] : [class_Int_Onumber__ring(_1259319), -(hAPP(c_Int_Oring__1__class_Oof__int(_1259319), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1259319), c_Int_OMin))], (4010 ^ _781215) ^ [_842056, _842058] : [_842058 = _842056, -(c_Orderings_Oord__class_Omax(_842058) = c_Orderings_Oord__class_Omax(_842056))], (40799 ^ _781215) ^ [_1580892, _1580894, _1580896] : [c_Com_Ocom_OWhile(_1580892, _1580894) = hAPP(c_Com_Ocom_OBODY, _1580896)], (17745 ^ _781215) ^ [_1098285, _1098287] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1098285)), hAPP(c_Int_Onat, _1098287)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1098287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098285), _1098287))], (10630 ^ _781215) ^ [_963143, _963145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963143), hAPP(c_Nat_OSuc, _963145))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963143), _963145)))], (50386 ^ _781215) ^ [_1805829, _1805831, _1805833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1805829), c_Nitpick_Oplus__frac(_1805829, _1805831, c_Nitpick_Ouminus__frac(_1805829, _1805833)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1805829, _1805831, _1805833))], (1438 ^ _781215) ^ [_802160, _802162] : [-(class_Finite__Set_Ofinite(_802160)), _802162 = _802160, class_Finite__Set_Ofinite(_802162)], (33208 ^ _781215) ^ [_1398309, _1398311, _1398313] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398309, tc_HOL_Obool)), _1398311), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398309, tc_HOL_Obool)), _1398313), _1398311)) = c_Orderings_Obot__class_Obot(tc_fun(_1398309, tc_HOL_Obool)))], (23694 ^ _781215) ^ [_1208406, _1208408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1208406), _1208408)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1208406), _1208408) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32968 ^ _781215) ^ [_1392651, _1392653, _1392655] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392651, tc_HOL_Obool)), _1392653), _1392655) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392651, tc_HOL_Obool)), _1392655), _1392653))], (11762 ^ _781215) ^ [_986218, _986220, _986222] : [class_Groups_Ogroup__add(_986218), 11765 ^ _781215 : [(11772 ^ _781215) ^ [] : [_986220 = _986222, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_986218), _986220), _986222) = c_Groups_Ozero__class_Ozero(_986218))], (11766 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_986218), _986220), _986222) = c_Groups_Ozero__class_Ozero(_986218), -(_986220 = _986222)]]], (50364 ^ _781215) ^ [_1805340, _1805342, _1805344] : [-(c_Nitpick_Otimes__frac(_1805340, _1805342, _1805344) = hAPP(hAPP(c_Nitpick_Ofrac(_1805340), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1805340), _1805342)), hAPP(c_Nitpick_Onum(_1805340), _1805344))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1805340), _1805342)), hAPP(c_Nitpick_Odenom(_1805340), _1805344))))], (21676 ^ _781215) ^ [_1170090, _1170092] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1170090)), c_Int_OBit1(_1170092)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1170090), _1170092)))], (40891 ^ _781215) ^ [_1582835, _1582837] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1582835, _1582837)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1582837)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16331 ^ _781215) ^ [_1069775, _1069777] : [class_Lattices_Obounded__lattice__bot(_1069775), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069775), c_Orderings_Obot__class_Obot(_1069775)), _1069777) = _1069777)], (51238 ^ _781215) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (2258 ^ _781215) ^ [_814420, _814422, _814424, _814426, _814428, _814430] : [-(c_SetInterval_Oord_OatLeast(_814430, _814426, _814422) = c_SetInterval_Oord_OatLeast(_814428, _814424, _814420)), _814430 = _814428, _814426 = _814424, _814422 = _814420], (23664 ^ _781215) ^ [_1207811, _1207813, _1207815, _1207817] : [class_Rings_Ocomm__semiring__1(_1207811), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1207811), hAPP(hAPP(c_Power_Opower__class_Opower(_1207811), _1207813), _1207815)), _1207817) = hAPP(hAPP(c_Power_Opower__class_Opower(_1207811), _1207813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1207815), _1207817)))], (18129 ^ _781215) ^ [_1105785, _1105787, _1105789] : [class_Orderings_Olinorder(_1105785), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105785), _1105787), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105785), _1105787), _1105789)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105785), _1105787), _1105789))], (51174 ^ _781215) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (15416 ^ _781215) ^ [_1051528, _1051530] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051528), _1051530))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051528), _1051530)), -(_1051528 = _1051530)], (10027 ^ _781215) ^ [_951634, _951636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951634), _951636)), -(_951636 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951634), 10030 ^ [_951634, _951636]))], (50538 ^ _781215) ^ [_1808834, _1808836, _1808838] : [50540 ^ _781215 : [(50543 ^ _781215) ^ [] : [hBOOL(hAPP(_1808836, 50539 ^ [_1808834, _1808836, _1808838]))], (50541 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808834), 50539 ^ [_1808834, _1808836, _1808838]), hAPP(c_List_Oset(_1808834), _1808838))))]], -(c_List_Olist__all(_1808834, _1808836, _1808838))], (17411 ^ _781215) ^ [_1092989, _1092991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1092989)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1092991)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092989)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1092991), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1092989))))], (6037 ^ _781215) ^ [_877924, _877926, _877928, _877930, _877932, _877934, _877936] : [c_Hoare__Mirabelle_Ohoare__derivs(_877924, _877926, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877924)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877924), _877928), _877930), _877932)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877924), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_877924, _877926, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877924)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877924), _877932), _877934), _877936)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877924), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_877924, _877926, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877924)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877924), _877928), c_Com_Ocom_OSemi(_877930, _877934)), _877936)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877924), tc_HOL_Obool)))))], (22126 ^ _781215) ^ [_1179978, _1179980] : [c_Nat__Transfer_Onat__set(_1179978), c_Nat__Transfer_Onat__set(_1179980), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1179978), _1179980) = 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), _1179978)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1179980))))], (14250 ^ _781215) ^ [_1030318] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1030318)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1030318)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23646 ^ _781215) ^ [_1207446, _1207448] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1207446), _1207448)), _1207446)))], (51626 ^ _781215) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (16685 ^ _781215) ^ [_1079809, _1079811, _1079813, _1079815] : [class_Lattices_Osemilattice__sup(_1079809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079809), _1079811)), hBOOL(hAPP(hAPP(c_member(_1079809), _1079813), _1079811)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079809), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1079809), _1079813), _1079815)), hAPP(hAPP(c_Finite__Set_Ofold(_1079809, _1079809, c_Lattices_Osemilattice__sup__class_Osup(_1079809)), _1079815), _1079811))))], (4930 ^ _781215) ^ [_856096, _856098] : [_856098 = _856096, -(c_Lazy__Sequence_Oyieldn(_856098) = c_Lazy__Sequence_Oyieldn(_856096))], (21672 ^ _781215) ^ [_1170014] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1170014)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1170014)))], (14708 ^ _781215) ^ [_1038418, _1038420, _1038422] : [class_Int_Onumber__ring(_1038418), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038418), hAPP(c_Int_Onumber__class_Onumber__of(_1038418), _1038420)), hAPP(c_Int_Onumber__class_Onumber__of(_1038418), _1038422)) = hAPP(c_Int_Onumber__class_Onumber__of(_1038418), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1038420), _1038422)))], (43051 ^ _781215) ^ [_1638173, _1638175, _1638177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1638173, _1638173), tc_HOL_Obool)), _1638175), hAPP(hAPP(c_Product__Type_OSigma(_1638173, _1638173), _1638177), hAPP(c_COMBK(tc_fun(_1638173, tc_HOL_Obool), _1638173), _1638177)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1638173), tc_List_Olist(_1638173)), tc_HOL_Obool)), c_List_Olistrel(_1638173, _1638175)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1638173), tc_List_Olist(_1638173)), c_List_Olists(_1638173, _1638177)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1638173), tc_HOL_Obool), tc_List_Olist(_1638173)), c_List_Olists(_1638173, _1638177))))))], (32246 ^ _781215) ^ [_1376950, _1376952, _1376954] : [_1376952 = c_Orderings_Obot__class_Obot(tc_fun(_1376950, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1376950, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1376950), _1376952), _1376954))], (27786 ^ _781215) ^ [_1287559, _1287561, _1287563, _1287565, _1287567] : [class_Fields_Ofield(_1287559), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287561), _1287563)), -(hAPP(_1287565, _1287567) = c_Groups_Ozero__class_Ozero(_1287559)), 27797 ^ _781215 : [(27804 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1287561), _1287567), _1287563))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287561, _1287559), _1287565), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1287561, tc_HOL_Obool)), _1287563), hAPP(hAPP(c_Set_Oinsert(_1287561), _1287567), c_Orderings_Obot__class_Obot(tc_fun(_1287561, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287561, _1287559), _1287565), _1287563))], (27798 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1287561), _1287567), _1287563)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287561, _1287559), _1287565), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1287561, tc_HOL_Obool)), _1287563), hAPP(hAPP(c_Set_Oinsert(_1287561), _1287567), c_Orderings_Obot__class_Obot(tc_fun(_1287561, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287559), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287561, _1287559), _1287565), _1287563)), hAPP(_1287565, _1287567)))]]], (34392 ^ _781215) ^ [_1425492, _1425494, _1425496] : [class_Lattices_Olattice(_1425492), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425492), _1425494)), -(_1425494 = c_Orderings_Obot__class_Obot(tc_fun(_1425492, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425492), _1425496)), -(_1425496 = c_Orderings_Obot__class_Obot(tc_fun(_1425492, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1425492, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1425492, tc_HOL_Obool)), _1425494), _1425496)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1425492), c_Big__Operators_Olattice__class_OInf__fin(_1425492, _1425494)), c_Big__Operators_Olattice__class_OInf__fin(_1425492, _1425496)))], (27207 ^ _781215) ^ [_1275894] : [-(_1275894 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1275894), 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)))))], (7830 ^ _781215) ^ [_913405, _913407, _913409, _913411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_913405, tc_HOL_Obool)), _913407), _913409)), hBOOL(hAPP(hAPP(c_member(_913405), _913411), _913407)), -(hBOOL(hAPP(hAPP(c_member(_913405), _913411), _913409)))], (18411 ^ _781215) ^ [_1110823, _1110825] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1110823), hAPP(c_Nat_OSuc, _1110825)) = 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)), _1110825)), _1110823))], (26121 ^ _781215) ^ [_1254922, _1254924, _1254926] : [class_Rings_Olinordered__idom(_1254922), 26124 ^ _781215 : [(26131 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254924), _1254926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254922), hAPP(c_Int_Oring__1__class_Oof__int(_1254922), _1254924)), hAPP(c_Int_Oring__1__class_Oof__int(_1254922), _1254926))))], (26125 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254922), hAPP(c_Int_Oring__1__class_Oof__int(_1254922), _1254924)), hAPP(c_Int_Oring__1__class_Oof__int(_1254922), _1254926))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254924), _1254926)))]]], (37145 ^ _781215) ^ [_1484222, _1484224, _1484226, _1484228, _1484230] : [_1484222 = c_Orderings_Obot__class_Obot(tc_fun(_1484224, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484226, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484224, tc_fun(_1484226, tc_HOL_Obool)), _1484222), _1484228)), _1484230) = _1484230)], (7907 ^ _781215) ^ [_914792, _914794] : [hAPP(c_Nat_OSuc, _914792) = hAPP(c_Nat_OSuc, _914794), -(_914792 = _914794)], (50611 ^ _781215) ^ [_1810204, _1810206, _1810208, _1810210, _1810212, _1810214] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1810204, _1810206, _1810208), _1810210), hAPP(hAPP(c_Product__Type_OPair(_1810204, _1810206), _1810212), _1810214)) = hAPP(hAPP(_1810210, _1810212), _1810214))], (30680 ^ _781215) ^ [_1342651, _1342653, _1342655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1342651)), 30683 ^ _781215 : [(30684 ^ _781215) ^ [_1342785] : [30686 ^ _781215 : [(30692 ^ _781215) ^ [] : [-(_1342785 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30688 ^ [_1342651, _1342653, _1342655, _1342785]), 30685 ^ [_1342651, _1342653, _1342655, _1342785]))], (30690 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30688 ^ [_1342651, _1342653, _1342655, _1342785]), _1342653)))], (30687 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30685 ^ [_1342651, _1342653, _1342655, _1342785]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1342651))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342785), _1342655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1342785), _1342651)), _1342655)))]]], (11944 ^ _781215) ^ [_988798] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988798), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _988798)], (48796 ^ _781215) ^ [_1766483, _1766485] : [_1766483 = _1766485, -(c_Random_Oinc__shift(_1766483, _1766485) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (49411 ^ _781215) ^ [_1780409, _1780411, _1780413] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1780409, _1780411, _1780411), _1780413), c_Relation_OId(_1780411)) = _1780413)], (18265 ^ _781215) ^ [_1108186, _1108188, _1108190, _1108192] : [class_Orderings_Olinorder(_1108186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108186), _1108188), _1108190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108186), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1108186), _1108188), _1108192)), _1108190)))], (45037 ^ _781215) ^ [_1684650, _1684652, _1684654] : [class_Lattices_Olattice(_1684650), -(c_Big__Operators_Olattice__class_OInf__fin(_1684650, hAPP(c_List_Oset(_1684650), hAPP(hAPP(c_List_Olist_OCons(_1684650), _1684652), _1684654))) = hAPP(c_List_Ofoldl(_1684650, _1684650, c_Lattices_Osemilattice__inf__class_Oinf(_1684650), _1684652), _1684654))], (23018 ^ _781215) ^ [_1196236, _1196238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196236)), -(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, _1196238, _1196236))))], (40913 ^ _781215) ^ [_1583286, _1583288, _1583290, _1583292] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1583286), _1583288)), 40919 ^ _781215 : [(40922 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1583290), hAPP(_1583292, 40918 ^ [_1583286, _1583288, _1583290, _1583292])))], (40920 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1583286), 40918 ^ [_1583286, _1583288, _1583290, _1583292]), _1583288)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1583290), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1583286, tc_fun(_1583290, tc_HOL_Obool)), _1583288), _1583292))))], (30939 ^ _781215) ^ [_1347539, _1347541] : [30947 ^ _781215 : [(30950 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1347541, 30946 ^ [_1347539, _1347541])))], (30948 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30946 ^ [_1347539, _1347541]), _1347539)))]], 30940 ^ _781215 : [(30941 ^ _781215) ^ [_1347607] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1347607), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1347539))), hBOOL(hAPP(_1347541, _1347607))]]], (49972 ^ _781215) ^ [_1794575, _1794577, _1794579, _1794581] : [-(hAPP(hAPP(c_Nat_Ocompow(_1794575, _1794575), _1794577), hAPP(hAPP(c_Nat_Ocompow(_1794575, _1794575), _1794579), _1794581)) = hAPP(hAPP(c_Nat_Ocompow(_1794575, _1794575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1794579), _1794577)), _1794581))], (21946 ^ _781215) ^ [] : [-(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))))))], (10238 ^ _781215) ^ [_955596, _955598] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955596), _955598) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _955596 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _955598 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (30012 ^ _781215) ^ [_1329187, _1329189, _1329191] : [-(c_Wellfounded_Omlex__prod(_1329187, _1329189, _1329191) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1329187), _1329187), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1329187, c_Wellfounded_Oless__than, _1329191)), hAPP(hAPP(c_COMBS(_1329187, _1329187, tc_prod(tc_Nat_Onat, _1329187)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1329187, tc_prod(tc_Nat_Onat, _1329187)), _1329187), c_Product__Type_OPair(tc_Nat_Onat, _1329187)), _1329189)), c_COMBI(_1329187))))], (47253 ^ _781215) ^ [_1731858, _1731860] : [class_Enum_Oenum(_1731858), 47256 ^ _781215 : [(47263 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731858), _1731860)), -(hBOOL(hAPP(_1731860, 47266 ^ [_1731858, _1731860])))], (47257 ^ _781215) ^ [] : [47258 ^ _781215 : [(47259 ^ _781215) ^ [_1731960] : [hBOOL(hAPP(_1731860, _1731960))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731858), _1731860)))]]], (43986 ^ _781215) ^ [_1660258, _1660260, _1660262, _1660264] : [-(hAPP(c_List_Olist_Olist__case(_1660258, _1660260, _1660262, _1660264), c_List_Olist_ONil(_1660260)) = _1660262)], (41255 ^ _781215) ^ [_1591295, _1591297, _1591299, _1591301, _1591303] : [c_Fun_Oinj__on(_1591295, _1591297, _1591299, c_Orderings_Otop__class_Otop(tc_fun(_1591295, tc_HOL_Obool))), c_Fun_Oinj__on(_1591301, _1591295, _1591303, c_Orderings_Otop__class_Otop(tc_fun(_1591301, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1591301, _1591297, hAPP(c_Fun_Ocomp(_1591295, _1591297, _1591301, _1591299), _1591303), c_Orderings_Otop__class_Otop(tc_fun(_1591301, tc_HOL_Obool))))], (16935 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (46670 ^ _781215) ^ [_1719476, _1719478] : [-(c_List_Oremdups(_1719476, c_List_Oremdups(_1719476, _1719478)) = c_List_Oremdups(_1719476, _1719478))], (24254 ^ _781215) ^ [_1218699, _1218701, _1218703] : [class_Rings_Olinordered__semidom(_1218699), hAPP(hAPP(c_Power_Opower__class_Opower(_1218699), _1218701), 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(_1218699), _1218703), 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(_1218699), c_Groups_Ozero__class_Ozero(_1218699)), _1218701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218699), c_Groups_Ozero__class_Ozero(_1218699)), _1218703)), -(_1218701 = _1218703)], (35515 ^ _781215) ^ [_1448633, _1448635, _1448637] : [class_Orderings_Oord(_1448633), 35518 ^ _781215 : [(35525 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448633), _1448637), _1448635)), -(hBOOL(hAPP(hAPP(c_member(_1448633), _1448635), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448633), _1448637))))], (35519 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1448633), _1448635), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448633), _1448637))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448633), _1448637), _1448635)))]]], (40209 ^ _781215) ^ [_1566429, _1566431, _1566433, _1566435, _1566437] : [-(hAPP(c_Relation_ODomain(_1566429, _1566431), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1566429, _1566431)), hAPP(hAPP(c_Product__Type_OPair(_1566429, _1566431), _1566433), _1566435)), _1566437)) = hAPP(hAPP(c_Set_Oinsert(_1566429), _1566433), hAPP(c_Relation_ODomain(_1566429, _1566431), _1566437)))], (14010 ^ _781215) ^ [_1025396, _1025398, _1025400] : [14011 ^ _781215 : [(14014 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025398), _1025400))], (14012 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1025396)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025396), _1025398)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025396), _1025400))))], (45404 ^ _781215) ^ [_1692450, _1692452, _1692454, _1692456, _1692458, _1692460] : [hAPP(hAPP(c_Map_Omap__of(_1692450, _1692452), _1692454), _1692456) = hAPP(c_Option_Ooption_OSome(_1692452), _1692458), hBOOL(hAPP(hAPP(_1692460, _1692456), _1692458)), -(hAPP(hAPP(c_Map_Omap__of(_1692450, _1692452), hAPP(c_List_Ofilter(tc_prod(_1692450, _1692452), hAPP(c_Product__Type_Oprod_Oprod__case(_1692450, _1692452, tc_HOL_Obool), _1692460)), _1692454)), _1692456) = hAPP(c_Option_Ooption_OSome(_1692452), _1692458))], (43453 ^ _781215) ^ [_1648433, _1648435, _1648437, _1648439, _1648441] : [class_Groups_Omonoid__add(_1648433), class_Groups_Oordered__ab__semigroup__add(_1648433), 43463 ^ _781215 : [(43466 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1648433), hAPP(_1648439, 43462 ^ [_1648433, _1648435, _1648437, _1648439, _1648441])), hAPP(_1648441, 43462 ^ [_1648433, _1648435, _1648437, _1648439, _1648441])))], (43464 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1648435), 43462 ^ [_1648433, _1648435, _1648437, _1648439, _1648441]), hAPP(c_List_Oset(_1648435), _1648437))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1648433), hAPP(c_List_Omonoid__add__class_Olistsum(_1648433), hAPP(hAPP(c_List_Omap(_1648435, _1648433), _1648439), _1648437))), hAPP(c_List_Omonoid__add__class_Olistsum(_1648433), hAPP(hAPP(c_List_Omap(_1648435, _1648433), _1648441), _1648437)))))], (27462 ^ _781215) ^ [_1281062, _1281064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1281062), 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)), _1281064)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1281062, _1281064) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1281062, _1281064)))], (35749 ^ _781215) ^ [_1453493, _1453495] : [class_Groups_Oordered__ab__group__add__abs(_1453493), -(hAPP(c_Groups_Oabs__class_Oabs(_1453493), hAPP(c_Groups_Ouminus__class_Ouminus(_1453493), _1453495)) = hAPP(c_Groups_Oabs__class_Oabs(_1453493), _1453495))], (51730 ^ _781215) ^ [_1826501, _1826503] : [hBOOL(_1826501), -(hBOOL(hAPP(hAPP(c_fdisj, _1826503), _1826501)))], (8890 ^ _781215) ^ [_931873, _931875, _931877, _931879, _931881] : [class_Orderings_Oord(_931873), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931875, _931873)), _931877), _931879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931873), hAPP(_931877, _931881)), hAPP(_931879, _931881))))], (17647 ^ _781215) ^ [_1096703, _1096705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096703)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096705)), 17654 ^ _781215 : [(17661 ^ _781215) ^ [] : [_1096703 = _1096705, -(hAPP(c_Int_Onat, _1096703) = hAPP(c_Int_Onat, _1096705))], (17655 ^ _781215) ^ [] : [hAPP(c_Int_Onat, _1096703) = hAPP(c_Int_Onat, _1096705), -(_1096703 = _1096705)]]], (16139 ^ _781215) ^ [_1066482, _1066484, _1066486, _1066488, _1066490] : [class_Lattices_Osemilattice__sup(_1066482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066482), _1066484), _1066486)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066482), _1066488), _1066490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066482), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066482), _1066484), _1066488)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066482), _1066486), _1066490))))], (41243 ^ _781215) ^ [_1590995, _1590997, _1590999, _1591001] : [-(hAPP(c_Map_Omap__of(_1590995, _1590997), hAPP(hAPP(c_List_Omap(_1590995, tc_prod(_1590995, _1590997)), hAPP(hAPP(c_COMBS(_1590995, _1590997, tc_prod(_1590995, _1590997)), c_Product__Type_OPair(_1590995, _1590997)), _1590999)), _1591001)) = c_Map_Orestrict__map(_1590995, _1590997, hAPP(c_Fun_Ocomp(_1590997, tc_Option_Ooption(_1590997), _1590995, c_Option_Ooption_OSome(_1590997)), _1590999), hAPP(c_List_Oset(_1590995), _1591001)))], (40445 ^ _781215) ^ [_1572934, _1572936, _1572938] : [-(c_Relation_Orefl__on(_1572934, _1572936, _1572938)), 40449 ^ _781215 : [(40452 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1572934, _1572934, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1572934, tc_fun(_1572934, tc_HOL_Obool), tc_fun(_1572934, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1572934, tc_HOL_Obool), tc_fun(_1572934, tc_HOL_Obool)), _1572934), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1572934)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572934), c_fconj), hAPP(hAPP(c_COMBC(_1572934, tc_fun(_1572934, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572934)), _1572936)))), hAPP(hAPP(c_COMBC(_1572934, tc_fun(_1572934, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572934)), _1572936))), 40448 ^ [_1572934, _1572936, _1572938]))], (40450 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572934, _1572934)), 40448 ^ [_1572934, _1572936, _1572938]), _1572938)))]], 40454 ^ _781215 : [(40457 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572934, _1572934)), hAPP(hAPP(c_Product__Type_OPair(_1572934, _1572934), 40453 ^ [_1572934, _1572936, _1572938]), 40453 ^ [_1572934, _1572936, _1572938])), _1572938))], (40455 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1572934), 40453 ^ [_1572934, _1572936, _1572938]), _1572936)))]]], (22090 ^ _781215) ^ [_1179138, _1179140, _1179142, _1179144, _1179146] : [_1179138 = c_Orderings_Obot__class_Obot(tc_fun(_1179140, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179140, tc_fun(_1179142, tc_HOL_Obool)), _1179138), hAPP(hAPP(c_COMBC(_1179140, tc_fun(_1179142, tc_HOL_Obool), tc_fun(_1179142, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1179142, tc_HOL_Obool), tc_fun(tc_fun(_1179142, tc_HOL_Obool), tc_fun(_1179142, tc_HOL_Obool)), _1179140), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1179142, tc_HOL_Obool))), _1179144)), _1179146)) = c_Orderings_Obot__class_Obot(tc_fun(_1179142, tc_HOL_Obool)))], (44958 ^ _781215) ^ [_1683028, _1683030, _1683032] : [class_Groups_Oab__semigroup__add(_1683028), -(c_List_Ofoldr(_1683028, _1683028, c_Groups_Oplus__class_Oplus(_1683028), _1683030, _1683032) = hAPP(c_List_Ofoldl(_1683028, _1683028, c_Groups_Oplus__class_Oplus(_1683028), _1683032), _1683030))], (46888 ^ _781215) ^ [_1724361, _1724363, _1724365] : [-(hAPP(c_List_Oset(tc_List_Olist(_1724361)), c_Enum_On__lists(_1724361, _1724363, _1724365)) = hAPP(c_Set_OCollect(tc_List_Olist(_1724361)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1724361), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1724361)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1724361), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1724361)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1724361)))), _1724363))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1724361), tc_fun(_1724361, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1724361, tc_HOL_Obool), tc_fun(tc_fun(_1724361, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1724361)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1724361, tc_HOL_Obool))), c_List_Oset(_1724361))), hAPP(c_List_Oset(_1724361), _1724365)))))], (46161 ^ _781215) ^ [_1707595] : [-(hAPP(c_List_Orev(_1707595), c_List_Olist_ONil(_1707595)) = c_List_Olist_ONil(_1707595))], (9899 ^ _781215) ^ [_949603, _949605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _949605)), _949603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949603), _949605))], (39789 ^ _781215) ^ [_1555608, _1555610] : [-(hAPP(c_Relation_ORange(_1555608, _1555610), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1555608, _1555610), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1555610, tc_HOL_Obool)))], (37639 ^ _781215) ^ [_1496324, _1496326, _1496328, _1496330, _1496332] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1496324, tc_fun(_1496326, tc_HOL_Obool)), _1496328), hAPP(hAPP(c_COMBS(_1496324, tc_fun(_1496326, tc_HOL_Obool), tc_fun(_1496326, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1496326, tc_HOL_Obool), tc_fun(tc_fun(_1496326, tc_HOL_Obool), tc_fun(_1496326, tc_HOL_Obool)), _1496324), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496326, tc_HOL_Obool))), _1496330)), _1496332)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496326, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1496326, tc_HOL_Obool), hAPP(c_Set_Oimage(_1496324, tc_fun(_1496326, tc_HOL_Obool), _1496330), _1496328))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1496326, tc_HOL_Obool), hAPP(c_Set_Oimage(_1496324, tc_fun(_1496326, tc_HOL_Obool), _1496332), _1496328))))], (35255 ^ _781215) ^ [_1443241, _1443243, _1443245, _1443247] : [c_Fun_Oinj__on(_1443241, _1443243, _1443245, _1443247), -(c_Fun_Oinj__on(_1443243, _1443241, c_Fun_Othe__inv__into(_1443241, _1443243, _1443247, _1443245), hAPP(c_Set_Oimage(_1443241, _1443243, _1443245), _1443247)))], (10350 ^ _781215) ^ [_957597, _957599, _957601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957597, tc_HOL_Obool)), _957599), _957601)), 10353 ^ _781215 : [(10356 ^ _781215) ^ [] : [_957599 = _957601], (10354 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957597, tc_HOL_Obool)), _957599), _957601)))]]], (42559 ^ _781215) ^ [_1625768, _1625770, _1625772, _1625774, _1625776] : [class_Orderings_Olinorder(_1625768), hBOOL(hAPP(c_List_Odistinct(_1625770), _1625772)), -(hBOOL(hAPP(c_List_Odistinct(_1625770), c_List_Olinorder__class_Oinsort__insert__key(_1625770, _1625768, _1625774, _1625776, _1625772))))], (16417 ^ _781215) ^ [_1071457, _1071459, _1071461, _1071463] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071457, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1071457), _1071459), _1071461)), _1071463) = hAPP(hAPP(c_Set_Oinsert(_1071457), _1071459), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071457, tc_HOL_Obool)), _1071461), _1071463)))], (12394 ^ _781215) ^ [_996818, _996820, _996822] : [class_Rings_Olinordered__ring__strict(_996818), 12397 ^ _781215 : [(12412 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996818), _996820), _996822)), c_Groups_Ozero__class_Ozero(_996818)))), 12413 ^ _781215 : [(12420 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996818), _996820), c_Groups_Ozero__class_Ozero(_996818))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996818), c_Groups_Ozero__class_Ozero(_996818)), _996822))], (12414 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996818), c_Groups_Ozero__class_Ozero(_996818)), _996820)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996818), _996822), c_Groups_Ozero__class_Ozero(_996818)))]]], (12398 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996818), _996820), _996822)), c_Groups_Ozero__class_Ozero(_996818))), 12403 ^ _781215 : [(12406 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996818), _996822), c_Groups_Ozero__class_Ozero(_996818))))], (12404 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996818), c_Groups_Ozero__class_Ozero(_996818)), _996820)))]], 12407 ^ _781215 : [(12410 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996818), c_Groups_Ozero__class_Ozero(_996818)), _996822)))], (12408 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996818), _996820), c_Groups_Ozero__class_Ozero(_996818))))]]]]], (51044 ^ _781215) ^ [_1819065, _1819067] : [class_Lattices_Obounded__lattice(_1819065), -(class_Lattices_Obounded__lattice(tc_fun(_1819067, _1819065)))], (10708 ^ _781215) ^ [_964640, _964642, _964644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964640), _964642)), 10711 ^ _781215 : [(10718 ^ _781215) ^ [] : [_964642 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964644), _964640), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964642), _964640) = _964644)], (10712 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964642), _964640) = _964644, -(_964642 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964644), _964640))]]], (38203 ^ _781215) ^ [_1508936, _1508938, _1508940] : [-(hAPP(c_Option_Omap(_1508936, _1508938), _1508940) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1508938), _1508936, c_Option_Ooption_ONone(_1508938), hAPP(hAPP(c_COMBB(_1508938, tc_Option_Ooption(_1508938), _1508936), c_Option_Ooption_OSome(_1508938)), _1508940)))], (6646 ^ _781215) ^ [_890052, _890054] : [-(hBOOL(hAPP(hAPP(c_member(_890052), 6647 ^ [_890052, _890054]), _890054))), -(_890054 = c_Orderings_Obot__class_Obot(tc_fun(_890052, tc_HOL_Obool)))], (9125 ^ _781215) ^ [_936034, _936036, _936038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936034), _936036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936038), _936034)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936038), _936036))))], (34920 ^ _781215) ^ [_1435851, _1435853, _1435855, _1435857] : [class_Groups_Ocomm__monoid__add(_1435851), 34923 ^ _781215 : [(34930 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1435853), _1435855))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1435853, _1435851), _1435857), _1435855) = c_Groups_Ozero__class_Ozero(_1435851))], (34924 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1435853), _1435855)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1435853, _1435851), _1435857), _1435855) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435851, _1435853, c_Groups_Oplus__class_Oplus(_1435851)), _1435857), c_Groups_Ozero__class_Ozero(_1435851)), _1435855))]]], (21590 ^ _781215) ^ [_1168555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1168555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1168555))))], (43710 ^ _781215) ^ [_1654242, _1654244, _1654246, _1654248] : [-(c_Map_Omap__upds(_1654242, _1654244, _1654246, _1654248, c_List_Olist_ONil(_1654244)) = _1654246)], (37993 ^ _781215) ^ [_1503694, _1503696, _1503698, _1503700] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1503694, tc_HOL_Obool), tc_fun(_1503696, tc_HOL_Obool)), _1503698), hAPP(hAPP(c_COMBC(tc_fun(_1503694, tc_HOL_Obool), tc_fun(_1503694, tc_fun(_1503696, tc_HOL_Obool)), tc_fun(_1503696, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1503694, tc_fun(_1503696, tc_HOL_Obool))), _1503700)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1503694, tc_fun(_1503696, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1503694, tc_HOL_Obool), _1503698)), _1503700))], (24208 ^ _781215) ^ [_1217838, _1217840] : [class_Rings_Ocomm__semiring__1(_1217838), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217838), _1217840), _1217840) = hAPP(hAPP(c_Power_Opower__class_Opower(_1217838), _1217840), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (40039 ^ _781215) ^ [_1562908, _1562910, _1562912] : [c_Wellfounded_Owf(_1562908, _1562910), -(c_Wellfounded_Owf(_1562908, c_Wellfounded_Omlex__prod(_1562908, _1562912, _1562910)))], (38949 ^ _781215) ^ [_1528756, _1528758, _1528760, _1528762, _1528764, _1528766, _1528768, _1528770] : [c_Finite__Set_Ofolding__image__simple(_1528756, _1528758, _1528760, _1528762, _1528764, _1528766), hBOOL(hAPP(c_Finite__Set_Ofinite(_1528758), _1528768)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1528758), _1528770)), 38963 ^ _781215 : [(38966 ^ _781215) ^ [] : [hAPP(_1528764, 38962 ^ [_1528756, _1528758, _1528760, _1528762, _1528764, _1528766, _1528768, _1528770]) = _1528762], (38964 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1528758), 38962 ^ [_1528756, _1528758, _1528760, _1528762, _1528764, _1528766, _1528768, _1528770]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1528758, tc_HOL_Obool)), _1528768), _1528770))))]], -(hAPP(_1528766, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528758, tc_HOL_Obool)), _1528768), _1528770)) = hAPP(hAPP(_1528760, hAPP(_1528766, _1528768)), hAPP(_1528766, _1528770)))], (44554 ^ _781215) ^ [_1674054, _1674056, _1674058] : [-(c_List_Obutlast(_1674054, hAPP(hAPP(c_List_Odrop(_1674054), _1674056), _1674058)) = hAPP(hAPP(c_List_Odrop(_1674054), _1674056), c_List_Obutlast(_1674054, _1674058)))], (35075 ^ _781215) ^ [_1439648, _1439650] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1439648), _1439650)), -(hAPP(c_Finite__Set_Ocard(_1439648), _1439650) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1439648, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1439648), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1439650))], (36754 ^ _781215) ^ [_1472395, _1472397, _1472399, _1472401, _1472403] : [c_Fun_Oinj__on(_1472395, _1472397, _1472399, c_Orderings_Otop__class_Otop(tc_fun(_1472395, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1472395, _1472397, _1472399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472395, tc_HOL_Obool)), _1472401), _1472403)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472397, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1472395, _1472397, _1472399), _1472401)), hAPP(c_Set_Oimage(_1472395, _1472397, _1472399), _1472403)))], (9935 ^ _781215) ^ [_950222, _950224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950222), _950224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950222), hAPP(c_Nat_OSuc, _950224))))], (36374 ^ _781215) ^ [_1464998, _1465000, _1465002, _1465004, _1465006] : [c_Fun_Oinj__on(_1464998, _1465000, _1465002, c_Orderings_Otop__class_Otop(tc_fun(_1464998, tc_HOL_Obool))), 36377 ^ _781215 : [(36384 ^ _781215) ^ [] : [_1465004 = _1465006, -(hAPP(_1465002, _1465004) = hAPP(_1465002, _1465006))], (36378 ^ _781215) ^ [] : [hAPP(_1465002, _1465004) = hAPP(_1465002, _1465006), -(_1465004 = _1465006)]]], (44447 ^ _781215) ^ [_1670939, _1670941, _1670943, _1670945, _1670947, _1670949, _1670951, _1670953] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1670939, _1670939)), hAPP(hAPP(c_Product__Type_OPair(_1670939, _1670939), _1670941), _1670943)), _1670945)), _1670947 = hAPP(hAPP(c_List_Oappend(_1670939), _1670949), hAPP(hAPP(c_List_Olist_OCons(_1670939), _1670941), _1670951)), _1670953 = hAPP(hAPP(c_List_Oappend(_1670939), _1670949), hAPP(hAPP(c_List_Olist_OCons(_1670939), _1670943), _1670951)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1670939), tc_List_Olist(_1670939))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1670939), tc_List_Olist(_1670939)), _1670947), _1670953)), c_List_Olistrel1(_1670939, _1670945))))], (3650 ^ _781215) ^ [_836480, _836482, _836484, _836486, _836488, _836490, _836492, _836494] : [-(c_Enum_Oproduct(_836494, _836490, _836486, _836482) = c_Enum_Oproduct(_836492, _836488, _836484, _836480)), _836494 = _836492, _836490 = _836488, _836486 = _836484, _836482 = _836480], (24416 ^ _781215) ^ [_1221451, _1221453, _1221455] : [class_Rings_Olinordered__idom(_1221451), 24419 ^ _781215 : [(24428 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221451), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221451), hAPP(hAPP(c_Power_Opower__class_Opower(_1221451), _1221453), 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(_1221451), _1221455), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1221451)))), _1221453 = c_Groups_Ozero__class_Ozero(_1221451), _1221455 = c_Groups_Ozero__class_Ozero(_1221451)], (24420 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221451), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221451), hAPP(hAPP(c_Power_Opower__class_Opower(_1221451), _1221453), 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(_1221451), _1221455), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1221451))), 24423 ^ _781215 : [(24426 ^ _781215) ^ [] : [-(_1221455 = c_Groups_Ozero__class_Ozero(_1221451))], (24424 ^ _781215) ^ [] : [-(_1221453 = c_Groups_Ozero__class_Ozero(_1221451))]]]]], (45968 ^ _781215) ^ [_1703013] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1703013) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1703013))))], (1218 ^ _781215) ^ [_799410, _799412] : [-(class_Divides_Oring__div(_799410)), _799412 = _799410, class_Divides_Oring__div(_799412)], (42977 ^ _781215) ^ [_1636489, _1636491, _1636493, _1636495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1636489), _1636491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636493, tc_HOL_Obool)), hAPP(c_List_Oset(_1636493), hAPP(hAPP(c_List_Otake(_1636493), _1636489), _1636495))), hAPP(c_List_Oset(_1636493), hAPP(hAPP(c_List_Otake(_1636493), _1636491), _1636495)))))], (15070 ^ _781215) ^ [_1045843, _1045845] : [class_Rings_Olinordered__idom(_1045843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045843), c_Groups_Ozero__class_Ozero(_1045843)), _1045845)), -(c_Groups_Osgn__class_Osgn(_1045843, _1045845) = c_Groups_Oone__class_Oone(_1045843))], (35301 ^ _781215) ^ [_1444224, _1444226, _1444228, _1444230, _1444232] : [class_Groups_Ocomm__monoid__add(_1444224), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444226), _1444228)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1444226, tc_HOL_Obool)), _1444230), _1444228)), 35315 ^ _781215 : [(35318 ^ _781215) ^ [] : [hAPP(_1444232, 35314 ^ [_1444224, _1444226, _1444228, _1444230, _1444232]) = c_Groups_Ozero__class_Ozero(_1444224)], (35316 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444226), 35314 ^ [_1444224, _1444226, _1444228, _1444230, _1444232]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1444226, tc_HOL_Obool)), _1444228), _1444230))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444226, _1444224), _1444232), _1444230) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444226, _1444224), _1444232), _1444228))], (1078 ^ _781215) ^ [_797660, _797662] : [-(class_Groups_Oordered__ab__group__add__abs(_797660)), _797662 = _797660, class_Groups_Oordered__ab__group__add__abs(_797662)], (45237 ^ _781215) ^ [_1688556, _1688558, _1688560] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688556)), _1688558), c_List_Olists(_1688556, _1688560)))), 45238 ^ _781215 : [(45241 ^ _781215) ^ [_1688684, _1688686] : [_1688558 = hAPP(hAPP(c_List_Olist_OCons(_1688556), _1688686), _1688684), hBOOL(hAPP(hAPP(c_member(_1688556), _1688686), _1688560)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688556)), _1688684), c_List_Olists(_1688556, _1688560)))], (45239 ^ _781215) ^ [] : [_1688558 = c_List_Olist_ONil(_1688556)]]], (22338 ^ _781215) ^ [_1184519, _1184521, _1184523, _1184525] : [class_Divides_Osemiring__div(_1184519), -(c_Divides_Odiv__class_Omod(_1184519, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184519), c_Divides_Odiv__class_Omod(_1184519, _1184521, _1184523)), _1184525), _1184523) = c_Divides_Odiv__class_Omod(_1184519, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184519), _1184521), _1184525), _1184523))], (38574 ^ _781215) ^ [_1518840, _1518842, _1518844, _1518846, _1518848, _1518850] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1518840, _1518842)), hAPP(hAPP(c_Product__Type_OPair(_1518840, _1518842), _1518844), _1518846)), hAPP(hAPP(c_Product__Type_OSigma(_1518840, _1518842), _1518848), _1518850))), -(hBOOL(hAPP(hAPP(c_member(_1518840), _1518844), _1518848)))], (7654 ^ _781215) ^ [_909855, _909857, _909859, _909861, _909863, _909865] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909855, tc_Option_Ooption(_909857)), c_Map_Orestrict__map(_909855, _909857, _909859, _909861)), _909863), _909865) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909855, tc_Option_Ooption(_909857)), c_Map_Orestrict__map(_909855, _909857, _909859, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909855, tc_HOL_Obool)), _909861), hAPP(hAPP(c_Set_Oinsert(_909855), _909863), c_Orderings_Obot__class_Obot(tc_fun(_909855, tc_HOL_Obool)))))), _909863), _909865))], (44258 ^ _781215) ^ [_1666307, _1666309, _1666311, _1666313, _1666315, _1666317] : [hAPP(hAPP(c_List_Oappend(_1666307), _1666309), _1666311) = _1666313, _1666315 = hAPP(hAPP(c_List_Oappend(_1666307), _1666311), _1666317), -(hAPP(hAPP(c_List_Oappend(_1666307), _1666309), _1666315) = hAPP(hAPP(c_List_Oappend(_1666307), _1666313), _1666317))], (22422 ^ _781215) ^ [_1186260, _1186262, _1186264] : [-(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, _1186260, _1186262)), _1186264), _1186262) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1186260), _1186264), _1186262))], (11478 ^ _781215) ^ [_981305] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _981305)))], (41000 ^ _781215) ^ [_1585395, _1585397, _1585399, _1585401] : [hAPP(c_List_Oset(_1585395), _1585397) = c_Map_Odom(_1585395, _1585399, _1585401), -(hAPP(c_Map_Omap__of(_1585395, _1585399), hAPP(hAPP(c_List_Omap(_1585395, tc_prod(_1585395, _1585399)), hAPP(hAPP(c_COMBS(_1585395, _1585399, tc_prod(_1585395, _1585399)), c_Product__Type_OPair(_1585395, _1585399)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1585399), _1585399, _1585395), c_Option_Othe(_1585399)), _1585401))), _1585397)) = _1585401)], (44080 ^ _781215) ^ [_1662640, _1662642, _1662644, _1662646, _1662648] : [hAPP(hAPP(c_List_Oappend(_1662640), _1662642), hAPP(hAPP(c_List_Olist_OCons(_1662640), _1662644), c_List_Olist_ONil(_1662640))) = hAPP(hAPP(c_List_Oappend(_1662640), _1662646), hAPP(hAPP(c_List_Olist_OCons(_1662640), _1662648), c_List_Olist_ONil(_1662640))), 44083 ^ _781215 : [(44086 ^ _781215) ^ [] : [-(_1662644 = _1662648)], (44084 ^ _781215) ^ [] : [-(_1662642 = _1662646)]]], (36317 ^ _781215) ^ [_1464002, _1464004, _1464006] : [class_Lattices_Oboolean__algebra(_1464002), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1464002), _1464004), _1464006) = c_Orderings_Obot__class_Obot(_1464002), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1464002), _1464004), _1464006) = c_Orderings_Otop__class_Otop(_1464002), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1464002), _1464004) = _1464006)], (47409 ^ _781215) ^ [_1734938, _1734940, _1734942] : [47411 ^ _781215 : [(47414 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1734940, 47410 ^ [_1734938, _1734940, _1734942])))], (47412 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734938), 47410 ^ [_1734938, _1734940, _1734942]), hAPP(c_List_Oset(_1734938), c_List_OdropWhile(_1734938, _1734940, _1734942)))))]], -(c_List_OtakeWhile(_1734938, _1734940, _1734942) = hAPP(c_List_Ofilter(_1734938, _1734940), _1734942))], (27882 ^ _781215) ^ [_1289574, _1289576, _1289578, _1289580] : [class_Rings_Odivision__ring(_1289574), -(_1289576 = c_Groups_Ozero__class_Ozero(_1289574)), 27889 ^ _781215 : [(27896 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289574), _1289578), _1289576) = _1289580, -(_1289578 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289574), _1289580), _1289576))], (27890 ^ _781215) ^ [] : [_1289578 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289574), _1289580), _1289576), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289574), _1289578), _1289576) = _1289580)]]], (9049 ^ _781215) ^ [_934771, _934773, _934775] : [class_Lattices_Oboolean__algebra(_934771), 9052 ^ _781215 : [(9059 ^ _781215) ^ [] : [_934773 = _934775, -(hAPP(c_Groups_Ouminus__class_Ouminus(_934771), _934773) = hAPP(c_Groups_Ouminus__class_Ouminus(_934771), _934775))], (9053 ^ _781215) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_934771), _934773) = hAPP(c_Groups_Ouminus__class_Ouminus(_934771), _934775), -(_934773 = _934775)]]], (41657 ^ _781215) ^ [_1600897, _1600899, _1600901, _1600903, _1600905, _1600907] : [c_Finite__Set_Ofolding(_1600897, _1600899, _1600901, _1600903), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600897), _1600905)), -(hAPP(_1600903, hAPP(hAPP(c_Set_Oinsert(_1600897), _1600907), _1600905)) = hAPP(c_Fun_Ocomp(_1600899, _1600899, _1600899, hAPP(_1600903, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1600897, tc_HOL_Obool)), _1600905), hAPP(hAPP(c_Set_Oinsert(_1600897), _1600907), c_Orderings_Obot__class_Obot(tc_fun(_1600897, tc_HOL_Obool)))))), hAPP(_1600901, _1600907)))], (21508 ^ _781215) ^ [_1167209, _1167211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1167209)), c_Int_OBit0(_1167211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1167209), _1167211)))], (11561 ^ _781215) ^ [_982885, _982887, _982889, _982891, _982893] : [-(hAPP(c_Set_Oimage(_982885, _982887, _982889), hAPP(hAPP(c_Set_Oinsert(_982885), _982891), _982893)) = hAPP(hAPP(c_Set_Oinsert(_982887), hAPP(_982889, _982891)), hAPP(c_Set_Oimage(_982885, _982887, _982889), _982893)))], (40279 ^ _781215) ^ [_1568764, _1568766] : [c_Wellfounded_Owf(_1568764, _1568766), -(c_Wellfounded_Owf(tc_List_Olist(_1568764), c_List_Olenlex(_1568764, _1568766)))], (3076 ^ _781215) ^ [_827443, _827445, _827447, _827449] : [-(c_List_Olexn(_827449, _827445) = c_List_Olexn(_827447, _827443)), _827449 = _827447, _827445 = _827443], (16836 ^ _781215) ^ [_1083549, _1083551] : [hBOOL(hAPP(hAPP(c_member(_1083549), _1083551), c_Orderings_Obot__class_Obot(tc_fun(_1083549, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1083549, tc_HOL_Obool)), _1083551)))], (44186 ^ _781215) ^ [_1664578, _1664580, _1664582] : [_1664578 = _1664580, -(_1664578 = hAPP(hAPP(c_List_Oappend(_1664582), c_List_Olist_ONil(_1664582)), _1664580))], (30656 ^ _781215) ^ [_1342201, _1342203, _1342205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1342201)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1342203), _1342205)), 30663 ^ _781215 : [(30664 ^ _781215) ^ [_1342391] : [30666 ^ _781215 : [(30672 ^ _781215) ^ [] : [-(_1342391 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30668 ^ [_1342201, _1342203, _1342205, _1342391]), 30665 ^ [_1342201, _1342203, _1342205, _1342391]))], (30670 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30668 ^ [_1342201, _1342203, _1342205, _1342391]), _1342205)))], (30667 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30665 ^ [_1342201, _1342203, _1342205, _1342391]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1342201))))]], -(_1342391 = _1342203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1342391), _1342201) = _1342203]]], (25978 ^ _781215) ^ [_1252423, _1252425, _1252427] : [class_Groups_Ocomm__monoid__mult(_1252423), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1252425, _1252423), _1252427), c_Orderings_Obot__class_Obot(tc_fun(_1252425, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1252423))], (13016 ^ _781215) ^ [_1007937, _1007939] : [class_Rings_Olinordered__idom(_1007937), 13019 ^ _781215 : [(13026 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007937), _1007939), c_Groups_Ozero__class_Ozero(_1007937))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007937), _1007939), hAPP(c_Groups_Ouminus__class_Ouminus(_1007937), _1007939))))], (13020 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007937), _1007939), hAPP(c_Groups_Ouminus__class_Ouminus(_1007937), _1007939))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007937), _1007939), c_Groups_Ozero__class_Ozero(_1007937))))]]], (50632 ^ _781215) ^ [_1810713, _1810715, _1810717] : [-(c_List_Olist__ex1(_1810713, _1810715, _1810717)), 50633 ^ _781215 : [(50634 ^ _781215) ^ [_1810807] : [hBOOL(hAPP(hAPP(c_member(_1810713), _1810807), hAPP(c_List_Oset(_1810713), _1810717))), hBOOL(hAPP(_1810715, _1810807)), 50642 ^ _781215 : [(50647 ^ _781215) ^ [] : [50641 ^ [_1810713, _1810715, _1810717, _1810807] = _1810807], (50645 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1810715, 50641 ^ [_1810713, _1810715, _1810717, _1810807])))], (50643 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810713), 50641 ^ [_1810713, _1810715, _1810717, _1810807]), hAPP(c_List_Oset(_1810713), _1810717))))]]]]], (16796 ^ _781215) ^ [_1082742, _1082744, _1082746, _1082748] : [hBOOL(hAPP(_1082742, _1082744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1082746, tc_HOL_Obool)), _1082742), _1082748)), -(hBOOL(hAPP(_1082748, _1082744)))], (37289 ^ _781215) ^ [_1487875, _1487877, _1487879, _1487881] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1487875, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37290 ^ [_1487875, _1487877, _1487879, _1487881])), _1487877) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1487875, 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), 37290 ^ [_1487875, _1487877, _1487879, _1487881]), _1487879))), _1487881), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1487875, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1487877) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1487875, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1487881))], (49477 ^ _781215) ^ [_1782049, _1782051, _1782053, _1782055] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1782049, _1782049)), hAPP(hAPP(c_Product__Type_OPair(_1782049, _1782049), _1782051), _1782053)), c_Transitive__Closure_Ortrancl(_1782049, _1782055))), hBOOL(hAPP(hAPP(c_member(_1782049), _1782053), c_Wellfounded_Oacc(_1782049, _1782055))), -(hBOOL(hAPP(hAPP(c_member(_1782049), _1782051), c_Wellfounded_Oacc(_1782049, _1782055))))], (44180 ^ _781215) ^ [_1664477, _1664479, _1664481] : [_1664479 = c_List_Olist_ONil(_1664477), -(hAPP(hAPP(c_List_Oappend(_1664477), _1664479), _1664481) = _1664481)], (37957 ^ _781215) ^ [_1503058, _1503060, _1503062, _1503064] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1503058, tc_fun(_1503060, tc_HOL_Obool)), _1503062), _1503064) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1503060, tc_HOL_Obool), hAPP(c_Set_Oimage(_1503058, tc_fun(_1503060, tc_HOL_Obool), _1503064), _1503062)))], (43505 ^ _781215) ^ [_1649447, _1649449, _1649451] : [43506 ^ _781215 : [(43507 ^ _781215) ^ [_1649501] : [hBOOL(hAPP(_1649447, _1649501))]], _1649449 = c_Hilbert__Choice_OEps(_1649451, _1649447), -(hBOOL(hAPP(_1649447, _1649449)))], (6345 ^ _781215) ^ [_884330, _884332] : [hBOOL(hAPP(hAPP(c_member(_884330), _884332), c_Orderings_Obot__class_Obot(tc_fun(_884330, tc_HOL_Obool))))], (3596 ^ _781215) ^ [_835693, _835695] : [_835695 = _835693, -(c_List_Otl(_835695) = c_List_Otl(_835693))], (43115 ^ _781215) ^ [_1639654, _1639656, _1639658] : [43117 ^ _781215 : [(43120 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1639654), 43116 ^ [_1639654, _1639656, _1639658]), _1639658))], (43118 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1639654), 43116 ^ [_1639654, _1639656, _1639658]), hAPP(c_List_Oset(_1639654), _1639656))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1639654)), _1639656), c_List_Olists(_1639654, _1639658))))], (41725 ^ _781215) ^ [_1602668, _1602670, _1602672, _1602674, _1602676, _1602678] : [class_Groups_Ocomm__monoid__add(_1602668), hBOOL(hAPP(c_Finite__Set_Ofinite(_1602670), _1602672)), 41735 ^ _781215 : [(41736 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602670), 41734 ^ [_1602668, _1602670, _1602672, _1602674, _1602676, _1602678]), _1602672)))], (41741 ^ _781215) ^ [] : [41734 ^ [_1602668, _1602670, _1602672, _1602674, _1602676, _1602678] = 41737 ^ [_1602668, _1602670, _1602672, _1602674, _1602676, _1602678]], (41745 ^ _781215) ^ [] : [hAPP(_1602676, hAPP(_1602674, 41734 ^ [_1602668, _1602670, _1602672, _1602674, _1602676, _1602678])) = c_Groups_Ozero__class_Ozero(_1602668)], (41743 ^ _781215) ^ [] : [-(hAPP(_1602674, 41734 ^ [_1602668, _1602670, _1602672, _1602674, _1602676, _1602678]) = hAPP(_1602674, 41737 ^ [_1602668, _1602670, _1602672, _1602674, _1602676, _1602678]))], (41739 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602670), 41737 ^ [_1602668, _1602670, _1602672, _1602674, _1602676, _1602678]), _1602672)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1602678, _1602668), _1602676), hAPP(c_Set_Oimage(_1602670, _1602678, _1602674), _1602672)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1602670, _1602668), hAPP(c_Fun_Ocomp(_1602678, _1602668, _1602670, _1602676), _1602674)), _1602672))], (25680 ^ _781215) ^ [_1243361] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1243361)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1243361)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5943 ^ _781215) ^ [_875831, _875833] : [c_Option_Oset(_875831, _875833) = c_Orderings_Obot__class_Obot(tc_fun(_875831, tc_HOL_Obool)), -(_875833 = c_Option_Ooption_ONone(_875831))], (45482 ^ _781215) ^ [_1694468, _1694470] : [class_Orderings_Olinorder(_1694468), c_List_Olinorder__class_Osorted(_1694468, _1694470), -(c_List_Olinorder__class_Osorted(_1694468, hAPP(c_List_Otl(_1694468), _1694470)))], (7004 ^ _781215) ^ [_897477, _897479, _897481, _897483, _897485, _897487, _897489] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_897477, tc_Option_Ooption(_897479)), _897481), _897483), hAPP(c_Option_Ooption_OSome(_897479), _897485)), _897487) = hAPP(c_Option_Ooption_OSome(_897479), _897489), 7009 ^ _781215 : [(7012 ^ _781215) ^ [] : [-(_897485 = _897489)], (7010 ^ _781215) ^ [] : [-(_897487 = _897483)]], 7013 ^ _781215 : [(7016 ^ _781215) ^ [] : [-(hAPP(_897481, _897487) = hAPP(c_Option_Ooption_OSome(_897479), _897489))], (7014 ^ _781215) ^ [] : [_897487 = _897483]]], (43363 ^ _781215) ^ [_1646221, _1646223, _1646225, _1646227, _1646229] : [class_Groups_Oab__group__add(_1646221), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1646221), hAPP(hAPP(c_List_Omap(_1646223, _1646221), hAPP(hAPP(c_COMBS(_1646223, _1646221, _1646221), hAPP(hAPP(c_COMBB(_1646221, tc_fun(_1646221, _1646221), _1646223), c_Groups_Ominus__class_Ominus(_1646221)), _1646225)), _1646227)), _1646229)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1646221), hAPP(c_List_Omonoid__add__class_Olistsum(_1646221), hAPP(hAPP(c_List_Omap(_1646223, _1646221), _1646225), _1646229))), hAPP(c_List_Omonoid__add__class_Olistsum(_1646221), hAPP(hAPP(c_List_Omap(_1646223, _1646221), _1646227), _1646229))))], (19094 ^ _781215) ^ [_1123714, _1123716, _1123718] : [class_Orderings_Olinorder(_1123714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123714), _1123716)), hBOOL(hAPP(hAPP(c_member(_1123714), _1123718), _1123716)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123714), _1123718), c_Big__Operators_Olattice_OInf__fin(_1123714, c_Orderings_Oord__class_Omin(_1123714), _1123716)) = _1123718)], (10086 ^ _781215) ^ [_952764, _952766, _952768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952764), _952766)), _952768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952764), _952768)))], (7788 ^ _781215) ^ [_912572, _912574, _912576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912572), _912574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912572), _912576)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912574), _912576))))], (26502 ^ _781215) ^ [_1262137, _1262139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262137)), 26505 ^ _781215 : [(26512 ^ _781215) ^ [] : [-(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), _1262139), _1262137)))), -(c_Divides_OnegDivAlg(_1262139, _1262137) = hAPP(c_Divides_Oadjust(_1262137), c_Divides_OnegDivAlg(_1262139, 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)))), _1262137))))], (26506 ^ _781215) ^ [] : [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), _1262139), _1262137))), -(c_Divides_OnegDivAlg(_1262139, _1262137) = 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), _1262139), _1262137)))]]], (38009 ^ _781215) ^ [_1504298, _1504300, _1504302] : [class_Complete__Lattice_Ocomplete__lattice(_1504298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1504298), _1504300)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1504298), _1504302), c_Complete__Lattice_OSup__class_OSup(_1504298, _1504300)) = hAPP(hAPP(c_Finite__Set_Ofold(_1504298, _1504298, c_Lattices_Osemilattice__sup__class_Osup(_1504298)), _1504302), _1504300))], (23628 ^ _781215) ^ [_1207035, _1207037] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207035)), _1207037) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1207035), _1207037)))], (16727 ^ _781215) ^ [_1080584, _1080586, _1080588, _1080590, _1080592, _1080594, _1080596, _1080598, _1080600] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1080584), _1080586)), 16733 ^ _781215 : [(16736 ^ _781215) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1080588, _1080590, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1080588)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1080588), hAPP(_1080598, 16732 ^ [_1080584, _1080586, _1080588, _1080590, _1080592, _1080594, _1080596, _1080598, _1080600])), hAPP(_1080594, 16732 ^ [_1080584, _1080586, _1080588, _1080590, _1080592, _1080594, _1080596, _1080598, _1080600])), hAPP(_1080600, 16732 ^ [_1080584, _1080586, _1080588, _1080590, _1080592, _1080594, _1080596, _1080598, _1080600]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1080588), tc_HOL_Obool))))], (16734 ^ _781215) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1080588, _1080590, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1080588)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1080588), hAPP(_1080592, 16732 ^ [_1080584, _1080586, _1080588, _1080590, _1080592, _1080594, _1080596, _1080598, _1080600])), hAPP(_1080594, 16732 ^ [_1080584, _1080586, _1080588, _1080590, _1080592, _1080594, _1080596, _1080598, _1080600])), hAPP(_1080596, 16732 ^ [_1080584, _1080586, _1080588, _1080590, _1080592, _1080594, _1080596, _1080598, _1080600]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1080588), tc_HOL_Obool)))))]], c_Hoare__Mirabelle_Ohoare__derivs(_1080588, _1080590, hAPP(c_Set_Oimage(_1080584, tc_Hoare__Mirabelle_Otriple(_1080588), hAPP(hAPP(c_COMBS(_1080584, tc_fun(_1080588, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1080588)), hAPP(hAPP(c_COMBS(_1080584, tc_Com_Ocom, tc_fun(tc_fun(_1080588, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1080588))), hAPP(hAPP(c_COMBB(tc_fun(_1080588, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1080588, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1080588))), _1080584), c_Hoare__Mirabelle_Otriple_Otriple(_1080588)), _1080592)), _1080594)), _1080596)), _1080586)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1080588, _1080590, hAPP(c_Set_Oimage(_1080584, tc_Hoare__Mirabelle_Otriple(_1080588), hAPP(hAPP(c_COMBS(_1080584, tc_fun(_1080588, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1080588)), hAPP(hAPP(c_COMBS(_1080584, tc_Com_Ocom, tc_fun(tc_fun(_1080588, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1080588))), hAPP(hAPP(c_COMBB(tc_fun(_1080588, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1080588, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1080588))), _1080584), c_Hoare__Mirabelle_Otriple_Otriple(_1080588)), _1080598)), _1080594)), _1080600)), _1080586)))], (37733 ^ _781215) ^ [_1498085, _1498087, _1498089, _1498091, _1498093, _1498095] : [c_Typedef_Otype__definition(_1498085, _1498087, _1498089, _1498091, _1498093), -(hBOOL(hAPP(hAPP(c_member(_1498087), hAPP(_1498089, _1498095)), _1498093)))], (11674 ^ _781215) ^ [_984873, _984875, _984877] : [class_Rings_Ono__zero__divisors(_984873), -(_984875 = c_Groups_Ozero__class_Ozero(_984873)), -(_984877 = c_Groups_Ozero__class_Ozero(_984873)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984873), _984875), _984877) = c_Groups_Ozero__class_Ozero(_984873)], (20665 ^ _781215) ^ [_1152001] : [class_Rings_Osemiring__1(_1152001), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1152001), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1152001))], (40841 ^ _781215) ^ [_1581578, _1581580, _1581582] : [40843 ^ _781215 : [(40846 ^ _781215) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1581578, hAPP(c_Nat_OSuc, _1581582), 40842 ^ [_1581578, _1581580, _1581582])], (40844 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1581578)), 40842 ^ [_1581578, _1581580, _1581582]), _1581580)))]], 40847 ^ _781215 : [(40848 ^ _781215) ^ [_1581751] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1581578)), _1581751), _1581580)), -(c_Hoare__Mirabelle_Otriple__valid(_1581578, _1581582, _1581751))]]], (46908 ^ _781215) ^ [_1724878, _1724880, _1724882, _1724884] : [-(hAPP(c_List_Oset(tc_prod(_1724878, _1724880)), c_Enum_Oproduct(_1724878, _1724880, _1724882, _1724884)) = hAPP(hAPP(c_Product__Type_OSigma(_1724878, _1724880), hAPP(c_List_Oset(_1724878), _1724882)), hAPP(c_COMBK(tc_fun(_1724880, tc_HOL_Obool), _1724878), hAPP(c_List_Oset(_1724880), _1724884))))], (16893 ^ _781215) ^ [_1084555, _1084557, _1084559] : [class_Lattices_Olattice(_1084555), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084555), _1084557)), hBOOL(hAPP(hAPP(c_member(_1084555), _1084559), _1084557)), 16904 ^ _781215 : [(16911 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1084555, tc_HOL_Obool)), _1084557), hAPP(hAPP(c_Set_Oinsert(_1084555), _1084559), c_Orderings_Obot__class_Obot(tc_fun(_1084555, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1084555, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1084555, _1084557) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1084555), _1084559), c_Big__Operators_Olattice__class_OSup__fin(_1084555, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1084555, tc_HOL_Obool)), _1084557), hAPP(hAPP(c_Set_Oinsert(_1084555), _1084559), c_Orderings_Obot__class_Obot(tc_fun(_1084555, tc_HOL_Obool)))))))], (16905 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1084555, tc_HOL_Obool)), _1084557), hAPP(hAPP(c_Set_Oinsert(_1084555), _1084559), c_Orderings_Obot__class_Obot(tc_fun(_1084555, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1084555, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1084555, _1084557) = _1084559)]]], (36570 ^ _781215) ^ [_1468507, _1468509] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468507), _1468509)), 36573 ^ _781215 : [(36580 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468507), c_Orderings_Otop__class_Otop(tc_fun(_1468507, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1468507), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468507, tc_HOL_Obool)), _1468509))))], (36574 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468507), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468507, tc_HOL_Obool)), _1468509))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1468507), c_Orderings_Otop__class_Otop(tc_fun(_1468507, tc_HOL_Obool)))))]]], (35575 ^ _781215) ^ [_1449737, _1449739] : [class_Groups_Oordered__ab__group__add(_1449737), -(hAPP(c_Set_Oimage(_1449737, _1449737, c_Groups_Ouminus__class_Ouminus(_1449737)), hAPP(c_SetInterval_Oord__class_OlessThan(_1449737), _1449739)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1449737), hAPP(c_Groups_Ouminus__class_Ouminus(_1449737), _1449739)))], (14520 ^ _781215) ^ [_1035147, _1035149, _1035151, _1035153, _1035155, _1035157] : [-(hBOOL(hAPP(_1035147, _1035149))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1035151), _1035149), _1035153), _1035155)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1035147, _1035157, _1035151)), _1035149), _1035153), _1035155)))], (15258 ^ _781215) ^ [] : [-(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))))], (48848 ^ _781215) ^ [_1767475, _1767477] : [-(c_Random_Opick(_1767475, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1767475), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1767475, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1767475, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1767475)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1767477)) = c_Random_Opick(_1767475, _1767477))], (38173 ^ _781215) ^ [_1508044, _1508046, _1508048, _1508050] : [-(c_HOL_OThe(tc_prod(_1508044, _1508046), hAPP(c_Product__Type_Oprod_Oprod__case(_1508044, _1508046, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1508044, tc_fun(_1508046, tc_HOL_Obool), tc_fun(_1508046, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1508046, tc_HOL_Obool), tc_fun(_1508046, tc_HOL_Obool)), _1508044), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1508046)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508044), c_fconj), hAPP(c_fequal, _1508048)))), hAPP(c_fequal, _1508050)))) = hAPP(hAPP(c_Product__Type_OPair(_1508044, _1508046), _1508048), _1508050))], (36173 ^ _781215) ^ [_1461287, _1461289] : [-(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), _1461287)), _1461289))))], (20671 ^ _781215) ^ [_1152088] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1152088)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1152088))))], (17369 ^ _781215) ^ [_1092309] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1092309)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39122 ^ _781215) ^ [_1532446, _1532448, _1532450, _1532452, _1532454] : [c_Finite__Set_Ofun__left__comm__idem(_1532446, _1532448, _1532450), -(hAPP(hAPP(_1532450, _1532452), hAPP(hAPP(_1532450, _1532452), _1532454)) = hAPP(hAPP(_1532450, _1532452), _1532454))], (17667 ^ _781215) ^ [_1097000] : [hBOOL(hAPP(_1097000, 17668 ^ [_1097000])), 17671 ^ _781215 : [(17672 ^ _781215) ^ [_1097094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1097094)), -(hBOOL(hAPP(_1097000, hAPP(c_Int_Onat, _1097094))))]]], (22294 ^ _781215) ^ [_1183537, _1183539, _1183541, _1183543, _1183545, _1183547] : [class_Divides_Osemiring__div(_1183537), c_Divides_Odiv__class_Omod(_1183537, _1183539, _1183541) = c_Divides_Odiv__class_Omod(_1183537, _1183543, _1183541), c_Divides_Odiv__class_Omod(_1183537, _1183545, _1183541) = c_Divides_Odiv__class_Omod(_1183537, _1183547, _1183541), -(c_Divides_Odiv__class_Omod(_1183537, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183537), _1183539), _1183545), _1183541) = c_Divides_Odiv__class_Omod(_1183537, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183537), _1183543), _1183547), _1183541))], (40122 ^ _781215) ^ [_1564551, _1564553] : [-(hAPP(c_Relation_ODomain(_1564551, _1564553), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564551, _1564553), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1564551, tc_HOL_Obool)))], (45552 ^ _781215) ^ [_1695664, _1695666, _1695668] : [class_Orderings_Olinorder(_1695664), c_List_Olinorder__class_Osorted(_1695664, _1695666), -(c_List_Olinorder__class_Osorted(_1695664, c_List_Olinorder__class_Oinsort__insert__key(_1695664, _1695664, c_COMBI(_1695664), _1695668, _1695666)))], (8384 ^ _781215) ^ [_922884, _922886, _922888, _922890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_922884, tc_HOL_Obool)), _922886), hAPP(hAPP(c_Set_Oinsert(_922884), _922888), _922890))), 8387 ^ _781215 : [(8394 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_922884), _922888), _922890))), 8397 ^ _781215 : [(8404 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_922884), _922888), _922886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922884, tc_HOL_Obool)), _922886), _922890)))], (8398 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_922884), _922888), _922886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_922884, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922884, tc_HOL_Obool)), _922886), hAPP(hAPP(c_Set_Oinsert(_922884), _922888), c_Orderings_Obot__class_Obot(tc_fun(_922884, tc_HOL_Obool))))), _922890)))]]], (8388 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_922884), _922888), _922890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_922884, tc_HOL_Obool)), _922886), _922890)))]]], (22390 ^ _781215) ^ [_1185633, _1185635, _1185637] : [class_Divides_Oring__div(_1185633), -(c_Divides_Odiv__class_Omod(_1185633, hAPP(c_Groups_Ouminus__class_Ouminus(_1185633), _1185635), _1185637) = c_Divides_Odiv__class_Omod(_1185633, hAPP(c_Groups_Ouminus__class_Ouminus(_1185633), c_Divides_Odiv__class_Omod(_1185633, _1185635, _1185637)), _1185637))], (17696 ^ _781215) ^ [_1097506] : [-(hBOOL(hAPP(_1097506, 17703 ^ [_1097506]))), 17697 ^ _781215 : [(17698 ^ _781215) ^ [_1097558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1097558)), hBOOL(hAPP(_1097506, hAPP(c_Int_Onat, _1097558)))]]], (43327 ^ _781215) ^ [_1645229, _1645231, _1645233] : [class_Groups_Omonoid__add(_1645229), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1645229), hAPP(hAPP(c_List_Olist_OCons(_1645229), _1645231), _1645233)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1645229), _1645231), hAPP(c_List_Omonoid__add__class_Olistsum(_1645229), _1645233)))], (35160 ^ _781215) ^ [_1441339, _1441341, _1441343, _1441345] : [c_Fun_Oinj__on(_1441339, tc_Option_Ooption(_1441341), c_Map_Omap__add(_1441339, _1441341, _1441343, _1441345), c_Map_Odom(_1441339, _1441341, _1441345)), -(c_Fun_Oinj__on(_1441339, tc_Option_Ooption(_1441341), _1441345, c_Map_Odom(_1441339, _1441341, _1441345)))], (41857 ^ _781215) ^ [_1605583, _1605585, _1605587, _1605589] : [-(hBOOL(hAPP(hAPP(c_member(_1605583), _1605585), hAPP(c_List_Oset(_1605583), _1605587)))), hBOOL(hAPP(hAPP(c_member(_1605583), _1605585), hAPP(c_List_Oset(_1605583), c_List_Oremove1(_1605583, _1605589, _1605587))))], (23094 ^ _781215) ^ [_1197417, _1197419] : [c_Nat__Transfer_Onat__set(_1197417), c_Nat__Transfer_Onat__set(_1197419), 23101 ^ _781215 : [(23108 ^ _781215) ^ [] : [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), _1197417)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1197417), _1197419)))], (23102 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1197417), _1197419)), -(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), _1197417)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197419))))]]], (25398 ^ _781215) ^ [_1238784] : [class_Int_Onumber__ring(_1238784), c_Int_Oiszero(_1238784, hAPP(c_Int_Onumber__class_Onumber__of(_1238784), c_Int_OMin))], (19956 ^ _781215) ^ [_1139144, _1139146, _1139148] : [class_Orderings_Olinorder(_1139144), hBOOL(hAPP(c_Finite__Set_Ofinite(_1139144), _1139146)), 19963 ^ _781215 : [(19970 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1139144, tc_HOL_Obool)), _1139146), hAPP(hAPP(c_Set_Oinsert(_1139144), _1139148), c_Orderings_Obot__class_Obot(tc_fun(_1139144, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1139144, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1139144, hAPP(hAPP(c_Set_Oinsert(_1139144), _1139148), _1139146)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1139144), _1139148), c_Big__Operators_Olinorder__class_OMax(_1139144, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1139144, tc_HOL_Obool)), _1139146), hAPP(hAPP(c_Set_Oinsert(_1139144), _1139148), c_Orderings_Obot__class_Obot(tc_fun(_1139144, tc_HOL_Obool)))))))], (19964 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1139144, tc_HOL_Obool)), _1139146), hAPP(hAPP(c_Set_Oinsert(_1139144), _1139148), c_Orderings_Obot__class_Obot(tc_fun(_1139144, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1139144, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1139144, hAPP(hAPP(c_Set_Oinsert(_1139144), _1139148), _1139146)) = _1139148)]]], (36440 ^ _781215) ^ [_1466067] : [c_Orderings_Otop__class_Otop(tc_fun(_1466067, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1466067, tc_HOL_Obool))], (14578 ^ _781215) ^ [_1036289, _1036291, _1036293, _1036295, _1036297] : [-(hBOOL(hAPP(_1036289, _1036291))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1036293), _1036291), _1036295)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1036289, _1036297, _1036293)), _1036291), _1036295)))], (28016 ^ _781215) ^ [_1291624, _1291626, _1291628, _1291630] : [class_Fields_Ofield(_1291624), -(_1291626 = c_Groups_Ozero__class_Ozero(_1291624)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1291624), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291624), _1291628), _1291626)), _1291630) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291624), hAPP(hAPP(c_Power_Opower__class_Opower(_1291624), _1291628), _1291630)), hAPP(hAPP(c_Power_Opower__class_Opower(_1291624), _1291626), _1291630)))], (30271 ^ _781215) ^ [_1334922, _1334924, _1334926, _1334928] : [class_Orderings_Oorder(_1334922), 30274 ^ _781215 : [(30283 ^ _781215) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1334922, _1334924, _1334926) = hAPP(hAPP(c_Set_Oinsert(_1334922), _1334928), c_Orderings_Obot__class_Obot(tc_fun(_1334922, tc_HOL_Obool)))), _1334924 = _1334926, _1334926 = _1334928], (30275 ^ _781215) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1334922, _1334924, _1334926) = hAPP(hAPP(c_Set_Oinsert(_1334922), _1334928), c_Orderings_Obot__class_Obot(tc_fun(_1334922, tc_HOL_Obool))), 30278 ^ _781215 : [(30281 ^ _781215) ^ [] : [-(_1334926 = _1334928)], (30279 ^ _781215) ^ [] : [-(_1334924 = _1334926)]]]]], (1938 ^ _781215) ^ [_809322, _809324, _809326, _809328, _809330, _809332, _809334, _809336] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_809336, _809332, _809328, _809324) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_809334, _809330, _809326, _809322)), _809336 = _809334, _809332 = _809330, _809328 = _809326, _809324 = _809322], (39312 ^ _781215) ^ [_1537965, _1537967, _1537969, _1537971, _1537973, _1537975] : [c_Finite__Set_Ofun__left__comm__idem(_1537965, _1537967, _1537969), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537965), _1537971)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1537965, _1537967, _1537969), _1537973), hAPP(hAPP(c_Set_Oinsert(_1537965), _1537975), _1537971)) = hAPP(hAPP(c_Finite__Set_Ofold(_1537965, _1537967, _1537969), hAPP(hAPP(_1537969, _1537975), _1537973)), _1537971))], (36438 ^ _781215) ^ [_1466010, _1466012] : [-(c_Sum__Type_OPlus(_1466010, _1466012, c_Orderings_Otop__class_Otop(tc_fun(_1466010, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1466012, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1466010, _1466012), tc_HOL_Obool)))], (40573 ^ _781215) ^ [_1576176, _1576178] : [class_Complete__Lattice_Ocomplete__lattice(_1576176), -(c_Complete__Lattice_OSup__class_OSup(_1576176, _1576178) = c_Complete__Lattice_OInf__class_OInf(_1576176, hAPP(c_Set_OCollect(_1576176), hAPP(hAPP(c_COMBB(tc_fun(_1576176, tc_HOL_Obool), tc_HOL_Obool, _1576176), c_HOL_OAll(_1576176)), hAPP(hAPP(c_COMBB(tc_fun(_1576176, tc_HOL_Obool), tc_fun(_1576176, tc_HOL_Obool), _1576176), hAPP(c_COMBS(_1576176, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1576176), c_fimplies), hAPP(hAPP(c_COMBC(_1576176, tc_fun(_1576176, tc_HOL_Obool), tc_HOL_Obool), c_member(_1576176)), _1576178)))), hAPP(c_COMBC(_1576176, _1576176, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1576176)))))))], (21386 ^ _781215) ^ [_1165062, _1165064] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1165062) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1165064), -(_1165062 = _1165064)], (47152 ^ _781215) ^ [_1730032, _1730034, _1730036] : [class_Enum_Oenum(_1730032), class_Enum_Oenum(_1730034), 47159 ^ _781215 : [(47166 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1730034), hAPP(hAPP(c_COMBB(tc_fun(_1730032, tc_HOL_Obool), tc_HOL_Obool, _1730034), c_Enum_Oenum__class_Oenum__all(_1730032)), hAPP(hAPP(c_COMBB(tc_fun(_1730032, tc_prod(_1730034, _1730032)), tc_fun(_1730032, tc_HOL_Obool), _1730034), hAPP(c_COMBB(tc_prod(_1730034, _1730032), tc_HOL_Obool, _1730032), _1730036)), c_Product__Type_OPair(_1730034, _1730032))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1730034, _1730032)), _1730036)))], (47160 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1730034, _1730032)), _1730036)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1730034), hAPP(hAPP(c_COMBB(tc_fun(_1730032, tc_HOL_Obool), tc_HOL_Obool, _1730034), c_Enum_Oenum__class_Oenum__all(_1730032)), hAPP(hAPP(c_COMBB(tc_fun(_1730032, tc_prod(_1730034, _1730032)), tc_fun(_1730032, tc_HOL_Obool), _1730034), hAPP(c_COMBB(tc_prod(_1730034, _1730032), tc_HOL_Obool, _1730032), _1730036)), c_Product__Type_OPair(_1730034, _1730032))))))]]], (21107 ^ _781215) ^ [_1159066, _1159068] : [class_Int_Onumber__ring(_1159066), class_Rings_Olinordered__idom(_1159066), 21114 ^ _781215 : [(21121 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159068), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159066), hAPP(c_Int_Onumber__class_Onumber__of(_1159066), _1159068)), c_Groups_Oone__class_Oone(_1159066))))], (21115 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159066), hAPP(c_Int_Onumber__class_Onumber__of(_1159066), _1159068)), c_Groups_Oone__class_Oone(_1159066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159068), c_Int_OBit1(c_Int_OPls))))]]], (24168 ^ _781215) ^ [_1217124, _1217126] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217124), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1217126)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1217124), 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)))), _1217126)))], (46309 ^ _781215) ^ [_1710734, _1710736, _1710738] : [-(hAPP(c_List_Orev(_1710734), hAPP(hAPP(c_List_Otake(_1710734), _1710736), _1710738)) = hAPP(hAPP(c_List_Odrop(_1710734), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710734)), _1710738)), _1710736)), hAPP(c_List_Orev(_1710734), _1710738)))], (16259 ^ _781215) ^ [_1068567, _1068569, _1068571] : [class_Lattices_Osemilattice__sup(_1068567), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068567), _1068569), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068567), _1068571), _1068569))))], (2410 ^ _781215) ^ [_816848, _816850, _816852, _816854] : [-(c_Divides_OnegDivAlg(_816854, _816850) = c_Divides_OnegDivAlg(_816852, _816848)), _816854 = _816852, _816850 = _816848], (47192 ^ _781215) ^ [_1730910, _1730912] : [class_Enum_Oenum(_1730910), 47195 ^ _781215 : [(47196 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1730910)), _1730912)), -(hBOOL(hAPP(_1730912, c_Option_Ooption_ONone(_1730910)))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1730910), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1730910), tc_HOL_Obool, _1730910), _1730912), c_Option_Ooption_OSome(_1730910)))))], (47206 ^ _781215) ^ [] : [47207 ^ _781215 : [(47210 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1730910), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1730910), tc_HOL_Obool, _1730910), _1730912), c_Option_Ooption_OSome(_1730910))))], (47208 ^ _781215) ^ [] : [hBOOL(hAPP(_1730912, c_Option_Ooption_ONone(_1730910)))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1730910)), _1730912)))]]], (37560 ^ _781215) ^ [_1494582] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494582, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1494582, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1494582, tc_HOL_Obool)))], (11590 ^ _781215) ^ [_983611, _983613, _983615, _983617] : [-(c_Nitpick_Ofold__graph_H(_983611, _983613, _983615, _983617, c_Orderings_Obot__class_Obot(tc_fun(_983611, tc_HOL_Obool)), _983617))], (2492 ^ _781215) ^ [_818225, _818227, _818229, _818231] : [-(c_Divides_OposDivAlg(_818231, _818227) = c_Divides_OposDivAlg(_818229, _818225)), _818231 = _818229, _818227 = _818225], (5911 ^ _781215) ^ [_875361, _875363] : [-(_875361 = hAPP(c_Option_Ooption_OSome(_875363), 5912 ^ [_875361, _875363])), -(_875361 = c_Option_Ooption_ONone(_875363))], (28732 ^ _781215) ^ [_1304930, _1304932] : [class_Fields_Olinordered__field__inverse__zero(_1304930), class_Int_Onumber__ring(_1304930), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304930), c_Groups_Ozero__class_Ozero(_1304930)), _1304932)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304930), c_Groups_Ozero__class_Ozero(_1304930)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304930), _1304932), hAPP(c_Int_Onumber__class_Onumber__of(_1304930), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (43293 ^ _781215) ^ [_1644510, _1644512] : [class_Groups_Ocomm__monoid__add(_1644510), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1644510), _1644512) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1644510), hAPP(c_List_Onth(_1644510), _1644512)), 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(_1644510)), _1644512))))], (21614 ^ _781215) ^ [_1168983, _1168985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1168983), _1168985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1168983)), c_Int_OBit1(_1168985))))], (15546 ^ _781215) ^ [_1053947, _1053949, _1053951, _1053953] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1053947, _1053949, _1053951), _1053953), c_Orderings_Obot__class_Obot(tc_fun(_1053947, tc_HOL_Obool))) = _1053953)], (41313 ^ _781215) ^ [_1592859, _1592861, _1592863, _1592865, _1592867, _1592869] : [-(hAPP(hAPP(c_Fun_Ocomp(_1592859, _1592861, _1592863, _1592865), _1592867), _1592869) = hAPP(_1592865, hAPP(_1592867, _1592869)))], (26310 ^ _781215) ^ [_1258582, _1258584] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1258582, _1258584)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1258584), _1258582))], (4360 ^ _781215) ^ [_847351, _847353, _847355, _847357] : [-(c_Relation_OId__on(_847357, _847353) = c_Relation_OId__on(_847355, _847351)), _847357 = _847355, _847353 = _847351], (38528 ^ _781215) ^ [_1517374, _1517376, _1517378, _1517380, _1517382] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1517374, _1517376), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517374, tc_HOL_Obool)), _1517378), _1517380)), hAPP(c_COMBK(tc_fun(_1517376, tc_HOL_Obool), _1517374), _1517382)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517374, _1517376), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517374, _1517376), _1517378), hAPP(c_COMBK(tc_fun(_1517376, tc_HOL_Obool), _1517374), _1517382))), hAPP(hAPP(c_Product__Type_OSigma(_1517374, _1517376), _1517380), hAPP(c_COMBK(tc_fun(_1517376, tc_HOL_Obool), _1517374), _1517382))))], (24768 ^ _781215) ^ [_1228253, _1228255, _1228257] : [class_Rings_Olinordered__semidom(_1228253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228253), c_Groups_Ozero__class_Ozero(_1228253)), _1228255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228253), c_Groups_Ozero__class_Ozero(_1228253)), hAPP(hAPP(c_Power_Opower__class_Opower(_1228253), _1228255), _1228257))))], (46554 ^ _781215) ^ [_1717279, _1717281, _1717283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717279)), c_List_OtakeWhile(_1717279, _1717281, _1717283))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717279)), _1717283))), hBOOL(hAPP(_1717281, hAPP(hAPP(c_List_Onth(_1717279), _1717283), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717279)), c_List_OtakeWhile(_1717279, _1717281, _1717283)))))], (40461 ^ _781215) ^ [_1573575, _1573577] : [c_Wellfounded_Owf(_1573575, _1573577), -(c_Wellfounded_Oacyclic(_1573575, _1573577))], (31028 ^ _781215) ^ [_1349066, _1349068, _1349070, _1349072, _1349074] : [class_Orderings_Olinorder(_1349066), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1349066, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349066, _1349068), _1349070)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349066, _1349072), _1349074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349066), _1349070), _1349068))), 31039 ^ _781215 : [(31042 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349066), _1349070), _1349074)))], (31040 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349066), _1349072), _1349068)))]]], (43199 ^ _781215) ^ [_1641837, _1641839, _1641841] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1641837)), _1641839), c_Wellfounded_Oacc(tc_List_Olist(_1641837), c_List_Olistrel1(_1641837, _1641841)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1641837)), _1641839), c_List_Olists(_1641837, c_Wellfounded_Oacc(_1641837, _1641841)))))], (4446 ^ _781215) ^ [_848660, _848662] : [_848662 = _848660, -(c_New__DSequence_Opos__not__seq(_848662) = c_New__DSequence_Opos__not__seq(_848660))], (49978 ^ _781215) ^ [_1794772, _1794774] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794772, _1794772), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1794774) = _1794774)], (51202 ^ _781215) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (34145 ^ _781215) ^ [_1419298, _1419300, _1419302, _1419304, _1419306, _1419308] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419298, tc_fun(_1419300, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1419298, tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_fun(_1419300, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419300, tc_fun(tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_fun(_1419300, tc_HOL_Obool)), _1419298), c_COMBC(_1419300, tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419300, tc_prod(_1419298, _1419300)), tc_fun(_1419300, tc_fun(tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_HOL_Obool)), _1419298), hAPP(c_COMBB(tc_prod(_1419298, _1419300), tc_fun(tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_HOL_Obool), _1419300), c_member(tc_prod(_1419298, _1419300)))), c_Product__Type_OPair(_1419298, _1419300)))), _1419302)), hAPP(hAPP(c_COMBC(_1419298, tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_fun(_1419300, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419300, tc_fun(tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_fun(_1419300, tc_HOL_Obool)), _1419298), c_COMBC(_1419300, tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419300, tc_prod(_1419298, _1419300)), tc_fun(_1419300, tc_fun(tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_HOL_Obool)), _1419298), hAPP(c_COMBB(tc_prod(_1419298, _1419300), tc_fun(tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool), tc_HOL_Obool), _1419300), c_member(tc_prod(_1419298, _1419300)))), c_Product__Type_OPair(_1419298, _1419300)))), _1419304)), _1419306), _1419308)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1419298, _1419300)), hAPP(hAPP(c_Product__Type_OPair(_1419298, _1419300), _1419306), _1419308)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1419298, _1419300), tc_HOL_Obool)), _1419302), _1419304))))], (7682 ^ _781215) ^ [_910441, _910443, _910445] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_910441), _910443)), hBOOL(hAPP(hAPP(c_member(_910441), _910445), _910443)), -(hAPP(c_Finite__Set_Ocard(_910441), _910443) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_910441), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910441, tc_HOL_Obool)), _910443), hAPP(hAPP(c_Set_Oinsert(_910441), _910445), c_Orderings_Obot__class_Obot(tc_fun(_910441, tc_HOL_Obool)))))))], (50816 ^ _781215) ^ [_1813962] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1813962))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1813962)))], (42447 ^ _781215) ^ [_1621995, _1621997, _1621999, _1622001, _1622003, _1622005] : [-(_1621995 = _1621997), -(hAPP(hAPP(c_Map_Omap__of(_1621999, _1622001), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1621999, _1622001)), hAPP(hAPP(c_Product__Type_OPair(_1621999, _1622001), _1621995), _1622003)), _1622005)), _1621997) = hAPP(hAPP(c_Map_Omap__of(_1621999, _1622001), _1622005), _1621997))], (33200 ^ _781215) ^ [_1398054, _1398056, _1398058, _1398060] : [hBOOL(hAPP(hAPP(c_member(_1398054), _1398056), _1398058)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398054, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1398054), _1398056), _1398060)), _1398058) = hAPP(hAPP(c_Set_Oinsert(_1398054), _1398056), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398054, tc_HOL_Obool)), _1398060), _1398058)))], (51160 ^ _781215) ^ [_1820587, _1820589] : [-(class_Enum_Oenum(tc_fun(_1820587, _1820589))), class_Enum_Oenum(_1820587), class_Enum_Oenum(_1820589)], (8640 ^ _781215) ^ [_927790, _927792, _927794] : [class_Rings_Oring(_927790), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927790), hAPP(c_Groups_Ouminus__class_Ouminus(_927790), _927792)), _927794) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927790), _927792), hAPP(c_Groups_Ouminus__class_Ouminus(_927790), _927794)))], (44754 ^ _781215) ^ [_1678977, _1678979, _1678981, _1678983, _1678985] : [-(hAPP(hAPP(c_List_Ozip(_1678977, _1678979), hAPP(hAPP(c_List_Oappend(_1678977), _1678981), _1678983)), _1678985) = hAPP(hAPP(c_List_Oappend(tc_prod(_1678977, _1678979)), hAPP(hAPP(c_List_Ozip(_1678977, _1678979), _1678981), hAPP(hAPP(c_List_Otake(_1678979), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678977)), _1678981)), _1678985))), hAPP(hAPP(c_List_Ozip(_1678977, _1678979), _1678983), hAPP(hAPP(c_List_Odrop(_1678979), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678977)), _1678981)), _1678985))))], (38183 ^ _781215) ^ [_1508374, _1508376, _1508378] : [-(c_HOL_OThe(tc_prod(_1508374, _1508376), hAPP(c_Product__Type_Oprod_Oprod__case(_1508374, _1508376, tc_HOL_Obool), _1508378)) = c_HOL_OThe(tc_prod(_1508374, _1508376), hAPP(hAPP(c_COMBS(tc_prod(_1508374, _1508376), _1508376, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1508374, tc_fun(_1508376, tc_HOL_Obool), tc_prod(_1508374, _1508376)), _1508378), c_Product__Type_Ofst(_1508374, _1508376))), c_Product__Type_Osnd(_1508374, _1508376))))], (36784 ^ _781215) ^ [_1473261, _1473263, _1473265, _1473267] : [c_Fun_Oinj__on(_1473261, _1473263, _1473265, c_Orderings_Otop__class_Otop(tc_fun(_1473261, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473263, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1473261, _1473263, _1473265), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1473261, tc_HOL_Obool)), _1473267))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1473263, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1473261, _1473263, _1473265), _1473267)))))], (48461 ^ _781215) ^ [_1759787, _1759789, _1759791] : [48463 ^ _781215 : [(48468 ^ _781215) ^ [] : [hBOOL(hAPP(_1759789, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 48462 ^ [_1759787, _1759789, _1759791]), _1759787)))], (48466 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1759789, 48462 ^ [_1759787, _1759789, _1759791])))], (48464 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48462 ^ [_1759787, _1759789, _1759791]), _1759787)))]], hBOOL(hAPP(_1759789, _1759791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1759791), _1759787)), -(hBOOL(hAPP(_1759789, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4422 ^ _781215) ^ [_848274, _848276] : [_848276 = _848274, -(c_List_Orotate1(_848276) = c_List_Orotate1(_848274))], (50846 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (20364 ^ _781215) ^ [_1146755] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1146755) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1146755 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10524 ^ _781215) ^ [_961118, _961120, _961122, _961124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961118, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_961118), _961120), _961122)), _961124)), 10527 ^ _781215 : [(10530 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961118, tc_HOL_Obool)), _961122), _961124)))], (10528 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_961118), _961120), _961124)))]]], (37219 ^ _781215) ^ [_1486127, _1486129, _1486131, _1486133, _1486135] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486127, tc_fun(_1486129, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1486127, tc_HOL_Obool)), _1486131), _1486133)), _1486135) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1486129, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486127, tc_fun(_1486129, tc_HOL_Obool)), _1486131), _1486135)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486127, tc_fun(_1486129, tc_HOL_Obool)), _1486133), _1486135)))], (41667 ^ _781215) ^ [_1601152, _1601154, _1601156, _1601158, _1601160, _1601162] : [c_Finite__Set_Ofolding(_1601152, _1601154, _1601156, _1601158), hBOOL(hAPP(c_Finite__Set_Ofinite(_1601152), _1601160)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1601152), _1601162)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1601152, tc_HOL_Obool)), _1601160), _1601162) = c_Orderings_Obot__class_Obot(tc_fun(_1601152, tc_HOL_Obool)), -(hAPP(_1601158, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1601152, tc_HOL_Obool)), _1601160), _1601162)) = hAPP(c_Fun_Ocomp(_1601154, _1601154, _1601154, hAPP(_1601158, _1601160)), hAPP(_1601158, _1601162)))], (16744 ^ _781215) ^ [_1081494, _1081496, _1081498, _1081500] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1081494, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1081494, tc_fun(_1081494, tc_HOL_Obool), tc_HOL_Obool), c_member(_1081494)), _1081496)), hAPP(hAPP(c_COMBC(_1081494, tc_fun(_1081494, tc_HOL_Obool), tc_HOL_Obool), c_member(_1081494)), _1081498)), _1081500)), -(hBOOL(hAPP(hAPP(c_member(_1081494), _1081500), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1081494, tc_HOL_Obool)), _1081496), _1081498))))], (46932 ^ _781215) ^ [_1725431, _1725433] : [class_Orderings_Olinorder(_1725431), -(c_List_Olinorder__class_Osort__key(_1725431, _1725431, c_COMBI(_1725431), _1725433) = hAPP(c_List_Ofoldl(tc_List_Olist(_1725431), _1725431, hAPP(c_COMBC(_1725431, tc_List_Olist(_1725431), tc_List_Olist(_1725431)), c_List_Olinorder__class_Oinsort__key(_1725431, _1725431, c_COMBI(_1725431))), c_List_Olist_ONil(_1725431)), _1725433))], (20490 ^ _781215) ^ [_1149019, _1149021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1149019), _1149021)), -(_1149021 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149019), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20493 ^ [_1149019, _1149021])))], (8718 ^ _781215) ^ [_929103, _929105, _929107, _929109, _929111] : [-(c_Map_Omap__add(_929103, _929105, _929107, c_Map_Omap__add(_929103, _929105, _929109, _929111)) = c_Map_Omap__add(_929103, _929105, c_Map_Omap__add(_929103, _929105, _929107, _929109), _929111))], (23660 ^ _781215) ^ [_1207705, _1207707, _1207709] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1207705), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1207707, _1207709)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1207705), _1207707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1207705), _1207709)))], (45165 ^ _781215) ^ [_1687391, _1687393, _1687395, _1687397] : [-(_1687391 = c_List_Olist_ONil(_1687393)), -(c_List_Olast(_1687395, hAPP(hAPP(c_List_Omap(_1687393, _1687395), _1687397), _1687391)) = hAPP(_1687397, c_List_Olast(_1687393, _1687391)))], (51662 ^ _781215) ^ [_1825519] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1825519)))], (51330 ^ _781215) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (24174 ^ _781215) ^ [_1217252, _1217254] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1217252))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1217254)) = 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)))), _1217252), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1217254)))], (15390 ^ _781215) ^ [_1051011, _1051013, _1051015] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1051011), _1051013)), _1051015) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1051011), _1051015)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1051013), _1051015)))], (1468 ^ _781215) ^ [_802535, _802537] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_802535)), _802537 = _802535, class_Groups_Oordered__cancel__ab__semigroup__add(_802537)], (11990 ^ _781215) ^ [_989436, _989438, _989440] : [11991 ^ _781215 : [(11994 ^ _781215) ^ [] : [_989436 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11992 ^ _781215) ^ [] : [_989438 = _989440]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989436), _989438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989436), _989440))], (34776 ^ _781215) ^ [_1432892, _1432894, _1432896] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1432892), _1432894)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432892, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1432892, _1432892, _1432896), _1432894)), _1432894)), c_Fun_Oinj__on(_1432892, _1432892, _1432896, _1432894), -(hAPP(c_Set_Oimage(_1432892, _1432892, _1432896), _1432894) = _1432894)], (45381 ^ _781215) ^ [_1691929, _1691931] : [c_List_Otranspose(_1691929, _1691931) = c_List_Olist_ONil(tc_List_Olist(_1691929)), 45384 ^ _781215 : [(45385 ^ _781215) ^ [_1692024] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1691929)), _1692024), hAPP(c_List_Oset(tc_List_Olist(_1691929)), _1691931))), -(_1692024 = c_List_Olist_ONil(_1691929))]]], (38718 ^ _781215) ^ [_1522902, _1522904, _1522906, _1522908] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1522902), _1522904)), 38724 ^ _781215 : [(38727 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1522906), hAPP(_1522908, 38723 ^ [_1522902, _1522904, _1522906, _1522908])))], (38725 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1522902), 38723 ^ [_1522902, _1522904, _1522906, _1522908]), _1522904)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1522902, _1522906)), hAPP(hAPP(c_Product__Type_OSigma(_1522902, _1522906), _1522904), _1522908))))], (42603 ^ _781215) ^ [_1626702, _1626704, _1626706, _1626708] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1626702), tc_List_Olist(_1626702))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626702), tc_List_Olist(_1626702)), _1626704), _1626706)), c_List_Olex(_1626702, _1626708)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1626702), tc_List_Olist(_1626702))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626702), tc_List_Olist(_1626702)), _1626704), _1626706)), c_List_Olexord(_1626702, _1626708))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626702)), _1626704) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626702)), _1626706)], (35553 ^ _781215) ^ [_1449304, _1449306] : [class_Orderings_Olinorder(_1449304), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1449304, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1449304), _1449306)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1449304), _1449306))], (2132 ^ _781215) ^ [_812445, _812447, _812449, _812451] : [-(c_SMT_Oz3div(_812451, _812447) = c_SMT_Oz3div(_812449, _812445)), _812451 = _812449, _812447 = _812445], (8410 ^ _781215) ^ [_923411, _923413, _923415, _923417] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_923411, tc_HOL_Obool)), _923413), hAPP(hAPP(c_Set_Oinsert(_923411), _923415), _923417)))), 8413 ^ _781215 : [(8416 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_923411, tc_HOL_Obool)), _923413), _923417))], (8414 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_923411), _923415), _923417)))]], 8417 ^ _781215 : [(8420 ^ _781215) ^ [] : [8421 ^ _781215 : [(8424 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_923411, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923411, tc_HOL_Obool)), _923413), hAPP(hAPP(c_Set_Oinsert(_923411), _923415), c_Orderings_Obot__class_Obot(tc_fun(_923411, tc_HOL_Obool))))), _923417))], (8422 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_923411), _923415), _923413)))]], 8425 ^ _781215 : [(8428 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_923411, tc_HOL_Obool)), _923413), _923417))], (8426 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_923411), _923415), _923413))]]], (8418 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_923411), _923415), _923417))]]], (39840 ^ _781215) ^ [_1556983, _1556985, _1556987, _1556989] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1556983, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1556983, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1556985, _1556983), _1556987)), hAPP(c_Relation_ORange(_1556985, _1556983), _1556989))), hAPP(c_Relation_ORange(_1556985, _1556983), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1556985, _1556983), tc_HOL_Obool)), _1556987), _1556989)))))], (16009 ^ _781215) ^ [_1063704, _1063706, _1063708, _1063710] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063704, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063704, tc_HOL_Obool)), _1063706), _1063708)), _1063710) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063704, tc_HOL_Obool)), _1063706), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063704, tc_HOL_Obool)), _1063708), _1063710)))], (41629 ^ _781215) ^ [_1600336, _1600338, _1600340, _1600342, _1600344, _1600346] : [c_Finite__Set_Ofolding(_1600336, _1600338, _1600340, _1600342), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600336), _1600344)), -(hBOOL(hAPP(hAPP(c_member(_1600336), _1600346), _1600344))), -(hAPP(_1600342, hAPP(hAPP(c_Set_Oinsert(_1600336), _1600346), _1600344)) = hAPP(c_Fun_Ocomp(_1600338, _1600338, _1600338, hAPP(_1600342, _1600344)), hAPP(_1600340, _1600346)))], (28712 ^ _781215) ^ [_1304580, _1304582] : [class_Fields_Olinordered__field__inverse__zero(_1304580), class_Int_Onumber__ring(_1304580), 28719 ^ _781215 : [(28726 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304580), c_Groups_Ozero__class_Ozero(_1304580)), _1304582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304580), c_Groups_Ozero__class_Ozero(_1304580)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304580), _1304582), hAPP(c_Int_Onumber__class_Onumber__of(_1304580), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (28720 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304580), c_Groups_Ozero__class_Ozero(_1304580)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304580), _1304582), hAPP(c_Int_Onumber__class_Onumber__of(_1304580), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304580), c_Groups_Ozero__class_Ozero(_1304580)), _1304582)))]]], (3764 ^ _781215) ^ [_838239, _838241, _838243, _838245] : [-(c_List_Oremdups(_838245, _838241) = c_List_Oremdups(_838243, _838239)), _838245 = _838243, _838241 = _838239], (15432 ^ _781215) ^ [_1051802, _1051804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051802), _1051804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051802), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1051804), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (8940 ^ _781215) ^ [_932888, _932890, _932892] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_932888, tc_HOL_Obool)), _932890) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_932888, tc_HOL_Obool)), _932892), -(_932890 = _932892)], (23905 ^ _781215) ^ [_1212168, _1212170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1212170), _1212168))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1212170), _1212168) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212170), _1212168)), _1212168)))], (29974 ^ _781215) ^ [_1328127, _1328129, _1328131, _1328133] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1328127, tc_HOL_Obool), tc_fun(_1328127, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1328127, tc_HOL_Obool), tc_fun(_1328127, tc_HOL_Obool)), _1328131), _1328133)), c_Wellfounded_Omax__ext(_1328127, _1328129))), -(c_Wellfounded_Omax__extp(_1328127, hAPP(hAPP(c_COMBC(_1328127, tc_fun(tc_prod(_1328127, _1328127), tc_HOL_Obool), tc_fun(_1328127, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1328127, tc_fun(tc_fun(tc_prod(_1328127, _1328127), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1328127, _1328127), tc_HOL_Obool), tc_fun(_1328127, tc_HOL_Obool)), _1328127), c_COMBC(_1328127, tc_fun(tc_prod(_1328127, _1328127), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1328127, tc_prod(_1328127, _1328127)), tc_fun(_1328127, tc_fun(tc_fun(tc_prod(_1328127, _1328127), tc_HOL_Obool), tc_HOL_Obool)), _1328127), hAPP(c_COMBB(tc_prod(_1328127, _1328127), tc_fun(tc_fun(tc_prod(_1328127, _1328127), tc_HOL_Obool), tc_HOL_Obool), _1328127), c_member(tc_prod(_1328127, _1328127)))), c_Product__Type_OPair(_1328127, _1328127)))), _1328129), _1328131, _1328133))], (1628 ^ _781215) ^ [_804535, _804537] : [-(class_Rings_Oordered__semiring(_804535)), _804537 = _804535, class_Rings_Oordered__semiring(_804537)], (22617 ^ _781215) ^ [_1189592, _1189594] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189592, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1189594)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189592, _1189594) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (33114 ^ _781215) ^ [_1396176, _1396178, _1396180, _1396182, _1396184] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396176, tc_fun(_1396178, tc_HOL_Obool)), _1396180), hAPP(hAPP(c_COMBB(tc_fun(_1396178, tc_HOL_Obool), tc_fun(_1396178, tc_HOL_Obool), _1396176), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396178, tc_HOL_Obool)), _1396182)), _1396184)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396178, tc_HOL_Obool)), _1396182), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396176, tc_fun(_1396178, tc_HOL_Obool)), _1396180), _1396184)))], (22282 ^ _781215) ^ [_1183267, _1183269, _1183271, _1183273] : [class_Divides_Osemiring__div(_1183267), -(c_Divides_Odiv__class_Omod(_1183267, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183267), _1183269), c_Divides_Odiv__class_Omod(_1183267, _1183271, _1183273)), _1183273) = c_Divides_Odiv__class_Omod(_1183267, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183267), _1183269), _1183271), _1183273))], (27034 ^ _781215) ^ [_1272529, _1272531, _1272533, _1272535, _1272537] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1272529, _1272531), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1272533), _1272535))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1272531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1272537)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1272529, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1272531), _1272537)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1272533), _1272537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1272531), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1272533, _1272537))), _1272535)))))], (36197 ^ _781215) ^ [_1461693, _1461695] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1461693), hAPP(hAPP(c_Power_Opower__class_Opower(_1461693), hAPP(c_Int_Onumber__class_Onumber__of(_1461693), c_Int_OMin)), _1461695)) = c_Groups_Oone__class_Oone(_1461693)), class_Int_Onumber__ring(_1461693), class_Rings_Olinordered__idom(_1461693)], (51442 ^ _781215) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (36983 ^ _781215) ^ [_1479434, _1479436, _1479438, _1479440] : [hBOOL(hAPP(hAPP(c_member(_1479436), _1479440), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479434, tc_fun(_1479436, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1479434, tc_HOL_Obool))), _1479438))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479434, tc_fun(_1479436, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1479434, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1479436, tc_HOL_Obool), tc_fun(_1479436, tc_HOL_Obool), _1479434), hAPP(c_COMBC(_1479436, tc_fun(_1479436, tc_HOL_Obool), tc_HOL_Obool), c_member(_1479436))), _1479438)), _1479440)))], (49966 ^ _781215) ^ [_1794472, _1794474, _1794476] : [c_Wellfounded_Owf(_1794472, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794472, _1794472), tc_HOL_Obool), _1794474), _1794476)), -(c_Wellfounded_Owf(_1794472, _1794476))], (5883 ^ _781215) ^ [_874830, _874832, _874834, _874836, _874838, _874840, _874842] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874830), _874832), _874834), _874836) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874830), _874838), _874840), _874842), 5886 ^ _781215 : [(5891 ^ _781215) ^ [] : [-(_874836 = _874842)], (5889 ^ _781215) ^ [] : [-(_874834 = _874840)], (5887 ^ _781215) ^ [] : [-(_874832 = _874838)]]], (1298 ^ _781215) ^ [_800410, _800412] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_800410)), _800412 = _800410, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_800412)], (35423 ^ _781215) ^ [_1446794, _1446796, _1446798] : [class_Orderings_Olinorder(_1446794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446794), _1446796), _1446798)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446794, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446794, _1446796), _1446798)), hAPP(c_SetInterval_Oord__class_OatLeast(_1446794), _1446798)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1446794), _1446796))], (39667 ^ _781215) ^ [_1552096, _1552098] : [-(hAPP(c_Set_Ovimage(_1552096, _1552096, c_Fun_Oid(_1552096)), _1552098) = _1552098)], (14300 ^ _781215) ^ [_1031315, _1031317] : [-(hBOOL(hAPP(_1031315, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1031315, _1031317)), 14308 ^ _781215 : [(14311 ^ _781215) ^ [_1031553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031553), 14307 ^ [_1031315, _1031317])), hBOOL(hAPP(_1031315, _1031553))], (14317 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1031315, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 14307 ^ [_1031315, _1031317]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (14309 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14307 ^ [_1031315, _1031317]), _1031317)))]]], (4950 ^ _781215) ^ [_856402, _856404, _856406, _856408] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_856408, _856404) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_856406, _856402)), _856408 = _856406, _856404 = _856402], (23678 ^ _781215) ^ [_1208092, _1208094, _1208096] : [-(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, _1208092, _1208094)), _1208096), _1208094) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1208092), _1208096), _1208094))], (18722 ^ _781215) ^ [_1116830, _1116832] : [class_Orderings_Olinorder(_1116830), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1116830), _1116832), _1116832) = _1116832)], (38556 ^ _781215) ^ [_1518354, _1518356] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518354, _1518354), tc_HOL_Obool)), c_Relation_OId__on(_1518354, _1518356)), hAPP(hAPP(c_Product__Type_OSigma(_1518354, _1518354), _1518356), hAPP(c_COMBK(tc_fun(_1518354, tc_HOL_Obool), _1518354), _1518356)))))], (13718 ^ _781215) ^ [_1020071, _1020073, _1020075, _1020077] : [class_Rings_Olinordered__ring__strict(_1020071), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020071), c_Groups_Ozero__class_Ozero(_1020071)), _1020073)), 13725 ^ _781215 : [(13732 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020071), _1020075), _1020077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020071), _1020073), _1020075)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020071), _1020073), _1020077))))], (13726 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020071), _1020073), _1020075)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020071), _1020073), _1020077))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020071), _1020075), _1020077)))]]], (10690 ^ _781215) ^ [_964229, _964231, _964233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964229), _964231)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964231), _964233)), _964229) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964231), _964229)), _964233))], (10884 ^ _781215) ^ [_968250, _968252, _968254] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_968250), _968252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_968250), _968252)), hAPP(c_Finite__Set_Ocard(_968250), hAPP(hAPP(c_Set_Oinsert(_968250), _968254), _968252)))))], (6138 ^ _781215) ^ [_879914] : [hAPP(c_Com_Ocom_OBODY, _879914) = c_Com_Ocom_OSKIP], (16043 ^ _781215) ^ [_1064553, _1064555, _1064557, _1064559] : [class_Lattices_Osemilattice__sup(_1064553), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064553), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064553), _1064555), _1064557)), _1064559) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064553), _1064555), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064553), _1064557), _1064559)))], (33515 ^ _781215) ^ [_1405293, _1405295, _1405297, _1405299, _1405301] : [class_Groups_Ocomm__monoid__mult(_1405293), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405295), _1405297)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405295), _1405299)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1405293), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405295, _1405293), _1405301), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405295, tc_HOL_Obool)), _1405297), _1405299))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405295, _1405293), _1405301), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1405295, tc_HOL_Obool)), _1405297), _1405299))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1405293), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405295, _1405293), _1405301), _1405297)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405295, _1405293), _1405301), _1405299)))], (38278 ^ _781215) ^ [_1510605, _1510607, _1510609, _1510611, _1510613] : [-(hAPP(c_Set_Ovimage(_1510605, _1510607, _1510609), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1510607, tc_HOL_Obool)), _1510611), _1510613)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1510605, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1510605, _1510607, _1510609), _1510611)), hAPP(c_Set_Ovimage(_1510605, _1510607, _1510609), _1510613)))], (24045 ^ _781215) ^ [_1214814, _1214816] : [class_Groups_Omonoid__mult(_1214814), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1214814), _1214816), 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(_1214814), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214814), _1214816), _1214816)), _1214816))], (13226 ^ _781215) ^ [_1011232] : [-(hAPP(c_Finite__Set_Ocard(_1011232), c_Orderings_Obot__class_Obot(tc_fun(_1011232, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7794 ^ _781215) ^ [_912695, _912697, _912699, _912701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912695), _912697)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912699), _912701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912695), _912699)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912697), _912701))))], (34360 ^ _781215) ^ [_1424970, _1424972, _1424974] : [class_Lattices_Olattice(_1424970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424970), _1424972)), -(_1424972 = c_Orderings_Obot__class_Obot(tc_fun(_1424970, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1424970, hAPP(hAPP(c_Set_Oinsert(_1424970), _1424974), _1424972)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1424970), _1424974), c_Big__Operators_Olattice__class_OInf__fin(_1424970, _1424972)))], (46062 ^ _781215) ^ [_1704923, _1704925, _1704927, _1704929] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1704923, tc_Nat_Onat), _1704923), c_Product__Type_Ofst(_1704923, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1704923, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1704923, 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(_1704923, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1704923, tc_Nat_Onat))), _1704925)), hAPP(hAPP(c_List_Ozip(_1704923, tc_Nat_Onat), _1704927), c_List_Oupt(_1704929, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704929), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704923)), _1704927)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1704923, tc_Nat_Onat), _1704923), c_Product__Type_Ofst(_1704923, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1704923, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1704923, 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(_1704923, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1704923, 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(_1704923, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1704923, tc_Nat_Onat))), _1704929))), _1704925)), hAPP(hAPP(c_List_Ozip(_1704923, tc_Nat_Onat), _1704927), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704923)), _1704927))))))], (40417 ^ _781215) ^ [_1571875, _1571877] : [c_Wellfounded_Owf(_1571875, _1571877), -(c_Wellfounded_OwfP(_1571875, hAPP(hAPP(c_COMBC(_1571875, tc_fun(tc_prod(_1571875, _1571875), tc_HOL_Obool), tc_fun(_1571875, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571875, tc_fun(tc_fun(tc_prod(_1571875, _1571875), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1571875, _1571875), tc_HOL_Obool), tc_fun(_1571875, tc_HOL_Obool)), _1571875), c_COMBC(_1571875, tc_fun(tc_prod(_1571875, _1571875), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571875, tc_prod(_1571875, _1571875)), tc_fun(_1571875, tc_fun(tc_fun(tc_prod(_1571875, _1571875), tc_HOL_Obool), tc_HOL_Obool)), _1571875), hAPP(c_COMBB(tc_prod(_1571875, _1571875), tc_fun(tc_fun(tc_prod(_1571875, _1571875), tc_HOL_Obool), tc_HOL_Obool), _1571875), c_member(tc_prod(_1571875, _1571875)))), c_Product__Type_OPair(_1571875, _1571875)))), _1571877)))], (5881 ^ _781215) ^ [_874761, _874763, _874765, _874767] : [-(hAPP(c_Option_Ooption_Ooption__case(_874761, _874763, _874765, _874767), c_Option_Ooption_ONone(_874763)) = _874765)], (41389 ^ _781215) ^ [_1594688, _1594690, _1594692, _1594694, _1594696, _1594698] : [class_Groups_Ocomm__monoid__add(_1594688), c_Fun_Oinj__on(_1594690, _1594692, _1594694, _1594696), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1594692, _1594688), _1594698), hAPP(c_Set_Oimage(_1594690, _1594692, _1594694), _1594696)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1594690, _1594688), hAPP(c_Fun_Ocomp(_1594692, _1594688, _1594690, _1594698), _1594694)), _1594696))], (21460 ^ _781215) ^ [_1166357, _1166359] : [c_Int_OBit0(_1166357) = c_Int_OBit0(_1166359), -(_1166357 = _1166359)], (1538 ^ _781215) ^ [_803410, _803412] : [-(class_Groups_Ocancel__ab__semigroup__add(_803410)), _803412 = _803410, class_Groups_Ocancel__ab__semigroup__add(_803412)], (34322 ^ _781215) ^ [_1424349, _1424351, _1424353] : [class_Lattices_Olattice(_1424349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424349), _1424351)), hBOOL(hAPP(hAPP(c_member(_1424349), _1424353), _1424351)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1424349), _1424353), c_Big__Operators_Olattice__class_OInf__fin(_1424349, _1424351)) = _1424353)], (11722 ^ _781215) ^ [_985589, _985591] : [class_Rings_Ocomm__semiring__1(_985589), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985589), c_Groups_Ozero__class_Ozero(_985589)), _985591) = c_Groups_Ozero__class_Ozero(_985589))], (6347 ^ _781215) ^ [_884367, _884369, _884371, _884373] : [hBOOL(hAPP(hAPP(c_member(_884367), _884369), hAPP(hAPP(c_Set_Oinsert(_884367), _884371), _884373))), -(_884369 = _884371), -(hBOOL(hAPP(hAPP(c_member(_884367), _884369), _884373)))], (7712 ^ _781215) ^ [_911068, _911070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _911068)), hAPP(c_Nat_OSuc, _911070))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911068), _911070)))], (11880 ^ _781215) ^ [_987915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _987915)), _987915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (38526 ^ _781215) ^ [_1517291, _1517293, _1517295, _1517297, _1517299] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1517291, _1517293), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517291, tc_HOL_Obool)), _1517295), _1517297)), _1517299) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517291, _1517293), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517291, _1517293), _1517295), _1517299)), hAPP(hAPP(c_Product__Type_OSigma(_1517291, _1517293), _1517297), _1517299)))], (51256 ^ _781215) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (25396 ^ _781215) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (22542 ^ _781215) ^ [_1188399, _1188401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1188399), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22545 ^ _781215 : [(22552 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1188401), _1188399)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22546 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1188401), _1188399)), 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)), _1188401)))]]], (6572 ^ _781215) ^ [_888580] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _888580), _888580)))], (33090 ^ _781215) ^ [_1395298, _1395300] : [c_Nat__Transfer_Onat__set(_1395298), c_Nat__Transfer_Onat__set(_1395300), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1395298), _1395300)))], (4594 ^ _781215) ^ [_850876, _850878, _850880, _850882, _850884, _850886] : [-(c_Nitpick_Oof__frac(_850886, _850882, _850878) = c_Nitpick_Oof__frac(_850884, _850880, _850876)), _850886 = _850884, _850882 = _850880, _850878 = _850876], (20687 ^ _781215) ^ [_1152338, _1152340] : [class_Rings_Oring__1(_1152338), -(hBOOL(hAPP(hAPP(c_member(_1152338), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1152338), _1152340)), c_Int_Oring__1__class_OInts(_1152338))))], (10580 ^ _781215) ^ [_962267, _962269] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962267)), _962269) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _962269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962267), _962269)))], (46664 ^ _781215) ^ [_1719357, _1719359] : [c_List_Oremdups(_1719357, _1719359) = _1719359, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719357)), c_List_Oremdups(_1719357, _1719359)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719357)), _1719359))], (20509 ^ _781215) ^ [_1149347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1149347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1149347))))], (45632 ^ _781215) ^ [_1696957, _1696959] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1696957, _1696959)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1696957), hAPP(c_Nat_OSuc, _1696959)))], (18673 ^ _781215) ^ [_1115756, _1115758, _1115760] : [class_Orderings_Olinorder(_1115756), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115756), _1115758)), hBOOL(hAPP(hAPP(c_member(_1115756), _1115760), _1115758)), 18684 ^ _781215 : [(18691 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1115756, tc_HOL_Obool)), _1115758), hAPP(hAPP(c_Set_Oinsert(_1115756), _1115760), c_Orderings_Obot__class_Obot(tc_fun(_1115756, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1115756, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1115756, c_Orderings_Oord__class_Omin(_1115756), _1115758) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1115756), _1115760), c_Big__Operators_Olattice_OInf__fin(_1115756, c_Orderings_Oord__class_Omin(_1115756), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1115756, tc_HOL_Obool)), _1115758), hAPP(hAPP(c_Set_Oinsert(_1115756), _1115760), c_Orderings_Obot__class_Obot(tc_fun(_1115756, tc_HOL_Obool)))))))], (18685 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1115756, tc_HOL_Obool)), _1115758), hAPP(hAPP(c_Set_Oinsert(_1115756), _1115760), c_Orderings_Obot__class_Obot(tc_fun(_1115756, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1115756, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1115756, c_Orderings_Oord__class_Omin(_1115756), _1115758) = _1115760)]]], (49782 ^ _781215) ^ [_1790202, _1790204, _1790206] : [c_Relation_Ototal__on(_1790202, _1790204, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1790202, _1790202), tc_HOL_Obool)), _1790206), c_Relation_OId(_1790202))), -(c_Relation_Ototal__on(_1790202, _1790204, _1790206))], (46085 ^ _781215) ^ [_1705797] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1705797)), c_List_Otranspose__rel(_1705797)), c_List_Olist_ONil(tc_List_Olist(_1705797)))), -(c_List_Otranspose(_1705797, c_List_Olist_ONil(tc_List_Olist(_1705797))) = c_List_Olist_ONil(tc_List_Olist(_1705797)))], (51212 ^ _781215) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (49085 ^ _781215) ^ [_1771644, _1771646, _1771648] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1771644, _1771644)), _1771646), _1771648)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1771644, _1771644)), _1771646), c_Transitive__Closure_Otrancl(_1771644, _1771648))))], (15817 ^ _781215) ^ [_1059508, _1059510, _1059512, _1059514, _1059516, _1059518] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1059508), _1059510)), _1059512) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1059514), _1059516)), _1059518), 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), _1059514), _1059516)), _1059518)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059512), _1059508)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1059518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1059514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059514), _1059508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059516), _1059510)))], (33102 ^ _781215) ^ [_1395500, _1395502, _1395504, _1395506] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395500, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1395500), _1395502), _1395504)), hAPP(hAPP(c_Set_Oinsert(_1395500), _1395502), _1395506)) = hAPP(hAPP(c_Set_Oinsert(_1395500), _1395502), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395500, tc_HOL_Obool)), _1395504), _1395506)))], (26033 ^ _781215) ^ [_1253309, _1253311, _1253313] : [class_Groups_Ocomm__monoid__add(_1253309), class_Groups_Ocomm__monoid__mult(_1253309), c_Nat__Transfer_Onat__set(_1253311), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1253309), _1253313), _1253311) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1253309), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1253309, tc_Nat_Onat), _1253313), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1253311)))], (8063 ^ _781215) ^ [_917149, _917151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917149), _917151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917149), hAPP(c_Nat_OSuc, _917151))))], (35249 ^ _781215) ^ [_1443118, _1443120, _1443122, _1443124] : [c_Fun_Oinj__on(_1443118, _1443120, _1443122, _1443124), -(hAPP(c_Set_Oimage(_1443120, _1443118, c_Fun_Othe__inv__into(_1443118, _1443120, _1443124, _1443122)), hAPP(c_Set_Oimage(_1443118, _1443120, _1443122), _1443124)) = _1443124)], (45428 ^ _781215) ^ [_1693349, _1693351, _1693353, _1693355, _1693357] : [class_Orderings_Olinorder(_1693349), hBOOL(hAPP(hAPP(c_member(_1693351), _1693353), hAPP(c_List_Oset(_1693351), _1693355))), c_List_Olinorder__class_Osorted(_1693349, hAPP(hAPP(c_List_Omap(_1693351, _1693349), _1693357), _1693355)), hAPP(c_List_Ohd(_1693351), hAPP(c_List_Ofilter(_1693351, hAPP(hAPP(c_COMBB(_1693349, tc_HOL_Obool, _1693351), hAPP(c_fequal, hAPP(_1693357, _1693353))), _1693357)), _1693355)) = _1693353, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1693351, _1693349, _1693357), _1693353), c_List_Oremove1(_1693351, _1693353, _1693355)) = _1693355)], (12968 ^ _781215) ^ [_1007121, _1007123] : [class_Groups_Oordered__ab__group__add(_1007121), 12971 ^ _781215 : [(12978 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007121), _1007123), c_Groups_Ozero__class_Ozero(_1007121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007121), c_Groups_Ozero__class_Ozero(_1007121)), hAPP(c_Groups_Ouminus__class_Ouminus(_1007121), _1007123))))], (12972 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007121), c_Groups_Ozero__class_Ozero(_1007121)), hAPP(c_Groups_Ouminus__class_Ouminus(_1007121), _1007123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007121), _1007123), c_Groups_Ozero__class_Ozero(_1007121))))]]], (21558 ^ _781215) ^ [_1168011] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1168011)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1168011)))], (2244 ^ _781215) ^ [_814199, _814201, _814203, _814205, _814207, _814209] : [-(c_SetInterval_Oord_OatMost(_814209, _814205, _814201) = c_SetInterval_Oord_OatMost(_814207, _814203, _814199)), _814209 = _814207, _814205 = _814203, _814201 = _814199], (36772 ^ _781215) ^ [_1472974, _1472976] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472974, 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(_1472974, tc_HOL_Obool)), tc_fun(_1472974, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1472974, tc_HOL_Obool)), tc_fun(_1472974, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472974, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1472976)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472974, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1472976))], (33194 ^ _781215) ^ [_1397883, _1397885, _1397887, _1397889] : [hBOOL(hAPP(hAPP(c_member(_1397883), _1397885), _1397887)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397883, tc_HOL_Obool)), _1397887), hAPP(hAPP(c_Set_Oinsert(_1397883), _1397885), _1397889)) = hAPP(hAPP(c_Set_Oinsert(_1397883), _1397885), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397883, tc_HOL_Obool)), _1397887), _1397889)))], (24272 ^ _781215) ^ [_1219006, _1219008] : [class_Rings_Olinordered__idom(_1219006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219006), hAPP(hAPP(c_Power_Opower__class_Opower(_1219006), _1219008), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1219006)))], (49000 ^ _781215) ^ [_1770130, _1770132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1770130), _1770132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1770130)), hAPP(c_Code__Numeral_Onat__of, _1770132))))], (4760 ^ _781215) ^ [_853325, _853327] : [_853327 = _853325, -(c_List_Oset(_853327) = c_List_Oset(_853325))], (51596 ^ _781215) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (45253 ^ _781215) ^ [_1688922, _1688924, _1688926, _1688928] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688922)), _1688924))), c_List_Ofoldr(tc_List_Olist(_1688926), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1688926)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1688926))), _1688928, 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(_1688922)), _1688924)), c_List_Ofoldr(tc_List_Olist(_1688926), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1688926)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1688926), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1688926)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1688926)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1688926), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1688926)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1688926), tc_List_Olist(_1688926), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1688926)))), _1688928), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (37231 ^ _781215) ^ [] : [-(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)))], (17279 ^ _781215) ^ [_1090704, _1090706] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090704) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090706), 17282 ^ _781215 : [(17289 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090704)))), 17292 ^ _781215 : [(17299 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090706)))), -(_1090704 = _1090706)], (17293 ^ _781215) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090706))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090704) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (17283 ^ _781215) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090706)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (4870 ^ _781215) ^ [_855108, _855110, _855112, _855114, _855116, _855118, _855120, _855122] : [-(c_New__Random__Sequence_Opos__empty(_855122, _855118, _855114, _855110) = c_New__Random__Sequence_Opos__empty(_855120, _855116, _855112, _855108)), _855122 = _855120, _855118 = _855116, _855114 = _855112, _855110 = _855108], (18934 ^ _781215) ^ [_1120679, _1120681, _1120683, _1120685] : [class_Orderings_Olinorder(_1120679), 18937 ^ _781215 : [(18938 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120679), _1120681), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1120679), _1120683), _1120685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120679), _1120681), _1120683))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120679), _1120681), _1120685)))], (18948 ^ _781215) ^ [] : [18949 ^ _781215 : [(18952 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120679), _1120681), _1120685))], (18950 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120679), _1120681), _1120683))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120679), _1120681), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1120679), _1120683), _1120685))))]]], (40355 ^ _781215) ^ [_1570382, _1570384] : [c_Wellfounded_Owf(_1570382, hAPP(c_Set_OCollect(tc_prod(_1570382, _1570382)), hAPP(c_Product__Type_Oprod_Oprod__case(_1570382, _1570382, tc_HOL_Obool), _1570384))), -(c_Wellfounded_OwfP(_1570382, _1570384))], (20358 ^ _781215) ^ [_1146679] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1146679)))], (39836 ^ _781215) ^ [_1556830, _1556832, _1556834, _1556836, _1556838] : [-(hAPP(c_Relation_ORange(_1556830, _1556832), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1556830, _1556832)), hAPP(hAPP(c_Product__Type_OPair(_1556830, _1556832), _1556834), _1556836)), _1556838)) = hAPP(hAPP(c_Set_Oinsert(_1556832), _1556836), hAPP(c_Relation_ORange(_1556830, _1556832), _1556838)))], (22136 ^ _781215) ^ [_1180154, _1180156] : [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), _1180154))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1180156)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1180154))) = 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), _1180156), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1180154)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31439 ^ _781215) ^ [_1357555, _1357557, _1357559] : [class_Rings_Oring__1(_1357555), -(hAPP(c_Int_Oring__1__class_Oof__int(_1357555), 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), _1357557), _1357559)), 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(_1357555), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1357555), _1357557)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1357555), _1357559)))], (27664 ^ _781215) ^ [_1284662, _1284664] : [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), _1284662), _1284664))), 27667 ^ _781215 : [(27674 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284664), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 27677 ^ _781215 : [(27686 ^ _781215) ^ [] : [-(c_Nitpick_Onorm__frac(_1284662, _1284664) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1284662), _1284664)), 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), _1284662))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1284664)))), -(_1284662 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1284664 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27678 ^ _781215) ^ [] : [27679 ^ _781215 : [(27682 ^ _781215) ^ [] : [_1284664 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (27680 ^ _781215) ^ [] : [_1284662 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1284662, _1284664) = 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)))]]], (27668 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284664), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1284662, _1284664) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1284662), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1284664)))]]], (6674 ^ _781215) ^ [_890449, _890451, _890453] : [_890449 = c_Orderings_Obot__class_Obot(tc_fun(_890451, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_890451), _890453), _890449))], (39438 ^ _781215) ^ [_1542454, _1542456, _1542458, _1542460, _1542462, _1542464] : [-(hBOOL(hAPP(hAPP(c_member(_1542454), _1542456), _1542458))), -(hAPP(c_Fun_Ooverride__on(_1542454, _1542460, _1542462, _1542464, _1542458), _1542456) = hAPP(_1542462, _1542456))], (50776 ^ _781215) ^ [_1813287] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1813287)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1813287), c_Int_OMin)))], (2442 ^ _781215) ^ [_817386, _817388, _817390, _817392, _817394, _817396, _817398, _817400, _817402, _817404] : [-(c_Product__Type_Oprod_Oprod__rec(_817404, _817400, _817396, _817392, _817388) = c_Product__Type_Oprod_Oprod__rec(_817402, _817398, _817394, _817390, _817386)), _817404 = _817402, _817400 = _817398, _817396 = _817394, _817392 = _817390, _817388 = _817386], (51224 ^ _781215) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (50547 ^ _781215) ^ [_1809037, _1809039, _1809041, _1809043] : [c_List_Olist__ex1(_1809037, _1809039, hAPP(hAPP(c_List_Olist_OCons(_1809037), _1809041), _1809043)), 50550 ^ _781215 : [(50557 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1809039, _1809041))), -(c_List_Olist__ex1(_1809037, _1809039, _1809043))], (50551 ^ _781215) ^ [] : [hBOOL(hAPP(_1809039, _1809041)), -(c_List_Olist__all(_1809037, hAPP(hAPP(c_COMBS(_1809037, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1809037), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1809037), c_fNot), _1809039))), hAPP(c_fequal, _1809041)), _1809043))]]], (51444 ^ _781215) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (50577 ^ _781215) ^ [_1809621, _1809623, _1809625] : [-(c_Product__Type_Ointernal__split(_1809621, _1809623, _1809625) = c_Product__Type_Oprod_Oprod__case(_1809621, _1809623, _1809625))], (25450 ^ _781215) ^ [_1239604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239604), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1239604)), c_Int_OMin)))], (4730 ^ _781215) ^ [_852900, _852902] : [_852902 = _852900, -(c_Finite__Set_Ofinite(_852902) = c_Finite__Set_Ofinite(_852900))], (21017 ^ _781215) ^ [_1157681] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1157681))) = 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)))), _1157681))], (50339 ^ _781215) ^ [_1804578, _1804580, _1804582, _1804584] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1804578, _1804580)), _1804582), hAPP(c_Relation_Oconverse(_1804580, _1804578), _1804584))), 50344 ^ _781215 : [(50347 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1804580, _1804578)), hAPP(hAPP(c_Product__Type_OPair(_1804580, _1804578), 50342 ^ [_1804578, _1804580, _1804582, _1804584]), 50343 ^ [_1804578, _1804580, _1804582, _1804584])), _1804584)))], (50345 ^ _781215) ^ [] : [-(_1804582 = hAPP(hAPP(c_Product__Type_OPair(_1804578, _1804580), 50343 ^ [_1804578, _1804580, _1804582, _1804584]), 50342 ^ [_1804578, _1804580, _1804582, _1804584]))]]], (32950 ^ _781215) ^ [_1392243, _1392245, _1392247, _1392249] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392243, tc_HOL_Obool)), _1392245), _1392247), _1392249)), -(hBOOL(hAPP(_1392245, _1392249)))], (2614 ^ _781215) ^ [_820058, _820060, _820062, _820064] : [-(c_Set_Othe__elem(_820064, _820060) = c_Set_Othe__elem(_820062, _820058)), _820064 = _820062, _820060 = _820058], (15755 ^ _781215) ^ [_1058305, _1058307, _1058309, _1058311, _1058313] : [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), _1058305), _1058307)), _1058309)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1058305), _1058311)), _1058313))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1058309), _1058305)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1058313), _1058305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1058307), _1058311)))], (416 ^ _781215) ^ [_787753, _787755, _787757, _787759] : [-(c_FunDef_Oreduction__pair(_787757, _787753)), c_FunDef_Oreduction__pair(_787759, _787755), _787759 = _787757, _787755 = _787753], (49091 ^ _781215) ^ [_1771769] : [-(c_Transitive__Closure_Otrancl(_1771769, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1771769, _1771769), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1771769, _1771769), tc_HOL_Obool)))], (40797 ^ _781215) ^ [_1580844, _1580846, _1580848] : [hAPP(c_Com_Ocom_OBODY, _1580844) = c_Com_Ocom_OWhile(_1580846, _1580848)], (48914 ^ _781215) ^ [_1768693, _1768695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1768693)), hAPP(c_Code__Numeral_Oof__nat, _1768695))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1768693), _1768695)))], (9313 ^ _781215) ^ [_939859, _939861, _939863] : [hBOOL(hAPP(hAPP(c_member(_939859), _939861), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_939859, tc_HOL_Obool)), _939863))), hBOOL(hAPP(hAPP(c_member(_939859), _939861), _939863))], (38129 ^ _781215) ^ [_1506996, _1506998] : [-(c_Set_Othe__elem(_1506996, _1506998) = c_HOL_OThe(_1506996, hAPP(hAPP(c_COMBB(tc_fun(_1506996, tc_HOL_Obool), tc_HOL_Obool, _1506996), hAPP(c_fequal, _1506998)), hAPP(hAPP(c_COMBC(_1506996, tc_fun(_1506996, tc_HOL_Obool), tc_fun(_1506996, tc_HOL_Obool)), c_Set_Oinsert(_1506996)), c_Orderings_Obot__class_Obot(tc_fun(_1506996, tc_HOL_Obool))))))], (36666 ^ _781215) ^ [_1470539, _1470541, _1470543, _1470545, _1470547] : [c_Fun_Oinj__on(_1470539, _1470541, _1470543, c_Orderings_Otop__class_Otop(tc_fun(_1470539, tc_HOL_Obool))), 36669 ^ _781215 : [(36676 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1470539), _1470545), _1470547)), -(hBOOL(hAPP(hAPP(c_member(_1470541), hAPP(_1470543, _1470545)), hAPP(c_Set_Oimage(_1470539, _1470541, _1470543), _1470547))))], (36670 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1470541), hAPP(_1470543, _1470545)), hAPP(c_Set_Oimage(_1470539, _1470541, _1470543), _1470547))), -(hBOOL(hAPP(hAPP(c_member(_1470539), _1470545), _1470547)))]]], (40285 ^ _781215) ^ [_1568851, _1568853, _1568855, _1568857] : [hBOOL(hAPP(hAPP(c_member(_1568851), _1568853), hAPP(c_Relation_ODomain(_1568851, _1568855), _1568857))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568851, _1568855)), hAPP(hAPP(c_Product__Type_OPair(_1568851, _1568855), _1568853), 40288 ^ [_1568851, _1568853, _1568855, _1568857])), _1568857)))], (42363 ^ _781215) ^ [_1620210, _1620212, _1620214, _1620216, _1620218, _1620220] : [c_List_Olistrelp(_1620210, _1620212, hAPP(hAPP(c_List_Olist_OCons(_1620210), _1620214), _1620216), hAPP(hAPP(c_List_Olist_OCons(_1620210), _1620218), _1620220)), 42366 ^ _781215 : [(42369 ^ _781215) ^ [] : [-(c_List_Olistrelp(_1620210, _1620212, _1620216, _1620220))], (42367 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1620212, _1620214), _1620218)))]]], (48820 ^ _781215) ^ [_1766860, _1766862] : [-(_1766860 = c_List_Olist_ONil(_1766862)), -(c_Random_Oselect__weight(_1766862, hAPP(hAPP(c_List_Omap(_1766862, tc_prod(tc_Code__Numeral_Ocode__numeral, _1766862)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1766862), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1766860)) = c_Random_Oselect(_1766862, _1766860))], (45375 ^ _781215) ^ [_1691747, _1691749] : [-(c_List_Ofoldr(tc_List_Olist(_1691747), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1691747)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1691747))), c_List_Otranspose(_1691747, _1691749), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1691747))), hAPP(c_List_Ofilter(tc_List_Olist(_1691747), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1691747)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1691747), tc_List_Olist(_1691747), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1691747)))), _1691749)))], (32160 ^ _781215) ^ [_1375035, _1375037, _1375039] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1375035), _1375037), _1375039) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1375035), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1375035, tc_Int_Oint), _1375037), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1375039))), class_Groups_Ocomm__monoid__add(_1375035), class_Groups_Ocomm__monoid__mult(_1375035)], (12124 ^ _781215) ^ [_991779, _991781, _991783] : [class_Groups_Oordered__comm__monoid__add(_991779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991779), c_Groups_Ozero__class_Ozero(_991779)), _991781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991779), c_Groups_Ozero__class_Ozero(_991779)), _991783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991779), c_Groups_Ozero__class_Ozero(_991779)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_991779), _991781), _991783))))], (44519 ^ _781215) ^ [_1673157, _1673159, _1673161, _1673163, _1673165] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1673157), tc_List_Olist(_1673157))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1673157), tc_List_Olist(_1673157)), hAPP(hAPP(c_List_Oappend(_1673157), _1673159), _1673161)), hAPP(hAPP(c_List_Oappend(_1673157), _1673159), _1673163))), c_List_Olexord(_1673157, _1673165))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1673157, _1673157)), hAPP(hAPP(c_Product__Type_OPair(_1673157, _1673157), 44524 ^ [_1673157, _1673159, _1673161, _1673163, _1673165]), 44524 ^ [_1673157, _1673159, _1673161, _1673163, _1673165])), _1673165))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1673157), tc_List_Olist(_1673157))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1673157), tc_List_Olist(_1673157)), _1673161), _1673163)), c_List_Olexord(_1673157, _1673165))))], (44834 ^ _781215) ^ [_1680400, _1680402, _1680404] : [hAPP(c_List_Orotate(_1680400, _1680402), _1680404) = c_List_Olist_ONil(_1680400), -(_1680404 = c_List_Olist_ONil(_1680400))], (11948 ^ _781215) ^ [_988856, _988858] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988856), _988858) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988858), _988856) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_988856 = _988858)], (4186 ^ _781215) ^ [_844752, _844754] : [_844754 = _844752, -(c_List_Omonoid__add__class_Olistsum(_844754) = c_List_Omonoid__add__class_Olistsum(_844752))], (4458 ^ _781215) ^ [_848830, _848832, _848834, _848836] : [-(c_Nat_Ocompow(_848836, _848832) = c_Nat_Ocompow(_848834, _848830)), _848836 = _848834, _848832 = _848830], (39813 ^ _781215) ^ [_1556261, _1556263, _1556265, _1556267] : [-(hAPP(c_Relation_ORange(_1556261, _1556263), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1556261, _1556263), tc_HOL_Obool)), _1556265), _1556267)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1556263, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1556261, _1556263), _1556265)), hAPP(c_Relation_ORange(_1556261, _1556263), _1556267)))], (3200 ^ _781215) ^ [_829405, _829407, _829409, _829411, _829413, _829415] : [-(c_List_Oset__Cons(_829415, _829411, _829407) = c_List_Oset__Cons(_829413, _829409, _829405)), _829415 = _829413, _829411 = _829409, _829407 = _829405], (22204 ^ _781215) ^ [_1181705, _1181707, _1181709] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181705), _1181707)), _1181709) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181705), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181707), _1181709))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181705), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181707, _1181709))), _1181709)))], (43134 ^ _781215) ^ [_1640109, _1640111, _1640113, _1640115, _1640117, _1640119, _1640121] : [-(hBOOL(hAPP(hAPP(c_member(_1640109), _1640111), hAPP(c_List_Oset(_1640109), _1640113)))), -(c_Map_Omap__upds(_1640109, _1640115, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1640109, tc_Option_Ooption(_1640115)), _1640117), _1640111), hAPP(c_Option_Ooption_OSome(_1640115), _1640119)), _1640113, _1640121) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1640109, tc_Option_Ooption(_1640115)), c_Map_Omap__upds(_1640109, _1640115, _1640117, _1640113, _1640121)), _1640111), hAPP(c_Option_Ooption_OSome(_1640115), _1640119)))], (6962 ^ _781215) ^ [_896595, _896597, _896599, _896601, _896603] : [-(_896595 = c_Option_Ooption_ONone(_896597)), -(c_Map_Odom(_896599, _896597, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_896599, tc_Option_Ooption(_896597)), _896601), _896603), _896595)) = hAPP(hAPP(c_Set_Oinsert(_896599), _896603), c_Map_Odom(_896599, _896597, _896601)))], (5576 ^ _781215) ^ [_869062, _869064] : [hAPP(_869062, 5577 ^ [_869062, _869064]) = hAPP(_869064, 5577 ^ [_869062, _869064]), -(_869062 = _869064)], (20400 ^ _781215) ^ [_1147304] : [20402 ^ _781215 : [(20405 ^ _781215) ^ [] : [hBOOL(hAPP(_1147304, 20401 ^ [_1147304]))], (20403 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20401 ^ [_1147304])))]], 20406 ^ _781215 : [(20407 ^ _781215) ^ [_1147431] : [-(hBOOL(hAPP(_1147304, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147431))))]]], (6844 ^ _781215) ^ [_893890, _893892, _893894, _893896, _893898, _893900, _893902, _893904] : [c_Finite__Set_Ofolding__image__simple(_893890, _893892, _893894, _893896, _893898, _893900), hBOOL(hAPP(c_Finite__Set_Ofinite(_893892), _893902)), hBOOL(hAPP(hAPP(c_member(_893892), _893904), _893902)), -(hAPP(_893900, _893902) = hAPP(hAPP(_893894, hAPP(_893898, _893904)), hAPP(_893900, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893892, tc_HOL_Obool)), _893902), hAPP(hAPP(c_Set_Oinsert(_893892), _893904), c_Orderings_Obot__class_Obot(tc_fun(_893892, tc_HOL_Obool)))))))], (4278 ^ _781215) ^ [_846138, _846140, _846142, _846144] : [-(c_List_Olistrel(_846144, _846140) = c_List_Olistrel(_846142, _846138)), _846144 = _846142, _846140 = _846138], (42423 ^ _781215) ^ [_1621466, _1621468, _1621470] : [hBOOL(hAPP(c_List_Odistinct(_1621466), hAPP(hAPP(c_List_Olist_OCons(_1621466), _1621468), _1621470))), 42426 ^ _781215 : [(42429 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1621466), _1621470)))], (42427 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1621466), _1621468), hAPP(c_List_Oset(_1621466), _1621470)))]]], (29668 ^ _781215) ^ [_1322000, _1322002, _1322004, _1322006] : [class_Fields_Ofield(_1322000), -(_1322002 = c_Groups_Ozero__class_Ozero(_1322000)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1322000), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322000), _1322004), _1322002)), _1322006) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1322000), _1322004), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322000), _1322002), _1322006))), _1322002))], (3508 ^ _781215) ^ [_834301, _834303, _834305, _834307] : [-(c_List_Otranspose(_834307, _834303) = c_List_Otranspose(_834305, _834301)), _834307 = _834305, _834303 = _834301], (44375 ^ _781215) ^ [_1669118, _1669120, _1669122, _1669124, _1669126, _1669128] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1669118), tc_List_Olist(_1669118))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1669118), tc_List_Olist(_1669118)), hAPP(hAPP(c_List_Oappend(_1669118), _1669120), _1669126)), hAPP(hAPP(c_List_Oappend(_1669118), _1669122), _1669128))), c_List_Olistrel1(_1669118, _1669124)))), 44376 ^ _781215 : [(44383 ^ _781215) ^ [] : [_1669120 = _1669122, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1669118), tc_List_Olist(_1669118))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1669118), tc_List_Olist(_1669118)), _1669126), _1669128)), c_List_Olistrel1(_1669118, _1669124)))], (44377 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1669118), tc_List_Olist(_1669118))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1669118), tc_List_Olist(_1669118)), _1669120), _1669122)), c_List_Olistrel1(_1669118, _1669124))), _1669126 = _1669128]]], (51376 ^ _781215) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (38552 ^ _781215) ^ [_1518161, _1518163, _1518165, _1518167, _1518169] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518161, _1518163), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518161, tc_HOL_Obool)), _1518165), _1518167)), hAPP(c_COMBK(tc_fun(_1518163, tc_HOL_Obool), _1518161), _1518169)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1518161, _1518163), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518161, _1518163), _1518165), hAPP(c_COMBK(tc_fun(_1518163, tc_HOL_Obool), _1518161), _1518169))), hAPP(hAPP(c_Product__Type_OSigma(_1518161, _1518163), _1518167), hAPP(c_COMBK(tc_fun(_1518163, tc_HOL_Obool), _1518161), _1518169))))], (5382 ^ _781215) ^ [_863444, _863446, _863448, _863450] : [-(c_Lazy__Sequence_Osmall__lazy_H(_863450, _863446) = c_Lazy__Sequence_Osmall__lazy_H(_863448, _863444)), _863450 = _863448, _863446 = _863444], (3918 ^ _781215) ^ [_840632, _840634, _840636, _840638, _840640, _840642] : [-(c_Predicate_ORangeP(_840642, _840638, _840634) = c_Predicate_ORangeP(_840640, _840636, _840632)), _840642 = _840640, _840638 = _840636, _840634 = _840632], (43357 ^ _781215) ^ [_1646038, _1646040, _1646042, _1646044, _1646046] : [class_Rings_Osemiring__0(_1646038), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1646038), hAPP(hAPP(c_List_Omap(_1646040, _1646038), hAPP(hAPP(c_COMBB(_1646038, _1646038, _1646040), hAPP(c_Groups_Otimes__class_Otimes(_1646038), _1646042)), _1646044)), _1646046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1646038), _1646042), hAPP(c_List_Omonoid__add__class_Olistsum(_1646038), hAPP(hAPP(c_List_Omap(_1646040, _1646038), _1646044), _1646046))))], (3630 ^ _781215) ^ [_836182, _836184, _836186, _836188] : [-(c_Enum_Oenum__the(_836188, _836184) = c_Enum_Oenum__the(_836186, _836182)), _836188 = _836186, _836184 = _836182], (39659 ^ _781215) ^ [_1551957, _1551959] : [-(hAPP(c_Fun_Oid(_1551957), _1551959) = _1551959)], (5474 ^ _781215) ^ [_864784, _864786] : [_864786 = _864784, -(c_COMBI(_864786) = c_COMBI(_864784))], (16497 ^ _781215) ^ [_1075181, _1075183, _1075185, _1075187, _1075189, _1075191, _1075193] : [c_Finite__Set_Ofun__left__comm(_1075181, _1075183, _1075185), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1075181, _1075183, _1075185, _1075187, _1075189), _1075191)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1075181, _1075183, _1075185, _1075187, _1075189), _1075193)), -(_1075193 = _1075191)], (2588 ^ _781215) ^ [_819675, _819677] : [_819677 = _819675, -(c_Nitpick_Oone__frac(_819677) = c_Nitpick_Oone__frac(_819675))], (13872 ^ _781215) ^ [_1022890, _1022892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1022890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1022892)), -(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), _1022892), _1022890))))], (43369 ^ _781215) ^ [_1646452, _1646454, _1646456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1646452), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1646454))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1646454), _1646452), _1646456)) = 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), _1646454)), _1646456)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1646454), _1646452)))], (9149 ^ _781215) ^ [_936409] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936409), _936409)))))], (29678 ^ _781215) ^ [_1322178, _1322180, _1322182, _1322184, _1322186] : [class_Fields_Ofield(_1322178), -(_1322180 = c_Groups_Ozero__class_Ozero(_1322178)), -(_1322182 = c_Groups_Ozero__class_Ozero(_1322178)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1322178), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322178), _1322184), _1322180)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322178), _1322186), _1322182)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322178), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1322178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322178), _1322184), _1322182)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322178), _1322186), _1322180))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322178), _1322180), _1322182)))], (44868 ^ _781215) ^ [_1681087, _1681089] : [hBOOL(hAPP(c_List_Odistinct(_1681087), _1681089)), -(hBOOL(hAPP(c_List_Odistinct(_1681087), hAPP(c_List_Otl(_1681087), _1681089))))], (33170 ^ _781215) ^ [_1397493, _1397495, _1397497, _1397499] : [hBOOL(hAPP(hAPP(c_member(_1397493), _1397495), _1397497)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397493, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1397493), _1397495), _1397499)), _1397497) = hAPP(hAPP(c_Set_Oinsert(_1397493), _1397495), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397493, tc_HOL_Obool)), _1397499), _1397497)))], (26149 ^ _781215) ^ [_1255435, _1255437, _1255439] : [class_Rings_Oring__1(_1255435), -(hAPP(c_Int_Oring__1__class_Oof__int(_1255435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255437), _1255439)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1255435), hAPP(c_Int_Oring__1__class_Oof__int(_1255435), _1255437)), hAPP(c_Int_Oring__1__class_Oof__int(_1255435), _1255439)))], (48948 ^ _781215) ^ [] : [-(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))))], (6217 ^ _781215) ^ [_881410, _881412, _881414, _881416] : [c_Finite__Set_Ofolding__one(_881410, _881412, _881414), -(hAPP(_881414, hAPP(hAPP(c_Set_Oinsert(_881410), _881416), c_Orderings_Obot__class_Obot(tc_fun(_881410, tc_HOL_Obool)))) = _881416)], (43724 ^ _781215) ^ [_1654446, _1654448, _1654450] : [43725 ^ _781215 : [(43728 ^ _781215) ^ [] : [_1654450 = c_List_Olist_ONil(_1654446)], (43726 ^ _781215) ^ [] : [_1654448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1654446), _1654448), _1654450) = c_List_Olist_ONil(_1654446))], (50884 ^ _781215) ^ [_1815159] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1815159)), c_Int_OPls))], (43339 ^ _781215) ^ [_1645479, _1645481, _1645483] : [class_Groups_Omonoid__add(_1645479), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1645479), hAPP(hAPP(c_List_Omap(_1645481, _1645479), hAPP(c_COMBK(_1645479, _1645481), c_Groups_Ozero__class_Ozero(_1645479))), _1645483)) = c_Groups_Ozero__class_Ozero(_1645479))], (36518 ^ _781215) ^ [_1467580, _1467582] : [class_Orderings_Otop(_1467580), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1467580), _1467582), c_Orderings_Otop__class_Otop(_1467580))))], (7736 ^ _781215) ^ [_911536, _911538, _911540] : [_911538 = _911540, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911536), _911538) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911536), _911540))], (42666 ^ _781215) ^ [_1628428, _1628430, _1628432, _1628434, _1628436] : [-(c_List_Olist_Olist__size(_1628428, _1628430, hAPP(hAPP(c_List_Omap(_1628432, _1628428), _1628434), _1628436)) = c_List_Olist_Olist__size(_1628432, hAPP(c_Fun_Ocomp(_1628428, tc_Nat_Onat, _1628432, _1628430), _1628434), _1628436))], (4798 ^ _781215) ^ [_853878, _853880] : [_853880 = _853878, -(c_Int_OBit0(_853880) = c_Int_OBit0(_853878))], (13582 ^ _781215) ^ [_1017460, _1017462, _1017464, _1017466] : [class_Rings_Olinordered__semiring__strict(_1017460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017460), _1017462), _1017464)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017460), _1017466), _1017464))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017460), c_Groups_Ozero__class_Ozero(_1017460)), _1017464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017460), _1017462), _1017466)))], (26934 ^ _781215) ^ [_1270726, _1270728] : [-(c_Divides_Odivmod__nat(_1270726, _1270728) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1270726), _1270728)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1270726, _1270728)))], (49427 ^ _781215) ^ [_1780762, _1780764, _1780766, _1780768, _1780770] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1780762), tc_List_Olist(_1780762))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1780762), tc_List_Olist(_1780762)), _1780764), _1780766)), c_List_Olistrel(_1780762, c_Transitive__Closure_Ortrancl(_1780762, _1780768)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1780762), tc_List_Olist(_1780762))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1780762), tc_List_Olist(_1780762)), _1780766), _1780770)), c_List_Olistrel(_1780762, c_Transitive__Closure_Ortrancl(_1780762, _1780768)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1780762), tc_List_Olist(_1780762))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1780762), tc_List_Olist(_1780762)), _1780764), _1780770)), c_List_Olistrel(_1780762, c_Transitive__Closure_Ortrancl(_1780762, _1780768)))))], (9663 ^ _781215) ^ [_945181, _945183, _945185, _945187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945181, tc_HOL_Obool)), _945183), _945185)), hBOOL(hAPP(hAPP(c_member(_945181), _945187), _945183)), -(hBOOL(hAPP(hAPP(c_member(_945181), _945187), _945185)))], (12210 ^ _781215) ^ [_993352, _993354, _993356, _993358, _993360] : [class_Rings_Oordered__semiring(_993352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993352), _993354), _993356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993352), _993358), _993360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993352), c_Groups_Ozero__class_Ozero(_993352)), _993356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993352), c_Groups_Ozero__class_Ozero(_993352)), _993358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993352), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993352), _993354), _993358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993352), _993356), _993360))))], (12324 ^ _781215) ^ [_995543, _995545, _995547] : [class_Rings_Oordered__ring(_995543), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995543), _995545), c_Groups_Ozero__class_Ozero(_995543))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995543), _995547), c_Groups_Ozero__class_Ozero(_995543))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995543), c_Groups_Ozero__class_Ozero(_995543)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995543), _995545), _995547))))], (15638 ^ _781215) ^ [_1056055, _1056057, _1056059, _1056061, _1056063, _1056065] : [c_Com_Ocom_OCall(_1056055, _1056057, _1056059) = c_Com_Ocom_OLocal(_1056061, _1056063, _1056065)], (43772 ^ _781215) ^ [_1655371, _1655373, _1655375, _1655377] : [_1655377 = c_List_Olist_ONil(_1655371), -(hAPP(hAPP(c_List_Omap(_1655371, _1655373), _1655375), _1655377) = c_List_Olist_ONil(_1655373))], (43660 ^ _781215) ^ [_1653321] : [class_Orderings_Olinorder(_1653321), -(c_List_Olinorder__class_Osorted__list__of__set(_1653321, c_Orderings_Obot__class_Obot(tc_fun(_1653321, tc_HOL_Obool))) = c_List_Olist_ONil(_1653321))], (20563 ^ _781215) ^ [_1150235] : [-(c_Int_OBit1(_1150235) = 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)), _1150235)), _1150235))], (4022 ^ _781215) ^ [_842226, _842228, _842230, _842232] : [-(c_Complete__Lattice_OInf__class_OInf(_842232, _842228) = c_Complete__Lattice_OInf__class_OInf(_842230, _842226)), _842232 = _842230, _842228 = _842226], (35261 ^ _781215) ^ [_1443354, _1443356, _1443358, _1443360, _1443362] : [c_Fun_Oinj__on(_1443354, _1443356, _1443358, _1443360), hBOOL(hAPP(hAPP(c_member(_1443356), _1443362), hAPP(c_Set_Oimage(_1443354, _1443356, _1443358), _1443360))), -(hAPP(_1443358, hAPP(c_Fun_Othe__inv__into(_1443354, _1443356, _1443360, _1443358), _1443362)) = _1443362)], (43704 ^ _781215) ^ [_1654149, _1654151] : [-(c_List_Olistrelp(_1654149, _1654151, c_List_Olist_ONil(_1654149), c_List_Olist_ONil(_1654149)))], (24674 ^ _781215) ^ [_1226633, _1226635, _1226637] : [class_Rings_Oring__1__no__zero__divisors(_1226633), -(_1226635 = c_Groups_Ozero__class_Ozero(_1226633)), hAPP(hAPP(c_Power_Opower__class_Opower(_1226633), _1226635), _1226637) = c_Groups_Ozero__class_Ozero(_1226633)], (51182 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (48956 ^ _781215) ^ [_1769375, _1769377] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1769375), _1769377) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1769375)), hAPP(c_Code__Numeral_Onat__of, _1769377))))], (1022 ^ _781215) ^ [_796864, _796866, _796868, _796870] : [-(c_FunDef_Ois__measure(_796868, _796864)), c_FunDef_Ois__measure(_796870, _796866), _796870 = _796868, _796866 = _796864], (25238 ^ _781215) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (51472 ^ _781215) ^ [_1823467, _1823469] : [-(class_Finite__Set_Ofinite(tc_sum(_1823467, _1823469))), class_Finite__Set_Ofinite(_1823467), class_Finite__Set_Ofinite(_1823469)], (17619 ^ _781215) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33188 ^ _781215) ^ [_1397806, _1397808, _1397810, _1397812] : [-(hBOOL(hAPP(hAPP(c_member(_1397806), _1397808), _1397810))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397806, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1397806), _1397808), _1397812)), _1397810) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397806, tc_HOL_Obool)), _1397812), _1397810))], (47460 ^ _781215) ^ [_1736180, _1736182] : [-(hBOOL(hAPP(c_List_Olistsp(_1736180, _1736182), c_List_Olist_ONil(_1736180))))], (37717 ^ _781215) ^ [_1497824, _1497826, _1497828, _1497830, _1497832, _1497834, _1497836] : [c_Typedef_Otype__definition(_1497824, _1497826, _1497828, _1497830, _1497832), 37720 ^ _781215 : [(37727 ^ _781215) ^ [] : [_1497834 = _1497836, -(hAPP(_1497828, _1497834) = hAPP(_1497828, _1497836))], (37721 ^ _781215) ^ [] : [hAPP(_1497828, _1497834) = hAPP(_1497828, _1497836), -(_1497834 = _1497836)]]], (42975 ^ _781215) ^ [_1636435, _1636437, _1636439, _1636441] : [-(hAPP(hAPP(c_List_Olist__update(_1636435, hAPP(hAPP(c_List_Olist_OCons(_1636435), _1636437), _1636439)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1636441) = hAPP(hAPP(c_List_Olist_OCons(_1636435), _1636441), _1636439))], (12310 ^ _781215) ^ [_995274, _995276, _995278, _995280] : [class_Rings_Oordered__semiring(_995274), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995274), _995276), _995278)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995274), c_Groups_Ozero__class_Ozero(_995274)), _995280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995274), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995274), _995276), _995280)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995274), _995278), _995280))))], (17799 ^ _781215) ^ [_1099127] : [class_Rings_Osemiring__1(_1099127), -(hBOOL(hAPP(hAPP(c_member(_1099127), c_Groups_Ozero__class_Ozero(_1099127)), c_Nat_Osemiring__1__class_ONats(_1099127))))], (22992 ^ _781215) ^ [_1195759, _1195761, _1195763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195759), _1195761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195763), 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), _1195761), _1195763)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195759), _1195763))))], (40265 ^ _781215) ^ [_1567997, _1567999] : [-(c_HOL_OThe(_1567997, hAPP(hAPP(c_COMBC(_1567997, _1567997, tc_HOL_Obool), c_fequal), _1567999)) = _1567999)], (42325 ^ _781215) ^ [_1619394, _1619396, _1619398, _1619400, _1619402, _1619404] : [-(hAPP(hAPP(c_List_Ozip(_1619394, _1619396), hAPP(hAPP(c_List_Olist_OCons(_1619394), _1619398), _1619400)), hAPP(hAPP(c_List_Olist_OCons(_1619396), _1619402), _1619404)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1619394, _1619396)), hAPP(hAPP(c_Product__Type_OPair(_1619394, _1619396), _1619398), _1619402)), hAPP(hAPP(c_List_Ozip(_1619394, _1619396), _1619400), _1619404)))], (20870 ^ _781215) ^ [_1155325, _1155327] : [class_Rings_Osemiring__1(_1155325), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1155325), hAPP(c_Nat_OSuc, _1155327)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155325), c_Groups_Oone__class_Oone(_1155325)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1155325), _1155327)))], (43474 ^ _781215) ^ [_1648941, _1648943] : [hBOOL(hAPP(_1648941, c_Hilbert__Choice_OEps(_1648943, _1648941))), -(hBOOL(hAPP(_1648941, 43477 ^ [_1648941, _1648943])))], (23618 ^ _781215) ^ [_1206738, _1206740, _1206742] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206738), _1206740)), _1206742) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206738), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1206740), _1206742))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206738), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1206740, _1206742))), _1206742)))], (38544 ^ _781215) ^ [_1517903, _1517905, _1517907] : [c_Equiv__Relations_Oequiv(_1517903, _1517905, _1517907), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517903, _1517903), tc_HOL_Obool)), _1517907), hAPP(hAPP(c_Product__Type_OSigma(_1517903, _1517903), _1517905), hAPP(c_COMBK(tc_fun(_1517903, tc_HOL_Obool), _1517903), _1517905)))))], (24372 ^ _781215) ^ [_1220680, _1220682] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220680))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220680), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220682)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23174 ^ _781215) ^ [_1198565, _1198567, _1198569, _1198571] : [class_Divides_Osemiring__div(_1198565), -(_1198567 = c_Groups_Ozero__class_Ozero(_1198565)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1198565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198565), _1198569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1198565), _1198567), _1198571))), _1198567) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198565), _1198571), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1198565), _1198569), _1198567)))], (15302 ^ _781215) ^ [_1049655, _1049657] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049655), _1049657) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049657), _1049655))], (33008 ^ _781215) ^ [_1393588, _1393590, _1393592, _1393594] : [class_Lattices_Osemilattice__inf(_1393588), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393588), _1393590), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393588), _1393592), _1393594)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393588), _1393592), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393588), _1393590), _1393594)))], (50962 ^ _781215) ^ [_1817202, _1817204, _1817206, _1817208] : [-(c_Lazy__Sequence_Oproduct(_1817202, _1817204, _1817206, _1817208) = hAPP(c_Lazy__Sequence_Obind(_1817202, tc_prod(_1817202, _1817204), _1817206), hAPP(hAPP(c_COMBB(tc_fun(_1817204, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1817202, _1817204))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1817202, _1817204)), _1817202), c_Lazy__Sequence_Obind(_1817204, tc_prod(_1817202, _1817204), _1817208)), hAPP(hAPP(c_COMBB(tc_fun(_1817204, tc_prod(_1817202, _1817204)), tc_fun(_1817204, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1817202, _1817204))), _1817202), hAPP(c_COMBB(tc_prod(_1817202, _1817204), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1817202, _1817204)), _1817204), c_Lazy__Sequence_Osingle(tc_prod(_1817202, _1817204)))), c_Product__Type_OPair(_1817202, _1817204)))))], (32776 ^ _781215) ^ [_1388155, _1388157, _1388159, _1388161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388155, tc_HOL_Obool)), _1388157), _1388159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388155, tc_HOL_Obool)), _1388157), _1388161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388155, tc_HOL_Obool)), _1388157), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388155, tc_HOL_Obool)), _1388159), _1388161))))], (246 ^ _781215) ^ [_784996, _784998] : [-(class_Fields_Ofield(_784996)), _784998 = _784996, class_Fields_Ofield(_784998)], (17593 ^ _781215) ^ [] : [-(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))))], (26336 ^ _781215) ^ [_1259069, _1259071, _1259073, _1259075, _1259077] : [class_Groups_Ocomm__monoid__mult(_1259069), hBOOL(hAPP(c_Finite__Set_Ofinite(_1259071), _1259073)), -(hBOOL(hAPP(hAPP(c_member(_1259071), _1259075), _1259073))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1259071, _1259069), _1259077), hAPP(hAPP(c_Set_Oinsert(_1259071), _1259075), _1259073)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1259069), hAPP(_1259077, _1259075)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1259071, _1259069), _1259077), _1259073)))], (25570 ^ _781215) ^ [_1241353, _1241355] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1241353, _1241355)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1241355), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1241353), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (15290 ^ _781215) ^ [_1049397, _1049399] : [-(hAPP(c_Set_Oimage(_1049397, _1049397, c_COMBI(_1049397)), _1049399) = _1049399)], (5843 ^ _781215) ^ [_874167, _874169] : [c_Option_Ois__none(_874167, _874169), -(_874169 = c_Option_Ooption_ONone(_874167))], (40932 ^ _781215) ^ [_1583934, _1583936, _1583938, _1583940, _1583942, _1583944, _1583946] : [c_Fun_Oinj__on(_1583934, _1583936, _1583938, c_Orderings_Otop__class_Otop(tc_fun(_1583934, tc_HOL_Obool))), hAPP(hAPP(c_Map_Omap__of(_1583934, _1583940), _1583942), _1583944) = hAPP(c_Option_Ooption_OSome(_1583940), _1583946), -(hAPP(hAPP(c_Map_Omap__of(_1583936, _1583940), hAPP(hAPP(c_List_Omap(tc_prod(_1583934, _1583940), tc_prod(_1583936, _1583940)), hAPP(c_Product__Type_Oprod_Oprod__case(_1583934, _1583940, tc_prod(_1583936, _1583940)), hAPP(hAPP(c_COMBB(_1583936, tc_fun(_1583940, tc_prod(_1583936, _1583940)), _1583934), c_Product__Type_OPair(_1583936, _1583940)), _1583938))), _1583942)), hAPP(_1583938, _1583944)) = hAPP(c_Option_Ooption_OSome(_1583940), _1583946))], (41327 ^ _781215) ^ [_1593210, _1593212, _1593214, _1593216, _1593218, _1593220, _1593222, _1593224, _1593226, _1593228, _1593230] : [hAPP(_1593210, hAPP(_1593212, _1593214)) = hAPP(_1593216, hAPP(_1593218, _1593220)), -(hAPP(hAPP(c_Fun_Ocomp(_1593222, _1593224, _1593226, _1593210), _1593212), _1593214) = hAPP(hAPP(c_Fun_Ocomp(_1593228, _1593224, _1593230, _1593216), _1593218), _1593220))], (16483 ^ _781215) ^ [_1073992, _1073994, _1073996] : [hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(_1073992, tc_HOL_Obool, hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_HOL_Obool))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_HOL_Obool)), tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1073992, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_HOL_OAll(_1073992)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_HOL_Obool))), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_HOL_Obool)), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_HOL_Obool), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, _1073992), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBC(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(_1073992, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBS(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1073992, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1073992), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1073992), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1073992), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1073992, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_Com_Ocom), c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1073992)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))), hAPP(hAPP(c_COMBC(tc_Com_Ocom, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_Natural_Oevaln)), _1073994))))))))), _1073996)), -(c_Hoare__Mirabelle_Otriple__valid(_1073992, _1073994, _1073996))], (38280 ^ _781215) ^ [_1510679, _1510681, _1510683] : [-(hAPP(c_Set_Ovimage(_1510679, _1510681, _1510683), c_Orderings_Otop__class_Otop(tc_fun(_1510681, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1510679, tc_HOL_Obool)))], (31547 ^ _781215) ^ [_1361096, _1361098, _1361100, _1361102, _1361104] : [class_Rings_Osemiring__0(_1361096), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361096), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361098, _1361096), _1361100), _1361102)), _1361104) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361098, _1361096), hAPP(hAPP(c_COMBC(_1361098, _1361096, _1361096), hAPP(hAPP(c_COMBB(_1361096, tc_fun(_1361096, _1361096), _1361098), c_Groups_Otimes__class_Otimes(_1361096)), _1361100)), _1361104)), _1361102))], (7374 ^ _781215) ^ [_905521, _905523, _905525] : [class_Orderings_Olinorder(_905521), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905521), _905523), _905525))), 7381 ^ _781215 : [(7388 ^ _781215) ^ [] : [_905525 = _905523, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905521), _905525), _905523))], (7382 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905521), _905525), _905523))), -(_905525 = _905523)]]], (39391 ^ _781215) ^ [_1541298, _1541300, _1541302, _1541304] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1541298), hAPP(c_Set_OCollect(_1541298), _1541300))), 39394 ^ _781215 : [(39395 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1541302), hAPP(c_Set_OCollect(_1541302), hAPP(hAPP(c_COMBB(tc_fun(_1541298, tc_HOL_Obool), tc_HOL_Obool, _1541302), c_HOL_OEx(_1541298)), hAPP(hAPP(c_COMBB(tc_fun(_1541298, tc_HOL_Obool), tc_fun(_1541298, tc_HOL_Obool), _1541302), hAPP(c_COMBS(_1541298, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541298), c_fconj), _1541300))), _1541304))))), 39398 ^ _781215 : [(39399 ^ _781215) ^ [_1541581] : [hBOOL(hAPP(_1541300, _1541581)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1541302), hAPP(c_Set_OCollect(_1541302), hAPP(hAPP(c_COMBC(_1541302, _1541298, tc_HOL_Obool), _1541304), _1541581)))))]]], (39405 ^ _781215) ^ [] : [39407 ^ _781215 : [(39410 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1541302), hAPP(c_Set_OCollect(_1541302), hAPP(hAPP(c_COMBC(_1541302, _1541298, tc_HOL_Obool), _1541304), 39406 ^ [_1541298, _1541300, _1541302, _1541304]))))], (39408 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1541300, 39406 ^ [_1541298, _1541300, _1541302, _1541304])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1541302), hAPP(c_Set_OCollect(_1541302), hAPP(hAPP(c_COMBB(tc_fun(_1541298, tc_HOL_Obool), tc_HOL_Obool, _1541302), c_HOL_OEx(_1541298)), hAPP(hAPP(c_COMBB(tc_fun(_1541298, tc_HOL_Obool), tc_fun(_1541298, tc_HOL_Obool), _1541302), hAPP(c_COMBS(_1541298, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541298), c_fconj), _1541300))), _1541304))))))]]], (31880 ^ _781215) ^ [_1368457, _1368459, _1368461, _1368463] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1368457), _1368459)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1368457, tc_HOL_Obool)), _1368459), _1368461)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1368457, tc_Nat_Onat), _1368463), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368457, tc_HOL_Obool)), _1368461), _1368459)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1368457, tc_Nat_Onat), _1368463), _1368461)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1368457, tc_Nat_Onat), _1368463), _1368459)))], (27858 ^ _781215) ^ [_1289074, _1289076, _1289078, _1289080] : [class_Rings_Odivision__ring(_1289074), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289074), _1289076), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289074), _1289078), _1289080)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289074), _1289076), _1289078)), _1289080))], (38035 ^ _781215) ^ [_1504682, _1504684, _1504686, _1504688] : [-(_1504682 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1504684, tc_HOL_Obool), tc_HOL_Obool))), 38041 ^ _781215 : [(38044 ^ _781215) ^ [] : [c_Fun_Oinj__on(_1504684, _1504686, _1504688, 38040 ^ [_1504682, _1504684, _1504686, _1504688])], (38042 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1504684, tc_HOL_Obool)), 38040 ^ [_1504682, _1504684, _1504686, _1504688]), _1504682)))]], -(c_Fun_Oinj__on(_1504684, _1504686, _1504688, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1504684, tc_HOL_Obool), _1504682)))], (21303 ^ _781215) ^ [_1163038, _1163040, _1163042, _1163044, _1163046] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1163038, tc_fun(_1163040, tc_HOL_Obool)), _1163042), _1163044), _1163046)), 21307 ^ _781215 : [(21310 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1163044, 21306 ^ [_1163038, _1163040, _1163042, _1163044, _1163046]), _1163046)))], (21308 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1163038), 21306 ^ [_1163038, _1163040, _1163042, _1163044, _1163046]), _1163042)))]]], (45460 ^ _781215) ^ [_1694003, _1694005, _1694007] : [class_Orderings_Olinorder(_1694003), -(c_List_Olinorder__class_Osorted(_1694003, hAPP(c_List_Ofilter(_1694003, hAPP(hAPP(c_COMBC(_1694003, _1694003, tc_HOL_Obool), c_fequal), hAPP(_1694005, _1694007))), _1694007)))], (20711 ^ _781215) ^ [_1152768, _1152770] : [class_Int_Onumber__ring(_1152768), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152768), hAPP(c_Int_Onumber__class_Onumber__of(_1152768), c_Int_OBit1(c_Int_OPls))), _1152770) = _1152770)], (30151 ^ _781215) ^ [_1332843, _1332845, _1332847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332843, tc_HOL_Obool)), _1332845), _1332847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1332843, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1332843), _1332845)), hAPP(c_Set_OPow(_1332843), _1332847))))], (23542 ^ _781215) ^ [_1205314, _1205316] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205314))), -(c_SMT_Oz3mod(_1205316, _1205314) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1205316, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205314)))], (17095 ^ _781215) ^ [_1087750] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087750))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087750) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22645 ^ _781215) ^ [_1190079, _1190081, _1190083] : [class_Divides_Osemiring__div(_1190079), -(_1190081 = c_Groups_Ozero__class_Ozero(_1190079)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190079), _1190083), _1190081)), _1190081) = _1190083)], (15572 ^ _781215) ^ [_1054622] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1054622) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1054622)))], (32978 ^ _781215) ^ [_1392873, _1392875, _1392877, _1392879] : [class_Lattices_Osemilattice__inf(_1392873), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1392873), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1392873), _1392875), _1392877)), _1392879) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1392873), _1392875), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1392873), _1392877), _1392879)))], (256 ^ _781215) ^ [_785121, _785123, _785125, _785127, _785129, _785131, _785133, _785135, _785137, _785139] : [-(c_Big__Operators_Ocomm__monoid__big(_785137, _785133, _785129, _785125, _785121)), c_Big__Operators_Ocomm__monoid__big(_785139, _785135, _785131, _785127, _785123), _785139 = _785137, _785135 = _785133, _785131 = _785129, _785127 = _785125, _785123 = _785121], (39842 ^ _781215) ^ [_1557065, _1557067, _1557069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557065, _1557065), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1557065, _1557065, _1557065), _1557067), _1557069)), _1557067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1557065, tc_HOL_Obool), tc_fun(_1557065, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1557065, tc_HOL_Obool), tc_fun(_1557065, tc_HOL_Obool), tc_fun(_1557065, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1557065, _1557067)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1557065, tc_HOL_Obool), tc_fun(_1557065, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1557065, _1557069)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1557065, tc_HOL_Obool), tc_fun(_1557065, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1557065, tc_HOL_Obool), tc_fun(_1557065, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1557065, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1557065, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1557065, tc_HOL_Obool), tc_fun(_1557065, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1557065, _1557067))))], (19242 ^ _781215) ^ [_1126503, _1126505] : [class_Orderings_Olinorder(_1126503), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126503), _1126505)), -(c_Big__Operators_Olinorder__class_OMin(_1126503, _1126505) = hAPP(c_Finite__Set_Ofold1(_1126503, c_Orderings_Oord__class_Omin(_1126503)), _1126505))], (5538 ^ _781215) ^ [_865766, _865768] : [_865768 = _865766, -(c_Set_Oinsert(_865768) = c_Set_Oinsert(_865766))], (38568 ^ _781215) ^ [_1518679, _1518681, _1518683, _1518685, _1518687, _1518689] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1518679, _1518681)), hAPP(hAPP(c_Product__Type_OPair(_1518679, _1518681), _1518683), _1518685)), hAPP(hAPP(c_Product__Type_OSigma(_1518679, _1518681), _1518687), _1518689))), -(hBOOL(hAPP(hAPP(c_member(_1518681), _1518685), hAPP(_1518689, _1518683))))], (16595 ^ _781215) ^ [_1077239, _1077241, _1077243] : [class_Lattices_Oab__semigroup__idem__mult(_1077239), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077239), _1077241)), -(_1077241 = c_Orderings_Obot__class_Obot(tc_fun(_1077239, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077239), _1077243)), -(_1077243 = c_Orderings_Obot__class_Obot(tc_fun(_1077239, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1077239, c_Groups_Otimes__class_Otimes(_1077239)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1077239, tc_HOL_Obool)), _1077241), _1077243)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077239), hAPP(c_Finite__Set_Ofold1(_1077239, c_Groups_Otimes__class_Otimes(_1077239)), _1077241)), hAPP(c_Finite__Set_Ofold1(_1077239, c_Groups_Otimes__class_Otimes(_1077239)), _1077243)))], (22779 ^ _781215) ^ [_1192386] : [c_Nat__Transfer_Onat__set(_1192386), 22782 ^ _781215 : [(22783 ^ _781215) ^ [_1192452] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1192452), _1192386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192452)))]]], (32381 ^ _781215) ^ [_1380180, _1380182, _1380184, _1380186, _1380188, _1380190, _1380192] : [c_Equiv__Relations_Oequiv(_1380180, _1380182, _1380184), hBOOL(hAPP(hAPP(c_member(tc_fun(_1380180, tc_HOL_Obool)), _1380186), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1380180), _1380182), _1380184))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1380180, tc_HOL_Obool)), _1380188), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1380180), _1380182), _1380184))), hBOOL(hAPP(hAPP(c_member(_1380180), _1380190), _1380186)), hBOOL(hAPP(hAPP(c_member(_1380180), _1380192), _1380188)), 32400 ^ _781215 : [(32407 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1380180, _1380180)), hAPP(hAPP(c_Product__Type_OPair(_1380180, _1380180), _1380190), _1380192)), _1380184)), -(_1380186 = _1380188)], (32401 ^ _781215) ^ [] : [_1380186 = _1380188, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1380180, _1380180)), hAPP(hAPP(c_Product__Type_OPair(_1380180, _1380180), _1380190), _1380192)), _1380184)))]]], (44696 ^ _781215) ^ [_1677463, _1677465, _1677467, _1677469, _1677471] : [-(hAPP(hAPP(c_List_Oappend(_1677463), _1677465), _1677467) = hAPP(hAPP(c_List_Oappend(_1677463), _1677469), _1677471)), 44699 ^ _781215 : [(44702 ^ _781215) ^ [] : [_1677465 = hAPP(hAPP(c_List_Otake(_1677463), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677463)), _1677465)), _1677469), _1677467 = hAPP(hAPP(c_List_Oappend(_1677463), hAPP(hAPP(c_List_Odrop(_1677463), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677463)), _1677465)), _1677469)), _1677471)], (44700 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677463)), _1677465)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677463)), _1677469))))]], 44707 ^ _781215 : [(44710 ^ _781215) ^ [] : [hAPP(hAPP(c_List_Otake(_1677463), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677463)), _1677469)), _1677465) = _1677469, hAPP(hAPP(c_List_Oappend(_1677463), hAPP(hAPP(c_List_Odrop(_1677463), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677463)), _1677469)), _1677465)), _1677467) = _1677471], (44708 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677463)), _1677465)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677463)), _1677469)))]]], (38003 ^ _781215) ^ [_1504157, _1504159, _1504161] : [class_Complete__Lattice_Ocomplete__lattice(_1504157), -(c_Complete__Lattice_OSup__class_OSup(_1504157, hAPP(hAPP(c_Set_Oinsert(_1504157), _1504159), hAPP(hAPP(c_Set_Oinsert(_1504157), _1504161), c_Orderings_Obot__class_Obot(tc_fun(_1504157, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1504157), _1504159), _1504161))], (9759 ^ _781215) ^ [_947011, _947013, _947015, _947017] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_947011), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947011), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947011), _947013), _947015)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947011), _947017), _947015))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947011), _947013), _947017)))], (44108 ^ _781215) ^ [_1663214, _1663216, _1663218] : [-(c_List_Olist_ONil(_1663214) = hAPP(hAPP(c_List_Oappend(_1663214), _1663216), _1663218)), _1663216 = c_List_Olist_ONil(_1663214), _1663218 = c_List_Olist_ONil(_1663214)], (8069 ^ _781215) ^ [_917252, _917254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917252), _917254)), -(hAPP(c_Nat_OSuc, _917252) = _917254), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _917252)), _917254)))], (44397 ^ _781215) ^ [_1669819, _1669821, _1669823] : [hBOOL(hAPP(c_List_Odistinct(_1669819), hAPP(hAPP(c_List_Oappend(_1669819), _1669821), _1669823))), 44400 ^ _781215 : [(44405 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1669819, tc_HOL_Obool)), hAPP(c_List_Oset(_1669819), _1669821)), hAPP(c_List_Oset(_1669819), _1669823)) = c_Orderings_Obot__class_Obot(tc_fun(_1669819, tc_HOL_Obool)))], (44403 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1669819), _1669823)))], (44401 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1669819), _1669821)))]]], (40498 ^ _781215) ^ [_1574235, _1574237] : [40500 ^ _781215 : [(40503 ^ _781215) ^ [] : [hBOOL(hAPP(_1574237, 40499 ^ [_1574235, _1574237]))], (40501 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1574235), 40499 ^ [_1574235, _1574237]), c_Orderings_Otop__class_Otop(tc_fun(_1574235, tc_HOL_Obool)))))]], 40504 ^ _781215 : [(40505 ^ _781215) ^ [_1574387] : [-(hBOOL(hAPP(_1574237, _1574387)))]]], (43942 ^ _781215) ^ [_1659025, _1659027] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1659025)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1659027)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1659025), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1659027)) = c_List_Olist_ONil(tc_Int_Oint))], (9167 ^ _781215) ^ [_936788, _936790, _936792] : [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, _936788)), _936790)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _936788)), _936792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936790), _936792)))], (46163 ^ _781215) ^ [_1707627, _1707629, _1707631] : [-(c_List_Oconcat(_1707627, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1707627)), _1707629), _1707631)) = hAPP(hAPP(c_List_Oappend(_1707627), c_List_Oconcat(_1707627, _1707629)), c_List_Oconcat(_1707627, _1707631)))], (14762 ^ _781215) ^ [_1039686, _1039688, _1039690, _1039692, _1039694, _1039696] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1039686, _1039688, _1039690)), _1039692), _1039694), _1039696)), 14767 ^ _781215 : [(14770 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1039688), _1039692), _1039694), _1039696)))], (14768 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1039686, _1039692)))]], 14771 ^ _781215 : [(14774 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1039690), _1039692), _1039694), _1039696)))], (14772 ^ _781215) ^ [] : [hBOOL(hAPP(_1039686, _1039692))]]], (27442 ^ _781215) ^ [_1280664, _1280666, _1280668, _1280670, _1280672] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1280664, _1280666, _1280668), _1280670), _1280672) = hAPP(hAPP(_1280670, hAPP(c_Product__Type_Ofst(_1280664, _1280666), _1280672)), hAPP(c_Product__Type_Osnd(_1280664, _1280666), _1280672)))], (4340 ^ _781215) ^ [_847053, _847055, _847057, _847059] : [-(c_Relation_ODomain(_847059, _847055) = c_Relation_ODomain(_847057, _847053)), _847059 = _847057, _847055 = _847053], (25798 ^ _781215) ^ [_1245917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1245917), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1245917 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 25801 ^ [_1245917]))))], (19152 ^ _781215) ^ [_1124965, _1124967] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1124965), _1124967)), _1124967) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1124965), _1124967))], (49660 ^ _781215) ^ [_1787239, _1787241] : [c_Wellfounded_Oacyclic(_1787239, hAPP(c_Relation_Oconverse(_1787239, _1787239), _1787241)), -(c_Wellfounded_Oacyclic(_1787239, _1787241))], (45418 ^ _781215) ^ [_1692919, _1692921, _1692923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692919), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1692921))), c_List_Otranspose(_1692921, _1692923)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1692921)), c_List_Otranspose(_1692921, _1692923)), _1692919) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692921), _1692921), hAPP(hAPP(c_COMBC(tc_List_Olist(_1692921), tc_Nat_Onat, _1692921), c_List_Onth(_1692921)), _1692919)), hAPP(c_List_Ofilter(tc_List_Olist(_1692921), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1692921)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692919)), c_Nat_Osize__class_Osize(tc_List_Olist(_1692921)))), _1692923)))], (35667 ^ _781215) ^ [_1451634, _1451636, _1451638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1451636), 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), _1451636), _1451638))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1451634))), _1451638)))], (3172 ^ _781215) ^ [_828963, _828965, _828967, _828969, _828971, _828973] : [-(c_Hilbert__Choice_OGreatestM(_828973, _828969, _828965) = c_Hilbert__Choice_OGreatestM(_828971, _828967, _828963)), _828973 = _828971, _828969 = _828967, _828965 = _828963], (51642 ^ _781215) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (49606 ^ _781215) ^ [_1785612] : [-(hAPP(c_Relation_Oconverse(_1785612, _1785612), c_Relation_OId(_1785612)) = c_Relation_OId(_1785612))], (38906 ^ _781215) ^ [_1527828, _1527830, _1527832, _1527834] : [c_Relation_Orefl__on(_1527828, _1527830, _1527832), hBOOL(hAPP(hAPP(c_member(_1527828), _1527834), _1527830)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1527828, _1527828)), hAPP(hAPP(c_Product__Type_OPair(_1527828, _1527828), _1527834), _1527834)), _1527832)))], (20436 ^ _781215) ^ [_1147966, _1147968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147966)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147968))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1147966), _1147968)))], (26789 ^ _781215) ^ [_1267886, _1267888, _1267890, _1267892, _1267894, _1267896, _1267898] : [hBOOL(hAPP(hAPP(c_member(_1267886), _1267888), hAPP(hAPP(_1267890, _1267892), _1267894))), -(hBOOL(hAPP(hAPP(c_member(_1267886), _1267888), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1267896, _1267898, tc_fun(_1267886, tc_HOL_Obool)), _1267890), hAPP(hAPP(c_Product__Type_OPair(_1267896, _1267898), _1267892), _1267894)))))], (45341 ^ _781215) ^ [_1690775, _1690777] : [-(hAPP(c_List_Ofilter(_1690775, _1690777), c_List_Olist_ONil(_1690775)) = c_List_Olist_ONil(_1690775))], (18782 ^ _781215) ^ [_1118048, _1118050] : [class_Orderings_Olinorder(_1118048), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1118048), _1118050), _1118050) = _1118050)], (15550 ^ _781215) ^ [_1054041, _1054043, _1054045, _1054047, _1054049] : [-(c_Map_Omap__comp(_1054041, _1054043, _1054045, _1054047, hAPP(c_COMBK(tc_Option_Ooption(_1054041), _1054045), c_Option_Ooption_ONone(_1054041)), _1054049) = c_Option_Ooption_ONone(_1054043))], (3624 ^ _781215) ^ [_836097, _836099] : [_836099 = _836097, -(c_Power_Opower__class_Opower(_836099) = c_Power_Opower__class_Opower(_836097))], (11118 ^ _781215) ^ [_973677, _973679, _973681] : [class_Rings_Ocomm__ring__1(_973677), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_973677), _973679), _973681) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973677), _973679), hAPP(c_Groups_Ouminus__class_Ouminus(_973677), _973681)))], (8037 ^ _781215) ^ [_916768, _916770] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916768), _916770))), 8040 ^ _781215 : [(8047 ^ _781215) ^ [] : [_916768 = _916770, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916768), hAPP(c_Nat_OSuc, _916770))))], (8041 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916768), hAPP(c_Nat_OSuc, _916770))), -(_916768 = _916770)]]], (46032 ^ _781215) ^ [_1704340, _1704342, _1704344, _1704346, _1704348] : [class_Orderings_Olinorder(_1704340), c_Fun_Oinj__on(_1704342, _1704340, _1704344, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1704342, tc_HOL_Obool)), hAPP(c_List_Oset(_1704342), _1704346)), hAPP(c_List_Oset(_1704342), _1704348))), c_List_Olinorder__class_Osorted(_1704340, hAPP(hAPP(c_List_Omap(_1704342, _1704340), _1704344), _1704346)), hBOOL(hAPP(c_List_Odistinct(_1704340), hAPP(hAPP(c_List_Omap(_1704342, _1704340), _1704344), _1704346))), c_List_Olinorder__class_Osorted(_1704340, hAPP(hAPP(c_List_Omap(_1704342, _1704340), _1704344), _1704348)), hBOOL(hAPP(c_List_Odistinct(_1704340), hAPP(hAPP(c_List_Omap(_1704342, _1704340), _1704344), _1704348))), hAPP(c_List_Oset(_1704342), _1704346) = hAPP(c_List_Oset(_1704342), _1704348), -(_1704346 = _1704348)], (40631 ^ _781215) ^ [_1577391, _1577393, _1577395, _1577397, _1577399] : [hBOOL(hAPP(_1577391, _1577393)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1577395), _1577393), _1577397)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1577391, _1577395)), _1577397), _1577399)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1577391, _1577395)), _1577393), _1577399)))], (494 ^ _781215) ^ [_788886, _788888] : [-(c_Nat__Transfer_Onat__set(_788886)), _788888 = _788886, c_Nat__Transfer_Onat__set(_788888)], (27564 ^ _781215) ^ [] : [-(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)))))], (23622 ^ _781215) ^ [_1206894, _1206896] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1206894), _1206896)), _1206896) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206894), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1206894, _1206896)))], (42407 ^ _781215) ^ [_1621066, _1621068, _1621070, _1621072, _1621074, _1621076] : [class_Orderings_Olinorder(_1621066), 42410 ^ _781215 : [(42417 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621066), hAPP(_1621068, _1621070)), hAPP(_1621068, _1621072)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1621074, _1621066, _1621068), _1621070), hAPP(hAPP(c_List_Olist_OCons(_1621074), _1621072), _1621076)) = hAPP(hAPP(c_List_Olist_OCons(_1621074), _1621072), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1621074, _1621066, _1621068), _1621070), _1621076)))], (42411 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621066), hAPP(_1621068, _1621070)), hAPP(_1621068, _1621072))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1621074, _1621066, _1621068), _1621070), hAPP(hAPP(c_List_Olist_OCons(_1621074), _1621072), _1621076)) = hAPP(hAPP(c_List_Olist_OCons(_1621074), _1621070), hAPP(hAPP(c_List_Olist_OCons(_1621074), _1621072), _1621076)))]]], (16917 ^ _781215) ^ [_1085061, _1085063, _1085065] : [-(c_Smallcheck_Oorelse(_1085061, _1085063, _1085065) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1085061), _1085061, _1085065, c_Option_Ooption_OSome(_1085061)), _1085063))], (50013 ^ _781215) ^ [_1795819, _1795821, _1795823] : [50014 ^ _781215 : [(50015 ^ _781215) ^ [_1795895] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1795819, _1795819)), _1795821), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1795819, _1795819), tc_HOL_Obool), _1795895), _1795823)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1795819, _1795819)), _1795821), c_Transitive__Closure_Ortrancl(_1795819, _1795823))))], (51286 ^ _781215) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (36153 ^ _781215) ^ [_1460998] : [_1460998 = 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), _1460998)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (45742 ^ _781215) ^ [_1698695, _1698697] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1698695, _1698697)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1698695), _1698697))], (46500 ^ _781215) ^ [_1716401, _1716403, _1716405] : [hBOOL(hAPP(c_List_Odistinct(_1716401), _1716403)), -(hBOOL(hAPP(c_List_Odistinct(_1716401), c_List_OtakeWhile(_1716401, _1716405, _1716403))))], (4406 ^ _781215) ^ [_848040, _848042] : [_848042 = _848040, -(c_Nat_Ofunpow(_848042) = c_Nat_Ofunpow(_848040))], (37544 ^ _781215) ^ [_1494199, _1494201, _1494203] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1494199, tc_HOL_Obool)), _1494201), _1494203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494199, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494199, tc_HOL_Obool), _1494203)), _1494201)))], (37450 ^ _781215) ^ [_1491948, _1491950, _1491952] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1491948, hAPP(hAPP(c_COMBC(_1491948, tc_fun(tc_prod(_1491948, _1491948), tc_HOL_Obool), tc_fun(_1491948, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491948, tc_fun(tc_fun(tc_prod(_1491948, _1491948), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1491948, _1491948), tc_HOL_Obool), tc_fun(_1491948, tc_HOL_Obool)), _1491948), c_COMBC(_1491948, tc_fun(tc_prod(_1491948, _1491948), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491948, tc_prod(_1491948, _1491948)), tc_fun(_1491948, tc_fun(tc_fun(tc_prod(_1491948, _1491948), tc_HOL_Obool), tc_HOL_Obool)), _1491948), hAPP(c_COMBB(tc_prod(_1491948, _1491948), tc_fun(tc_fun(tc_prod(_1491948, _1491948), tc_HOL_Obool), tc_HOL_Obool), _1491948), c_member(tc_prod(_1491948, _1491948)))), c_Product__Type_OPair(_1491948, _1491948)))), _1491950)), _1491952)), -(hBOOL(hAPP(hAPP(c_member(_1491948), _1491952), c_Wellfounded_Oacc(_1491948, _1491950))))], (43708 ^ _781215) ^ [_1654211, _1654213] : [-(c_List_Olist_Olist__size(_1654211, _1654213, c_List_Olist_ONil(_1654211)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25805 ^ _781215) ^ [_1246030, _1246032] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1246030, _1246032))))], (39088 ^ _781215) ^ [_1531620, _1531622] : [-(hAPP(c_Set_OCollect(_1531620), hAPP(hAPP(c_COMBC(_1531620, tc_fun(_1531620, tc_HOL_Obool), tc_HOL_Obool), c_member(_1531620)), _1531622)) = _1531622)], (26875 ^ _781215) ^ [_1269518, _1269520, _1269522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269518, tc_fun(_1269518, tc_HOL_Obool))), _1269520), _1269522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269518, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1269518, _1269522)), c_Wellfounded_Oaccp(_1269518, _1269520))))], (51634 ^ _781215) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (29060 ^ _781215) ^ [_1311040, _1311042, _1311044] : [class_Fields_Olinordered__field(_1311040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311040), c_Groups_Ozero__class_Ozero(_1311040)), _1311042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311040), _1311044), c_Groups_Ozero__class_Ozero(_1311040))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311040), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311040), _1311042), _1311044)), c_Groups_Ozero__class_Ozero(_1311040))))], (16037 ^ _781215) ^ [_1064410, _1064412, _1064414, _1064416] : [class_Lattices_Olattice(_1064410), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064410), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064410), _1064412), _1064414)), _1064416) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064410), _1064412), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064410), _1064414), _1064416)))], (36790 ^ _781215) ^ [] : [-(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))))], (14425 ^ _781215) ^ [_1033473, _1033475] : [class_Groups_Osgn__if(_1033473), 14428 ^ _781215 : [(14435 ^ _781215) ^ [] : [-(_1033475 = c_Groups_Ozero__class_Ozero(_1033473)), 14438 ^ _781215 : [(14445 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033473), c_Groups_Ozero__class_Ozero(_1033473)), _1033475))), -(c_Groups_Osgn__class_Osgn(_1033473, _1033475) = hAPP(c_Groups_Ouminus__class_Ouminus(_1033473), c_Groups_Oone__class_Oone(_1033473)))], (14439 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033473), c_Groups_Ozero__class_Ozero(_1033473)), _1033475)), -(c_Groups_Osgn__class_Osgn(_1033473, _1033475) = c_Groups_Oone__class_Oone(_1033473))]]], (14429 ^ _781215) ^ [] : [_1033475 = c_Groups_Ozero__class_Ozero(_1033473), -(c_Groups_Osgn__class_Osgn(_1033473, _1033475) = c_Groups_Ozero__class_Ozero(_1033473))]]], (41100 ^ _781215) ^ [_1587619, _1587621, _1587623, _1587625, _1587627] : [hAPP(hAPP(c_Map_Omap__of(_1587619, _1587621), _1587623), _1587625) = hAPP(c_Option_Ooption_OSome(_1587621), _1587627), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587619, _1587621)), hAPP(hAPP(c_Product__Type_OPair(_1587619, _1587621), _1587625), _1587627)), hAPP(c_List_Oset(tc_prod(_1587619, _1587621)), _1587623))))], (51352 ^ _781215) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (45954 ^ _781215) ^ [_1702792, _1702794] : [class_Orderings_Olinorder(_1702792), hBOOL(hAPP(c_Finite__Set_Ofinite(_1702792), _1702794)), 45961 ^ _781215 : [(45966 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1702792), c_List_Olinorder__class_Osorted__list__of__set(_1702792, _1702794))))], (45964 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1702792, c_List_Olinorder__class_Osorted__list__of__set(_1702792, _1702794)))], (45962 ^ _781215) ^ [] : [-(hAPP(c_List_Oset(_1702792), c_List_Olinorder__class_Osorted__list__of__set(_1702792, _1702794)) = _1702794)]]], (29494 ^ _781215) ^ [_1318798, _1318800, _1318802, _1318804] : [class_Fields_Olinordered__field(_1318798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318798), c_Groups_Ozero__class_Ozero(_1318798)), _1318800)), 29501 ^ _781215 : [(29508 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318798), _1318802), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318798), _1318804), _1318800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318798), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318798), _1318802), _1318800)), _1318804)))], (29502 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318798), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318798), _1318802), _1318800)), _1318804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318798), _1318802), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318798), _1318804), _1318800))))]]], (5222 ^ _781215) ^ [_860902, _860904] : [_860904 = _860902, -(c_Groups_Ominus__class_Ominus(_860904) = c_Groups_Ominus__class_Ominus(_860902))], (21692 ^ _781215) ^ [_1170372] : [-(c_Int_Opred(c_Int_OBit1(_1170372)) = c_Int_OBit0(_1170372))], (25360 ^ _781215) ^ [_1238299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1238299))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1238299)))], (34126 ^ _781215) ^ [_1418909, _1418911, _1418913] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1418909), _1418911)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418909), _1418913)), 34136 ^ _781215 : [(34139 ^ _781215) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (34137 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418909), 34135 ^ [_1418909, _1418911, _1418913]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418909, tc_HOL_Obool)), _1418911), _1418913))))]], -(hAPP(c_Finite__Set_Ocard(_1418909), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1418909, tc_HOL_Obool)), _1418911), _1418913)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1418909), _1418911)), hAPP(c_Finite__Set_Ocard(_1418909), _1418913)))], (22206 ^ _781215) ^ [_1181778, _1181780, _1181782] : [-(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), _1181778), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181780), _1181778))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181780, _1181778))), _1181782) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181780), _1181782))], (41227 ^ _781215) ^ [_1590747, _1590749] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1590747), _1590749) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1590747, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1590749), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (29180 ^ _781215) ^ [_1313179, _1313181, _1313183, _1313185] : [class_Fields_Ofield__inverse__zero(_1313179), -(_1313181 = c_Groups_Ozero__class_Ozero(_1313179)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313179), _1313181), _1313183)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313179), _1313181), _1313185)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313179), _1313183), _1313185))], (51020 ^ _781215) ^ [_1818563] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1818563) = c_Lazy__Sequence_Osmall__lazy_H(_1818563, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1818563)))], (3696 ^ _781215) ^ [_837231, _837233, _837235, _837237, _837239, _837241] : [-(c_Enum_On__lists(_837241, _837237, _837233) = c_Enum_On__lists(_837239, _837235, _837231)), _837241 = _837239, _837237 = _837235, _837233 = _837231], (51068 ^ _781215) ^ [_1819381, _1819383] : [class_Lattices_Olattice(_1819381), -(class_Lattices_Osemilattice__sup(tc_fun(_1819383, _1819381)))], (49704 ^ _781215) ^ [_1788172, _1788174, _1788176] : [c_Relation_Orefl__on(_1788172, _1788174, _1788176), -(c_Relation_Orefl__on(_1788172, _1788174, hAPP(c_Relation_Oconverse(_1788172, _1788172), _1788176)))], (33164 ^ _781215) ^ [_1397399, _1397401, _1397403, _1397405] : [-(hBOOL(hAPP(hAPP(c_member(_1397399), _1397401), _1397403))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397399, tc_HOL_Obool)), _1397403), hAPP(hAPP(c_Set_Oinsert(_1397399), _1397401), _1397405)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397399, tc_HOL_Obool)), _1397403), _1397405))], (46696 ^ _781215) ^ [_1719990, _1719992] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1719990), _1719992) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1719990)), c_List_Oembed__list(_1719992))))], (8524 ^ _781215) ^ [_925876, _925878] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925876, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_925876, tc_HOL_Obool))), _925878)))], (39532 ^ _781215) ^ [_1546139, _1546141, _1546143] : [class_Lattices_Odistrib__lattice(_1546139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546139), _1546141)), -(_1546141 = c_Orderings_Obot__class_Obot(tc_fun(_1546139, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546139), _1546143)), -(_1546143 = c_Orderings_Obot__class_Obot(tc_fun(_1546139, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1546139), c_Big__Operators_Olattice__class_OSup__fin(_1546139, _1546141)), c_Big__Operators_Olattice__class_OSup__fin(_1546139, _1546143)) = c_Big__Operators_Olattice__class_OSup__fin(_1546139, hAPP(c_Set_OCollect(_1546139), hAPP(hAPP(c_COMBB(tc_fun(_1546139, tc_HOL_Obool), tc_HOL_Obool, _1546139), c_HOL_OEx(_1546139)), hAPP(hAPP(c_COMBB(tc_fun(_1546139, tc_fun(_1546139, tc_HOL_Obool)), tc_fun(_1546139, tc_HOL_Obool), _1546139), hAPP(c_COMBB(tc_fun(_1546139, tc_HOL_Obool), tc_HOL_Obool, _1546139), c_HOL_OEx(_1546139))), hAPP(hAPP(c_COMBC(_1546139, tc_fun(_1546139, tc_fun(_1546139, tc_HOL_Obool)), tc_fun(_1546139, tc_fun(_1546139, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1546139, tc_fun(tc_fun(_1546139, tc_HOL_Obool), tc_fun(_1546139, tc_HOL_Obool))), tc_fun(tc_fun(_1546139, tc_fun(_1546139, tc_HOL_Obool)), tc_fun(_1546139, tc_fun(_1546139, tc_HOL_Obool))), _1546139), c_COMBS(_1546139, tc_fun(_1546139, tc_HOL_Obool), tc_fun(_1546139, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1546139, tc_fun(_1546139, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1546139, tc_fun(tc_fun(_1546139, tc_HOL_Obool), tc_fun(_1546139, tc_HOL_Obool))), _1546139), hAPP(c_COMBB(tc_fun(_1546139, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1546139, tc_HOL_Obool), tc_fun(_1546139, tc_HOL_Obool)), _1546139), c_COMBS(_1546139, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1546139, tc_fun(_1546139, tc_HOL_Obool)), tc_fun(_1546139, tc_fun(_1546139, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1546139), hAPP(c_COMBB(tc_fun(_1546139, tc_HOL_Obool), tc_fun(_1546139, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1546139), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546139), c_fconj))), hAPP(hAPP(c_COMBC(_1546139, tc_fun(_1546139, tc_fun(_1546139, _1546139)), tc_fun(_1546139, tc_fun(_1546139, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1546139, _1546139), tc_fun(_1546139, tc_HOL_Obool)), tc_fun(tc_fun(_1546139, tc_fun(_1546139, _1546139)), tc_fun(_1546139, tc_fun(_1546139, tc_HOL_Obool))), _1546139), c_COMBB(tc_fun(_1546139, _1546139), tc_fun(_1546139, tc_HOL_Obool), _1546139)), hAPP(hAPP(c_COMBB(tc_fun(_1546139, tc_HOL_Obool), tc_fun(tc_fun(_1546139, _1546139), tc_fun(_1546139, tc_HOL_Obool)), _1546139), c_COMBB(_1546139, tc_HOL_Obool, _1546139)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1546139)))))), hAPP(hAPP(c_COMBC(_1546139, tc_fun(_1546139, tc_HOL_Obool), tc_fun(_1546139, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1546139, tc_HOL_Obool), tc_fun(_1546139, tc_HOL_Obool)), _1546139), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1546139)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546139), c_fconj), hAPP(hAPP(c_COMBC(_1546139, tc_fun(_1546139, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546139)), _1546141)))), hAPP(hAPP(c_COMBC(_1546139, tc_fun(_1546139, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546139)), _1546143))))))))], (45273 ^ _781215) ^ [_1689412, _1689414, _1689416, _1689418] : [-(hAPP(c_List_Ofilter(_1689412, _1689414), hAPP(c_List_Ofilter(_1689412, _1689416), _1689418)) = hAPP(c_List_Ofilter(_1689412, hAPP(hAPP(c_COMBS(_1689412, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1689412), c_fconj), _1689416)), _1689414)), _1689418))], (39673 ^ _781215) ^ [_1552183, _1552185] : [-(c_Product__Type_Omap__pair(_1552183, _1552183, _1552185, _1552185, c_COMBI(_1552183), c_COMBI(_1552185)) = c_Fun_Oid(tc_prod(_1552183, _1552185)))], (15544 ^ _781215) ^ [_1053898, _1053900, _1053902, _1053904] : [-(hAPP(c_Map_Orestrict__map(_1053898, _1053900, hAPP(c_COMBK(tc_Option_Ooption(_1053900), _1053898), c_Option_Ooption_ONone(_1053900)), _1053902), _1053904) = c_Option_Ooption_ONone(_1053900))], (36171 ^ _781215) ^ [_1461232, _1461234] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1461232), _1461234))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1461232))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1461234))))], (43894 ^ _781215) ^ [_1657726, _1657728, _1657730, _1657732] : [-(hAPP(hAPP(c_List_Otake(_1657726), _1657728), hAPP(hAPP(c_List_Olist_OCons(_1657726), _1657730), _1657732)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1657726), c_List_Olist_ONil(_1657726), hAPP(hAPP(c_COMBB(tc_List_Olist(_1657726), tc_List_Olist(_1657726), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1657726), _1657730)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1657726), tc_List_Olist(_1657726)), c_List_Otake(_1657726)), _1657732)), _1657728))], (9803 ^ _781215) ^ [_947781, _947783] : [class_Orderings_Obot(_947781), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947781), c_Orderings_Obot__class_Obot(_947781)), _947783)))], (11448 ^ _781215) ^ [_980822, _980824] : [_980822 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _980822), _980824) = _980824)], (38445 ^ _781215) ^ [_1514972] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1514972), c_Int_OInteg)), -(_1514972 = hAPP(c_Int_ORep__Integ, 38448 ^ [_1514972]))], (39683 ^ _781215) ^ [_1552384, _1552386, _1552388, _1552390] : [-(c_Product__Type_Oapsnd(_1552384, _1552386, _1552388, _1552390) = c_Product__Type_Omap__pair(_1552388, _1552388, _1552384, _1552386, c_Fun_Oid(_1552388), _1552390))], (11058 ^ _781215) ^ [_972248, _972250, _972252, _972254, _972256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972248), _972250)), 11061 ^ _781215 : [(11068 ^ _781215) ^ [] : [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), _972250), _972248)), _972252)), _972254) = _972256, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972250), _972252)), _972254) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972248), _972252)), _972256))], (11062 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972250), _972252)), _972254) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972248), _972252)), _972256), -(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), _972250), _972248)), _972252)), _972254) = _972256)]]], (41076 ^ _781215) ^ [_1587030, _1587032, _1587034, _1587036, _1587038, _1587040] : [-(hBOOL(hAPP(hAPP(c_member(_1587030), _1587032), hAPP(c_List_Oset(_1587030), _1587034)))), -(hAPP(hAPP(c_List_Omap(_1587030, _1587036), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1587030, _1587036), _1587038), _1587032), _1587040)), _1587034) = hAPP(hAPP(c_List_Omap(_1587030, _1587036), _1587038), _1587034))], (30996 ^ _781215) ^ [_1348616, _1348618, _1348620] : [class_Orderings_Oorder(_1348616), 30999 ^ _781215 : [(31006 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348616), _1348618), _1348620))), -(c_Orderings_Obot__class_Obot(tc_fun(_1348616, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1348616, _1348618), _1348620))], (31000 ^ _781215) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1348616, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1348616, _1348618), _1348620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348616), _1348618), _1348620))]]], (41417 ^ _781215) ^ [_1595250, _1595252, _1595254, _1595256, _1595258, _1595260] : [class_Groups_Ocomm__monoid__mult(_1595250), c_Fun_Oinj__on(_1595252, _1595254, _1595256, _1595258), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1595254, _1595250), _1595260), hAPP(c_Set_Oimage(_1595252, _1595254, _1595256), _1595258)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1595252, _1595250), hAPP(c_Fun_Ocomp(_1595254, _1595250, _1595252, _1595260), _1595256)), _1595258))], (21370 ^ _781215) ^ [_1164602, _1164604, _1164606, _1164608, _1164610] : [21372 ^ _781215 : [(21378 ^ _781215) ^ [] : [hBOOL(hAPP(_1164610, 21374 ^ [_1164602, _1164604, _1164606, _1164608, _1164610]))], (21376 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1164602), 21374 ^ [_1164602, _1164604, _1164606, _1164608, _1164610]), hAPP(_1164608, 21371 ^ [_1164602, _1164604, _1164606, _1164608, _1164610]))))], (21373 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1164604), 21371 ^ [_1164602, _1164604, _1164606, _1164608, _1164610]), _1164606)))]], 21379 ^ _781215 : [(21380 ^ _781215) ^ [_1164912] : [hBOOL(hAPP(hAPP(c_member(_1164602), _1164912), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1164604, tc_fun(_1164602, tc_HOL_Obool)), _1164606), _1164608))), -(hBOOL(hAPP(_1164610, _1164912)))]]], (22655 ^ _781215) ^ [_1190207, _1190209, _1190211] : [class_Divides_Osemiring__div(_1190207), -(_1190209 = c_Groups_Ozero__class_Ozero(_1190207)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190207), _1190209), _1190211)), _1190209) = _1190211)], (51098 ^ _781215) ^ [_1819776, _1819778] : [-(class_Finite__Set_Ofinite(tc_fun(_1819776, _1819778))), class_Finite__Set_Ofinite(_1819776), class_Finite__Set_Ofinite(_1819778)], (17991 ^ _781215) ^ [_1102377, _1102379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102377), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1102377), _1102379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1102377))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1102379))))], (38308 ^ _781215) ^ [_1511353, _1511355, _1511357, _1511359, _1511361, _1511363] : [-(hAPP(c_Set_Ovimage(_1511353, _1511355, _1511357), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1511359, tc_fun(_1511355, tc_HOL_Obool)), _1511361), _1511363)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1511359, tc_fun(_1511353, tc_HOL_Obool)), _1511361), hAPP(hAPP(c_COMBB(tc_fun(_1511355, tc_HOL_Obool), tc_fun(_1511353, tc_HOL_Obool), _1511359), c_Set_Ovimage(_1511353, _1511355, _1511357)), _1511363)))], (6106 ^ _781215) ^ [_879359, _879361] : [hBOOL(hAPP(c_Com_OWT, _879359)), hBOOL(hAPP(c_Com_OWT, _879361)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_879359, _879361))))], (49832 ^ _781215) ^ [_1791056, _1791058, _1791060, _1791062, _1791064, _1791066] : [c_Relation_Osingle__valued(_1791056, _1791058, _1791060), hBOOL(hAPP(hAPP(c_member(tc_prod(_1791056, _1791058)), hAPP(hAPP(c_Product__Type_OPair(_1791056, _1791058), _1791062), _1791064)), _1791060)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1791056, _1791058)), hAPP(hAPP(c_Product__Type_OPair(_1791056, _1791058), _1791062), _1791066)), _1791060)), -(_1791064 = _1791066)], (29706 ^ _781215) ^ [_1322672, _1322674, _1322676, _1322678] : [class_Fields_Ofield(_1322672), -(_1322674 = c_Groups_Ozero__class_Ozero(_1322672)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322672), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322672), _1322676), _1322674)), _1322678) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322672), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322672), _1322676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322672), _1322674), _1322678))), _1322674))], (23931 ^ _781215) ^ [_1212588, _1212590, _1212592] : [hBOOL(hAPP(_1212588, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1212590), _1212592))), 23934 ^ _781215 : [(23941 ^ _781215) ^ [] : [-(_1212592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 23944 ^ _781215 : [(23945 ^ _781215) ^ [_1212840, _1212842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1212840), _1212592)), _1212590 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1212592), _1212842)), _1212840), -(hBOOL(hAPP(_1212588, _1212842)))]]], (23935 ^ _781215) ^ [] : [_1212592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1212588, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (4864 ^ _781215) ^ [_855023, _855025] : [_855025 = _855023, -(c_HOL_Oequal__class_Oequal(_855025) = c_HOL_Oequal__class_Oequal(_855023))], (9797 ^ _781215) ^ [_947686, _947688] : [class_Groups_Ocomm__monoid__mult(_947686), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947686), _947688), c_Groups_Oone__class_Oone(_947686)) = _947688)], (19938 ^ _781215) ^ [_1138907, _1138909, _1138911] : [class_Orderings_Olinorder(_1138907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1138907), _1138909)), -(hBOOL(hAPP(hAPP(c_member(_1138907), _1138911), _1138909))), -(_1138909 = c_Orderings_Obot__class_Obot(tc_fun(_1138907, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1138907, hAPP(hAPP(c_Set_Oinsert(_1138907), _1138911), _1138909)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1138907), _1138911), c_Big__Operators_Olinorder__class_OMax(_1138907, _1138909)))], (30163 ^ _781215) ^ [_1333108, _1333110] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333108), _1333110)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1333108, tc_HOL_Obool)), hAPP(c_Set_OPow(_1333108), _1333110))))], (24702 ^ _781215) ^ [_1227034] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1227034) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (42291 ^ _781215) ^ [_1617874, _1617876, _1617878, _1617880] : [-(hBOOL(hAPP(hAPP(c_member(_1617874), _1617876), hAPP(c_List_Oset(_1617874), _1617878)))), hBOOL(hAPP(hAPP(c_member(_1617874), _1617876), hAPP(c_List_Oset(_1617874), c_List_Osublist(_1617874, _1617878, _1617880))))], (23432 ^ _781215) ^ [_1203439, _1203441, _1203443, _1203445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203441)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203441), _1203443)), -(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), _1203443), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1203445, _1203439))), _1203441)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1203443), _1203439))))], (19876 ^ _781215) ^ [_1137765, _1137767, _1137769] : [class_Orderings_Olinorder(_1137765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1137765), _1137767)), -(c_Big__Operators_Olinorder__class_OMax(_1137765, hAPP(hAPP(c_Set_Oinsert(_1137765), _1137769), _1137767)) = hAPP(hAPP(c_Finite__Set_Ofold(_1137765, _1137765, c_Orderings_Oord__class_Omax(_1137765)), _1137769), _1137767))], (48946 ^ _781215) ^ [_1769224, _1769226] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1769224)), hAPP(c_Code__Numeral_Oof__nat, _1769226)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1769224), _1769226)))], (49794 ^ _781215) ^ [_1790430] : [-(c_Relation_Osingle__valued(_1790430, _1790430, c_Relation_OId(_1790430)))], (46856 ^ _781215) ^ [_1723641, _1723643] : [hBOOL(hAPP(c_List_Odistinct(_1723641), _1723643)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1723641, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1723641), tc_fun(_1723641, tc_HOL_Obool)), c_List_Oset(_1723641)), c_Enum_Osublists(_1723641, _1723643)))))], (36586 ^ _781215) ^ [_1468785, _1468787] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468785, tc_HOL_Obool)), _1468787), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468785, tc_HOL_Obool)), _1468787)) = c_Orderings_Otop__class_Otop(tc_fun(_1468785, tc_HOL_Obool)))], (38464 ^ _781215) ^ [_1515402, _1515404, _1515406, _1515408, _1515410, _1515412] : [hBOOL(hAPP(hAPP(c_member(_1515402), _1515404), _1515406)), 38467 ^ _781215 : [(38474 ^ _781215) ^ [] : [_1515410 = _1515412, -(hAPP(hAPP(c_Product__Type_OSigma(_1515408, _1515402), _1515410), hAPP(c_COMBK(tc_fun(_1515402, tc_HOL_Obool), _1515408), _1515406)) = hAPP(hAPP(c_Product__Type_OSigma(_1515408, _1515402), _1515412), hAPP(c_COMBK(tc_fun(_1515402, tc_HOL_Obool), _1515408), _1515406)))], (38468 ^ _781215) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1515408, _1515402), _1515410), hAPP(c_COMBK(tc_fun(_1515402, tc_HOL_Obool), _1515408), _1515406)) = hAPP(hAPP(c_Product__Type_OSigma(_1515408, _1515402), _1515412), hAPP(c_COMBK(tc_fun(_1515402, tc_HOL_Obool), _1515408), _1515406)), -(_1515410 = _1515412)]]], (44726 ^ _781215) ^ [_1678257, _1678259, _1678261, _1678263] : [-(hAPP(c_List_Orotate1(_1678259), hAPP(hAPP(c_List_Olist_OCons(_1678259), _1678261), _1678263)) = hAPP(hAPP(c_List_Oappend(_1678259), _1678263), hAPP(hAPP(c_List_Olist_OCons(_1678259), _1678261), c_List_Olist_ONil(_1678259))))], (38430 ^ _781215) ^ [_1514514, _1514516, _1514518, _1514520, _1514522, _1514524] : [-(hAPP(c_Set_Oimage(_1514514, tc_prod(_1514516, _1514518), hAPP(hAPP(c_COMBS(_1514514, _1514518, tc_prod(_1514516, _1514518)), hAPP(hAPP(c_COMBB(_1514516, tc_fun(_1514518, tc_prod(_1514516, _1514518)), _1514514), c_Product__Type_OPair(_1514516, _1514518)), _1514520)), _1514522)), _1514524) = hAPP(hAPP(c_Product__Type_OSigma(_1514516, _1514518), hAPP(c_Set_Oimage(_1514514, _1514516, _1514520), _1514524)), hAPP(hAPP(c_COMBB(tc_fun(_1514514, tc_HOL_Obool), tc_fun(_1514518, tc_HOL_Obool), _1514516), c_Set_Oimage(_1514514, _1514518, _1514522)), hAPP(hAPP(c_COMBC(_1514516, tc_fun(_1514514, tc_HOL_Obool), tc_fun(_1514514, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514514, tc_HOL_Obool), tc_fun(tc_fun(_1514514, tc_HOL_Obool), tc_fun(_1514514, tc_HOL_Obool)), _1514516), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1514514, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1514516, tc_HOL_Obool), tc_fun(_1514514, tc_HOL_Obool), _1514516), c_Set_Ovimage(_1514514, _1514516, _1514520)), hAPP(hAPP(c_COMBC(_1514516, tc_fun(_1514516, tc_HOL_Obool), tc_fun(_1514516, tc_HOL_Obool)), c_Set_Oinsert(_1514516)), c_Orderings_Obot__class_Obot(tc_fun(_1514516, tc_HOL_Obool)))))), _1514524))))], (20328 ^ _781215) ^ [_1146142, _1146144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1146142)), c_Int_OBit1(_1146144))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1146142), _1146144)))], (21879 ^ _781215) ^ [_1174202, _1174204, _1174206, _1174208, _1174210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174202, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174204, tc_fun(_1174202, tc_HOL_Obool)), _1174206), _1174208)), _1174210)), 21882 ^ _781215 : [(21883 ^ _781215) ^ [_1174335] : [hBOOL(hAPP(hAPP(c_member(_1174204), _1174335), _1174206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174202, tc_HOL_Obool)), hAPP(_1174208, _1174335)), _1174210)))]]], (32836 ^ _781215) ^ [_1389747, _1389749, _1389751, _1389753] : [class_Lattices_Odistrib__lattice(_1389747), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1389747), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1389747), _1389749), _1389751)), _1389753) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1389747), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1389747), _1389749), _1389753)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1389747), _1389751), _1389753)))], (25984 ^ _781215) ^ [_1252532, _1252534, _1252536] : [class_Groups_Ocomm__monoid__mult(_1252532), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1252534, _1252532), _1252536), c_Orderings_Obot__class_Obot(tc_fun(_1252534, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1252532))], (26179 ^ _781215) ^ [_1256004, _1256006] : [class_Rings_Oring__1(_1256004), -(hBOOL(hAPP(hAPP(c_member(_1256004), hAPP(c_Int_Oring__1__class_Oof__int(_1256004), _1256006)), c_Int_Oring__1__class_OInts(_1256004))))], (36804 ^ _781215) ^ [_1474453, _1474455, _1474457] : [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), _1474453), _1474455))), -(hBOOL(hAPP(hAPP(_1474457, _1474453), _1474455))), 36811 ^ _781215 : [(36814 ^ _781215) ^ [] : [-(36810 ^ [_1474453, _1474455, _1474457] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1474457, 36810 ^ [_1474453, _1474455, _1474457]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 36809 ^ [_1474453, _1474455, _1474457], 36810 ^ [_1474453, _1474455, _1474457]))))], (36820 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1474457, 36809 ^ [_1474453, _1474455, _1474457]), 36810 ^ [_1474453, _1474455, _1474457]))], (36812 ^ _781215) ^ [] : [-(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), 36809 ^ [_1474453, _1474455, _1474457]), 36810 ^ [_1474453, _1474455, _1474457]))))]]], (17931 ^ _781215) ^ [_1101371, _1101373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101373)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1101371)), hAPP(c_Int_Onat, _1101373)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1101371), _1101373)))], (20078 ^ _781215) ^ [_1141537, _1141539, _1141541] : [class_Orderings_Olinorder(_1141537), hAPP(_1141539, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1141537), 20083 ^ [_1141537, _1141539, _1141541]), 20084 ^ [_1141537, _1141539, _1141541])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1141537), hAPP(_1141539, 20083 ^ [_1141537, _1141539, _1141541])), hAPP(_1141539, 20084 ^ [_1141537, _1141539, _1141541])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1141537), _1141541)), -(_1141541 = c_Orderings_Obot__class_Obot(tc_fun(_1141537, tc_HOL_Obool))), -(hAPP(_1141539, c_Big__Operators_Olinorder__class_OMax(_1141537, _1141541)) = c_Big__Operators_Olinorder__class_OMax(_1141537, hAPP(c_Set_Oimage(_1141537, _1141537, _1141539), _1141541)))], (51384 ^ _781215) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (11660 ^ _781215) ^ [_984701, _984703, _984705] : [class_Rings_Ono__zero__divisors(_984701), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984701), _984703), _984705) = c_Groups_Ozero__class_Ozero(_984701), -(_984703 = c_Groups_Ozero__class_Ozero(_984701)), -(_984705 = c_Groups_Ozero__class_Ozero(_984701))], (24095 ^ _781215) ^ [_1215731, _1215733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1215731)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1215731), _1215733)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1215733), _1215731) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1215733), _1215731)), _1215731)))], (27732 ^ _781215) ^ [_1286025, _1286027, _1286029, _1286031, _1286033, _1286035] : [-(c_Product__Type_Oprod_Oprod__rec(_1286025, _1286027, _1286029, _1286031, hAPP(hAPP(c_Product__Type_OPair(_1286025, _1286027), _1286033), _1286035)) = hAPP(hAPP(_1286031, _1286033), _1286035))], (48301 ^ _781215) ^ [_1755891, _1755893, _1755895, _1755897, _1755899] : [-(hAPP(hAPP(c_List_Olist_OCons(_1755891), _1755893), _1755895) = hAPP(c_List_Ofilter(_1755891, _1755897), _1755899)), 48302 ^ _781215 : [(48303 ^ _781215) ^ [_1756019, _1756021] : [_1755899 = hAPP(hAPP(c_List_Oappend(_1755891), _1756021), hAPP(hAPP(c_List_Olist_OCons(_1755891), _1755893), _1756019)), 48309 ^ _781215 : [(48312 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1755897, 48308 ^ [_1755891, _1755893, _1755895, _1755897, _1755899, _1756019, _1756021])))], (48310 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1755891), 48308 ^ [_1755891, _1755893, _1755895, _1755897, _1755899, _1756019, _1756021]), hAPP(c_List_Oset(_1755891), _1756021))))]], hBOOL(hAPP(_1755897, _1755893)), _1755895 = hAPP(c_List_Ofilter(_1755891, _1755897), _1756019)]]], (17429 ^ _781215) ^ [_1093271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093271), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093271)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (30127 ^ _781215) ^ [_1332292, _1332294, _1332296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332292, tc_HOL_Obool)), _1332294), _1332296)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1332292, tc_HOL_Obool)), _1332294), hAPP(c_Set_OPow(_1332292), _1332296))))], (50421 ^ _781215) ^ [_1806576, _1806578, _1806580] : [c_List_Olist__all(_1806576, _1806578, _1806580), 50424 ^ _781215 : [(50425 ^ _781215) ^ [_1806665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1806665), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806576)), _1806580))), -(hBOOL(hAPP(_1806578, hAPP(hAPP(c_List_Onth(_1806576), _1806580), _1806665))))]]], (26865 ^ _781215) ^ [_1269453, _1269455] : [-(c_Divides_Odivmod__nat(_1269455, _1269453) = 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), _1269455), _1269453), _1269453))), -(_1269453 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1269455), _1269453)))], (44327 ^ _781215) ^ [_1667873, _1667875, _1667877, _1667879] : [-(hAPP(hAPP(c_List_Oappend(_1667873), hAPP(hAPP(c_List_Olist_OCons(_1667873), _1667875), _1667877)), _1667879) = hAPP(hAPP(c_List_Olist_OCons(_1667873), _1667875), hAPP(hAPP(c_List_Oappend(_1667873), _1667877), _1667879)))], (46982 ^ _781215) ^ [_1726332, _1726334, _1726336, _1726338] : [class_Orderings_Olinorder(_1726332), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726334)), c_List_Olinorder__class_Osort__key(_1726334, _1726332, _1726336, _1726338)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726334)), _1726338))], (20160 ^ _781215) ^ [_1143111, _1143113, _1143115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143111)), 20166 ^ _781215 : [(20169 ^ _781215) ^ [] : [hBOOL(hAPP(_1143113, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 20165 ^ [_1143111, _1143113, _1143115]), _1143111)))], (20167 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1143113, 20165 ^ [_1143111, _1143113, _1143115])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143115)), 20174 ^ _781215 : [(20175 ^ _781215) ^ [_1143400] : [hBOOL(hAPP(_1143113, _1143400)), -(hBOOL(hAPP(_1143113, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1143400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1143115), _1143111)))))]]], (6080 ^ _781215) ^ [_878917, _878919, _878921, _878923] : [c_Com_Ocom_OSemi(_878917, _878919) = c_Com_Ocom_OSemi(_878921, _878923), 6083 ^ _781215 : [(6086 ^ _781215) ^ [] : [-(_878919 = _878923)], (6084 ^ _781215) ^ [] : [-(_878917 = _878921)]]], (36484 ^ _781215) ^ [_1466930, _1466932] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1466930, _1466932)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1466930, _1466932), tc_HOL_Obool)))), 36487 ^ _781215 : [(36490 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1466932), c_Orderings_Otop__class_Otop(tc_fun(_1466932, tc_HOL_Obool)))))], (36488 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1466930), c_Orderings_Otop__class_Otop(tc_fun(_1466930, tc_HOL_Obool)))))]]], (44467 ^ _781215) ^ [_1671567, _1671569, _1671571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1671567), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671569)), _1671571))), -(hAPP(hAPP(c_List_Otake(_1671569), hAPP(c_Nat_OSuc, _1671567)), _1671571) = hAPP(hAPP(c_List_Oappend(_1671569), hAPP(hAPP(c_List_Otake(_1671569), _1671567), _1671571)), hAPP(hAPP(c_List_Olist_OCons(_1671569), hAPP(hAPP(c_List_Onth(_1671569), _1671571), _1671567)), c_List_Olist_ONil(_1671569))))], (50218 ^ _781215) ^ [_1801439, _1801441, _1801443] : [hBOOL(hAPP(hAPP(c_member(_1801439), _1801441), hAPP(c_List_Oset(_1801439), _1801443))), 50223 ^ _781215 : [(50226 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1801439), _1801441), hAPP(c_List_Oset(_1801439), 50221 ^ [_1801439, _1801441, _1801443])))], (50224 ^ _781215) ^ [] : [-(_1801443 = hAPP(hAPP(c_List_Oappend(_1801439), 50221 ^ [_1801439, _1801441, _1801443]), hAPP(hAPP(c_List_Olist_OCons(_1801439), _1801441), 50222 ^ [_1801439, _1801441, _1801443])))]]], (47561 ^ _781215) ^ [_1738292, _1738294, _1738296] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1738292)), _1738296), c_List_Olists(_1738292, _1738294))), -(hBOOL(hAPP(c_List_Olistsp(_1738292, hAPP(hAPP(c_COMBC(_1738292, tc_fun(_1738292, tc_HOL_Obool), tc_HOL_Obool), c_member(_1738292)), _1738294)), _1738296)))], (18627 ^ _781215) ^ [_1114845, _1114847] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114845), _1114847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114845)), _1114847)))], (6659 ^ _781215) ^ [_890234, _890236] : [6660 ^ _781215 : [(6661 ^ _781215) ^ [_890287] : [hBOOL(hAPP(hAPP(c_member(_890234), _890287), _890236))]], _890236 = c_Orderings_Obot__class_Obot(tc_fun(_890234, tc_HOL_Obool))], (10126 ^ _781215) ^ [_953583, _953585, _953587, _953589, _953591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953583, tc_HOL_Obool)), _953585), _953587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953583, tc_HOL_Obool)), _953589), _953591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953583, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953583, tc_HOL_Obool)), _953585), _953591)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953583, tc_HOL_Obool)), _953587), _953589))))], (9033 ^ _781215) ^ [_934488, _934490, _934492] : [class_Lattices_Oboolean__algebra(_934488), 9036 ^ _781215 : [(9043 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934488), _934492), _934490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934488), hAPP(c_Groups_Ouminus__class_Ouminus(_934488), _934490)), hAPP(c_Groups_Ouminus__class_Ouminus(_934488), _934492))))], (9037 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934488), hAPP(c_Groups_Ouminus__class_Ouminus(_934488), _934490)), hAPP(c_Groups_Ouminus__class_Ouminus(_934488), _934492))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934488), _934492), _934490)))]]], (26191 ^ _781215) ^ [_1256232, _1256234, _1256236] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1256232), _1256234)), 26194 ^ _781215 : [(26195 ^ _781215) ^ [] : [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(_1256232, tc_Nat_Onat), _1256236), _1256234))), 26198 ^ _781215 : [(26199 ^ _781215) ^ [_1256400] : [hBOOL(hAPP(hAPP(c_member(_1256232), _1256400), _1256234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1256236, _1256400))))]]], (26205 ^ _781215) ^ [] : [26207 ^ _781215 : [(26210 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1256236, 26206 ^ [_1256232, _1256234, _1256236])))], (26208 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1256232), 26206 ^ [_1256232, _1256234, _1256236]), _1256234)))]], -(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(_1256232, tc_Nat_Onat), _1256236), _1256234))))]]], (51584 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (36893 ^ _781215) ^ [_1476515, _1476517, _1476519, _1476521, _1476523, _1476525, _1476527, _1476529] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1476515, tc_fun(_1476517, tc_fun(_1476519, tc_HOL_Obool))), _1476521), _1476523), _1476525), _1476527)), hBOOL(hAPP(hAPP(c_member(_1476515), _1476529), _1476521)), -(hBOOL(hAPP(hAPP(hAPP(_1476523, _1476529), _1476525), _1476527)))], (46638 ^ _781215) ^ [_1718913] : [-(c_List_Oremdups(_1718913, c_List_Olist_ONil(_1718913)) = c_List_Olist_ONil(_1718913))], (51390 ^ _781215) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (10450 ^ _781215) ^ [_959506, _959508, _959510] : [class_Rings_Olinordered__semidom(_959506), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959506), c_Groups_Oone__class_Oone(_959506)), _959508)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959506), c_Groups_Oone__class_Oone(_959506)), _959510)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959506), c_Groups_Oone__class_Oone(_959506)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959506), _959508), _959510))))], (33108 ^ _781215) ^ [_1395887, _1395889, _1395891, _1395893, _1395895] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395887, tc_HOL_Obool)), _1395889), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395891, tc_fun(_1395887, tc_HOL_Obool)), _1395893), _1395895)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395891, tc_fun(_1395887, tc_HOL_Obool)), _1395893), hAPP(hAPP(c_COMBB(tc_fun(_1395887, tc_HOL_Obool), tc_fun(_1395887, tc_HOL_Obool), _1395891), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395887, tc_HOL_Obool)), _1395889)), _1395895)))], (16017 ^ _781215) ^ [_1063959, _1063961] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063959, tc_HOL_Obool)), _1063961), _1063961) = _1063961)], (7187 ^ _781215) ^ [_901592, _901594, _901596, _901598] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_901592, _901594), _901596), _901598), hAPP(_901596, _901598)) = _901596)], (47036 ^ _781215) ^ [_1727283, _1727285] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1727283, _1727285)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1727285), tc_fun(_1727283, _1727285)), hAPP(hAPP(c_COMBB(tc_fun(_1727283, tc_Option_Ooption(_1727285)), tc_fun(_1727283, _1727285), tc_List_Olist(_1727285)), c_Fun_Ocomp(tc_Option_Ooption(_1727285), _1727285, _1727283, c_Option_Othe(_1727285))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1727283, _1727285)), tc_fun(_1727283, tc_Option_Ooption(_1727285)), tc_List_Olist(_1727285)), c_Map_Omap__of(_1727283, _1727285)), hAPP(c_List_Ozip(_1727283, _1727285), c_Enum_Oenum__class_Oenum(_1727283))))), c_Enum_On__lists(_1727285, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727283)), c_Enum_Oenum__class_Oenum(_1727283)), c_Enum_Oenum__class_Oenum(_1727285)))), class_Enum_Oenum(_1727283), class_HOL_Oequal(_1727283), class_Enum_Oenum(_1727285)], (37035 ^ _781215) ^ [_1481072, _1481074, _1481076, _1481078, _1481080] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481072, tc_HOL_Obool)), _1481074), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481076, tc_fun(_1481072, tc_HOL_Obool)), _1481078), _1481080)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481076, tc_fun(_1481072, tc_HOL_Obool)), _1481078), hAPP(hAPP(c_COMBB(tc_fun(_1481072, tc_HOL_Obool), tc_fun(_1481072, tc_HOL_Obool), _1481076), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481072, tc_HOL_Obool)), _1481074)), _1481080)))], (35743 ^ _781215) ^ [_1453388, _1453390] : [class_Rings_Olinordered__idom(_1453388), -(hAPP(c_Groups_Oabs__class_Oabs(_1453388), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1453388), _1453390)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1453388), _1453390))], (30171 ^ _781215) ^ [_1333276, _1333278] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1333276, _1333278) = 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), _1333276), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1333278))))], (7198 ^ _781215) ^ [_901842, _901844, _901846, _901848, _901850] : [hAPP(_901842, _901844) = c_Option_Ooption_ONone(_901846), -(c_Map_Oran(_901848, _901846, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_901848, tc_Option_Ooption(_901846)), _901842), _901844), hAPP(c_Option_Ooption_OSome(_901846), _901850))) = hAPP(hAPP(c_Set_Oinsert(_901846), _901850), c_Map_Oran(_901848, _901846, _901842)))], (48021 ^ _781215) ^ [_1748448, _1748450] : [-(c_Wellfounded_Owf(_1748448, c_List_Omeasures(_1748448, _1748450)))], (10582 ^ _781215) ^ [_962313, _962315] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962313), hAPP(c_Nat_OSuc, _962315)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _962313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _962313), _962315)))], (16750 ^ _781215) ^ [_1081693, _1081695, _1081697, _1081699] : [hBOOL(hAPP(hAPP(c_member(_1081693), _1081699), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1081693, tc_HOL_Obool)), _1081695), _1081697))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1081693, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1081693, tc_fun(_1081693, tc_HOL_Obool), tc_HOL_Obool), c_member(_1081693)), _1081695)), hAPP(hAPP(c_COMBC(_1081693, tc_fun(_1081693, tc_HOL_Obool), tc_HOL_Obool), c_member(_1081693)), _1081697)), _1081699)))], (7822 ^ _781215) ^ [_913215, _913217] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913215), _913217)), _913215) = _913217)], (50349 ^ _781215) ^ [_1804831, _1804833, _1804835, _1804837, _1804839, _1804841] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1804831, _1804833)), _1804835), hAPP(hAPP(c_Relation_Orel__comp(_1804831, _1804837, _1804833), _1804839), _1804841))), 50355 ^ _781215 : [(50360 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1804837, _1804833)), hAPP(hAPP(c_Product__Type_OPair(_1804837, _1804833), 50353 ^ [_1804831, _1804833, _1804835, _1804837, _1804839, _1804841]), 50354 ^ [_1804831, _1804833, _1804835, _1804837, _1804839, _1804841])), _1804841)))], (50358 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1804831, _1804837)), hAPP(hAPP(c_Product__Type_OPair(_1804831, _1804837), 50352 ^ [_1804831, _1804833, _1804835, _1804837, _1804839, _1804841]), 50353 ^ [_1804831, _1804833, _1804835, _1804837, _1804839, _1804841])), _1804839)))], (50356 ^ _781215) ^ [] : [-(_1804835 = hAPP(hAPP(c_Product__Type_OPair(_1804831, _1804833), 50352 ^ [_1804831, _1804833, _1804835, _1804837, _1804839, _1804841]), 50354 ^ [_1804831, _1804833, _1804835, _1804837, _1804839, _1804841]))]]], (40887 ^ _781215) ^ [_1582667, _1582669] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1582667, tc_HOL_Obool), _1582669) = hAPP(c_Set_OCollect(_1582667), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1582667, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1582667), c_HOL_OAll(tc_fun(_1582667, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1582667, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1582667, tc_HOL_Obool), tc_HOL_Obool), _1582667), hAPP(c_COMBS(tc_fun(_1582667, 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(_1582667, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1582667, tc_HOL_Obool), tc_fun(tc_fun(_1582667, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1582667, tc_HOL_Obool))), _1582669)))), c_member(_1582667)))))], (31401 ^ _781215) ^ [_1356621, _1356623] : [-(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)), _1356621)), 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), _1356623), _1356621))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1356621), _1356623))], (31272 ^ _781215) ^ [_1353988, _1353990, _1353992] : [class_Orderings_Olinorder(_1353988), 31275 ^ _781215 : [(31282 ^ _781215) ^ [] : [_1353990 = _1353992, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1353988), _1353990) = hAPP(c_SetInterval_Oord__class_OlessThan(_1353988), _1353992))], (31276 ^ _781215) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1353988), _1353990) = hAPP(c_SetInterval_Oord__class_OlessThan(_1353988), _1353992), -(_1353990 = _1353992)]]], (1058 ^ _781215) ^ [_797410, _797412] : [-(class_Lattices_Obounded__lattice(_797410)), _797412 = _797410, class_Lattices_Obounded__lattice(_797412)], (21341 ^ _781215) ^ [_1163966, _1163968] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1163966) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1163968), -(_1163966 = _1163968)], (14924 ^ _781215) ^ [_1042945, _1042947, _1042949] : [c_Com_Ocom_OCond(_1042945, _1042947, _1042949) = c_Com_Ocom_OSKIP], (19516 ^ _781215) ^ [_1131277, _1131279] : [class_Orderings_Olinorder(_1131277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131277), _1131279)), -(_1131279 = c_Orderings_Obot__class_Obot(tc_fun(_1131277, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1131277), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1131277), 19529 ^ [_1131277, _1131279]), 19530 ^ [_1131277, _1131279])), hAPP(hAPP(c_Set_Oinsert(_1131277), 19529 ^ [_1131277, _1131279]), hAPP(hAPP(c_Set_Oinsert(_1131277), 19530 ^ [_1131277, _1131279]), c_Orderings_Obot__class_Obot(tc_fun(_1131277, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1131277), c_Big__Operators_Olattice_OInf__fin(_1131277, c_Orderings_Oord__class_Omin(_1131277), _1131279)), _1131279)))], (25776 ^ _781215) ^ [_1245225, _1245227, _1245229, _1245231, _1245233, _1245235] : [class_Groups_Ocomm__monoid__mult(_1245225), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245227), _1245229)), 25783 ^ _781215 : [(25790 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1245227), _1245231), _1245229))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1245227, _1245225), hAPP(hAPP(c_COMBC(_1245227, _1245225, _1245225), hAPP(hAPP(c_COMBS(_1245227, _1245225, tc_fun(_1245225, _1245225)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1245225, tc_fun(_1245225, _1245225)), _1245227), c_If(_1245225)), hAPP(hAPP(c_COMBC(_1245227, _1245227, tc_HOL_Obool), c_fequal), _1245231))), _1245233)), _1245235)), _1245229) = hAPP(hAPP(c_Power_Opower__class_Opower(_1245225), _1245235), hAPP(c_Finite__Set_Ocard(_1245227), _1245229)))], (25784 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1245227), _1245231), _1245229)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1245227, _1245225), hAPP(hAPP(c_COMBC(_1245227, _1245225, _1245225), hAPP(hAPP(c_COMBS(_1245227, _1245225, tc_fun(_1245225, _1245225)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1245225, tc_fun(_1245225, _1245225)), _1245227), c_If(_1245225)), hAPP(hAPP(c_COMBC(_1245227, _1245227, tc_HOL_Obool), c_fequal), _1245231))), _1245233)), _1245235)), _1245229) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245225), hAPP(_1245233, _1245231)), hAPP(hAPP(c_Power_Opower__class_Opower(_1245225), _1245235), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1245227), _1245229)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (39026 ^ _781215) ^ [_1530426, _1530428, _1530430, _1530432] : [-(hAPP(c_Set_OCollect(tc_prod(_1530426, _1530428)), hAPP(c_Product__Type_Oprod_Oprod__case(_1530426, _1530428, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1530426, tc_fun(_1530428, tc_HOL_Obool), tc_fun(_1530428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1530428, tc_HOL_Obool), tc_fun(_1530428, tc_HOL_Obool)), _1530426), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1530428)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1530426), c_fconj), _1530430))), _1530432))) = hAPP(hAPP(c_Product__Type_OSigma(_1530426, _1530428), hAPP(c_Set_OCollect(_1530426), _1530430)), hAPP(c_COMBK(tc_fun(_1530428, tc_HOL_Obool), _1530426), hAPP(c_Set_OCollect(_1530428), _1530432))))], (37641 ^ _781215) ^ [_1496453, _1496455, _1496457] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496453, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496453, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1496453, tc_HOL_Obool), _1496455)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1496453, tc_HOL_Obool), _1496457))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1496453, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1496453, tc_HOL_Obool), tc_HOL_Obool)), _1496455), _1496457)))))], (11498 ^ _781215) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38151 ^ _781215) ^ [_1507516, _1507518, _1507520] : [38153 ^ _781215 : [(38156 ^ _781215) ^ [] : [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(_1507518, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 38152 ^ [_1507516, _1507518, _1507520]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1507518, 38152 ^ [_1507516, _1507518, _1507520])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38154 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 38152 ^ [_1507516, _1507518, _1507520]), _1507516)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1507518, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1507520)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1507520), hAPP(_1507518, _1507516))), 38166 ^ _781215 : [(38169 ^ _781215) ^ [] : [-(hAPP(_1507518, 38165 ^ [_1507516, _1507518, _1507520]) = _1507520)], (38167 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 38165 ^ [_1507516, _1507518, _1507520]), _1507516)))]]], (37181 ^ _781215) ^ [_1485054, _1485056, _1485058, _1485060, _1485062] : [_1485054 = c_Orderings_Obot__class_Obot(tc_fun(_1485056, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1485056, tc_fun(_1485058, tc_HOL_Obool)), _1485054), hAPP(hAPP(c_COMBC(_1485056, tc_fun(_1485058, tc_HOL_Obool), tc_fun(_1485058, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485058, tc_HOL_Obool), tc_fun(tc_fun(_1485058, tc_HOL_Obool), tc_fun(_1485058, tc_HOL_Obool)), _1485056), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485058, tc_HOL_Obool))), _1485060)), _1485062)) = c_Orderings_Otop__class_Otop(tc_fun(_1485058, tc_HOL_Obool)))], (16387 ^ _781215) ^ [_1070891, _1070893] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1070891, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1070891, tc_HOL_Obool))), _1070893) = _1070893)], (8832 ^ _781215) ^ [_930938, _930940, _930942, _930944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930938, tc_HOL_Obool)), _930940), _930942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930938, tc_HOL_Obool)), _930942), _930944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930938, tc_HOL_Obool)), _930940), _930944)))], (29950 ^ _781215) ^ [] : [-(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)))], (21718 ^ _781215) ^ [_1170754] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1170754)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170754)), 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))))], (16067 ^ _781215) ^ [_1065125, _1065127, _1065129] : [class_Lattices_Osemilattice__sup(_1065125), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065125), _1065127), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065125), _1065127), _1065129)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065125), _1065127), _1065129))], (11424 ^ _781215) ^ [_980371, _980373, _980375, _980377, _980379, _980381] : [hBOOL(hAPP(hAPP(c_member(_980371), _980373), _980375)), -(hAPP(c_Set_Oimage(_980371, _980377, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_980371, _980377), _980379), _980373), _980381)), _980375) = hAPP(hAPP(c_Set_Oinsert(_980377), _980381), hAPP(c_Set_Oimage(_980371, _980377, _980379), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980371, tc_HOL_Obool)), _980375), hAPP(hAPP(c_Set_Oinsert(_980371), _980373), c_Orderings_Obot__class_Obot(tc_fun(_980371, tc_HOL_Obool)))))))], (31114 ^ _781215) ^ [_1350713, _1350715, _1350717, _1350719] : [class_Orderings_Olinorder(_1350713), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350713), _1350715), _1350717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350713), _1350717), _1350719)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350713, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1350713, _1350715), _1350717)), c_SetInterval_Oord__class_OatLeastAtMost(_1350713, _1350717, _1350719)) = c_SetInterval_Oord__class_OatLeastAtMost(_1350713, _1350715, _1350719))], (44898 ^ _781215) ^ [_1681717, _1681719, _1681721] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1681717, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681719)), _1681721)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1681719, _1681717), _1681721) = _1681721)], (42937 ^ _781215) ^ [_1635444, _1635446, _1635448, _1635450, _1635452, _1635454] : [-(hAPP(hAPP(c_List_Omap(_1635444, _1635446), _1635448), hAPP(hAPP(c_List_Olist__update(_1635444, _1635450), _1635452), _1635454)) = hAPP(hAPP(c_List_Olist__update(_1635446, hAPP(hAPP(c_List_Omap(_1635444, _1635446), _1635448), _1635450)), _1635452), hAPP(_1635448, _1635454)))], (39687 ^ _781215) ^ [_1552470, _1552472, _1552474, _1552476] : [class_Groups_Ocomm__monoid__add(_1552470), c_Fun_Oinj__on(_1552472, _1552470, _1552474, _1552476), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1552472, _1552470), _1552474), _1552476) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1552470, _1552470), c_Fun_Oid(_1552470)), hAPP(c_Set_Oimage(_1552472, _1552470, _1552474), _1552476)))], (50485 ^ _781215) ^ [_1807845, _1807847, _1807849, _1807851] : [-(c_List_Olist__all(_1807845, _1807847, hAPP(hAPP(c_List_Oappend(_1807845), _1807849), _1807851))), c_List_Olist__all(_1807845, _1807847, _1807849), c_List_Olist__all(_1807845, _1807847, _1807851)], (24732 ^ _781215) ^ [_1227499, _1227501, _1227503] : [class_Groups_Omonoid__mult(_1227499), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227499), hAPP(hAPP(c_Power_Opower__class_Opower(_1227499), _1227501), _1227503)), _1227501) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227499), _1227501), hAPP(hAPP(c_Power_Opower__class_Opower(_1227499), _1227501), _1227503)))], (11854 ^ _781215) ^ [_987539] : [class_Groups_Ogroup__add(_987539), -(hAPP(c_Groups_Ouminus__class_Ouminus(_987539), c_Groups_Ozero__class_Ozero(_987539)) = c_Groups_Ozero__class_Ozero(_987539))], (39002 ^ _781215) ^ [_1529963, _1529965] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1529963))), -(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)), _1529963))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1529965)))) = 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)), _1529963))), 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, _1529965))))))], (26622 ^ _781215) ^ [_1264272, _1264274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264272), 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)), _1264274)), -(c_Divides_OnegDivAlg(_1264272, _1264274) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1264272), _1264274)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1264272, _1264274)))], (5924 ^ _781215) ^ [_875522, _875524] : [-(_875522 = c_Option_Ooption_ONone(_875524)), -(_875522 = hAPP(c_Option_Ooption_OSome(_875524), 5927 ^ [_875522, _875524]))], (14994 ^ _781215) ^ [_1044229, _1044231, _1044233, _1044235] : [class_Int_Onumber__ring(_1044229), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044229), hAPP(c_Int_Onumber__class_Onumber__of(_1044229), _1044231)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044229), _1044233), hAPP(c_Int_Onumber__class_Onumber__of(_1044229), _1044235))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044229), hAPP(c_Int_Onumber__class_Onumber__of(_1044229), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1044231), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1044235)))), _1044233))], (11928 ^ _781215) ^ [_988579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988579), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_988579 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50938 ^ _781215) ^ [_1816557, _1816559, _1816561, _1816563] : [-(c_New__Random__Sequence_Opos__map(_1816557, _1816559, _1816561, _1816563) = c_New__Random__Sequence_Opos__bind(_1816557, _1816559, _1816563, hAPP(c_Fun_Ocomp(_1816559, 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(_1816559))))), _1816557, c_New__Random__Sequence_Opos__single(_1816559)), _1816561)))], (45345 ^ _781215) ^ [_1690873, _1690875, _1690877] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1690873), tc_List_Olist(_1690873)), c_List_Opartition(_1690873, _1690875, _1690877)) = hAPP(c_List_Ofilter(_1690873, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1690873, c_fNot), _1690875)), _1690877))], (5772 ^ _781215) ^ [_872612, _872614, _872616] : [_872614 = _872616, -(hAPP(c_Option_Ooption_OSome(_872612), _872614) = hAPP(c_Option_Ooption_OSome(_872612), _872616))], (43001 ^ _781215) ^ [_1637090, _1637092, _1637094, _1637096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1637090), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637092)), _1637094))), 43004 ^ _781215 : [(43011 ^ _781215) ^ [] : [hAPP(hAPP(c_List_Onth(_1637092), _1637094), _1637090) = _1637096, -(hAPP(hAPP(c_List_Olist__update(_1637092, _1637094), _1637090), _1637096) = _1637094)], (43005 ^ _781215) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1637092, _1637094), _1637090), _1637096) = _1637094, -(hAPP(hAPP(c_List_Onth(_1637092), _1637094), _1637090) = _1637096)]]], (46769 ^ _781215) ^ [_1721546, _1721548, _1721550] : [-(hAPP(hAPP(c_List_Oappend(_1721546), c_List_OtakeWhile(_1721546, _1721548, _1721550)), c_List_OdropWhile(_1721546, _1721548, _1721550)) = _1721550)], (51588 ^ _781215) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (49219 ^ _781215) ^ [_1775719, _1775721] : [-(c_Transitive__Closure_Otrancl(_1775719, c_Transitive__Closure_Ortrancl(_1775719, _1775721)) = c_Transitive__Closure_Ortrancl(_1775719, _1775721))], (51288 ^ _781215) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (51314 ^ _781215) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (25919 ^ _781215) ^ [_1251369, _1251371, _1251373] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1251369), _1251371), _1251373) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1251369), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1251369, tc_Int_Oint), _1251371), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1251373))), class_Groups_Ocomm__monoid__add(_1251369), class_Groups_Ocomm__monoid__mult(_1251369)], (33785 ^ _781215) ^ [_1411309, _1411311, _1411313] : [class_Lattices_Olattice(_1411309), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411309), _1411311)), -(_1411311 = c_Orderings_Obot__class_Obot(tc_fun(_1411309, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411309), _1411313)), -(_1411313 = c_Orderings_Obot__class_Obot(tc_fun(_1411309, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411309, tc_HOL_Obool)), _1411311), _1411313) = c_Orderings_Obot__class_Obot(tc_fun(_1411309, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1411309, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411309, tc_HOL_Obool)), _1411311), _1411313)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1411309), c_Big__Operators_Olattice__class_OSup__fin(_1411309, _1411311)), c_Big__Operators_Olattice__class_OSup__fin(_1411309, _1411313)))], (44088 ^ _781215) ^ [_1662817, _1662819, _1662821, _1662823, _1662825] : [-(hAPP(hAPP(c_List_Oappend(_1662817), _1662819), hAPP(hAPP(c_List_Olist_OCons(_1662817), _1662821), c_List_Olist_ONil(_1662817))) = hAPP(hAPP(c_List_Oappend(_1662817), _1662823), hAPP(hAPP(c_List_Olist_OCons(_1662817), _1662825), c_List_Olist_ONil(_1662817)))), _1662819 = _1662823, _1662821 = _1662825], (38328 ^ _781215) ^ [_1511933, _1511935, _1511937, _1511939, _1511941] : [hAPP(_1511939, _1511935) = _1511941, -(hBOOL(hAPP(hAPP(c_member(_1511933), _1511935), hAPP(c_Set_Ovimage(_1511933, _1511937, _1511939), hAPP(hAPP(c_Set_Oinsert(_1511937), _1511941), c_Orderings_Obot__class_Obot(tc_fun(_1511937, tc_HOL_Obool)))))))], (14822 ^ _781215) ^ [_1040955, _1040957, _1040959, _1040961, _1040963] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1040955, _1040957, _1040959)), _1040961), _1040963)), 14827 ^ _781215 : [(14830 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1040957), _1040961), _1040963)))], (14828 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1040955, _1040961)))]], 14831 ^ _781215 : [(14834 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1040959), _1040961), _1040963)))], (14832 ^ _781215) ^ [] : [hBOOL(hAPP(_1040955, _1040961))]]], (38225 ^ _781215) ^ [_1509423, _1509425, _1509427, _1509429] : [_1509429 = c_Option_Ooption_ONone(_1509423), -(hAPP(hAPP(c_Option_Omap(_1509423, _1509425), _1509427), _1509429) = c_Option_Ooption_ONone(_1509425))], (41525 ^ _781215) ^ [_1597849, _1597851, _1597853, _1597855, _1597857, _1597859] : [c_Finite__Set_Ofolding(_1597849, _1597851, _1597853, _1597855), -(hAPP(c_Fun_Ocomp(_1597851, _1597851, _1597851, hAPP(_1597853, _1597857)), hAPP(_1597853, _1597859)) = hAPP(c_Fun_Ocomp(_1597851, _1597851, _1597851, hAPP(_1597853, _1597859)), hAPP(_1597853, _1597857)))], (11454 ^ _781215) ^ [_980905, _980907] : [-(_980905 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _980905), _980907) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980905), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _980907)))], (35055 ^ _781215) ^ [_1438984, _1438986, _1438988, _1438990, _1438992] : [class_Groups_Ocomm__monoid__mult(_1438984), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438986), _1438988)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438986), _1438990)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1438984), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1438984, _1438986, c_Groups_Otimes__class_Otimes(_1438984)), _1438992), c_Groups_Oone__class_Oone(_1438984)), _1438988)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1438984, _1438986, c_Groups_Otimes__class_Otimes(_1438984)), _1438992), c_Groups_Oone__class_Oone(_1438984)), _1438990)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1438984), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1438984, _1438986, c_Groups_Otimes__class_Otimes(_1438984)), _1438992), c_Groups_Oone__class_Oone(_1438984)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1438986, tc_HOL_Obool)), _1438988), _1438990))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1438984, _1438986, c_Groups_Otimes__class_Otimes(_1438984)), _1438992), c_Groups_Oone__class_Oone(_1438984)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438986, tc_HOL_Obool)), _1438988), _1438990))))], (38294 ^ _781215) ^ [_1511007, _1511009, _1511011, _1511013, _1511015] : [hBOOL(hAPP(hAPP(c_member(_1511007), _1511009), hAPP(c_Set_Ovimage(_1511007, _1511011, _1511013), _1511015))), -(hBOOL(hAPP(hAPP(c_member(_1511011), hAPP(_1511013, _1511009)), _1511015)))], (49020 ^ _781215) ^ [_1770492] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1770492), 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, _1770492)) = _1770492)], (19092 ^ _781215) ^ [_1123666, _1123668] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1123666), hAPP(c_Nat_OSuc, _1123668)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1123668), 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)), _1123668)), _1123666))], (29296 ^ _781215) ^ [_1315001, _1315003, _1315005, _1315007, _1315009] : [class_Fields_Olinordered__field(_1315001), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315001), c_Groups_Ozero__class_Ozero(_1315001)), _1315003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315001), _1315003), _1315005)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315001), c_Groups_Ozero__class_Ozero(_1315001)), _1315007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315001), _1315007), _1315009)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315001), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315001), _1315003), _1315009)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315001), _1315005), _1315007))))], (43299 ^ _781215) ^ [_1644643, _1644645, _1644647, _1644649] : [43301 ^ _781215 : [(43304 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1644647, 43300 ^ [_1644643, _1644645, _1644647, _1644649])), hAPP(_1644649, 43300 ^ [_1644643, _1644645, _1644647, _1644649])))], (43302 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1644643), 43300 ^ [_1644643, _1644645, _1644647, _1644649]), hAPP(c_List_Oset(_1644643), _1644645))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1644643, _1644647, _1644645)), c_List_Olist_Olist__size(_1644643, _1644649, _1644645))))], (16049 ^ _781215) ^ [_1064696, _1064698, _1064700, _1064702] : [class_Lattices_Osemilattice__sup(_1064696), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064696), _1064698), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064696), _1064700), _1064702)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064696), _1064700), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064696), _1064698), _1064702)))], (16055 ^ _781215) ^ [_1064839, _1064841, _1064843, _1064845] : [class_Lattices_Olattice(_1064839), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064839), _1064841), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064839), _1064843), _1064845)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064839), _1064843), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064839), _1064841), _1064845)))], (22412 ^ _781215) ^ [_1186021, _1186023] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186021)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186023)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1186021), _1186023))], (10420 ^ _781215) ^ [_958923, _958925, _958927, _958929] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_958923, _958925)), c_Sum__Type_OPlus(_958923, _958925, _958927, _958929))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_958923), _958927)))], (25742 ^ _781215) ^ [_1244621, _1244623, _1244625, _1244627] : [hBOOL(hAPP(hAPP(_1244625, _1244627), _1244623)), -(hBOOL(hAPP(hAPP(c_member(_1244621), _1244623), c_SetInterval_Oord_OgreaterThan(_1244621, _1244625, _1244627))))], (35198 ^ _781215) ^ [_1442056, _1442058, _1442060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1442056, 35199 ^ [_1442056, _1442058, _1442060])), hAPP(_1442058, 35199 ^ [_1442056, _1442058, _1442060]))), -(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), _1442058), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1442060))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1442056), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1442060))) = 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)), _1442058)), _1442056)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1442060)))], (44407 ^ _781215) ^ [_1670036, _1670038, _1670040] : [-(hBOOL(hAPP(c_List_Odistinct(_1670036), hAPP(hAPP(c_List_Oappend(_1670036), _1670038), _1670040)))), hBOOL(hAPP(c_List_Odistinct(_1670036), _1670038)), hBOOL(hAPP(c_List_Odistinct(_1670036), _1670040)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1670036, tc_HOL_Obool)), hAPP(c_List_Oset(_1670036), _1670038)), hAPP(c_List_Oset(_1670036), _1670040)) = c_Orderings_Obot__class_Obot(tc_fun(_1670036, tc_HOL_Obool))], (42829 ^ _781215) ^ [_1632210, _1632212, _1632214] : [-(hAPP(c_List_Oset(_1632210), c_List_Osublist(_1632210, _1632212, _1632214)) = hAPP(c_Set_OCollect(_1632210), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1632210), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1632210, 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)), _1632210), 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)), _1632210), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1632210, tc_fun(tc_Nat_Onat, _1632210), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1632210, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1632210), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1632210), c_COMBB(_1632210, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1632210), _1632212))))), 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(_1632210)), _1632212)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1632214))))))], (6229 ^ _781215) ^ [_881661, _881663, _881665, _881667] : [_881665 = _881667, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_881661, _881663, hAPP(hAPP(c_Set_Oinsert(_881661), _881665), c_Orderings_Obot__class_Obot(tc_fun(_881661, tc_HOL_Obool)))), _881667)))], (33410 ^ _781215) ^ [_1403136, _1403138, _1403140] : [class_Orderings_Oorder(_1403136), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1403136, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1403136), _1403138)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1403136, _1403138, _1403140)) = c_Orderings_Obot__class_Obot(tc_fun(_1403136, tc_HOL_Obool)))], (12052 ^ _781215) ^ [_990547, _990549, _990551] : [class_Groups_Oordered__comm__monoid__add(_990547), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990547), _990549), c_Groups_Ozero__class_Ozero(_990547))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990547), _990551), c_Groups_Ozero__class_Ozero(_990547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_990547), _990549), _990551)), c_Groups_Ozero__class_Ozero(_990547))))], (29850 ^ _781215) ^ [_1325476, _1325478, _1325480, _1325482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1325476), _1325478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1325480), _1325482)), -(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), _1325476), _1325480)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1325478), _1325482))), c_FunDef_Opair__leq)))], (20677 ^ _781215) ^ [_1152198, _1152200] : [c_Int_Oiszero(_1152198, hAPP(c_Int_Onumber__class_Onumber__of(_1152198), c_Int_OBit1(_1152200))), class_Int_Onumber__ring(_1152198), class_Int_Oring__char__0(_1152198)], (3812 ^ _781215) ^ [_838979, _838981, _838983, _838985, _838987, _838989, _838991, _838993] : [-(c_List_Omaps(_838993, _838989, _838985, _838981) = c_List_Omaps(_838991, _838987, _838983, _838979)), _838993 = _838991, _838989 = _838987, _838985 = _838983, _838981 = _838979], (34980 ^ _781215) ^ [_1437109, _1437111, _1437113, _1437115, _1437117] : [c_Fun_Oinj__on(_1437109, _1437111, _1437113, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437109, tc_HOL_Obool)), _1437115), _1437117)), 34983 ^ _781215 : [(34988 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437111, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1437109, _1437111, _1437113), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1437109, tc_HOL_Obool)), _1437115), _1437117))), hAPP(c_Set_Oimage(_1437109, _1437111, _1437113), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1437109, tc_HOL_Obool)), _1437117), _1437115))) = c_Orderings_Obot__class_Obot(tc_fun(_1437111, tc_HOL_Obool)))], (34986 ^ _781215) ^ [] : [-(c_Fun_Oinj__on(_1437109, _1437111, _1437113, _1437117))], (34984 ^ _781215) ^ [] : [-(c_Fun_Oinj__on(_1437109, _1437111, _1437113, _1437115))]]], (12726 ^ _781215) ^ [_1002795, _1002797, _1002799] : [class_Rings_Olinordered__semiring__strict(_1002795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002795), _1002797), c_Groups_Ozero__class_Ozero(_1002795))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002795), c_Groups_Ozero__class_Ozero(_1002795)), _1002799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002795), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002795), _1002797), _1002799)), c_Groups_Ozero__class_Ozero(_1002795))))], (19054 ^ _781215) ^ [_1122764, _1122766, _1122768] : [class_Orderings_Olinorder(_1122764), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122764), _1122766), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1122764), _1122766), _1122768)) = _1122766)], (42903 ^ _781215) ^ [_1634667, _1634669, _1634671] : [-(hAPP(hAPP(c_List_Olist__update(_1634667, _1634669), _1634671), hAPP(hAPP(c_List_Onth(_1634667), _1634669), _1634671)) = _1634669)], (11342 ^ _781215) ^ [_978618, _978620, _978622, _978624] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_978618), _978620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978618, tc_HOL_Obool)), _978620), _978622)), hBOOL(hAPP(_978624, c_Orderings_Obot__class_Obot(tc_fun(_978618, tc_HOL_Obool)))), 11357 ^ _781215 : [(11358 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_978618), 11356 ^ [_978618, _978620, _978622, _978624])))], (11362 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_978618), 11355 ^ [_978618, _978620, _978622, _978624]), 11356 ^ [_978618, _978620, _978622, _978624]))], (11366 ^ _781215) ^ [] : [hBOOL(hAPP(_978624, hAPP(hAPP(c_Set_Oinsert(_978618), 11355 ^ [_978618, _978620, _978622, _978624]), 11356 ^ [_978618, _978620, _978622, _978624])))], (11364 ^ _781215) ^ [] : [-(hBOOL(hAPP(_978624, 11356 ^ [_978618, _978620, _978622, _978624])))], (11360 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_978618), 11355 ^ [_978618, _978620, _978622, _978624]), _978622)))]], -(hBOOL(hAPP(_978624, _978620)))], (27812 ^ _781215) ^ [_1288138, _1288140, _1288142, _1288144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1288138), _1288140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1288142), _1288144)), -(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), _1288138), _1288142)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1288140), _1288144))), c_FunDef_Opair__less)))], (45562 ^ _781215) ^ [_1695811, _1695813] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1695811, _1695813))))], (20488 ^ _781215) ^ [_1148944, _1148946, _1148948] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148944)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148946)), _1148948)) = 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), _1148944), _1148946))), _1148948))], (21950 ^ _781215) ^ [_1176176] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1176176), 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, _1176176)))], (45391 ^ _781215) ^ [_1692139, _1692141] : [45393 ^ _781215 : [(45396 ^ _781215) ^ [] : [45392 ^ [_1692139, _1692141] = c_List_Olist_ONil(_1692139)], (45394 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692139)), 45392 ^ [_1692139, _1692141]), hAPP(c_List_Oset(tc_List_Olist(_1692139)), _1692141))))]], -(c_List_Otranspose(_1692139, _1692141) = c_List_Olist_ONil(tc_List_Olist(_1692139)))], (43033 ^ _781215) ^ [_1637680, _1637682, _1637684, _1637686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1637680), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637682)), _1637684))), -(hBOOL(hAPP(hAPP(c_member(_1637682), _1637686), hAPP(c_List_Oset(_1637682), hAPP(hAPP(c_List_Olist__update(_1637682, _1637684), _1637680), _1637686)))))], (21546 ^ _781215) ^ [_1167783, _1167785] : [c_Int_OBit0(_1167783) = c_Int_OBit1(_1167785)], (4810 ^ _781215) ^ [_854048, _854050] : [_854050 = _854048, -(c_Int_OBit1(_854050) = c_Int_OBit1(_854048))], (35673 ^ _781215) ^ [_1451781, _1451783, _1451785, _1451787] : [class_Groups_Oordered__ab__group__add__abs(_1451781), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1451781), hAPP(c_Groups_Oabs__class_Oabs(_1451781), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1451783, _1451781), _1451785), _1451787))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1451783, _1451781), hAPP(hAPP(c_COMBB(_1451781, _1451781, _1451783), c_Groups_Oabs__class_Oabs(_1451781)), _1451785)), _1451787))))], (6665 ^ _781215) ^ [_890343, _890345] : [-(_890345 = c_Orderings_Obot__class_Obot(tc_fun(_890343, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_890343), 6668 ^ [_890343, _890345]), _890345)))], (48322 ^ _781215) ^ [_1756417, _1756419, _1756421, _1756423, _1756425, _1756427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1756417, tc_HOL_Obool)), _1756419), _1756421)), 48328 ^ _781215 : [(48331 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1756423, tc_HOL_Obool)), hAPP(_1756425, 48327 ^ [_1756417, _1756419, _1756421, _1756423, _1756425, _1756427])), hAPP(_1756427, 48327 ^ [_1756417, _1756419, _1756421, _1756423, _1756425, _1756427])))], (48329 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756417), 48327 ^ [_1756417, _1756419, _1756421, _1756423, _1756425, _1756427]), _1756419)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1756417, _1756423), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1756417, _1756423), _1756419), _1756425)), hAPP(hAPP(c_Product__Type_OSigma(_1756417, _1756423), _1756421), _1756427))))], (16699 ^ _781215) ^ [_1080076, _1080078, _1080080, _1080082] : [class_Lattices_Osemilattice__sup(_1080076), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080076), _1080078)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1080076, _1080076, c_Lattices_Osemilattice__sup__class_Osup(_1080076)), _1080080), hAPP(hAPP(c_Set_Oinsert(_1080076), _1080082), _1080078)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1080076), _1080082), hAPP(hAPP(c_Finite__Set_Ofold(_1080076, _1080076, c_Lattices_Osemilattice__sup__class_Osup(_1080076)), _1080080), _1080078)))], (45371 ^ _781215) ^ [_1691565, _1691567, _1691569] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691565)), hAPP(c_List_Ofilter(_1691565, _1691567), _1691569)) = 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(_1691565)), _1691569)))), hAPP(hAPP(c_COMBB(_1691565, tc_HOL_Obool, tc_Nat_Onat), _1691567), hAPP(c_List_Onth(_1691565), _1691569))))))], (43389 ^ _781215) ^ [_1646975, _1646977] : [class_Groups_Ocomm__monoid__add(_1646975), hBOOL(hAPP(c_List_Odistinct(_1646975), _1646977)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1646975), _1646977) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1646975, _1646975), c_COMBI(_1646975)), hAPP(c_List_Oset(_1646975), _1646977)))], (21798 ^ _781215) ^ [_1172302] : [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), _1172302))), 21801 ^ _781215 : [(21804 ^ _781215) ^ [] : [-(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(_1172302)))))], (21802 ^ _781215) ^ [] : [-(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(_1172302)))))]]], (21556 ^ _781215) ^ [_1167968, _1167970] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1167968)), c_Int_OBit0(_1167970)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1167968), _1167970)))], (37398 ^ _781215) ^ [_1490989, _1490991, _1490993] : [c_Equiv__Relations_Oequivp(_1490989, _1490991), -(hBOOL(hAPP(hAPP(_1490991, _1490993), _1490993)))], (30467 ^ _781215) ^ [_1338597, _1338599] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1338597, _1338597)), hAPP(hAPP(c_Product__Type_OPair(_1338597, _1338597), 30468 ^ [_1338597, _1338599]), 30468 ^ [_1338597, _1338599])), _1338599))), -(c_Relation_Oirrefl(_1338597, _1338599))], (50954 ^ _781215) ^ [_1816932, _1816934, _1816936, _1816938, _1816940] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1816932), _1816934), _1816936), _1816938), _1816940) = c_New__DSequence_Opos__single(_1816932, _1816934))], (39038 ^ _781215) ^ [_1530804] : [class_Orderings_Olinorder(_1530804), -(c_Finite__Set_Ofun__left__comm__idem(_1530804, _1530804, c_Orderings_Oord__class_Omax(_1530804)))], (6142 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (51578 ^ _781215) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (49083 ^ _781215) ^ [_1771575, _1771577] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1771575, _1771575), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1771575, _1771577)), hAPP(hAPP(c_Product__Type_OSigma(_1771575, _1771575), hAPP(c_Relation_OField(_1771575), _1771577)), hAPP(c_COMBK(tc_fun(_1771575, tc_HOL_Obool), _1771575), hAPP(c_Relation_OField(_1771575), _1771577))))))], (18401 ^ _781215) ^ [_1110620] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1110620), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45946 ^ _781215) ^ [_1702591, _1702593] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1702591, _1702593) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1702591), _1702593)))], (17441 ^ _781215) ^ [_1093423, _1093425, _1093427] : [class_Lattices_Olattice(_1093423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093423), _1093425)), -(hBOOL(hAPP(hAPP(c_member(_1093423), _1093427), _1093425))), -(_1093425 = c_Orderings_Obot__class_Obot(tc_fun(_1093423, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1093423, hAPP(hAPP(c_Set_Oinsert(_1093423), _1093427), _1093425)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1093423), _1093427), c_Big__Operators_Olattice__class_OSup__fin(_1093423, _1093425)))], (760 ^ _781215) ^ [_792941, _792943, _792945, _792947, _792949, _792951] : [-(c_List_Olist__ex(_792949, _792945, _792941)), c_List_Olist__ex(_792951, _792947, _792943), _792951 = _792949, _792947 = _792945, _792943 = _792941], (32762 ^ _781215) ^ [_1387865, _1387867, _1387869] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387865, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1387865, tc_HOL_Obool)), _1387867), _1387869)), _1387869)))], (33659 ^ _781215) ^ [_1408609, _1408611, _1408613, _1408615, _1408617] : [class_Groups_Ocomm__monoid__add(_1408609), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408611), _1408613)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408611), _1408615)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408611, tc_HOL_Obool)), _1408613), _1408615) = c_Orderings_Obot__class_Obot(tc_fun(_1408611, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1408611, _1408609), _1408617), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408611, tc_HOL_Obool)), _1408613), _1408615)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1408609), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1408611, _1408609), _1408617), _1408613)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1408611, _1408609), _1408617), _1408615)))], (5949 ^ _781215) ^ [_875924, _875926] : [_875926 = c_Option_Ooption_ONone(_875924), -(c_Option_Oset(_875924, _875926) = c_Orderings_Obot__class_Obot(tc_fun(_875924, tc_HOL_Obool)))], (22228 ^ _781215) ^ [_1182270, _1182272, _1182274] : [class_Divides_Osemiring__div(_1182270), -(c_Divides_Odiv__class_Omod(_1182270, c_Divides_Odiv__class_Omod(_1182270, _1182272, _1182274), _1182274) = c_Divides_Odiv__class_Omod(_1182270, _1182272, _1182274))], (29156 ^ _781215) ^ [_1312730, _1312732, _1312734, _1312736, _1312738] : [class_Fields_Ofield(_1312730), -(_1312732 = c_Groups_Ozero__class_Ozero(_1312730)), -(_1312734 = c_Groups_Ozero__class_Ozero(_1312730)), 29167 ^ _781215 : [(29174 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312730), _1312736), _1312734) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312730), _1312738), _1312732), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312730), _1312736), _1312732) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312730), _1312738), _1312734))], (29168 ^ _781215) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312730), _1312736), _1312732) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312730), _1312738), _1312734), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312730), _1312736), _1312734) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312730), _1312738), _1312732))]]], (48986 ^ _781215) ^ [_1769908, _1769910] : [hAPP(c_Code__Numeral_Onat__of, _1769908) = hAPP(c_Code__Numeral_Onat__of, _1769910), -(_1769908 = _1769910)], (38697 ^ _781215) ^ [_1522205, _1522207, _1522209, _1522211] : [-(c_Fun_Oinj__on(_1522205, tc_prod(_1522207, _1522205), 38695 ^ [_1522205, _1522207, _1522209, _1522211], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1522207, tc_fun(_1522205, tc_HOL_Obool)), _1522209), _1522211)))], (44427 ^ _781215) ^ [_1670479, _1670481, _1670483, _1670485] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670479), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670481)), _1670483)))), -(hAPP(hAPP(c_List_Onth(_1670481), hAPP(hAPP(c_List_Oappend(_1670481), _1670483), _1670485)), _1670479) = hAPP(hAPP(c_List_Onth(_1670481), _1670485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1670479), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670481)), _1670483))))], (6653 ^ _781215) ^ [_890103, _890105] : [_890105 = c_Orderings_Obot__class_Obot(tc_fun(_890103, tc_HOL_Obool)), 6656 ^ _781215 : [(6657 ^ _781215) ^ [_890183] : [hBOOL(hAPP(hAPP(c_member(_890103), _890183), _890105))]]], (9267 ^ _781215) ^ [_938936, _938938, _938940] : [class_Groups_Oordered__ab__group__add(_938936), 9270 ^ _781215 : [(9277 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938936), _938940), _938938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938936), hAPP(c_Groups_Ouminus__class_Ouminus(_938936), _938938)), hAPP(c_Groups_Ouminus__class_Ouminus(_938936), _938940))))], (9271 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938936), hAPP(c_Groups_Ouminus__class_Ouminus(_938936), _938938)), hAPP(c_Groups_Ouminus__class_Ouminus(_938936), _938940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938936), _938940), _938938)))]]], (16097 ^ _781215) ^ [_1065718, _1065720, _1065722] : [class_Lattices_Osemilattice__sup(_1065718), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065718), _1065720), _1065722) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065718), _1065722), _1065720))], (33338 ^ _781215) ^ [_1401442, _1401444, _1401446, _1401448, _1401450] : [class_Orderings_Olinorder(_1401442), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401442, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1401442, _1401444), _1401446)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1401442, _1401448), _1401450)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1401442, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1401442), _1401444), _1401448)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1401442), _1401446), _1401450)))], (9405 ^ _781215) ^ [_941584, _941586, _941588] : [class_Orderings_Oorder(_941584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941584), _941586), _941588)), -(_941588 = _941586), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941584), _941586), _941588)))], (42631 ^ _781215) ^ [_1627547, _1627549, _1627551] : [_1627547 = _1627549, 42634 ^ _781215 : [(42637 ^ _781215) ^ [_1627695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627695), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627551)), _1627547))), -(hAPP(hAPP(c_List_Onth(_1627551), _1627547), _1627695) = hAPP(hAPP(c_List_Onth(_1627551), _1627549), _1627695))], (42635 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627551)), _1627547) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627551)), _1627549))]]], (6413 ^ _781215) ^ [_885543, _885545, _885547] : [hBOOL(hAPP(_885547, _885545)), -(hBOOL(hAPP(hAPP(c_member(_885543), _885545), _885547)))], (21889 ^ _781215) ^ [_1174460, _1174462, _1174464, _1174466, _1174468] : [21891 ^ _781215 : [(21894 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174460, tc_HOL_Obool)), hAPP(_1174466, 21890 ^ [_1174460, _1174462, _1174464, _1174466, _1174468])), _1174468))], (21892 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1174462), 21890 ^ [_1174460, _1174462, _1174464, _1174466, _1174468]), _1174464)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174460, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174462, tc_fun(_1174460, tc_HOL_Obool)), _1174464), _1174466)), _1174468)))], (39334 ^ _781215) ^ [_1538495, _1538497, _1538499, _1538501, _1538503] : [-(c_Map_Odom(_1538495, _1538497, c_Fun_Ooverride__on(_1538495, tc_Option_Ooption(_1538497), _1538499, _1538501, _1538503)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1538495, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1538495, tc_HOL_Obool)), c_Map_Odom(_1538495, _1538497, _1538499)), hAPP(c_Set_OCollect(_1538495), hAPP(hAPP(c_COMBC(_1538495, tc_fun(_1538495, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538495)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1538495, tc_HOL_Obool)), _1538503), c_Map_Odom(_1538495, _1538497, _1538501)))))), hAPP(c_Set_OCollect(_1538495), hAPP(hAPP(c_COMBC(_1538495, tc_fun(_1538495, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538495)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1538495, tc_HOL_Obool)), _1538503), c_Map_Odom(_1538495, _1538497, _1538501))))))], (8191 ^ _781215) ^ [_919376, _919378, _919380, _919382] : [class_Groups_Oordered__cancel__ab__semigroup__add(_919376), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919376), _919378), _919380)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919376), _919382), _919378)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919376), _919382), _919380))))], (20762 ^ _781215) ^ [_1153614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153614)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1153614)) = _1153614)], (50459 ^ _781215) ^ [_1807409, _1807411, _1807413, _1807415] : [c_List_Olist__all(_1807409, _1807411, hAPP(hAPP(c_List_Olist_OCons(_1807409), _1807413), _1807415)), 50462 ^ _781215 : [(50465 ^ _781215) ^ [] : [-(c_List_Olist__all(_1807409, _1807411, _1807415))], (50463 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1807411, _1807413)))]]], (30768 ^ _781215) ^ [_1344438, _1344440, _1344442] : [-(hAPP(c_Relation_OField(_1344438), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1344438, _1344438), tc_HOL_Obool)), _1344440), _1344442)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1344438, tc_HOL_Obool)), hAPP(c_Relation_OField(_1344438), _1344440)), hAPP(c_Relation_OField(_1344438), _1344442)))], (5802 ^ _781215) ^ [_873471, _873473] : [c_Option_Ois__none(_873471, hAPP(c_Option_Ooption_OSome(_873471), _873473))], (33134 ^ _781215) ^ [_1396717, _1396719] : [class_Lattices_Oboolean__algebra(_1396717), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1396717), hAPP(c_Groups_Ouminus__class_Ouminus(_1396717), _1396719)), _1396719) = c_Orderings_Obot__class_Obot(_1396717))], (42341 ^ _781215) ^ [_1619762, _1619764, _1619766] : [_1619762 = hAPP(hAPP(c_List_Olist_OCons(_1619764), _1619766), _1619762)], (6181 ^ _781215) ^ [_880813, _880815] : [class_Finite__Set_Ofinite(_880813), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_880813), _880815)))], (10782 ^ _781215) ^ [_966069, _966071, _966073, _966075, _966077] : [hBOOL(hAPP(hAPP(c_member(_966069), _966071), c_Map_Odom(_966069, _966073, _966075))), -(hAPP(c_Map_Omap__add(_966069, _966073, _966077, _966075), _966071) = hAPP(_966075, _966071))], (43205 ^ _781215) ^ [_1641980, _1641982, _1641984] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1641980)), _1641982), c_List_Olists(_1641980, c_Wellfounded_Oacc(_1641980, _1641984)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1641980)), _1641982), c_Wellfounded_Oacc(tc_List_Olist(_1641980), c_List_Olistrel1(_1641980, _1641984)))))], (2216 ^ _781215) ^ [_813725, _813727, _813729, _813731, _813733, _813735, _813737, _813739, _813741, _813743] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_813743, _813739, _813735, _813731, _813727) = c_SetInterval_Oord_OgreaterThanAtMost(_813741, _813737, _813733, _813729, _813725)), _813743 = _813741, _813739 = _813737, _813735 = _813733, _813731 = _813729, _813727 = _813725], (24144 ^ _781215) ^ [_1216622, _1216624, _1216626] : [-(hBOOL(hAPP(_1216622, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1216624), _1216626)))), 24145 ^ _781215 : [(24152 ^ _781215) ^ [_1216790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216626), _1216790)), _1216624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1216624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216626), hAPP(c_Nat_OSuc, _1216790)))), hBOOL(hAPP(_1216622, _1216790))], (24146 ^ _781215) ^ [] : [_1216626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1216622, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (14894 ^ _781215) ^ [_1042328, _1042330, _1042332] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1042328, _1042330, _1042332)))), hBOOL(hAPP(c_Com_OWT, _1042330)), hBOOL(hAPP(c_Com_OWT, _1042332))], (44505 ^ _781215) ^ [_1672752, _1672754, _1672756, _1672758] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1672752), tc_List_Olist(_1672752))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1672752), tc_List_Olist(_1672752)), _1672754), _1672756)), c_List_Olistrel1(_1672752, _1672758))), 44510 ^ _781215 : [(44517 ^ _781215) ^ [] : [-(_1672756 = hAPP(hAPP(c_List_Oappend(_1672752), 44512 ^ [_1672752, _1672754, _1672756, _1672758]), hAPP(hAPP(c_List_Olist_OCons(_1672752), 44509 ^ [_1672752, _1672754, _1672756, _1672758]), 44513 ^ [_1672752, _1672754, _1672756, _1672758])))], (44515 ^ _781215) ^ [] : [-(_1672754 = hAPP(hAPP(c_List_Oappend(_1672752), 44512 ^ [_1672752, _1672754, _1672756, _1672758]), hAPP(hAPP(c_List_Olist_OCons(_1672752), 44508 ^ [_1672752, _1672754, _1672756, _1672758]), 44513 ^ [_1672752, _1672754, _1672756, _1672758])))], (44511 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1672752, _1672752)), hAPP(hAPP(c_Product__Type_OPair(_1672752, _1672752), 44508 ^ [_1672752, _1672754, _1672756, _1672758]), 44509 ^ [_1672752, _1672754, _1672756, _1672758])), _1672758)))]]], (43706 ^ _781215) ^ [_1654180, _1654182] : [-(c_List_Olistrelp(_1654180, _1654182, c_List_Olist_ONil(_1654180), c_List_Olist_ONil(_1654180)))], (15869 ^ _781215) ^ [_1060387, _1060389] : [c_Hoare__Mirabelle_Ostate__not__singleton, c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _1060387, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_Com_Ostate), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies)), c_Natural_Oevalc(_1060389))))), c_fequal))), _1060389), c_fequal)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _1060387, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _1060389)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (42273 ^ _781215) ^ [_1617452, _1617454, _1617456, _1617458] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1617452), tc_List_Olist(_1617452))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1617452), tc_List_Olist(_1617452)), _1617454), _1617456)), c_List_Olistrel(_1617452, _1617458))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617452)), _1617454) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617452)), _1617456))], (16945 ^ _781215) ^ [_1085427] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1085427), c_Int_OPls) = _1085427)], (24656 ^ _781215) ^ [_1226294, _1226296, _1226298, _1226300] : [class_Rings_Olinordered__semidom(_1226294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1226296), _1226298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226294), c_Groups_Ozero__class_Ozero(_1226294)), _1226300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226294), _1226300), c_Groups_Oone__class_Oone(_1226294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226294), hAPP(hAPP(c_Power_Opower__class_Opower(_1226294), _1226300), _1226298)), hAPP(hAPP(c_Power_Opower__class_Opower(_1226294), _1226300), _1226296))))], (10788 ^ _781215) ^ [_966192, _966194, _966196, _966198, _966200] : [-(hBOOL(hAPP(hAPP(c_member(_966192), _966194), c_Map_Odom(_966192, _966196, _966198)))), -(hAPP(c_Map_Omap__add(_966192, _966196, _966200, _966198), _966194) = hAPP(_966200, _966194))], (47860 ^ _781215) ^ [_1744974, _1744976, _1744978, _1744980, _1744982] : [47862 ^ _781215 : [(47865 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1744974, _1744976, tc_HOL_Obool), _1744982), 47861 ^ [_1744974, _1744976, _1744978, _1744980, _1744982]))], (47863 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1744974, _1744976)), 47861 ^ [_1744974, _1744976, _1744978, _1744980, _1744982]), hAPP(c_List_Oset(tc_prod(_1744974, _1744976)), hAPP(hAPP(c_List_Ozip(_1744974, _1744976), _1744978), _1744980)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744974)), _1744978) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744976)), _1744980), -(c_List_Olist__all2(_1744974, _1744976, _1744982, _1744978, _1744980))], (51502 ^ _781215) ^ [_1823854] : [-(class_HOL_Oequal(tc_Option_Ooption(_1823854)))], (7879 ^ _781215) ^ [_914311] : [-(hAPP(c_Nat_OSuc, _914311) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _914311))], (25064 ^ _781215) ^ [_1233586, _1233588, _1233590] : [class_Rings_Oring__1(_1233586), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1233586), hAPP(c_Groups_Ouminus__class_Ouminus(_1233586), _1233588)), _1233590) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1233586), hAPP(hAPP(c_Power_Opower__class_Opower(_1233586), hAPP(c_Groups_Ouminus__class_Ouminus(_1233586), c_Groups_Oone__class_Oone(_1233586))), _1233590)), hAPP(hAPP(c_Power_Opower__class_Opower(_1233586), _1233588), _1233590)))], (23042 ^ _781215) ^ [_1196617, _1196619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196617), 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, _1196619, _1196617)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21744 ^ _781215) ^ [_1171275, _1171277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171275), _1171277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1171275)), c_Int_OBit0(_1171277))))], (15608 ^ _781215) ^ [_1055373, _1055375, _1055377] : [hBOOL(hAPP(c_Com_OWT, _1055373)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1055375, _1055377, _1055373))))], (47892 ^ _781215) ^ [_1745784, _1745786, _1745788] : [-(hBOOL(hAPP(hAPP(c_member(_1745784), _1745786), hAPP(c_List_Oset(_1745784), _1745788)))), -(c_List_Oinsert(_1745784, _1745786, _1745788) = hAPP(hAPP(c_List_Olist_OCons(_1745784), _1745786), _1745788))], (41885 ^ _781215) ^ [_1606188, _1606190, _1606192, _1606194, _1606196, _1606198, _1606200, _1606202] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1606188, _1606190), _1606192), _1606194), hAPP(hAPP(c_List_Ozip(_1606188, _1606190), _1606196), hAPP(hAPP(c_List_Omap(_1606198, _1606190), _1606200), _1606202))) = hAPP(hAPP(c_List_Omap(tc_prod(_1606188, _1606198), _1606192), hAPP(c_Product__Type_Oprod_Oprod__case(_1606188, _1606198, _1606192), hAPP(hAPP(c_COMBB(tc_fun(_1606198, tc_prod(_1606188, _1606190)), tc_fun(_1606198, _1606192), _1606188), hAPP(c_COMBB(tc_prod(_1606188, _1606190), _1606192, _1606198), _1606194)), hAPP(hAPP(c_COMBC(_1606188, tc_fun(_1606198, _1606190), tc_fun(_1606198, tc_prod(_1606188, _1606190))), hAPP(hAPP(c_COMBB(tc_fun(_1606190, tc_prod(_1606188, _1606190)), tc_fun(tc_fun(_1606198, _1606190), tc_fun(_1606198, tc_prod(_1606188, _1606190))), _1606188), c_COMBB(_1606190, tc_prod(_1606188, _1606190), _1606198)), c_Product__Type_OPair(_1606188, _1606190))), _1606200)))), hAPP(hAPP(c_List_Ozip(_1606188, _1606198), _1606196), _1606202)))], (32914 ^ _781215) ^ [_1391405, _1391407, _1391409, _1391411] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1391405, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1391405, tc_fun(_1391405, tc_HOL_Obool), tc_HOL_Obool), c_member(_1391405)), _1391407)), hAPP(hAPP(c_COMBC(_1391405, tc_fun(_1391405, tc_HOL_Obool), tc_HOL_Obool), c_member(_1391405)), _1391409)), _1391411)), -(hBOOL(hAPP(hAPP(c_member(_1391405), _1391411), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1391405, tc_HOL_Obool)), _1391407), _1391409))))], (23150 ^ _781215) ^ [_1198252, _1198254] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198252, _1198254) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198252, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198254)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51298 ^ _781215) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (37921 ^ _781215) ^ [_1502237, _1502239, _1502241] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1502237, tc_HOL_Obool)), _1502239), _1502241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502237, tc_HOL_Obool)), _1502239), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502237, tc_HOL_Obool), _1502241))))], (21087 ^ _781215) ^ [_1158761, _1158763] : [class_Int_Onumber__ring(_1158761), class_Rings_Olinordered__idom(_1158761), 21094 ^ _781215 : [(21101 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1158763)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158761), c_Groups_Oone__class_Oone(_1158761)), hAPP(c_Int_Onumber__class_Onumber__of(_1158761), _1158763))))], (21095 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158761), c_Groups_Oone__class_Oone(_1158761)), hAPP(c_Int_Onumber__class_Onumber__of(_1158761), _1158763))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1158763)))]]], (9809 ^ _781215) ^ [_947874, _947876, _947878, _947880, _947882] : [class_Groups_Oordered__ab__group__add(_947874), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947874), _947876), _947878) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947874), _947880), _947882), 9816 ^ _781215 : [(9823 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947874), _947880), _947882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947874), _947876), _947878)))], (9817 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947874), _947876), _947878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947874), _947880), _947882)))]]], (31264 ^ _781215) ^ [_1353809] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1353809))))], (23595 ^ _781215) ^ [_1206339] : [23597 ^ _781215 : [(23600 ^ _781215) ^ [_1206449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 23596 ^ [_1206339, _1206449]), _1206449))], (23598 ^ _781215) ^ [_1206415] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 23596 ^ [_1206339, _1206415]), _1206339)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1206339)))], (18093 ^ _781215) ^ [_1104916, _1104918, _1104920, _1104922] : [-(hAPP(c_Nat_Onat_Onat__rec(_1104916, _1104918, _1104920), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104922)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1104916), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1104922))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1104916, _1104916), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1104916, tc_fun(_1104916, _1104916)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1104916, tc_fun(_1104916, _1104916)), tc_Int_Oint), c_If(_1104916)), c_Nat__Numeral_Oneg)), _1104918)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1104916, _1104916), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1104916, _1104916), tc_Int_Oint), _1104920), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1104916, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1104916, _1104918, _1104920)), c_Int_Onat)))))], (36636 ^ _781215) ^ [_1470000, _1470002, _1470004, _1470006] : [c_Fun_Oinj__on(_1470000, _1470002, _1470004, c_Orderings_Otop__class_Otop(tc_fun(_1470000, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1470000, tc_fun(_1470006, _1470002), hAPP(hAPP(c_COMBB(_1470002, tc_fun(_1470006, _1470002), _1470000), c_COMBK(_1470002, _1470006)), _1470004), c_Orderings_Otop__class_Otop(tc_fun(_1470000, tc_HOL_Obool))))], (21466 ^ _781215) ^ [_1166438, _1166440] : [_1166438 = _1166440, -(c_Int_OBit0(_1166438) = c_Int_OBit0(_1166440))], (35093 ^ _781215) ^ [_1439963, _1439965, _1439967, _1439969] : [-(_1439963 = c_Orderings_Obot__class_Obot(tc_fun(_1439965, tc_HOL_Obool))), 35096 ^ _781215 : [(35097 ^ _781215) ^ [] : [-(hAPP(c_Set_Oimage(_1439967, _1439965, 35104 ^ [_1439963, _1439965, _1439967, _1439969]), _1439969) = _1439963), 35098 ^ _781215 : [(35099 ^ _781215) ^ [_1440104] : [c_Fun_Oinj__on(_1439965, _1439967, _1440104, _1439963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439967, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1439965, _1439967, _1440104), _1439963)), _1439969))]]], (35108 ^ _781215) ^ [] : [35109 ^ _781215 : [(35110 ^ _781215) ^ [_1440296] : [hAPP(c_Set_Oimage(_1439967, _1439965, _1440296), _1439969) = _1439963]], 35112 ^ _781215 : [(35115 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439967, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1439965, _1439967, 35111 ^ [_1439963, _1439965, _1439967, _1439969]), _1439963)), _1439969)))], (35113 ^ _781215) ^ [] : [-(c_Fun_Oinj__on(_1439965, _1439967, 35111 ^ [_1439963, _1439965, _1439967, _1439969], _1439963))]]]]], (5658 ^ _781215) ^ [_870488, _870490, _870492] : [c_Orderings_Obot__class_Obot(tc_fun(_870488, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_870488), _870490), _870492)], (26590 ^ _781215) ^ [_1263689, _1263691, _1263693, _1263695, _1263697, _1263699] : [hBOOL(hAPP(hAPP(_1263689, _1263691), _1263693)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263695, tc_fun(_1263697, tc_HOL_Obool))), _1263689), _1263699)), -(hBOOL(hAPP(hAPP(_1263699, _1263691), _1263693)))], (39885 ^ _781215) ^ [_1559983, _1559985, _1559987, _1559989, _1559991, _1559993, _1559995, _1559997] : [hBOOL(hAPP(hAPP(_1559983, _1559985), _1559987)), hBOOL(hAPP(hAPP(_1559989, _1559987), _1559991)), -(c_Predicate_Opred__comp(_1559993, _1559995, _1559997, _1559983, _1559989, _1559985, _1559991))], (36568 ^ _781215) ^ [_1468466] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468466, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1468466, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1468466, tc_HOL_Obool)))], (42094 ^ _781215) ^ [_1611720, _1611722, _1611724, _1611726] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611720)), _1611722) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611724)), _1611726), -(hAPP(hAPP(c_List_Omap(tc_prod(_1611720, _1611724), _1611724), c_Product__Type_Osnd(_1611720, _1611724)), hAPP(hAPP(c_List_Ozip(_1611720, _1611724), _1611722), _1611726)) = _1611726)], (20856 ^ _781215) ^ [_1155110] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155110))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13420 ^ _781215) ^ [_1014476, _1014478, _1014480, _1014482] : [c_Finite__Set_Ofolding__one(_1014476, _1014478, _1014480), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014476), _1014482)), -(hAPP(_1014480, _1014482) = hAPP(c_Finite__Set_Ofold1(_1014476, _1014478), _1014482))], (34476 ^ _781215) ^ [_1426919, _1426921, _1426923] : [class_Lattices_Olattice(_1426919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426919), _1426921)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426919), _1426923)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426919, tc_HOL_Obool)), _1426921), _1426923) = c_Orderings_Obot__class_Obot(tc_fun(_1426919, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426919), c_Big__Operators_Olattice__class_OInf__fin(_1426919, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426919, tc_HOL_Obool)), _1426921), _1426923))), c_Big__Operators_Olattice__class_OInf__fin(_1426919, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426919, tc_HOL_Obool)), _1426921), _1426923))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426919), c_Big__Operators_Olattice__class_OInf__fin(_1426919, _1426921)), c_Big__Operators_Olattice__class_OInf__fin(_1426919, _1426923)))], (49744 ^ _781215) ^ [_1789309, _1789311, _1789313] : [c_Relation_Orefl__on(_1789309, _1789311, _1789313), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1789309, _1789309), tc_HOL_Obool)), _1789313), hAPP(hAPP(c_Relation_Orel__comp(_1789309, _1789309, _1789309), hAPP(c_Relation_Oconverse(_1789309, _1789309), _1789313)), _1789313))))], (30139 ^ _781215) ^ [_1332552, _1332554] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1332552, tc_HOL_Obool)), _1332554), hAPP(c_Set_OPow(_1332552), _1332554))))], (39452 ^ _781215) ^ [_1543055] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1543055) = 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), _1543055), c_Int_Onat)))))], (16931 ^ _781215) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (12616 ^ _781215) ^ [_1000758, _1000760, _1000762, _1000764] : [class_Rings_Olinordered__ring__strict(_1000758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000758), c_Groups_Ozero__class_Ozero(_1000758)), _1000760)), 12623 ^ _781215 : [(12630 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000758), _1000762), _1000764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000758), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000758), _1000760), _1000762)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000758), _1000760), _1000764))))], (12624 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000758), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000758), _1000760), _1000762)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000758), _1000760), _1000764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000758), _1000762), _1000764)))]]], (21528 ^ _781215) ^ [_1167522] : [c_Int_OPls = _1167522, -(c_Int_OPls = c_Int_OBit0(_1167522))], (29940 ^ _781215) ^ [_1327125] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1327125)), -(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))), _1327125)), c_FunDef_Omax__weak)))], (33210 ^ _781215) ^ [_1398363, _1398365, _1398367] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398363, tc_HOL_Obool)), _1398365), _1398367) = c_Orderings_Obot__class_Obot(tc_fun(_1398363, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398363, tc_HOL_Obool)), _1398365), _1398367) = _1398365)], (49549 ^ _781215) ^ [_1784053] : [-(c_Relation_OId(_1784053) = hAPP(c_Set_OCollect(tc_prod(_1784053, _1784053)), hAPP(hAPP(c_COMBB(tc_fun(_1784053, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1784053, _1784053)), c_HOL_OEx(_1784053)), hAPP(hAPP(c_COMBC(tc_prod(_1784053, _1784053), tc_fun(_1784053, tc_prod(_1784053, _1784053)), tc_fun(_1784053, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1784053, _1784053), tc_HOL_Obool), tc_fun(tc_fun(_1784053, tc_prod(_1784053, _1784053)), tc_fun(_1784053, tc_HOL_Obool)), tc_prod(_1784053, _1784053)), c_COMBB(tc_prod(_1784053, _1784053), tc_HOL_Obool, _1784053)), c_fequal)), hAPP(hAPP(c_COMBS(_1784053, _1784053, tc_prod(_1784053, _1784053)), c_Product__Type_OPair(_1784053, _1784053)), c_COMBI(_1784053))))))], (51328 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (40007 ^ _781215) ^ [_1562244, _1562246, _1562248] : [c_Wellfounded_Owf(_1562244, _1562246), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562244, _1562244)), hAPP(hAPP(c_Product__Type_OPair(_1562244, _1562244), _1562248), _1562248)), _1562246))], (11052 ^ _781215) ^ [_972047, _972049, _972051, _972053, _972055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972047), _972049)), -(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), _972049), _972051)), _972053)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _972047), _972051)), _972055)) = 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), _972049), _972047)), _972051)), _972053)), _972055))], (23732 ^ _781215) ^ [_1209119, _1209121] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1209119, _1209121)) = _1209121, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1209119), _1209121) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8001 ^ _781215) ^ [_916162, _916164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916164), hAPP(c_Nat_OSuc, _916162))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916162), _916164))], (32022 ^ _781215) ^ [_1371749, _1371751, _1371753, _1371755, _1371757] : [class_Rings_Oring(_1371749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371751), _1371753)), hBOOL(hAPP(hAPP(c_member(_1371751), _1371755), _1371753)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371751, _1371749), _1371757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371751, tc_HOL_Obool)), _1371753), hAPP(hAPP(c_Set_Oinsert(_1371751), _1371755), c_Orderings_Obot__class_Obot(tc_fun(_1371751, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1371749), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371751, _1371749), _1371757), _1371753)), hAPP(_1371757, _1371755)))], (37711 ^ _781215) ^ [_1497721, _1497723, _1497725, _1497727, _1497729, _1497731] : [c_Typedef_Otype__definition(_1497721, _1497723, _1497725, _1497727, _1497729), -(hAPP(_1497727, hAPP(_1497725, _1497731)) = _1497731)], (37195 ^ _781215) ^ [_1485483, _1485485, _1485487, _1485489, _1485491] : [_1485483 = c_Orderings_Obot__class_Obot(tc_fun(_1485485, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1485485, tc_fun(_1485487, tc_HOL_Obool)), _1485483), hAPP(hAPP(c_COMBC(_1485485, tc_fun(_1485487, tc_HOL_Obool), tc_fun(_1485487, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485487, tc_HOL_Obool), tc_fun(tc_fun(_1485487, tc_HOL_Obool), tc_fun(_1485487, tc_HOL_Obool)), _1485485), c_Groups_Ominus__class_Ominus(tc_fun(_1485487, tc_HOL_Obool))), _1485489)), _1485491)) = c_Orderings_Otop__class_Otop(tc_fun(_1485487, tc_HOL_Obool)))], (39763 ^ _781215) ^ [_1554889, _1554891, _1554893, _1554895] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1554889, _1554891, _1554893), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1554889, _1554891), tc_HOL_Obool))), _1554895) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1554889, _1554893), tc_HOL_Obool)))], (44920 ^ _781215) ^ [_1682127, _1682129, _1682131] : [-(hAPP(c_List_Orotate(_1682127, _1682129), _1682131) = hAPP(hAPP(c_List_Oappend(_1682127), hAPP(hAPP(c_List_Odrop(_1682127), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1682129, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682127)), _1682131))), _1682131)), hAPP(hAPP(c_List_Otake(_1682127), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1682129, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682127)), _1682131))), _1682131)))], (39879 ^ _781215) ^ [_1559354, _1559356, _1559358, _1559360, _1559362, _1559364, _1559366] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559354, _1559358)), hAPP(hAPP(c_Product__Type_OPair(_1559354, _1559358), _1559364), _1559366)), hAPP(hAPP(c_Relation_Orel__comp(_1559354, _1559356, _1559358), _1559360), _1559362))), -(c_Predicate_Opred__comp(_1559354, _1559356, _1559358, hAPP(hAPP(c_COMBC(_1559354, tc_fun(tc_prod(_1559354, _1559356), tc_HOL_Obool), tc_fun(_1559356, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559356, tc_fun(tc_fun(tc_prod(_1559354, _1559356), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1559354, _1559356), tc_HOL_Obool), tc_fun(_1559356, tc_HOL_Obool)), _1559354), c_COMBC(_1559356, tc_fun(tc_prod(_1559354, _1559356), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559356, tc_prod(_1559354, _1559356)), tc_fun(_1559356, tc_fun(tc_fun(tc_prod(_1559354, _1559356), tc_HOL_Obool), tc_HOL_Obool)), _1559354), hAPP(c_COMBB(tc_prod(_1559354, _1559356), tc_fun(tc_fun(tc_prod(_1559354, _1559356), tc_HOL_Obool), tc_HOL_Obool), _1559356), c_member(tc_prod(_1559354, _1559356)))), c_Product__Type_OPair(_1559354, _1559356)))), _1559360), hAPP(hAPP(c_COMBC(_1559356, tc_fun(tc_prod(_1559356, _1559358), tc_HOL_Obool), tc_fun(_1559358, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559358, tc_fun(tc_fun(tc_prod(_1559356, _1559358), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1559356, _1559358), tc_HOL_Obool), tc_fun(_1559358, tc_HOL_Obool)), _1559356), c_COMBC(_1559358, tc_fun(tc_prod(_1559356, _1559358), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559358, tc_prod(_1559356, _1559358)), tc_fun(_1559358, tc_fun(tc_fun(tc_prod(_1559356, _1559358), tc_HOL_Obool), tc_HOL_Obool)), _1559356), hAPP(c_COMBB(tc_prod(_1559356, _1559358), tc_fun(tc_fun(tc_prod(_1559356, _1559358), tc_HOL_Obool), tc_HOL_Obool), _1559358), c_member(tc_prod(_1559356, _1559358)))), c_Product__Type_OPair(_1559356, _1559358)))), _1559362), _1559364, _1559366))], (46064 ^ _781215) ^ [_1705128, _1705130, _1705132] : [46065 ^ _781215 : [(46068 ^ _781215) ^ [] : [_1705132 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46066 ^ _781215) ^ [] : [-(_1705128 = c_List_Olist_ONil(tc_List_Olist(_1705130)))]], 46072 ^ _781215 : [(46075 ^ _781215) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705130)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1705130)), _1705128), 46071 ^ [_1705128, _1705130, _1705132])) = _1705132], (46073 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46071 ^ [_1705128, _1705130, _1705132]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705130))), _1705128))))]], -(c_List_Otranspose(_1705130, _1705128) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1705130)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1705130)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1705130), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1705130)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1705130)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1705130), hAPP(hAPP(c_COMBB(tc_List_Olist(_1705130), tc_fun(tc_Nat_Onat, _1705130), tc_Nat_Onat), c_List_Onth(_1705130)), hAPP(c_List_Onth(tc_List_Olist(_1705130)), _1705128))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705130))), _1705128)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1705132)))], (38067 ^ _781215) ^ [_1505321, _1505323, _1505325] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1505321), _1505323), _1505325) = c_Nitpick_OAbs__Frac(_1505321, c_Nitpick_Onorm__frac(_1505323, _1505325)))], (25562 ^ _781215) ^ [] : [-(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)))], (25320 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (17359 ^ _781215) ^ [_1092150, _1092152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1092150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1092152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1092150, _1092152))))], (1508 ^ _781215) ^ [_803035, _803037] : [-(class_Rings_Olinordered__semiring__strict(_803035)), _803037 = _803035, class_Rings_Olinordered__semiring__strict(_803037)], (35172 ^ _781215) ^ [_1441583, _1441585, _1441587] : [-(c_Fun_Oinj__on(tc_prod(_1441583, _1441585), tc_prod(_1441585, _1441583), hAPP(c_Product__Type_Oprod_Oprod__case(_1441583, _1441585, tc_prod(_1441585, _1441583)), hAPP(c_COMBC(_1441585, _1441583, tc_prod(_1441585, _1441583)), c_Product__Type_OPair(_1441585, _1441583))), _1441587))], (1458 ^ _781215) ^ [_802410, _802412] : [-(class_Enum_Oenum(_802410)), _802412 = _802410, class_Enum_Oenum(_802412)], (20249 ^ _781215) ^ [_1144701, _1144703] : [-(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), _1144701))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144703))))], (36301 ^ _781215) ^ [_1463784, _1463786] : [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), _1463784), _1463786))), 36304 ^ _781215 : [(36311 ^ _781215) ^ [] : [-(_1463786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1463784, _1463786) = c_Nitpick_Onat__gcd(_1463786, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1463784, _1463786)))], (36305 ^ _781215) ^ [] : [_1463786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1463784, _1463786) = _1463784)]]], (20717 ^ _781215) ^ [_1152869, _1152871] : [class_Int_Onumber__ring(_1152869), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152869), _1152871), hAPP(c_Int_Onumber__class_Onumber__of(_1152869), c_Int_OBit1(c_Int_OPls))) = _1152871)], (44540 ^ _781215) ^ [_1673814, _1673816] : [-(hAPP(hAPP(c_List_Odrop(_1673814), _1673816), c_List_Olist_ONil(_1673814)) = c_List_Olist_ONil(_1673814))], (3366 ^ _781215) ^ [_832006, _832008, _832010, _832012] : [-(c_List_Oupto(_832012, _832008) = c_List_Oupto(_832010, _832006)), _832012 = _832010, _832008 = _832006], (29956 ^ _781215) ^ [_1327310, _1327312, _1327314, _1327316, _1327318, _1327320] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1327310, tc_HOL_Obool), tc_fun(_1327310, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1327310, tc_HOL_Obool), tc_fun(_1327310, tc_HOL_Obool)), _1327312), _1327314)), c_Wellfounded_Omax__ext(_1327310, _1327316))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1327310, tc_HOL_Obool), tc_fun(_1327310, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1327310, tc_HOL_Obool), tc_fun(_1327310, tc_HOL_Obool)), _1327318), _1327320)), c_Wellfounded_Omax__ext(_1327310, _1327316))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1327310, tc_HOL_Obool), tc_fun(_1327310, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1327310, tc_HOL_Obool), tc_fun(_1327310, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327310, tc_HOL_Obool)), _1327312), _1327318)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327310, tc_HOL_Obool)), _1327314), _1327320))), c_Wellfounded_Omax__ext(_1327310, _1327316))))], (40930 ^ _781215) ^ [_1583667, _1583669, _1583671, _1583673] : [-(c_Map_Omap__add(_1583667, _1583669, _1583671, hAPP(c_Map_Omap__of(_1583667, _1583669), _1583673)) = c_List_Ofoldr(tc_prod(_1583667, _1583669), tc_fun(_1583667, tc_Option_Ooption(_1583669)), hAPP(c_Product__Type_Oprod_Oprod__case(_1583667, _1583669, tc_fun(tc_fun(_1583667, tc_Option_Ooption(_1583669)), tc_fun(_1583667, tc_Option_Ooption(_1583669)))), hAPP(hAPP(c_COMBC(_1583667, tc_fun(_1583669, tc_Option_Ooption(_1583669)), tc_fun(_1583669, tc_fun(tc_fun(_1583667, tc_Option_Ooption(_1583669)), tc_fun(_1583667, tc_Option_Ooption(_1583669))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1583669), tc_fun(tc_fun(_1583667, tc_Option_Ooption(_1583669)), tc_fun(_1583667, tc_Option_Ooption(_1583669)))), tc_fun(tc_fun(_1583669, tc_Option_Ooption(_1583669)), tc_fun(_1583669, tc_fun(tc_fun(_1583667, tc_Option_Ooption(_1583669)), tc_fun(_1583667, tc_Option_Ooption(_1583669))))), _1583667), c_COMBB(tc_Option_Ooption(_1583669), tc_fun(tc_fun(_1583667, tc_Option_Ooption(_1583669)), tc_fun(_1583667, tc_Option_Ooption(_1583669))), _1583669)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1583667, tc_Option_Ooption(_1583669)), tc_fun(tc_Option_Ooption(_1583669), tc_fun(_1583667, tc_Option_Ooption(_1583669)))), tc_fun(tc_Option_Ooption(_1583669), tc_fun(tc_fun(_1583667, tc_Option_Ooption(_1583669)), tc_fun(_1583667, tc_Option_Ooption(_1583669)))), _1583667), c_COMBC(tc_fun(_1583667, tc_Option_Ooption(_1583669)), tc_Option_Ooption(_1583669), tc_fun(_1583667, tc_Option_Ooption(_1583669)))), hAPP(c_COMBC(tc_fun(_1583667, tc_Option_Ooption(_1583669)), _1583667, tc_fun(tc_Option_Ooption(_1583669), tc_fun(_1583667, tc_Option_Ooption(_1583669)))), c_Fun_Ofun__upd(_1583667, tc_Option_Ooption(_1583669)))))), c_Option_Ooption_OSome(_1583669))), _1583673, _1583671))], (11942 ^ _781215) ^ [_988772] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _988772) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33032 ^ _781215) ^ [_1394106, _1394108, _1394110] : [class_Lattices_Osemilattice__inf(_1394106), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1394106), _1394108), _1394110) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1394106), _1394110), _1394108))], (25314 ^ _781215) ^ [_1237556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1237556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1237556))))], (9077 ^ _781215) ^ [_935254, _935256] : [class_Lattices_Oab__semigroup__idem__mult(_935254), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935254), _935256), _935256) = _935256)], (42150 ^ _781215) ^ [_1612848, _1612850] : [-(c_List_Olenlex(_1612848, _1612850) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1612848), tc_List_Olist(_1612848))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1612848), tc_List_Olist(_1612848), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1612848), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612848), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool)), tc_List_Olist(_1612848)), c_COMBS(tc_List_Olist(_1612848), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612848), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1612848)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1612848)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1612848), tc_fun(tc_List_Olist(_1612848), tc_Nat_Onat), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1612848), tc_Nat_Onat), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool)), tc_List_Olist(_1612848)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1612848))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1612848)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1612848))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1612848)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1612848), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612848), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool)), tc_List_Olist(_1612848)), c_COMBS(tc_List_Olist(_1612848), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612848), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1612848)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1612848)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1612848), tc_fun(tc_List_Olist(_1612848), tc_Nat_Onat), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1612848), tc_Nat_Onat), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool)), tc_List_Olist(_1612848)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1612848))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1612848)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1612848))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1612848)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1612848), tc_fun(tc_prod(tc_List_Olist(_1612848), tc_List_Olist(_1612848)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612848), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1612848), tc_List_Olist(_1612848)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1612848), tc_List_Olist(_1612848)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1612848), tc_HOL_Obool)), tc_List_Olist(_1612848)), c_COMBC(tc_List_Olist(_1612848), tc_fun(tc_prod(tc_List_Olist(_1612848), tc_List_Olist(_1612848)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1612848), tc_prod(tc_List_Olist(_1612848), tc_List_Olist(_1612848))), tc_fun(tc_List_Olist(_1612848), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1612848), tc_List_Olist(_1612848)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1612848)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1612848), tc_List_Olist(_1612848)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1612848), tc_List_Olist(_1612848)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1612848)), c_member(tc_prod(tc_List_Olist(_1612848), tc_List_Olist(_1612848))))), c_Product__Type_OPair(tc_List_Olist(_1612848), tc_List_Olist(_1612848))))), c_List_Olex(_1612848, _1612850)))))))], (33044 ^ _781215) ^ [_1394324, _1394326, _1394328] : [class_Lattices_Osemilattice__inf(_1394324), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1394324), _1394326), _1394328) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1394324), _1394328), _1394326))], (33925 ^ _781215) ^ [_1413931, _1413933, _1413935] : [class_Orderings_Olinorder(_1413931), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413931), _1413933)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413931), _1413935)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413931, tc_HOL_Obool)), _1413933), _1413935) = c_Orderings_Obot__class_Obot(tc_fun(_1413931, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1413931), c_Big__Operators_Olattice_OInf__fin(_1413931, c_Orderings_Oord__class_Omin(_1413931), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413931, tc_HOL_Obool)), _1413933), _1413935))), c_Big__Operators_Olattice_OInf__fin(_1413931, c_Orderings_Oord__class_Omin(_1413931), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413931, tc_HOL_Obool)), _1413933), _1413935))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1413931), c_Big__Operators_Olattice_OInf__fin(_1413931, c_Orderings_Oord__class_Omin(_1413931), _1413933)), c_Big__Operators_Olattice_OInf__fin(_1413931, c_Orderings_Oord__class_Omin(_1413931), _1413935)))], (39242 ^ _781215) ^ [_1535194, _1535196] : [-(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), _1535194)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1535196))))))], (32268 ^ _781215) ^ [_1377464, _1377466, _1377468, _1377470] : [hBOOL(hAPP(hAPP(c_member(_1377464), _1377466), _1377468)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1377464, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1377464, _1377464, _1377470), hAPP(hAPP(c_Set_Oinsert(_1377464), _1377466), c_Orderings_Obot__class_Obot(tc_fun(_1377464, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377464), _1377468), _1377470))))], (51496 ^ _781215) ^ [_1823779] : [class_Finite__Set_Ofinite(_1823779), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1823779)))], (27060 ^ _781215) ^ [_1273026, _1273028, _1273030] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1273026, _1273028), _1273030)), -(c_Divides_Odivmod__nat(_1273026, _1273028) = _1273030)], (33987 ^ _781215) ^ [_1415170, _1415172, _1415174, _1415176, _1415178, _1415180, _1415182, _1415184, _1415186, _1415188] : [c_Equiv__Relations_Ocongruent2(_1415170, _1415172, _1415174, _1415176, _1415178, _1415180), hBOOL(hAPP(hAPP(c_member(tc_prod(_1415170, _1415170)), hAPP(hAPP(c_Product__Type_OPair(_1415170, _1415170), _1415182), _1415184)), _1415176)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1415172, _1415172)), hAPP(hAPP(c_Product__Type_OPair(_1415172, _1415172), _1415186), _1415188)), _1415178)), -(hAPP(hAPP(_1415180, _1415182), _1415186) = hAPP(hAPP(_1415180, _1415184), _1415188))], (30305 ^ _781215) ^ [_1335506, _1335508, _1335510, _1335512, _1335514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1335506, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1335508, _1335506, _1335510), _1335512)), _1335514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1335506, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1335508, tc_HOL_Obool), tc_fun(_1335506, tc_HOL_Obool), c_Set_Oimage(_1335508, _1335506, _1335510)), hAPP(c_Set_OPow(_1335508), _1335512))), hAPP(c_Set_OPow(_1335506), _1335514))))], (20854 ^ _781215) ^ [_1155076] : [-(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), _1155076))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24584 ^ _781215) ^ [_1224953, _1224955] : [class_Rings_Oring__1(_1224953), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1224953), hAPP(c_Groups_Ouminus__class_Ouminus(_1224953), c_Groups_Oone__class_Oone(_1224953))), 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)))), _1224955))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1224953), c_Groups_Oone__class_Oone(_1224953)))], (24552 ^ _781215) ^ [_1224241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1224241)), -(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), _1224241), 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)))))))], (24394 ^ _781215) ^ [_1221055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1221055)), -(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), _1221055), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (40382 ^ _781215) ^ [_1571100, _1571102] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1571100, _1571102), 40383 ^ [_1571100, _1571102])), -(c_Wellfounded_OwfP(_1571100, _1571102))], (26896 ^ _781215) ^ [_1270025, _1270027, _1270029, _1270031, _1270033, _1270035] : [hAPP(hAPP(c_Product__Type_OPair(_1270025, _1270027), _1270029), _1270031) = hAPP(hAPP(c_Product__Type_OPair(_1270025, _1270027), _1270033), _1270035), 26899 ^ _781215 : [(26902 ^ _781215) ^ [] : [-(_1270031 = _1270035)], (26900 ^ _781215) ^ [] : [-(_1270029 = _1270033)]]], (51056 ^ _781215) ^ [_1819223, _1819225] : [class_Lattices_Obounded__lattice(_1819223), -(class_Lattices_Obounded__lattice__top(tc_fun(_1819225, _1819223)))], (48599 ^ _781215) ^ [_1762558, _1762560, _1762562] : [c_Wellfounded_Owf(_1762558, _1762560), hBOOL(hAPP(hAPP(c_member(tc_prod(_1762558, _1762558)), hAPP(hAPP(c_Product__Type_OPair(_1762558, _1762558), hAPP(_1762562, hAPP(c_Nat_OSuc, 48602 ^ [_1762558, _1762560, _1762562]))), hAPP(_1762562, 48602 ^ [_1762558, _1762560, _1762562]))), _1762560))], (32264 ^ _781215) ^ [_1377331, _1377333] : [-(c_Relation_OId__on(_1377331, _1377333) = hAPP(c_Product__Type_Oprod_Oprod__case(_1377331, _1377331, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1377331, tc_HOL_Obool, tc_fun(_1377331, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377331, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1377331, tc_HOL_Obool)), _1377331), c_COMBC(_1377331, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377331, tc_HOL_Obool), tc_fun(_1377331, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1377331), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1377331), c_fconj)), c_fequal))), _1377333)))], (36331 ^ _781215) ^ [_1464237, _1464239, _1464241, _1464243, _1464245] : [class_Groups_Ocomm__monoid__add(_1464237), class_Groups_Ocomm__monoid__mult(_1464237), _1464239 = _1464241, c_Nat__Transfer_Onat__set(_1464241), 36349 ^ _781215 : [(36352 ^ _781215) ^ [] : [hAPP(_1464243, 36348 ^ [_1464237, _1464239, _1464241, _1464243, _1464245]) = hAPP(_1464245, 36348 ^ [_1464237, _1464239, _1464241, _1464243, _1464245])], (36350 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36348 ^ [_1464237, _1464239, _1464241, _1464243, _1464245])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1464237), _1464243), _1464239) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1464237), _1464245), _1464241))], (19232 ^ _781215) ^ [_1126340, _1126342] : [class_Orderings_Olinorder(_1126340), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126340), _1126342)), -(c_Big__Operators_Olattice_OInf__fin(_1126340, c_Orderings_Oord__class_Omin(_1126340), _1126342) = hAPP(c_Finite__Set_Ofold1(_1126340, c_Orderings_Oord__class_Omin(_1126340)), _1126342))], (26486 ^ _781215) ^ [_1261789, _1261791] : [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), _1261789))), 26489 ^ _781215 : [(26496 ^ _781215) ^ [] : [-(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), _1261791)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261789))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261791), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261789)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261789)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261791), 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), _1261789)))))], (26490 ^ _781215) ^ [] : [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), _1261791)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261789)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261791), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261789)) = 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), _1261791)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261789))))]]], (6790 ^ _781215) ^ [_892839, _892841, _892843, _892845] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_892839, _892841, _892843), _892845)), _892843 = c_Orderings_Obot__class_Obot(tc_fun(_892839, tc_HOL_Obool))], (50651 ^ _781215) ^ [_1811142, _1811144, _1811146, _1811148] : [class_Rings_Olinordered__semidom(_1811142), 50657 ^ _781215 : [(50660 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1811142), c_Groups_Ozero__class_Ozero(_1811142)), hAPP(_1811148, 50656 ^ [_1811142, _1811144, _1811146, _1811148])))], (50658 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1811144), 50656 ^ [_1811142, _1811144, _1811146, _1811148]), _1811146)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1811142), c_Groups_Ozero__class_Ozero(_1811142)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1811144, _1811142), _1811148), _1811146))))], (49860 ^ _781215) ^ [_1791731, _1791733, _1791735] : [49863 ^ _781215 : [(49869 ^ _781215) ^ [] : [49862 ^ [_1791731, _1791733, _1791735] = 49865 ^ [_1791731, _1791733, _1791735]], (49867 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1791731, _1791733)), hAPP(hAPP(c_Product__Type_OPair(_1791731, _1791733), 49861 ^ [_1791731, _1791733, _1791735]), 49865 ^ [_1791731, _1791733, _1791735])), _1791735)))], (49864 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1791731, _1791733)), hAPP(hAPP(c_Product__Type_OPair(_1791731, _1791733), 49861 ^ [_1791731, _1791733, _1791735]), 49862 ^ [_1791731, _1791733, _1791735])), _1791735)))]], -(c_Relation_Osingle__valued(_1791731, _1791733, _1791735))], (23650 ^ _781215) ^ [_1207525, _1207527, _1207529] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1207525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1207527), _1207529)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1207525), _1207527)), _1207529))], (26928 ^ _781215) ^ [_1270627, _1270629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1270627), _1270629)), -(c_Divides_Odivmod__nat(_1270627, _1270629) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1270627))], (15614 ^ _781215) ^ [_1055486, _1055488, _1055490] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1055486, _1055488, _1055490))), -(hBOOL(hAPP(c_Com_OWT, _1055490)))], (22574 ^ _781215) ^ [_1188856, _1188858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1188856, _1188858)), _1188856)))], (49012 ^ _781215) ^ [_1770346] : [-(hAPP(c_Code__Numeral_Onat__of, _1770346) = c_Code__Numeral_Onat__of__aux(_1770346, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50902 ^ _781215) ^ [_1815529, _1815531, _1815533, _1815535, _1815537, _1815539, _1815541] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1815529, _1815531, _1815533, _1815535), _1815537), _1815539), _1815541) = c_New__DSequence_Opos__bind(_1815529, _1815531, hAPP(hAPP(hAPP(_1815533, _1815537), _1815539), _1815541), hAPP(hAPP(c_COMBC(_1815529, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1815531))), hAPP(hAPP(c_COMBC(_1815529, 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(_1815531)))), hAPP(hAPP(c_COMBC(_1815529, 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(_1815531))))), _1815535), _1815537)), _1815539)), _1815541)))], (46469 ^ _781215) ^ [_1715750, _1715752, _1715754] : [c_List_OtakeWhile(_1715750, _1715752, _1715754) = _1715754, 46472 ^ _781215 : [(46473 ^ _781215) ^ [_1715837] : [hBOOL(hAPP(hAPP(c_member(_1715750), _1715837), hAPP(c_List_Oset(_1715750), _1715754))), -(hBOOL(hAPP(_1715752, _1715837)))]]], (40267 ^ _781215) ^ [_1568056, _1568058, _1568060, _1568062] : [hBOOL(hAPP(c_Predicate_ODomainP(_1568056, _1568058, hAPP(hAPP(c_COMBC(_1568056, tc_fun(tc_prod(_1568056, _1568058), tc_HOL_Obool), tc_fun(_1568058, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568058, tc_fun(tc_fun(tc_prod(_1568056, _1568058), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1568056, _1568058), tc_HOL_Obool), tc_fun(_1568058, tc_HOL_Obool)), _1568056), c_COMBC(_1568058, tc_fun(tc_prod(_1568056, _1568058), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568058, tc_prod(_1568056, _1568058)), tc_fun(_1568058, tc_fun(tc_fun(tc_prod(_1568056, _1568058), tc_HOL_Obool), tc_HOL_Obool)), _1568056), hAPP(c_COMBB(tc_prod(_1568056, _1568058), tc_fun(tc_fun(tc_prod(_1568056, _1568058), tc_HOL_Obool), tc_HOL_Obool), _1568058), c_member(tc_prod(_1568056, _1568058)))), c_Product__Type_OPair(_1568056, _1568058)))), _1568060)), _1568062)), -(hBOOL(hAPP(hAPP(c_member(_1568056), _1568062), hAPP(c_Relation_ODomain(_1568056, _1568058), _1568060))))], (49495 ^ _781215) ^ [_1782486, _1782488, _1782490, _1782492] : [-(c_Wellfounded_Owf(_1782486, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1782486, _1782486)), hAPP(hAPP(c_Product__Type_OPair(_1782486, _1782486), _1782488), _1782490)), _1782492))), c_Wellfounded_Owf(_1782486, _1782492), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782486, _1782486)), hAPP(hAPP(c_Product__Type_OPair(_1782486, _1782486), _1782490), _1782488)), c_Transitive__Closure_Ortrancl(_1782486, _1782492))))], (11866 ^ _781215) ^ [_987744] : [hAPP(c_Nat_OSuc, _987744) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44033 ^ _781215) ^ [_1661605, _1661607, _1661609, _1661611, _1661613] : [-(hAPP(hAPP(c_List_Oappend(_1661605), _1661607), _1661609) = hAPP(hAPP(c_List_Olist_OCons(_1661605), _1661611), _1661613)), 44034 ^ _781215 : [(44041 ^ _781215) ^ [_1661788] : [_1661607 = hAPP(hAPP(c_List_Olist_OCons(_1661605), _1661611), _1661788), hAPP(hAPP(c_List_Oappend(_1661605), _1661788), _1661609) = _1661613], (44035 ^ _781215) ^ [] : [_1661607 = c_List_Olist_ONil(_1661605), _1661609 = hAPP(hAPP(c_List_Olist_OCons(_1661605), _1661611), _1661613)]]], (50664 ^ _781215) ^ [_1811438, _1811440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50665 ^ [_1811438, _1811440]), hAPP(_1811438, 50665 ^ [_1811438, _1811440]))), -(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)), _1811438)), _1811440)))))], (47677 ^ _781215) ^ [_1741156, _1741158, _1741160] : [_1741156 = _1741158, -(c_List_Olist__all2(_1741160, _1741160, c_fequal, _1741156, _1741158))], (50782 ^ _781215) ^ [_1813382] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1813382), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1813382)), c_Int_OMin)))], (38836 ^ _781215) ^ [_1526169, _1526171, _1526173, _1526175, _1526177, _1526179, _1526181, _1526183] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526169, _1526171)), _1526173), hAPP(c_Set_Oimage(tc_prod(_1526175, _1526177), tc_prod(_1526169, _1526171), c_Product__Type_Omap__pair(_1526175, _1526169, _1526177, _1526171, _1526179, _1526181)), _1526183))), 38841 ^ _781215 : [(38844 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526175, _1526177)), hAPP(hAPP(c_Product__Type_OPair(_1526175, _1526177), 38839 ^ [_1526169, _1526171, _1526173, _1526175, _1526177, _1526179, _1526181, _1526183]), 38840 ^ [_1526169, _1526171, _1526173, _1526175, _1526177, _1526179, _1526181, _1526183])), _1526183)))], (38842 ^ _781215) ^ [] : [-(_1526173 = hAPP(hAPP(c_Product__Type_OPair(_1526169, _1526171), hAPP(_1526179, 38839 ^ [_1526169, _1526171, _1526173, _1526175, _1526177, _1526179, _1526181, _1526183])), hAPP(_1526181, 38840 ^ [_1526169, _1526171, _1526173, _1526175, _1526177, _1526179, _1526181, _1526183])))]]], (11270 ^ _781215) ^ [_977173, _977175, _977177, _977179] : [class_Rings_Ocomm__semiring__1(_977173), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977173), _977175), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977173), _977177), _977179)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977173), _977175), _977177)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977173), _977175), _977179)))], (31471 ^ _781215) ^ [_1358526, _1358528] : [-(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), _1358526), _1358528)), 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), _1358526), _1358528))], (46187 ^ _781215) ^ [_1708156, _1708158] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708156)), hAPP(c_List_Orev(_1708156), _1708158)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708156)), _1708158))], (31519 ^ _781215) ^ [_1360070, _1360072, _1360074] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360070, tc_Nat_Onat), _1360072), _1360074) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360070, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1360070), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1360072)), _1360074)))], (43896 ^ _781215) ^ [_1657824, _1657826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1657824), _1657826)), -(c_List_Oupto(_1657824, _1657826) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1657824), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1657824), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1657826)))], (34520 ^ _781215) ^ [_1427744, _1427746, _1427748] : [class_Lattices_Olattice(_1427744), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427744), _1427746)), -(hBOOL(hAPP(hAPP(c_member(_1427744), _1427748), _1427746))), -(c_Big__Operators_Olattice__class_OInf__fin(_1427744, hAPP(hAPP(c_Set_Oinsert(_1427744), _1427748), _1427746)) = hAPP(hAPP(c_Finite__Set_Ofold(_1427744, _1427744, c_Lattices_Osemilattice__inf__class_Oinf(_1427744)), _1427748), _1427746))], (1258 ^ _781215) ^ [_799910, _799912] : [-(class_Groups_Oabs__if(_799910)), _799912 = _799910, class_Groups_Oabs__if(_799912)], (45283 ^ _781215) ^ [_1689582, _1689584, _1689586, _1689588, _1689590, _1689592] : [class_Orderings_Olinorder(_1689582), -(hBOOL(hAPP(_1689584, _1689586))), -(hAPP(c_List_Ofilter(_1689588, _1689584), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1689588, _1689582, _1689590), _1689586), _1689592)) = hAPP(c_List_Ofilter(_1689588, _1689584), _1689592))], (35693 ^ _781215) ^ [_1452318, _1452320, _1452322, _1452324] : [class_Fields_Olinordered__field(_1452318), -(hAPP(c_Groups_Oabs__class_Oabs(_1452318), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1452320, _1452318), _1452322), _1452324)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1452320, _1452318), hAPP(hAPP(c_COMBB(_1452318, _1452318, _1452320), c_Groups_Oabs__class_Oabs(_1452318)), _1452322)), _1452324))], (26942 ^ _781215) ^ [_1270930, _1270932, _1270934, _1270936] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1270930, _1270932, _1270934), hAPP(hAPP(c_COMBB(tc_fun(_1270932, tc_prod(_1270930, _1270932)), tc_fun(_1270932, _1270934), _1270930), hAPP(c_COMBB(tc_prod(_1270930, _1270932), _1270934, _1270932), _1270936)), c_Product__Type_OPair(_1270930, _1270932))) = _1270936)], (40142 ^ _781215) ^ [_1564996, _1564998, _1565000, _1565002] : [-(hAPP(c_Relation_ODomain(_1564996, _1564998), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564996, _1564998), tc_HOL_Obool)), _1565000), _1565002)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1564996, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1564996, _1564998), _1565000)), hAPP(c_Relation_ODomain(_1564996, _1564998), _1565002)))], (33442 ^ _781215) ^ [_1403850, _1403852, _1403854, _1403856] : [class_Lattices_Osemilattice__inf(_1403850), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403850), _1403852)), hBOOL(hAPP(hAPP(c_member(_1403850), _1403854), _1403852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403850), hAPP(hAPP(c_Finite__Set_Ofold(_1403850, _1403850, c_Lattices_Osemilattice__inf__class_Oinf(_1403850)), _1403856), _1403852)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1403850), _1403854), _1403856))))], (858 ^ _781215) ^ [_794470, _794472, _794474, _794476, _794478, _794480] : [-(c_Equiv__Relations_Oequiv(_794478, _794474, _794470)), c_Equiv__Relations_Oequiv(_794480, _794476, _794472), _794480 = _794478, _794476 = _794474, _794472 = _794470], (5452 ^ _781215) ^ [_864465, _864467] : [_864467 = _864465, -(tc_Option_Ooption(_864467) = tc_Option_Ooption(_864465))], (10642 ^ _781215) ^ [_963362, _963364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963362), _963364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963362)), _963364)))], (41903 ^ _781215) ^ [_1606928, _1606930, _1606932, _1606934, _1606936, _1606938] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606928, _1606930)), hAPP(hAPP(c_Product__Type_OPair(_1606928, _1606930), _1606932), _1606934)), hAPP(c_List_Oset(tc_prod(_1606928, _1606930)), hAPP(hAPP(c_List_Ozip(_1606928, _1606930), _1606936), _1606938)))), -(hBOOL(hAPP(hAPP(c_member(_1606928), _1606932), hAPP(c_List_Oset(_1606928), _1606936))))], (38398 ^ _781215) ^ [_1513518, _1513520, _1513522, _1513524, _1513526, _1513528] : [hBOOL(hAPP(hAPP(c_member(_1513518), _1513520), _1513522)), 38401 ^ _781215 : [(38408 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513518), _1513524), _1513522))), -(hAPP(c_Set_Ovimage(_1513526, _1513518, hAPP(hAPP(c_COMBC(_1513526, _1513518, _1513518), hAPP(hAPP(c_COMBC(_1513526, _1513518, tc_fun(_1513518, _1513518)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1513518, tc_fun(_1513518, _1513518)), _1513526), c_If(_1513518)), hAPP(hAPP(c_COMBC(_1513526, tc_fun(_1513526, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513526)), _1513528))), _1513520)), _1513524)), _1513522) = _1513528)], (38402 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1513518), _1513524), _1513522)), -(hAPP(c_Set_Ovimage(_1513526, _1513518, hAPP(hAPP(c_COMBC(_1513526, _1513518, _1513518), hAPP(hAPP(c_COMBC(_1513526, _1513518, tc_fun(_1513518, _1513518)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1513518, tc_fun(_1513518, _1513518)), _1513526), c_If(_1513518)), hAPP(hAPP(c_COMBC(_1513526, tc_fun(_1513526, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513526)), _1513528))), _1513520)), _1513524)), _1513522) = c_Orderings_Otop__class_Otop(tc_fun(_1513526, tc_HOL_Obool)))]]], (21738 ^ _781215) ^ [_1171174, _1171176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1171174)), c_Int_OBit0(_1171176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171174), _1171176)))], (17621 ^ _781215) ^ [_1096340] : [class_Rings_Osemiring__1(_1096340), c_Int_Oiszero(_1096340, c_Groups_Oone__class_Oone(_1096340))], (51420 ^ _781215) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (15470 ^ _781215) ^ [_1052539, _1052541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052539), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052541), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052539), _1052541)))], (50860 ^ _781215) ^ [_1814711, _1814713] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1814711)), c_Int_OBit0(_1814713))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1814711), _1814713)))], (12154 ^ _781215) ^ [_992317, _992319] : [class_Groups_Olinordered__ab__group__add(_992317), 12157 ^ _781215 : [(12164 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992317), c_Groups_Ozero__class_Ozero(_992317)), _992319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992317), c_Groups_Ozero__class_Ozero(_992317)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_992317), _992319), _992319))))], (12158 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992317), c_Groups_Ozero__class_Ozero(_992317)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_992317), _992319), _992319))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992317), c_Groups_Ozero__class_Ozero(_992317)), _992319)))]]], (46988 ^ _781215) ^ [_1726449, _1726451, _1726453] : [class_Orderings_Olinorder(_1726449), -(c_List_Olinorder__class_Osort__key(_1726451, _1726449, _1726453, c_List_Olist_ONil(_1726451)) = c_List_Olist_ONil(_1726451))], (42401 ^ _781215) ^ [_1621000, _1621002, _1621004, _1621006] : [-(_1621000 = _1621002), -(c_List_Oremove1(_1621004, _1621000, hAPP(hAPP(c_List_Olist_OCons(_1621004), _1621002), _1621006)) = hAPP(hAPP(c_List_Olist_OCons(_1621004), _1621002), c_List_Oremove1(_1621004, _1621000, _1621006)))], (40686 ^ _781215) ^ [_1578534, _1578536, _1578538, _1578540] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1578534, _1578536)), _1578538), _1578540), _1578538))), 40687 ^ _781215 : [(40690 ^ _781215) ^ [_1578648] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1578536), _1578538), _1578540), _1578648)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1578534, _1578536)), _1578648), _1578540), _1578538))], (40688 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1578534, _1578538)))]]], (49149 ^ _781215) ^ [_1773194, _1773196, _1773198, _1773200] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773194, _1773194)), _1773196), c_Transitive__Closure_Otrancl(_1773194, _1773198))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1773194, _1773194), tc_HOL_Obool)), _1773198), _1773200)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773194, _1773194)), _1773196), c_Transitive__Closure_Otrancl(_1773194, _1773200))))], (51366 ^ _781215) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (48972 ^ _781215) ^ [_1769670] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1769670)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1769670))], (25472 ^ _781215) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (39830 ^ _781215) ^ [_1556670, _1556672, _1556674, _1556676] : [39831 ^ _781215 : [(39832 ^ _781215) ^ [_1556745] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1556674, _1556670)), hAPP(hAPP(c_Product__Type_OPair(_1556674, _1556670), _1556745), _1556672)), _1556676))]], -(hBOOL(hAPP(hAPP(c_member(_1556670), _1556672), hAPP(c_Relation_ORange(_1556674, _1556670), _1556676))))], (22418 ^ _781215) ^ [_1186158, _1186160, _1186162] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186158), _1186160), _1186162) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186158), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1186160, _1186162)), _1186162))], (32644 ^ _781215) ^ [_1385765, _1385767, _1385769, _1385771] : [class_Lattices_Osemilattice__inf(_1385765), 32647 ^ _781215 : [(32656 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385765), _1385767), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1385765), _1385769), _1385771)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385765), _1385767), _1385769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385765), _1385767), _1385771))], (32648 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385765), _1385767), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1385765), _1385769), _1385771))), 32651 ^ _781215 : [(32654 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385765), _1385767), _1385771)))], (32652 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385765), _1385767), _1385769)))]]]]], (16109 ^ _781215) ^ [_1065918, _1065920] : [class_Lattices_Osemilattice__sup(_1065918), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065918), _1065920), _1065920) = _1065920)], (23074 ^ _781215) ^ [_1197144, _1197146] : [c_Nat__Transfer_Onat__set(_1197144), c_Nat__Transfer_Onat__set(_1197146), 23081 ^ _781215 : [(23088 ^ _781215) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197144) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197146), -(_1197144 = _1197146)], (23082 ^ _781215) ^ [] : [_1197144 = _1197146, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197144) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197146))]]], (21584 ^ _781215) ^ [_1168472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1168472))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1168472)))], (49167 ^ _781215) ^ [_1773673, _1773675, _1773677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1773673, _1773673), tc_HOL_Obool)), _1773675), _1773677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1773673, _1773673), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1773673, _1773673, _1773673), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1773673, _1773673), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1773673, _1773675)), _1773677)), _1773675)), _1773677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1773673, _1773673), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1773673, _1773675)), _1773677)))], (37267 ^ _781215) ^ [_1487435, _1487437, _1487439, _1487441, _1487443] : [class_Complete__Lattice_Ocomplete__lattice(_1487435), hBOOL(hAPP(hAPP(c_member(_1487437), _1487439), _1487441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1487435), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1487437, _1487435), _1487441), _1487443)), hAPP(_1487443, _1487439))))], (35805 ^ _781215) ^ [_1454421, _1454423] : [class_Groups_Oordered__ab__group__add__abs(_1454421), 35808 ^ _781215 : [(35815 ^ _781215) ^ [] : [_1454423 = c_Groups_Ozero__class_Ozero(_1454421), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454421), hAPP(c_Groups_Oabs__class_Oabs(_1454421), _1454423)), c_Groups_Ozero__class_Ozero(_1454421))))], (35809 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454421), hAPP(c_Groups_Oabs__class_Oabs(_1454421), _1454423)), c_Groups_Ozero__class_Ozero(_1454421))), -(_1454423 = c_Groups_Ozero__class_Ozero(_1454421))]]], (1338 ^ _781215) ^ [_800910, _800912] : [-(class_Lattices_Obounded__lattice__bot(_800910)), _800912 = _800910, class_Lattices_Obounded__lattice__bot(_800912)], (8343 ^ _781215) ^ [_921878, _921880, _921882, _921884] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_921878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921878), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921878), _921880), _921882)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921878), _921880), _921884))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921878), _921882), _921884)))], (41819 ^ _781215) ^ [_1604888, _1604890, _1604892, _1604894, _1604896] : [hBOOL(hAPP(hAPP(c_member(_1604888), _1604890), hAPP(c_List_Oset(_1604888), _1604892))), -(hAPP(hAPP(c_Map_Omap__of(_1604888, _1604894), hAPP(hAPP(c_List_Ozip(_1604888, _1604894), _1604892), hAPP(hAPP(c_List_Omap(_1604888, _1604894), _1604896), _1604892))), _1604890) = hAPP(c_Option_Ooption_OSome(_1604894), hAPP(_1604896, _1604890)))], (46338 ^ _781215) ^ [_1711917, _1711919, _1711921] : [46340 ^ _781215 : [(46343 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1711917), tc_List_Olist(_1711917), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1711917), tc_fun(tc_List_Olist(_1711917), tc_Nat_Onat), tc_fun(tc_List_Olist(_1711917), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1711917), tc_Nat_Onat), tc_fun(tc_List_Olist(_1711917), tc_HOL_Obool)), tc_List_Olist(_1711917)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1711917))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1711917)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1711917))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1711917)))), 46339 ^ [_1711917, _1711919, _1711921]))], (46341 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711917), tc_List_Olist(_1711917))), 46339 ^ [_1711917, _1711919, _1711921]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1711917), tc_List_Olist(_1711917))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1711917), tc_List_Olist(_1711917)), _1711919), _1711921)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1711917))), _1711919) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1711917))), _1711921), 46348 ^ _781215 : [(46355 ^ _781215) ^ [] : [_1711919 = _1711921, -(c_List_Oconcat(_1711917, _1711919) = c_List_Oconcat(_1711917, _1711921))], (46349 ^ _781215) ^ [] : [c_List_Oconcat(_1711917, _1711919) = c_List_Oconcat(_1711917, _1711921), -(_1711919 = _1711921)]]], (20635 ^ _781215) ^ [_1151485, _1151487, _1151489] : [class_Rings_Osemiring__1(_1151485), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1151487), _1151489)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151485), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151485), _1151487)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151485), _1151489)))], (44118 ^ _781215) ^ [_1663377, _1663379] : [-(hAPP(hAPP(c_List_Oappend(_1663377), _1663379), c_List_Olist_ONil(_1663377)) = _1663379)], (20376 ^ _781215) ^ [] : [-(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))], (45361 ^ _781215) ^ [_1691259, _1691261, _1691263] : [-(c_List_Opartition(_1691259, _1691261, _1691263) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691259), tc_List_Olist(_1691259)), hAPP(c_List_Ofilter(_1691259, _1691261), _1691263)), hAPP(c_List_Ofilter(_1691259, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1691259, c_fNot), _1691261)), _1691263)))], (9853 ^ _781215) ^ [_948722, _948724, _948726] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_948722), _948724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_948722, tc_HOL_Obool)), _948726), _948724)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_948722), _948726)))], (31226 ^ _781215) ^ [_1352993, _1352995, _1352997] : [class_Orderings_Olinorder(_1352993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352993), _1352995), _1352997)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352993, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1352993), _1352995)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1352993, _1352995, _1352997)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1352993), _1352997))], (6291 ^ _781215) ^ [_883022, _883024, _883026] : [hBOOL(hAPP(hAPP(c_member(_883022), _883024), c_Option_Oset(_883022, _883026))), -(_883026 = hAPP(c_Option_Ooption_OSome(_883022), _883024))], (24938 ^ _781215) ^ [_1231262, _1231264, _1231266, _1231268] : [class_Rings_Olinordered__semidom(_1231262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231262), hAPP(hAPP(c_Power_Opower__class_Opower(_1231262), _1231264), hAPP(c_Nat_OSuc, _1231266))), hAPP(hAPP(c_Power_Opower__class_Opower(_1231262), _1231268), hAPP(c_Nat_OSuc, _1231266)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231262), c_Groups_Ozero__class_Ozero(_1231262)), _1231268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231262), _1231264), _1231268)))], (43493 ^ _781215) ^ [_1649250, _1649252] : [43494 ^ _781215 : [(43495 ^ _781215) ^ [_1649296] : [hBOOL(hAPP(_1649250, _1649296))]], -(hBOOL(hAPP(_1649250, c_Hilbert__Choice_OEps(_1649252, _1649250))))], (29658 ^ _781215) ^ [_1321822, _1321824, _1321826, _1321828] : [class_Fields_Ofield__inverse__zero(_1321822), -(_1321824 = c_Groups_Ozero__class_Ozero(_1321822)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1321822), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321822), _1321826), _1321824)), _1321828) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321822), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1321822), _1321826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321822), _1321828), _1321824))), _1321824))], (44532 ^ _781215) ^ [_1673570, _1673572, _1673574, _1673576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673570), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673572)), _1673574))), -(hAPP(hAPP(c_List_Olist__update(_1673572, _1673574), _1673570), _1673576) = hAPP(hAPP(c_List_Oappend(_1673572), hAPP(hAPP(c_List_Otake(_1673572), _1673570), _1673574)), hAPP(hAPP(c_List_Olist_OCons(_1673572), _1673576), hAPP(hAPP(c_List_Odrop(_1673572), hAPP(c_Nat_OSuc, _1673570)), _1673574))))], (10984 ^ _781215) ^ [_970448, _970450, _970452] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_970448), _970450)), -(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(_970448), _970452)), hAPP(c_Finite__Set_Ocard(_970448), _970450))), hAPP(c_Finite__Set_Ocard(_970448), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970448, tc_HOL_Obool)), _970452), _970450)))))], (21827 ^ _781215) ^ [_1172961, _1172963, _1172965, _1172967] : [c_Orderings_Obot__class_Obot(tc_fun(_1172961, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1172963, tc_fun(_1172961, tc_HOL_Obool)), _1172965), _1172967), 21830 ^ _781215 : [(21831 ^ _781215) ^ [_1173077] : [hBOOL(hAPP(hAPP(c_member(_1172963), _1173077), _1172965)), -(hAPP(_1172967, _1173077) = c_Orderings_Obot__class_Obot(tc_fun(_1172961, tc_HOL_Obool)))]]], (9089 ^ _781215) ^ [_935436, _935438] : [class_Lattices_Oboolean__algebra(_935436), -(hAPP(c_Groups_Ouminus__class_Ouminus(_935436), hAPP(c_Groups_Ouminus__class_Ouminus(_935436), _935438)) = _935438)], (23700 ^ _781215) ^ [_1208517, _1208519, _1208521] : [_1208517 = 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), _1208517), _1208519)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1208517), _1208521)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11688 ^ _781215) ^ [_985093, _985095, _985097] : [class_Rings_Oring__no__zero__divisors(_985093), 11691 ^ _781215 : [(11692 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985093), _985095), _985097) = c_Groups_Ozero__class_Ozero(_985093), -(_985095 = c_Groups_Ozero__class_Ozero(_985093)), -(_985097 = c_Groups_Ozero__class_Ozero(_985093))], (11702 ^ _781215) ^ [] : [11703 ^ _781215 : [(11706 ^ _781215) ^ [] : [_985097 = c_Groups_Ozero__class_Ozero(_985093)], (11704 ^ _781215) ^ [] : [_985095 = c_Groups_Ozero__class_Ozero(_985093)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985093), _985095), _985097) = c_Groups_Ozero__class_Ozero(_985093))]]], (22430 ^ _781215) ^ [_1186438, _1186440] : [class_Divides_Osemiring__div(_1186438), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1186438), _1186440), c_Groups_Ozero__class_Ozero(_1186438)) = c_Groups_Ozero__class_Ozero(_1186438))], (42201 ^ _781215) ^ [_1614763, _1614765, _1614767, _1614769, _1614771] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614763)), _1614765) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614767)), _1614769), 42204 ^ _781215 : [(42212 ^ _781215) ^ [] : [42213 ^ _781215 : [(42214 ^ _781215) ^ [_1615055] : [hAPP(hAPP(c_Map_Omap__of(_1614763, _1614767), hAPP(hAPP(c_List_Ozip(_1614763, _1614767), _1614765), _1614769)), _1614771) = hAPP(c_Option_Ooption_OSome(_1614767), _1615055)]], -(hBOOL(hAPP(hAPP(c_member(_1614763), _1614771), hAPP(c_List_Oset(_1614763), _1614765))))], (42205 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1614763), _1614771), hAPP(c_List_Oset(_1614763), _1614765))), -(hAPP(hAPP(c_Map_Omap__of(_1614763, _1614767), hAPP(hAPP(c_List_Ozip(_1614763, _1614767), _1614765), _1614769)), _1614771) = hAPP(c_Option_Ooption_OSome(_1614767), 42208 ^ [_1614763, _1614765, _1614767, _1614769, _1614771]))]]], (12008 ^ _781215) ^ [_989709, _989711, _989713] : [12009 ^ _781215 : [(12012 ^ _781215) ^ [] : [_989711 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12010 ^ _781215) ^ [] : [_989709 = _989713]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989709), _989711) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989713), _989711))], (35841 ^ _781215) ^ [_1454984, _1454986] : [class_Groups_Oordered__ab__group__add__abs(_1454984), 35844 ^ _781215 : [(35851 ^ _781215) ^ [] : [-(_1454986 = c_Groups_Ozero__class_Ozero(_1454984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454984), c_Groups_Ozero__class_Ozero(_1454984)), hAPP(c_Groups_Oabs__class_Oabs(_1454984), _1454986))))], (35845 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454984), c_Groups_Ozero__class_Ozero(_1454984)), hAPP(c_Groups_Oabs__class_Oabs(_1454984), _1454986))), _1454986 = c_Groups_Ozero__class_Ozero(_1454984)]]], (11152 ^ _781215) ^ [_974490, _974492, _974494, _974496] : [class_Rings_Ocomm__semiring__1(_974490), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974490), _974492), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974490), _974494), _974496)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974490), _974494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974490), _974492), _974496)))], (7656 ^ _781215) ^ [_909950, _909952, _909954, _909956] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_909950), _909952)), hBOOL(hAPP(hAPP(c_member(_909950), _909954), _909952)), -(hBOOL(hAPP(hAPP(c_member(_909950), _909954), _909956))), -(hAPP(c_Finite__Set_Ocard(_909950), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909950, tc_HOL_Obool)), _909952), hAPP(hAPP(c_Set_Oinsert(_909950), _909954), _909956))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_909950), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909950, tc_HOL_Obool)), _909952), _909956))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (50092 ^ _781215) ^ [_1797746, _1797748, _1797750, _1797752, _1797754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1797746, _1797746)), hAPP(hAPP(c_Product__Type_OPair(_1797746, _1797746), _1797748), _1797750)), c_Transitive__Closure_Ortrancl(_1797746, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1797746, _1797746), tc_HOL_Obool)), _1797752), _1797754)))), 50098 ^ _781215 : [(50104 ^ _781215) ^ [] : [50100 ^ [_1797746, _1797748, _1797750, _1797752, _1797754] = 50097 ^ [_1797746, _1797748, _1797750, _1797752, _1797754]], (50102 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1797746, _1797746)), hAPP(hAPP(c_Product__Type_OPair(_1797746, _1797746), 50100 ^ [_1797746, _1797748, _1797750, _1797752, _1797754]), 50097 ^ [_1797746, _1797748, _1797750, _1797752, _1797754])), _1797754)))], (50099 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1797746, _1797746)), hAPP(hAPP(c_Product__Type_OPair(_1797746, _1797746), 50097 ^ [_1797746, _1797748, _1797750, _1797752, _1797754]), _1797750)), c_Transitive__Closure_Ortrancl(_1797746, _1797752))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1797746, _1797746)), hAPP(hAPP(c_Product__Type_OPair(_1797746, _1797746), _1797748), _1797750)), c_Transitive__Closure_Ortrancl(_1797746, _1797752))))], (50673 ^ _781215) ^ [_1811616, _1811618, _1811620, _1811622] : [class_HOL_Oequal(_1811616), class_Enum_Oenum(_1811618), 50680 ^ _781215 : [(50681 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1811618, _1811616)), _1811620), _1811622)), 50684 ^ _781215 : [(50685 ^ _781215) ^ [_1811838] : [hBOOL(hAPP(hAPP(c_member(_1811618), _1811838), hAPP(c_List_Oset(_1811618), c_Enum_Oenum__class_Oenum(_1811618)))), -(hAPP(_1811620, _1811838) = hAPP(_1811622, _1811838))]]], (50691 ^ _781215) ^ [] : [50693 ^ _781215 : [(50696 ^ _781215) ^ [] : [hAPP(_1811620, 50692 ^ [_1811616, _1811618, _1811620, _1811622]) = hAPP(_1811622, 50692 ^ [_1811616, _1811618, _1811620, _1811622])], (50694 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1811618), 50692 ^ [_1811616, _1811618, _1811620, _1811622]), hAPP(c_List_Oset(_1811618), c_Enum_Oenum__class_Oenum(_1811618)))))]], -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1811618, _1811616)), _1811620), _1811622)))]]], (36472 ^ _781215) ^ [_1466699, _1466701] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1466699, _1466701)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1466699, _1466701), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1466701), c_Orderings_Otop__class_Otop(tc_fun(_1466701, tc_HOL_Obool)))))], (35445 ^ _781215) ^ [_1447267, _1447269, _1447271, _1447273] : [class_Orderings_Olinorder(_1447267), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447267, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1447267), _1447269)), c_SetInterval_Oord__class_OatLeastAtMost(_1447267, _1447271, _1447273)) = c_SetInterval_Oord__class_OatLeastAtMost(_1447267, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1447267), _1447269), _1447271), _1447273))], (45320 ^ _781215) ^ [_1690388, _1690390, _1690392] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1690388), tc_List_Olist(_1690388)), c_List_Opartition(_1690388, _1690390, _1690392)) = hAPP(c_List_Ofilter(_1690388, _1690390), _1690392))], (51228 ^ _781215) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (37090 ^ _781215) ^ [_1483027, _1483029, _1483031, _1483033, _1483035] : [class_Complete__Lattice_Ocomplete__lattice(_1483027), class_Orderings_Olinorder(_1483027), 37097 ^ _781215 : [(37107 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1483027), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483029, _1483027), _1483031), _1483033)), _1483035))), 37108 ^ _781215 : [(37109 ^ _781215) ^ [_1483375] : [hBOOL(hAPP(hAPP(c_member(_1483029), _1483375), _1483031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1483027), hAPP(_1483033, _1483375)), _1483035))]]], (37098 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1483027), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483029, _1483027), _1483031), _1483033)), _1483035)), 37102 ^ _781215 : [(37105 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1483027), hAPP(_1483033, 37101 ^ [_1483027, _1483029, _1483031, _1483033, _1483035])), _1483035)))], (37103 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1483029), 37101 ^ [_1483027, _1483029, _1483031, _1483033, _1483035]), _1483031)))]]]]], (5332 ^ _781215) ^ [_862683, _862685, _862687, _862689, _862691, _862693] : [-(c_New__DSequence_Opos__union(_862693, _862689, _862685) = c_New__DSequence_Opos__union(_862691, _862687, _862683)), _862693 = _862691, _862689 = _862687, _862685 = _862683], (28156 ^ _781215) ^ [_1294018, _1294020, _1294022, _1294024] : [class_Fields_Ofield__inverse__zero(_1294018), class_Int_Onumber(_1294018), 28163 ^ _781215 : [(28164 ^ _781215) ^ [] : [_1294020 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294018), _1294022), hAPP(c_Int_Onumber__class_Onumber__of(_1294018), _1294024)), 28167 ^ _781215 : [(28174 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1294018), _1294024) = c_Groups_Ozero__class_Ozero(_1294018), -(_1294020 = c_Groups_Ozero__class_Ozero(_1294018))], (28168 ^ _781215) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1294018), _1294024) = c_Groups_Ozero__class_Ozero(_1294018)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294018), _1294020), hAPP(c_Int_Onumber__class_Onumber__of(_1294018), _1294024)) = _1294022)]]], (28180 ^ _781215) ^ [] : [-(_1294020 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294018), _1294022), hAPP(c_Int_Onumber__class_Onumber__of(_1294018), _1294024))), 28183 ^ _781215 : [(28186 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294018), _1294020), hAPP(c_Int_Onumber__class_Onumber__of(_1294018), _1294024)) = _1294022], (28184 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1294018), _1294024) = c_Groups_Ozero__class_Ozero(_1294018)]], 28187 ^ _781215 : [(28190 ^ _781215) ^ [] : [_1294020 = c_Groups_Ozero__class_Ozero(_1294018)], (28188 ^ _781215) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1294018), _1294024) = c_Groups_Ozero__class_Ozero(_1294018))]]]]], (26600 ^ _781215) ^ [_1263880, _1263882, _1263884, _1263886, _1263888, _1263890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263880, tc_fun(_1263882, tc_HOL_Obool))), _1263884), _1263886)), hBOOL(hAPP(hAPP(_1263884, _1263888), _1263890)), -(hBOOL(hAPP(hAPP(_1263886, _1263888), _1263890)))], (14389 ^ _781215) ^ [_1032906, _1032908, _1032910] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCall(_1032906, _1032908, _1032910)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31290 ^ _781215) ^ [_1354313] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1354313)) = _1354313)], (16221 ^ _781215) ^ [_1067931, _1067933, _1067935, _1067937] : [class_Lattices_Osemilattice__sup(_1067931), 16224 ^ _781215 : [(16233 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067931), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067931), _1067933), _1067935)), _1067937))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067931), _1067933), _1067937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067931), _1067935), _1067937))], (16225 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067931), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067931), _1067933), _1067935)), _1067937)), 16228 ^ _781215 : [(16231 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067931), _1067935), _1067937)))], (16229 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067931), _1067933), _1067937)))]]]]], (22414 ^ _781215) ^ [_1186064, _1186066] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1186064), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186066)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186064)), _1186066))], (4748 ^ _781215) ^ [_853155, _853157] : [_853157 = _853155, -(c_Groups_Oabs__class_Oabs(_853157) = c_Groups_Oabs__class_Oabs(_853155))], (46896 ^ _781215) ^ [_1724662, _1724664, _1724666] : [-(c_Enum_Oproduct(_1724662, _1724664, c_List_Olist_ONil(_1724662), _1724666) = c_List_Olist_ONil(tc_prod(_1724662, _1724664)))], (38217 ^ _781215) ^ [_1509259, _1509261, _1509263] : [-(hAPP(hAPP(c_Option_Omap(_1509259, _1509261), _1509263), c_Option_Ooption_ONone(_1509259)) = c_Option_Ooption_ONone(_1509261))], (20997 ^ _781215) ^ [_1157354, _1157356, _1157358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157354), _1157356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1157358)), -(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), _1157358)), _1157354)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157358)), _1157356))))], (49810 ^ _781215) ^ [_1790693, _1790695] : [-(c_Relation_Osingle__valued(_1790693, _1790693, c_Relation_OId__on(_1790693, _1790695)))], (46530 ^ _781215) ^ [_1716882, _1716884, _1716886, _1716888] : [-(hBOOL(hAPP(_1716882, _1716884))), -(c_List_OtakeWhile(_1716886, _1716882, hAPP(hAPP(c_List_Olist_OCons(_1716886), _1716884), _1716888)) = c_List_Olist_ONil(_1716886))], (48725 ^ _781215) ^ [_1765119, _1765121, _1765123, _1765125, _1765127, _1765129, _1765131, _1765133, _1765135] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1765119, _1765121, _1765123, _1765125), hAPP(hAPP(c_Product__Type_Oscomp(_1765119, _1765127, _1765129, tc_prod(_1765121, _1765123)), _1765131), _1765133)), _1765135) = hAPP(hAPP(c_Product__Type_Oscomp(_1765119, _1765127, _1765129, _1765125), _1765131), hAPP(hAPP(c_COMBC(_1765127, tc_fun(_1765121, tc_fun(_1765123, _1765125)), tc_fun(_1765129, _1765125)), hAPP(hAPP(c_COMBB(tc_fun(_1765129, tc_prod(_1765121, _1765123)), tc_fun(tc_fun(_1765121, tc_fun(_1765123, _1765125)), tc_fun(_1765129, _1765125)), _1765127), c_Product__Type_Oscomp(_1765129, _1765121, _1765123, _1765125)), _1765133)), _1765135)))], (8307 ^ _781215) ^ [_921348, _921350, _921352, _921354, _921356] : [class_Groups_Oab__group__add(_921348), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_921348), _921350), _921352) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_921348), _921354), _921356), 8314 ^ _781215 : [(8321 ^ _781215) ^ [] : [_921354 = _921356, -(_921350 = _921352)], (8315 ^ _781215) ^ [] : [_921350 = _921352, -(_921354 = _921356)]]], (46252 ^ _781215) ^ [_1709516, _1709518] : [c_List_Olist_ONil(_1709516) = c_List_Oconcat(_1709516, _1709518), 46255 ^ _781215 : [(46256 ^ _781215) ^ [_1709607] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709516)), _1709607), hAPP(c_List_Oset(tc_List_Olist(_1709516)), _1709518))), -(_1709607 = c_List_Olist_ONil(_1709516))]]], (25821 ^ _781215) ^ [_1247460, _1247462, _1247464, _1247466] : [hAPP(hAPP(c_COMBC(_1247460, tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_fun(_1247462, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1247462, tc_fun(tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_fun(_1247462, tc_HOL_Obool)), _1247460), c_COMBC(_1247462, tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1247462, tc_prod(_1247460, _1247462)), tc_fun(_1247462, tc_fun(tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_HOL_Obool)), _1247460), hAPP(c_COMBB(tc_prod(_1247460, _1247462), tc_fun(tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_HOL_Obool), _1247462), c_member(tc_prod(_1247460, _1247462)))), c_Product__Type_OPair(_1247460, _1247462)))), _1247464) = hAPP(hAPP(c_COMBC(_1247460, tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_fun(_1247462, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1247462, tc_fun(tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_fun(_1247462, tc_HOL_Obool)), _1247460), c_COMBC(_1247462, tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1247462, tc_prod(_1247460, _1247462)), tc_fun(_1247462, tc_fun(tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_HOL_Obool)), _1247460), hAPP(c_COMBB(tc_prod(_1247460, _1247462), tc_fun(tc_fun(tc_prod(_1247460, _1247462), tc_HOL_Obool), tc_HOL_Obool), _1247462), c_member(tc_prod(_1247460, _1247462)))), c_Product__Type_OPair(_1247460, _1247462)))), _1247466), -(_1247464 = _1247466)], (24222 ^ _781215) ^ [_1218079, _1218081] : [class_Rings_Oring__1(_1218079), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1218079), hAPP(c_Groups_Ouminus__class_Ouminus(_1218079), _1218081)), 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(_1218079), _1218081), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35587 ^ _781215) ^ [_1449983, _1449985, _1449987] : [class_Orderings_Oorder(_1449983), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449983, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1449983, _1449985, _1449987)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1449983), _1449987)) = c_Orderings_Obot__class_Obot(tc_fun(_1449983, tc_HOL_Obool)))], (20360 ^ _781215) ^ [] : [-(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)))))], (33026 ^ _781215) ^ [_1393981, _1393983, _1393985] : [class_Lattices_Osemilattice__inf(_1393981), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393981), _1393983), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393981), _1393983), _1393985)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393981), _1393983), _1393985))], (7608 ^ _781215) ^ [_909025, _909027, _909029, _909031, _909033, _909035] : [-(_909025 = _909027), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909029, _909031), _909033), _909027), _909035), _909025) = hAPP(_909033, _909025))], (33380 ^ _781215) ^ [_1402411, _1402413, _1402415, _1402417] : [class_Orderings_Oorder(_1402411), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402411, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1402411, _1402413, _1402415)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1402411, _1402415), _1402417)) = c_Orderings_Obot__class_Obot(tc_fun(_1402411, tc_HOL_Obool)))], (27440 ^ _781215) ^ [_1280605, _1280607, _1280609, _1280611, _1280613] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1280605, _1280607, _1280609), _1280611), _1280613) = hAPP(hAPP(_1280611, hAPP(c_Product__Type_Ofst(_1280605, _1280607), _1280613)), hAPP(c_Product__Type_Osnd(_1280605, _1280607), _1280613)))], (7620 ^ _781215) ^ [_909198, _909200, _909202, _909204, _909206, _909208] : [_909198 = _909200, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909202, _909204), _909206), _909200), _909208), _909198) = _909208)], (16756 ^ _781215) ^ [_1081916, _1081918, _1081920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081916, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1081916, tc_fun(_1081916, tc_HOL_Obool), tc_HOL_Obool), c_member(_1081916)), _1081918)), hAPP(hAPP(c_COMBC(_1081916, tc_fun(_1081916, tc_HOL_Obool), tc_HOL_Obool), c_member(_1081916)), _1081920))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081916, tc_HOL_Obool)), _1081918), _1081920)))], (50228 ^ _781215) ^ [_1801694, _1801696, _1801698] : [-(hBOOL(hAPP(hAPP(c_member(_1801694), _1801696), hAPP(c_List_Oset(_1801694), _1801698)))), 50229 ^ _781215 : [(50230 ^ _781215) ^ [_1801783] : [50231 ^ _781215 : [(50232 ^ _781215) ^ [_1801856] : [_1801698 = hAPP(hAPP(c_List_Oappend(_1801694), _1801783), hAPP(hAPP(c_List_Olist_OCons(_1801694), _1801696), _1801856))]], -(hBOOL(hAPP(hAPP(c_member(_1801694), _1801696), hAPP(c_List_Oset(_1801694), _1801783))))]]], (48898 ^ _781215) ^ [] : [-(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))], (21554 ^ _781215) ^ [_1167927, _1167929] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1167927)), _1167929) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1167927), _1167929)))], (49209 ^ _781215) ^ [_1775509, _1775511] : [-(c_Transitive__Closure_Otrancl(_1775509, _1775511) = hAPP(hAPP(c_Relation_Orel__comp(_1775509, _1775509, _1775509), c_Transitive__Closure_Ortrancl(_1775509, _1775511)), _1775511))], (44792 ^ _781215) ^ [_1679840, _1679842, _1679844] : [_1679840 = c_List_Olist_ONil(_1679842), -(hAPP(c_List_Ohd(_1679842), hAPP(hAPP(c_List_Oappend(_1679842), _1679840), _1679844)) = hAPP(c_List_Ohd(_1679842), _1679844))], (15154 ^ _781215) ^ [_1047191, _1047193] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047191)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047193)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1047191), _1047193)))], (46229 ^ _781215) ^ [_1708989, _1708991, _1708993] : [-(hAPP(c_List_Orev(_1708989), hAPP(c_List_Ofilter(_1708989, _1708991), _1708993)) = hAPP(c_List_Ofilter(_1708989, _1708991), hAPP(c_List_Orev(_1708989), _1708993)))], (22216 ^ _781215) ^ [_1182075] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182075), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51334 ^ _781215) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (12482 ^ _781215) ^ [_998362, _998364, _998366, _998368] : [class_Rings_Olinordered__semidom(_998362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998362), c_Groups_Ozero__class_Ozero(_998362)), _998364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998362), _998366), _998368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998362), _998366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998362), _998364), _998368))))], (40374 ^ _781215) ^ [_1570955] : [-(c_Wellfounded_OwfP(_1570955, hAPP(c_COMBK(tc_fun(_1570955, tc_HOL_Obool), _1570955), hAPP(c_COMBK(tc_HOL_Obool, _1570955), c_fFalse))))], (10438 ^ _781215) ^ [_959268, _959270, _959272] : [class_Groups_Oab__group__add(_959268), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959268), _959270), _959272) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959268), _959270), hAPP(c_Groups_Ouminus__class_Ouminus(_959268), _959272)))], (51374 ^ _781215) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (21940 ^ _781215) ^ [_1175981, _1175983, _1175985, _1175987, _1175989] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175981, tc_fun(_1175983, tc_HOL_Obool)), _1175985), hAPP(hAPP(c_COMBC(_1175981, tc_fun(_1175983, tc_HOL_Obool), tc_fun(_1175983, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1175983, tc_HOL_Obool), tc_fun(tc_fun(_1175983, tc_HOL_Obool), tc_fun(_1175983, tc_HOL_Obool)), _1175981), c_Groups_Ominus__class_Ominus(tc_fun(_1175983, tc_HOL_Obool))), _1175987)), _1175989)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1175983, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175981, tc_fun(_1175983, tc_HOL_Obool)), _1175985), _1175987)), _1175989))], (27870 ^ _781215) ^ [_1289376, _1289378] : [class_Rings_Odivision__ring(_1289376), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289376), c_Groups_Ozero__class_Ozero(_1289376)), _1289378) = c_Groups_Ozero__class_Ozero(_1289376))], (38100 ^ _781215) ^ [_1506214, _1506216, _1506218] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1506214, tc_HOL_Obool)), _1506216)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1506214), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1506214, tc_HOL_Obool), _1506216))), 38110 ^ _781215 : [(38113 ^ _781215) ^ [] : [hAPP(c_Finite__Set_Ocard(_1506214), 38109 ^ [_1506214, _1506216, _1506218]) = _1506218], (38111 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1506214, tc_HOL_Obool)), 38109 ^ [_1506214, _1506216, _1506218]), _1506216)))]], 38117 ^ _781215 : [(38121 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1506214, tc_HOL_Obool)), 38119 ^ [_1506214, _1506216, _1506218]), _1506216)))], (38123 ^ _781215) ^ [] : [38116 ^ [_1506214, _1506216, _1506218] = 38119 ^ [_1506214, _1506216, _1506218]], (38125 ^ _781215) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506214, tc_HOL_Obool)), 38116 ^ [_1506214, _1506216, _1506218]), 38119 ^ [_1506214, _1506216, _1506218]) = c_Orderings_Obot__class_Obot(tc_fun(_1506214, tc_HOL_Obool))], (38118 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1506214, tc_HOL_Obool)), 38116 ^ [_1506214, _1506216, _1506218]), _1506216)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1506218), hAPP(c_Finite__Set_Ocard(tc_fun(_1506214, tc_HOL_Obool)), _1506216)) = hAPP(c_Finite__Set_Ocard(_1506214), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1506214, tc_HOL_Obool), _1506216)))], (34724 ^ _781215) ^ [_1431891, _1431893, _1431895, _1431897, _1431899] : [c_Fun_Oinj__on(_1431891, _1431893, _1431895, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431891, tc_HOL_Obool)), _1431897), _1431899)), 34727 ^ _781215 : [(34734 ^ _781215) ^ [] : [_1431897 = _1431899, -(hAPP(c_Set_Oimage(_1431891, _1431893, _1431895), _1431897) = hAPP(c_Set_Oimage(_1431891, _1431893, _1431895), _1431899))], (34728 ^ _781215) ^ [] : [hAPP(c_Set_Oimage(_1431891, _1431893, _1431895), _1431897) = hAPP(c_Set_Oimage(_1431891, _1431893, _1431895), _1431899), -(_1431897 = _1431899)]]], (42983 ^ _781215) ^ [_1636652, _1636654, _1636656, _1636658, _1636660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636652, tc_HOL_Obool)), hAPP(c_List_Oset(_1636652), _1636654)), _1636656)), hBOOL(hAPP(hAPP(c_member(_1636652), _1636658), _1636656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636652, tc_HOL_Obool)), hAPP(c_List_Oset(_1636652), hAPP(hAPP(c_List_Olist__update(_1636652, _1636654), _1636660), _1636658))), _1636656)))], (44630 ^ _781215) ^ [_1675843, _1675845, _1675847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675843)), _1675845)), _1675847)), -(hAPP(hAPP(c_List_Odrop(_1675843), _1675847), _1675845) = c_List_Olist_ONil(_1675843))], (46014 ^ _781215) ^ [_1704013, _1704015, _1704017, _1704019] : [class_Orderings_Olinorder(_1704013), c_List_Olinorder__class_Osorted(_1704013, _1704015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1704017), _1704019)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704019), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704013)), _1704015))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1704013), hAPP(hAPP(c_List_Onth(_1704013), _1704015), _1704017)), hAPP(hAPP(c_List_Onth(_1704013), _1704015), _1704019))))], (9863 ^ _781215) ^ [_948891, _948893, _948895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_948891, tc_HOL_Obool)), _948893), _948895)), hBOOL(hAPP(c_Finite__Set_Ofinite(_948891), _948895)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_948891), _948893)))], (19726 ^ _781215) ^ [_1135243, _1135245, _1135247] : [class_Orderings_Olinorder(_1135243), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135243), _1135245)), -(_1135245 = c_Orderings_Obot__class_Obot(tc_fun(_1135243, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1135243, c_Orderings_Oord__class_Omax(_1135243), hAPP(hAPP(c_Set_Oinsert(_1135243), _1135247), _1135245)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1135243), _1135247), c_Big__Operators_Olattice_OSup__fin(_1135243, c_Orderings_Oord__class_Omax(_1135243), _1135245)))], (37404 ^ _781215) ^ [_1491093, _1491095] : [c_Equiv__Relations_Oequivp(_1491093, _1491095), 37407 ^ _781215 : [(37414 ^ _781215) ^ [_1491286, _1491288] : [hAPP(_1491095, _1491288) = hAPP(_1491095, _1491286), -(hBOOL(hAPP(hAPP(_1491095, _1491288), _1491286)))], (37408 ^ _781215) ^ [_1491187, _1491189] : [hBOOL(hAPP(hAPP(_1491095, _1491189), _1491187)), -(hAPP(_1491095, _1491189) = hAPP(_1491095, _1491187))]]], (3966 ^ _781215) ^ [_841380, _841382] : [_841382 = _841380, -(c_List_Odistinct(_841382) = c_List_Odistinct(_841380))], (5587 ^ _781215) ^ [_869254] : [c_Hoare__Mirabelle_Ostate__not__singleton, c_Com_OWT__bodies, hBOOL(hAPP(c_Com_OWT, _869254)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _869254)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (21860 ^ _781215) ^ [_1173719, _1173721, _1173723, _1173725] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1173719, tc_fun(_1173721, tc_HOL_Obool)), _1173723), _1173725) = c_Orderings_Obot__class_Obot(tc_fun(_1173721, tc_HOL_Obool)), 21863 ^ _781215 : [(21864 ^ _781215) ^ [_1173835] : [hBOOL(hAPP(hAPP(c_member(_1173719), _1173835), _1173723)), -(hAPP(_1173725, _1173835) = c_Orderings_Obot__class_Obot(tc_fun(_1173721, tc_HOL_Obool)))]]], (14080 ^ _781215) ^ [_1026736, _1026738, _1026740] : [class_Lattices_Oab__semigroup__idem__mult(_1026736), -(_1026738 = c_Orderings_Obot__class_Obot(tc_fun(_1026736, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1026736), _1026738)), -(hAPP(c_Finite__Set_Ofold1(_1026736, c_Groups_Otimes__class_Otimes(_1026736)), hAPP(hAPP(c_Set_Oinsert(_1026736), _1026740), _1026738)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026736), _1026740), hAPP(c_Finite__Set_Ofold1(_1026736, c_Groups_Otimes__class_Otimes(_1026736)), _1026738)))], (50830 ^ _781215) ^ [_1814192, _1814194] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1814192)), c_Int_OBit1(_1814194)))], (46121 ^ _781215) ^ [_1706818, _1706820, _1706822] : [hAPP(hAPP(c_List_Olist_OCons(_1706818), _1706820), c_List_Olist_ONil(_1706818)) = hAPP(c_List_Orev(_1706818), _1706822), -(_1706822 = hAPP(hAPP(c_List_Olist_OCons(_1706818), _1706820), c_List_Olist_ONil(_1706818)))], (44538 ^ _781215) ^ [_1673763, _1673765, _1673767] : [-(hAPP(hAPP(c_List_Oappend(_1673763), hAPP(hAPP(c_List_Otake(_1673763), _1673765), _1673767)), hAPP(hAPP(c_List_Odrop(_1673763), _1673765), _1673767)) = _1673767)], (32568 ^ _781215) ^ [_1384371, _1384373, _1384375, _1384377] : [hBOOL(hAPP(_1384371, _1384373)), hBOOL(hAPP(_1384375, _1384373)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384377, tc_HOL_Obool)), _1384371), _1384375), _1384373)))], (13284 ^ _781215) ^ [_1012134, _1012136, _1012138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012134), _1012136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1012138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012134), _1012138)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012136), _1012138))))], (22004 ^ _781215) ^ [_1177316, _1177318, _1177320, _1177322, _1177324] : [_1177316 = c_Orderings_Obot__class_Obot(tc_fun(_1177318, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1177320), _1177322), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1177318, tc_fun(_1177320, tc_HOL_Obool)), _1177316), _1177324)) = hAPP(hAPP(c_Set_Oinsert(_1177320), _1177322), c_Orderings_Obot__class_Obot(tc_fun(_1177320, tc_HOL_Obool))))], (51510 ^ _781215) ^ [_1823953] : [-(class_Nat_Osize(tc_Option_Ooption(_1823953)))], (39160 ^ _781215) ^ [_1533069, _1533071, _1533073] : [-(hAPP(hAPP(c_Set_Oinsert(_1533069), _1533071), _1533073) = hAPP(c_Set_OCollect(_1533069), hAPP(hAPP(c_COMBS(_1533069, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533069), c_fdisj), hAPP(hAPP(c_COMBC(_1533069, _1533069, tc_HOL_Obool), c_fequal), _1533071))), hAPP(hAPP(c_COMBC(_1533069, tc_fun(_1533069, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533069)), _1533073))))], (43908 ^ _781215) ^ [_1657999, _1658001, _1658003] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1657999)), -(c_List_Osublist(_1658001, hAPP(hAPP(c_List_Olist_OCons(_1658001), _1658003), c_List_Olist_ONil(_1658001)), _1657999) = hAPP(hAPP(c_List_Olist_OCons(_1658001), _1658003), c_List_Olist_ONil(_1658001)))], (50048 ^ _781215) ^ [_1796675, _1796677] : [-(c_Transitive__Closure_Ortrancl(_1796675, _1796677) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1796675, _1796675), 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(_1796675, _1796675), tc_HOL_Obool), tc_fun(tc_prod(_1796675, _1796675), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1796675, _1796675), tc_HOL_Obool)), _1796677)))], (5611 ^ _781215) ^ [_869584, _869586, _869588, _869590] : [c_Hoare__Mirabelle_Ohoare__derivs(_869584, _869586, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_869584)), _869588), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_869584), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_869584, _869586, _869590), -(c_Hoare__Mirabelle_Ohoare__derivs(_869584, _869586, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_869584)), _869588), _869590)))], (6162 ^ _781215) ^ [_880369, _880371, _880373, _880375, _880377, _880379, _880381] : [c_Map_Omap__comp(_880369, _880371, _880373, _880375, _880377, _880379) = hAPP(c_Option_Ooption_OSome(_880371), _880381), 6166 ^ _781215 : [(6169 ^ _781215) ^ [] : [-(hAPP(_880375, 6165 ^ [_880369, _880371, _880373, _880375, _880377, _880379, _880381]) = hAPP(c_Option_Ooption_OSome(_880371), _880381))], (6167 ^ _781215) ^ [] : [-(hAPP(_880377, _880379) = hAPP(c_Option_Ooption_OSome(_880369), 6165 ^ [_880369, _880371, _880373, _880375, _880377, _880379, _880381]))]]], (22420 ^ _781215) ^ [_1186209, _1186211, _1186213] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1186209), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1186211, _1186213)), _1186213) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1186209), _1186211), _1186213))], (16167 ^ _781215) ^ [_1067002, _1067004, _1067006, _1067008] : [class_Lattices_Osemilattice__sup(_1067002), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067002), _1067004), _1067006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067002), _1067008), _1067006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067002), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067002), _1067004), _1067008)), _1067006)))], (49984 ^ _781215) ^ [_1794960, _1794962, _1794964] : [-(hAPP(hAPP(c_Nat_Ocompow(_1794960, _1794960), hAPP(c_Nat_OSuc, _1794962)), _1794964) = hAPP(c_Fun_Ocomp(_1794960, _1794960, _1794960, _1794964), hAPP(hAPP(c_Nat_Ocompow(_1794960, _1794960), _1794962), _1794964)))], (50366 ^ _781215) ^ [_1805411, _1805413, _1805415] : [-(c_Nitpick_Oof__frac(_1805413, _1805411, _1805415) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1805411), hAPP(c_Int_Oring__1__class_Oof__int(_1805411), hAPP(c_Nitpick_Onum(_1805413), _1805415))), hAPP(c_Int_Oring__1__class_Oof__int(_1805411), hAPP(c_Nitpick_Odenom(_1805413), _1805415)))), class_Rings_Oinverse(_1805411), class_Rings_Oring__1(_1805411)], (46652 ^ _781215) ^ [_1719138, _1719140] : [hBOOL(hAPP(c_List_Odistinct(_1719138), _1719140)), -(c_List_Oremdups(_1719138, _1719140) = _1719140)], (48402 ^ _781215) ^ [_1758426, _1758428, _1758430, _1758432] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1758426, tc_HOL_Obool), tc_fun(_1758426, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1758426, tc_HOL_Obool), tc_fun(_1758426, tc_HOL_Obool)), _1758428), _1758430)), c_Wellfounded_Omax__ext(_1758426, _1758432)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1758426), _1758428)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1758426), _1758430)), -(_1758430 = c_Orderings_Obot__class_Obot(tc_fun(_1758426, tc_HOL_Obool))), 48416 ^ _781215 : [(48419 ^ _781215) ^ [_1758831] : [hBOOL(hAPP(hAPP(c_member(_1758426), _1758831), _1758430)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1758426, _1758426)), hAPP(hAPP(c_Product__Type_OPair(_1758426, _1758426), 48415 ^ [_1758426, _1758428, _1758430, _1758432]), _1758831)), _1758432))], (48417 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758426), 48415 ^ [_1758426, _1758428, _1758430, _1758432]), _1758428)))]]], (46744 ^ _781215) ^ [_1721072, _1721074, _1721076, _1721078] : [-(hBOOL(hAPP(_1721072, _1721074))), -(c_List_OdropWhile(_1721076, _1721072, hAPP(hAPP(c_List_Olist_OCons(_1721076), _1721074), _1721078)) = hAPP(hAPP(c_List_Olist_OCons(_1721076), _1721074), _1721078))], (11242 ^ _781215) ^ [_976596, _976598, _976600, _976602] : [class_Rings_Ocomm__semiring__1(_976596), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976596), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976596), _976598), _976600)), _976602) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976596), _976598), _976602)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976596), _976600), _976602)))], (19402 ^ _781215) ^ [_1129214, _1129216, _1129218] : [class_Orderings_Olinorder(_1129214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1129214), _1129216)), -(c_Big__Operators_Olinorder__class_OMin(_1129214, hAPP(hAPP(c_Set_Oinsert(_1129214), _1129218), _1129216)) = hAPP(hAPP(c_Finite__Set_Ofold(_1129214, _1129214, c_Orderings_Oord__class_Omin(_1129214)), _1129218), _1129216))], (45312 ^ _781215) ^ [_1690138, _1690140, _1690142] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690138)), hAPP(c_List_Ofilter(_1690138, _1690140), _1690142))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690138)), hAPP(c_List_Ofilter(_1690138, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1690138), c_fNot), _1690140)), _1690142))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690138)), _1690142))], (44968 ^ _781215) ^ [_1683282, _1683284, _1683286, _1683288, _1683290, _1683292] : [-(hAPP(c_List_Ofoldl(_1683282, _1683284, _1683286, _1683288), hAPP(hAPP(c_List_Oappend(_1683284), _1683290), _1683292)) = hAPP(c_List_Ofoldl(_1683282, _1683284, _1683286, hAPP(c_List_Ofoldl(_1683282, _1683284, _1683286, _1683288), _1683290)), _1683292))], (19740 ^ _781215) ^ [_1135463, _1135465, _1135467] : [class_Orderings_Olinorder(_1135463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135463), _1135465)), -(_1135467 = c_Orderings_Obot__class_Obot(tc_fun(_1135463, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1135463, tc_HOL_Obool)), _1135467), _1135465)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1135463), c_Big__Operators_Olattice_OSup__fin(_1135463, c_Orderings_Oord__class_Omax(_1135463), _1135467)), c_Big__Operators_Olattice_OSup__fin(_1135463, c_Orderings_Oord__class_Omax(_1135463), _1135465)) = c_Big__Operators_Olattice_OSup__fin(_1135463, c_Orderings_Oord__class_Omax(_1135463), _1135465))], (23813 ^ _781215) ^ [_1210472, _1210474] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1210472, _1210474)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210472), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210474)))], (27766 ^ _781215) ^ [_1287025, _1287027, _1287029] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1287025, tc_HOL_Obool), tc_fun(_1287025, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1287025, tc_HOL_Obool), tc_fun(_1287025, tc_HOL_Obool)), _1287027), _1287029)), c_Wellfounded_Ofinite__psubset(_1287025)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1287025, tc_HOL_Obool)), _1287027), _1287029)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287025), _1287029))], (51316 ^ _781215) ^ [] : [-(class_HOL_Oequal(tc_Int_Oint))], (8740 ^ _781215) ^ [_929459, _929461, _929463] : [_929459 = _929461, 8743 ^ _781215 : [(8746 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929463, tc_HOL_Obool)), _929461), _929459)))], (8744 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929463, tc_HOL_Obool)), _929459), _929461)))]]], (31463 ^ _781215) ^ [_1358299, _1358301] : [-(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), _1358299), _1358301)), 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), _1358301), _1358299)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37842 ^ _781215) ^ [_1500455, _1500457, _1500459, _1500461] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500455, tc_fun(_1500457, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1500455, tc_HOL_Obool), _1500459)), _1500461) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1500455, tc_HOL_Obool), tc_fun(_1500457, tc_HOL_Obool)), _1500459), hAPP(hAPP(c_COMBC(tc_fun(_1500455, tc_HOL_Obool), tc_fun(_1500455, tc_fun(_1500457, tc_HOL_Obool)), tc_fun(_1500457, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500455, tc_fun(_1500457, tc_HOL_Obool))), _1500461)))], (41701 ^ _781215) ^ [_1602129, _1602131, _1602133, _1602135, _1602137] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1602129, _1602131, _1602133), _1602135), _1602137)), 41704 ^ _781215 : [(41707 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1602133, _1602137)))], (41705 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1602131, _1602135), _1602137)))]]], (38816 ^ _781215) ^ [_1525513, _1525515, _1525517, _1525519, _1525521, _1525523, _1525525] : [-(hAPP(c_Product__Type_Ofst(_1525513, _1525515), hAPP(c_Product__Type_Omap__pair(_1525517, _1525513, _1525519, _1525515, _1525521, _1525523), _1525525)) = hAPP(_1525521, hAPP(c_Product__Type_Ofst(_1525517, _1525519), _1525525)))], (48686 ^ _781215) ^ [_1764188, _1764190, _1764192, _1764194] : [48687 ^ _781215 : [(48690 ^ _781215) ^ [] : [c_List_Olist__ex(_1764188, _1764190, _1764194)], (48688 ^ _781215) ^ [] : [hBOOL(hAPP(_1764190, _1764192))]], -(c_List_Olist__ex(_1764188, _1764190, hAPP(hAPP(c_List_Olist_OCons(_1764188), _1764192), _1764194)))], (21762 ^ _781215) ^ [_1171620, _1171622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1171620)), c_Int_OBit1(_1171622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171620), _1171622)))], (44580 ^ _781215) ^ [_1674766, _1674768, _1674770, _1674772] : [-(hAPP(hAPP(c_List_Odrop(_1674766), _1674768), hAPP(hAPP(c_List_Odrop(_1674766), _1674770), _1674772)) = hAPP(hAPP(c_List_Odrop(_1674766), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1674768), _1674770)), _1674772))], (45101 ^ _781215) ^ [_1686449, _1686451, _1686453, _1686455] : [-(_1686449 = c_List_Olist_ONil(_1686451)), 45104 ^ _781215 : [(45111 ^ _781215) ^ [] : [-(_1686453 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686451)), _1686449)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1686451, hAPP(hAPP(c_List_Olist__update(_1686451, _1686449), _1686453), _1686455)) = c_List_Olast(_1686451, _1686449))], (45105 ^ _781215) ^ [] : [_1686453 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686451)), _1686449)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1686451, hAPP(hAPP(c_List_Olist__update(_1686451, _1686449), _1686453), _1686455)) = _1686455)]]], (11868 ^ _781215) ^ [_987779] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _987779)], (21422 ^ _781215) ^ [_1165672, _1165674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1165672), _1165674)), -(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)), _1165672)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1165674))))], (11500 ^ _781215) ^ [_981593, _981595, _981597, _981599, _981601, _981603] : [hBOOL(hAPP(hAPP(c_member(_981593), _981595), _981597)), _981599 = hAPP(_981601, _981595), -(hBOOL(hAPP(hAPP(c_member(_981603), _981599), hAPP(c_Set_Oimage(_981593, _981603, _981601), _981597))))], (40996 ^ _781215) ^ [_1585342] : [-(hAPP(c_List_Omap(_1585342, _1585342), c_Fun_Oid(_1585342)) = c_Fun_Oid(tc_List_Olist(_1585342)))], (51388 ^ _781215) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (21792 ^ _781215) ^ [_1172163, _1172165] : [class_Int_Onumber__ring(_1172163), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172163), c_Groups_Oone__class_Oone(_1172163)), c_Groups_Oone__class_Oone(_1172163))), hAPP(c_Int_Onumber__class_Onumber__of(_1172163), _1172165)) = hAPP(c_Int_Onumber__class_Onumber__of(_1172163), c_Int_OBit0(_1172165)))], (33641 ^ _781215) ^ [_1408253, _1408255, _1408257, _1408259, _1408261] : [c_Finite__Set_Ofolding__one(_1408253, _1408255, _1408257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408253), _1408259)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408253), _1408261)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408253, tc_HOL_Obool)), _1408259), _1408261) = c_Orderings_Obot__class_Obot(tc_fun(_1408253, tc_HOL_Obool))), -(hAPP(hAPP(_1408255, hAPP(_1408257, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408253, tc_HOL_Obool)), _1408259), _1408261))), hAPP(_1408257, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408253, tc_HOL_Obool)), _1408259), _1408261))) = hAPP(hAPP(_1408255, hAPP(_1408257, _1408259)), hAPP(_1408257, _1408261)))], (45734 ^ _781215) ^ [_1698529, _1698531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1698529), _1698531)), -(c_List_Oupt(_1698529, hAPP(c_Nat_OSuc, _1698531)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1698529, _1698531)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1698531), c_List_Olist_ONil(tc_Nat_Onat))))], (22276 ^ _781215) ^ [_1183124, _1183126, _1183128, _1183130] : [class_Divides_Osemiring__div(_1183124), -(c_Divides_Odiv__class_Omod(_1183124, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183124), _1183126), _1183128), _1183130) = c_Divides_Odiv__class_Omod(_1183124, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183124), c_Divides_Odiv__class_Omod(_1183124, _1183126, _1183130)), c_Divides_Odiv__class_Omod(_1183124, _1183128, _1183130)), _1183130))], (45215 ^ _781215) ^ [_1688193, _1688195] : [-(_1688193 = c_List_Olist_ONil(_1688195)), -(c_List_Olast(_1688195, _1688193) = hAPP(hAPP(c_List_Onth(_1688195), _1688193), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688195)), _1688193)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (23418 ^ _781215) ^ [_1203192, _1203194, _1203196, _1203198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203194), _1203196)), -(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), _1203196), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1203198, _1203192))), _1203194))))], (4488 ^ _781215) ^ [_849277, _849279] : [_849279 = _849277, -(c_Relation_OId(_849279) = c_Relation_OId(_849277))], (40033 ^ _781215) ^ [_1562790, _1562792, _1562794] : [c_Wellfounded_Owf(_1562790, _1562792), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562790, _1562790)), hAPP(hAPP(c_Product__Type_OPair(_1562790, _1562790), _1562794), _1562794)), _1562792))], (35433 ^ _781215) ^ [_1446993, _1446995, _1446997] : [class_Orderings_Oorder(_1446993), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446993, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446993, _1446995), _1446997)), hAPP(c_SetInterval_Oord__class_OatLeast(_1446993), _1446997)) = c_Orderings_Obot__class_Obot(tc_fun(_1446993, tc_HOL_Obool)))], (15582 ^ _781215) ^ [_1054829, _1054831, _1054833] : [_1054833 = hAPP(c_COMBK(tc_Option_Ooption(_1054831), _1054829), c_Option_Ooption_ONone(_1054831)), -(c_Map_Odom(_1054829, _1054831, _1054833) = c_Orderings_Obot__class_Obot(tc_fun(_1054829, tc_HOL_Obool)))], (32616 ^ _781215) ^ [_1385295, _1385297, _1385299] : [class_Lattices_Olattice(_1385295), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385295), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1385295), _1385297), _1385299)), _1385299)))], (7053 ^ _781215) ^ [_898486, _898488, _898490, _898492, _898494] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_898486, _898488)), _898490), _898492), _898494)), 7057 ^ _781215 : [(7060 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _898488), 7056 ^ [_898486, _898488, _898490, _898492, _898494]), _898492), _898494)))], (7058 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _898486), _898490), _898492), 7056 ^ [_898486, _898488, _898490, _898492, _898494])))]]], (20356 ^ _781215) ^ [_1146641] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1146641)) = _1146641)], (15634 ^ _781215) ^ [_1055928, _1055930, _1055932, _1055934, _1055936] : [c_Com_Ocom_OSemi(_1055928, _1055930) = c_Com_Ocom_OLocal(_1055932, _1055934, _1055936)], (42758 ^ _781215) ^ [_1630710, _1630712, _1630714] : [hBOOL(hAPP(hAPP(c_member(_1630710), _1630712), hAPP(c_List_Oset(_1630710), _1630714))), 42762 ^ _781215 : [(42765 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1630710), _1630714), 42761 ^ [_1630710, _1630712, _1630714]) = _1630712)], (42763 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42761 ^ [_1630710, _1630712, _1630714]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630710)), _1630714))))]]], (31415 ^ _781215) ^ [_1356946, _1356948, _1356950] : [class_Orderings_Olinorder(_1356946), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356946), _1356948), _1356950)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1356946, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1356946), _1356948)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1356946, _1356948), _1356950)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1356946), _1356950))], (27514 ^ _781215) ^ [_1281960, _1281962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1281962), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1281960, _1281962) = 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), _1281960), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1281962)))))], (45835 ^ _781215) ^ [_1700442, _1700444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700442)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700444))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700442), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700444)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700442)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700442)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700444))))], (47450 ^ _781215) ^ [_1735903, _1735905, _1735907, _1735909] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1735903)), _1735905), c_List_Olists(_1735903, _1735907))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1735903)), _1735905), c_List_Olists(_1735903, _1735909))), -(hBOOL(hAPP(c_List_Olistsp(_1735903, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1735903, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1735903, tc_fun(_1735903, tc_HOL_Obool), tc_HOL_Obool), c_member(_1735903)), _1735907)), hAPP(hAPP(c_COMBC(_1735903, tc_fun(_1735903, tc_HOL_Obool), tc_HOL_Obool), c_member(_1735903)), _1735909))), _1735905)))], (13526 ^ _781215) ^ [_1016384, _1016386, _1016388, _1016390] : [class_Rings_Olinordered__semiring__strict(_1016384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016384), _1016386), _1016388)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016384), _1016386), _1016390))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016384), c_Groups_Ozero__class_Ozero(_1016384)), _1016386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016384), _1016388), _1016390)))], (37739 ^ _781215) ^ [_1498196, _1498198, _1498200, _1498202, _1498204, _1498206] : [c_Typedef_Otype__definition(_1498196, _1498198, _1498200, _1498202, _1498204), hBOOL(hAPP(hAPP(c_member(_1498198), _1498206), _1498204)), -(hAPP(_1498200, hAPP(_1498202, _1498206)) = _1498206)], (27339 ^ _781215) ^ [_1278163, _1278165, _1278167, _1278169] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1278163), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1278165), _1278167)))), -(hBOOL(hAPP(hAPP(hAPP(_1278169, _1278163), _1278165), _1278167))), 27347 ^ _781215 : [(27350 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 27345 ^ [_1278163, _1278165, _1278167, _1278169]), 27346 ^ [_1278163, _1278165, _1278167, _1278169]))), hAPP(27344 ^ [_1278163, _1278165, _1278167, _1278169], 27346 ^ [_1278163, _1278165, _1278167, _1278169]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1278169, 27344 ^ [_1278163, _1278165, _1278167, _1278169]), 27345 ^ [_1278163, _1278165, _1278167, _1278169]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 27346 ^ [_1278163, _1278165, _1278167, _1278169]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (27360 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1278169, 27344 ^ [_1278163, _1278165, _1278167, _1278169]), 27345 ^ [_1278163, _1278165, _1278167, _1278169]), 27346 ^ [_1278163, _1278165, _1278167, _1278169]))], (27348 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), 27344 ^ [_1278163, _1278165, _1278167, _1278169]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 27345 ^ [_1278163, _1278165, _1278167, _1278169]), 27346 ^ [_1278163, _1278165, _1278167, _1278169])))))]]], (21211 ^ _781215) ^ [_1160897, _1160899, _1160901, _1160903, _1160905] : [class_Complete__Lattice_Ocomplete__lattice(_1160897), hBOOL(hAPP(c_Finite__Set_Ofinite(_1160899), _1160901)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1160897), _1160903), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1160899, _1160897), _1160901), _1160905)) = hAPP(hAPP(c_Finite__Set_Ofold(_1160899, _1160897, hAPP(hAPP(c_COMBB(_1160897, tc_fun(_1160897, _1160897), _1160899), c_Lattices_Osemilattice__sup__class_Osup(_1160897)), _1160905)), _1160903), _1160901))], (10064 ^ _781215) ^ [_952339, _952341, _952343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952339), _952341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952339), _952343)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952341), _952343))))], (39741 ^ _781215) ^ [_1554095, _1554097, _1554099, _1554101, _1554103, _1554105, _1554107] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1554095, _1554097, _1554099), _1554101), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1554103, tc_fun(tc_prod(_1554097, _1554099), tc_HOL_Obool)), _1554105), _1554107)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1554103, tc_fun(tc_prod(_1554095, _1554099), tc_HOL_Obool)), _1554105), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1554097, _1554099), tc_HOL_Obool), tc_fun(tc_prod(_1554095, _1554099), tc_HOL_Obool), _1554103), hAPP(c_Relation_Orel__comp(_1554095, _1554097, _1554099), _1554101)), _1554107)))], (49565 ^ _781215) ^ [_1784454, _1784456, _1784458, _1784460, _1784462] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1784454, _1784454)), hAPP(hAPP(c_Product__Type_OPair(_1784454, _1784454), _1784456), _1784458)), c_Transitive__Closure_Ortrancl(_1784454, _1784460))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1784454, _1784454), tc_HOL_Obool)), _1784460), hAPP(hAPP(c_Product__Type_OSigma(_1784454, _1784454), _1784462), hAPP(c_COMBK(tc_fun(_1784454, tc_HOL_Obool), _1784454), _1784462)))), -(_1784456 = _1784458), -(hBOOL(hAPP(hAPP(c_member(_1784454), _1784456), _1784462)))], (31397 ^ _781215) ^ [_1356489, _1356491, _1356493, _1356495] : [-(hAPP(c_Relation_OImage(_1356489, _1356491, _1356493), _1356495) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1356489, tc_fun(_1356491, tc_HOL_Obool)), _1356495), hAPP(hAPP(c_COMBB(tc_fun(_1356489, tc_HOL_Obool), tc_fun(_1356491, tc_HOL_Obool), _1356489), c_Relation_OImage(_1356489, _1356491, _1356493)), hAPP(hAPP(c_COMBC(_1356489, tc_fun(_1356489, tc_HOL_Obool), tc_fun(_1356489, tc_HOL_Obool)), c_Set_Oinsert(_1356489)), c_Orderings_Obot__class_Obot(tc_fun(_1356489, tc_HOL_Obool))))))], (48998 ^ _781215) ^ [_1770084] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1770084)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (38884 ^ _781215) ^ [_1527397] : [-(c_Relation_Orefl__on(_1527397, c_Orderings_Obot__class_Obot(tc_fun(_1527397, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527397, _1527397), tc_HOL_Obool))))], (5372 ^ _781215) ^ [_863295, _863297, _863299, _863301] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_863301, _863297) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_863299, _863295)), _863301 = _863299, _863297 = _863295], (46771 ^ _781215) ^ [_1721588, _1721590, _1721592] : [-(c_List_OdropWhile(_1721588, _1721590, _1721592) = c_List_Olist_ONil(_1721588)), hBOOL(hAPP(_1721590, hAPP(c_List_Ohd(_1721588), c_List_OdropWhile(_1721588, _1721590, _1721592))))], (7857 ^ _781215) ^ [_913929, _913931] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913929), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913929), _913931)))))], (17337 ^ _781215) ^ [_1091687, _1091689, _1091691] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091687))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091687)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091689)), _1091691)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091689)), _1091691))], (39244 ^ _781215) ^ [_1535236, _1535238, _1535240, _1535242, _1535244, _1535246, _1535248] : [class_Groups_Ocomm__monoid__add(_1535236), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535238), _1535240)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535242), _1535244)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1535238, _1535236), hAPP(hAPP(c_COMBS(_1535238, tc_fun(_1535242, tc_HOL_Obool), _1535236), hAPP(hAPP(c_COMBB(tc_fun(_1535242, _1535236), tc_fun(tc_fun(_1535242, tc_HOL_Obool), _1535236), _1535238), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1535242, _1535236)), _1535246)), hAPP(hAPP(c_COMBB(tc_fun(_1535242, tc_HOL_Obool), tc_fun(_1535242, tc_HOL_Obool), _1535238), c_Set_OCollect(_1535242)), hAPP(hAPP(c_COMBB(tc_fun(_1535242, tc_HOL_Obool), tc_fun(_1535242, tc_HOL_Obool), _1535238), hAPP(c_COMBS(_1535242, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535242), c_fconj), hAPP(hAPP(c_COMBC(_1535242, tc_fun(_1535242, tc_HOL_Obool), tc_HOL_Obool), c_member(_1535242)), _1535244)))), _1535248)))), _1535240) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1535242, _1535236), hAPP(hAPP(c_COMBS(_1535242, tc_fun(_1535238, tc_HOL_Obool), _1535236), hAPP(hAPP(c_COMBB(tc_fun(_1535238, _1535236), tc_fun(tc_fun(_1535238, tc_HOL_Obool), _1535236), _1535242), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1535238, _1535236)), hAPP(c_COMBC(_1535238, _1535242, _1535236), _1535246))), hAPP(hAPP(c_COMBB(tc_fun(_1535238, tc_HOL_Obool), tc_fun(_1535238, tc_HOL_Obool), _1535242), c_Set_OCollect(_1535238)), hAPP(hAPP(c_COMBB(tc_fun(_1535238, tc_HOL_Obool), tc_fun(_1535238, tc_HOL_Obool), _1535242), hAPP(c_COMBS(_1535238, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535238), c_fconj), hAPP(hAPP(c_COMBC(_1535238, tc_fun(_1535238, tc_HOL_Obool), tc_HOL_Obool), c_member(_1535238)), _1535240)))), hAPP(c_COMBC(_1535238, _1535242, tc_HOL_Obool), _1535248))))), _1535244))], (21472 ^ _781215) ^ [_1166540, _1166542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1166540)), c_Int_OBit0(_1166542))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1166540), _1166542)))], (20253 ^ _781215) ^ [_1144797, _1144799] : [c_Int_OBit1(_1144797) = c_Int_OBit1(_1144799), -(_1144797 = _1144799)], (47470 ^ _781215) ^ [_1736382, _1736384, _1736386, _1736388] : [-(hBOOL(hAPP(c_List_Olistsp(_1736382, _1736384), hAPP(hAPP(c_List_Oappend(_1736382), _1736386), _1736388)))), hBOOL(hAPP(c_List_Olistsp(_1736382, _1736384), _1736386)), hBOOL(hAPP(c_List_Olistsp(_1736382, _1736384), _1736388))], (33254 ^ _781215) ^ [_1399687, _1399689, _1399691] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399687, tc_HOL_Obool)), _1399689), _1399691) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399687, tc_HOL_Obool)), _1399689), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1399687, tc_HOL_Obool)), _1399691)))], (25178 ^ _781215) ^ [_1235678, _1235680] : [c_Nat__Transfer_Ois__nat(_1235678), c_Nat__Transfer_Onat__set(_1235680), 25185 ^ _781215 : [(25192 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1235678)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1235680))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1235678), _1235680)))], (25186 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1235678), _1235680)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1235678)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1235680))))]]], (36446 ^ _781215) ^ [_1466192, _1466194] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466192, tc_HOL_Obool)), _1466194), c_Orderings_Otop__class_Otop(tc_fun(_1466192, tc_HOL_Obool)))))], (36159 ^ _781215) ^ [_1461097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1461097), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1461097) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1461097))], (20058 ^ _781215) ^ [_1141122, _1141124, _1141126] : [class_Orderings_Olinorder(_1141122), hAPP(_1141124, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1141122), 20063 ^ [_1141122, _1141124, _1141126]), 20064 ^ [_1141122, _1141124, _1141126])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1141122), hAPP(_1141124, 20063 ^ [_1141122, _1141124, _1141126])), hAPP(_1141124, 20064 ^ [_1141122, _1141124, _1141126])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1141122), _1141126)), -(_1141126 = c_Orderings_Obot__class_Obot(tc_fun(_1141122, tc_HOL_Obool))), -(hAPP(_1141124, c_Big__Operators_Olattice_OSup__fin(_1141122, c_Orderings_Oord__class_Omax(_1141122), _1141126)) = c_Big__Operators_Olattice_OSup__fin(_1141122, c_Orderings_Oord__class_Omax(_1141122), hAPP(c_Set_Oimage(_1141122, _1141122, _1141124), _1141126)))], (9923 ^ _781215) ^ [_950006, _950008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _950006)), hAPP(c_Nat_OSuc, _950008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950006), _950008)))], (36428 ^ _781215) ^ [_1465854] : [-(hAPP(c_Set_OPow(_1465854), c_Orderings_Otop__class_Otop(tc_fun(_1465854, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1465854, tc_HOL_Obool), tc_HOL_Obool)))], (31513 ^ _781215) ^ [_1359955, _1359957, _1359959] : [class_Groups_Ocomm__monoid__add(_1359955), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359957, _1359955), hAPP(c_COMBK(_1359955, _1359957), c_Groups_Ozero__class_Ozero(_1359955))), _1359959) = c_Groups_Ozero__class_Ozero(_1359955))], (15444 ^ _781215) ^ [_1052033, _1052035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052033), _1052035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052033), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1052035)))], (39190 ^ _781215) ^ [_1533927, _1533929, _1533931] : [hBOOL(hAPP(_1533927, _1533929)), -(hAPP(c_Set_OCollect(_1533931), hAPP(hAPP(c_COMBS(_1533931, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533931), c_fconj), hAPP(c_fequal, _1533929))), _1533927)) = hAPP(hAPP(c_Set_Oinsert(_1533931), _1533929), c_Orderings_Obot__class_Obot(tc_fun(_1533931, tc_HOL_Obool))))], (49654 ^ _781215) ^ [_1787103, _1787105, _1787107] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1787105, _1787103)), _1787107)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1787103, _1787105)), hAPP(c_Relation_Oconverse(_1787105, _1787103), _1787107))))], (32970 ^ _781215) ^ [_1392700, _1392702] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392700, tc_HOL_Obool)), _1392702), _1392702) = _1392702)], (21181 ^ _781215) ^ [_1160333, _1160335, _1160337] : [hBOOL(hAPP(_1160333, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160335), _1160337)))), 21184 ^ _781215 : [(21191 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160335), _1160337)), -(hBOOL(hAPP(_1160333, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21185 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1160337), _1160335)), -(hBOOL(hAPP(_1160333, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1160335)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1160337)))))]]], (6357 ^ _781215) ^ [_884507, _884509, _884511, _884513] : [6358 ^ _781215 : [(6361 ^ _781215) ^ [] : [_884509 = _884513], (6359 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_884507), _884509), _884511))]], -(hBOOL(hAPP(hAPP(c_member(_884507), _884509), hAPP(hAPP(c_Set_Oinsert(_884507), _884513), _884511))))], (25462 ^ _781215) ^ [_1239800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1239800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1239800))))], (39671 ^ _781215) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (7957 ^ _781215) ^ [_915376, _915378, _915380] : [7958 ^ _781215 : [(7961 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_915380, _915378), _915376))], (7959 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915376), _915378)))]], 7964 ^ _781215 : [(7967 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_915380, _915378), _915376))], (7965 ^ _781215) ^ [] : [-(_915376 = _915378)]], 7970 ^ _781215 : [(7973 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_915380, _915378), _915376))], (7971 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915378), _915376)))]], -(hBOOL(hAPP(hAPP(_915380, _915378), _915376)))], (21502 ^ _781215) ^ [_1167087, _1167089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1167087), _1167089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1167087)), c_Int_OBit0(_1167089))))], (10358 ^ _781215) ^ [_957746, _957748, _957750] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957746, tc_HOL_Obool)), _957748), _957750))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957746, tc_HOL_Obool)), _957748), _957750)), -(_957748 = _957750)], (51570 ^ _781215) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (9137 ^ _781215) ^ [_936280, _936282] : [_936280 = _936282, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936280), _936282)))], (46133 ^ _781215) ^ [_1707074, _1707076] : [-(hAPP(c_List_Orev(_1707074), c_List_Oconcat(_1707074, _1707076)) = c_List_Oconcat(_1707074, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707074), tc_List_Olist(_1707074)), c_List_Orev(_1707074)), hAPP(c_List_Orev(tc_List_Olist(_1707074)), _1707076))))], (48900 ^ _781215) ^ [_1768401, _1768403] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1768401)), hAPP(c_Code__Numeral_Oof__nat, _1768403)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1768401), _1768403)))], (22214 ^ _781215) ^ [_1181994, _1181996, _1181998] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181994), _1181996)), _1181998) = 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), _1181994), _1181998)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181996), _1181998))), 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, _1181994, _1181998)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181996, _1181998))), _1181998)))], (22066 ^ _781215) ^ [_1178601, _1178603, _1178605, _1178607, _1178609] : [_1178601 = c_Orderings_Obot__class_Obot(tc_fun(_1178603, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1178605, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1178603, tc_fun(_1178605, tc_HOL_Obool)), _1178601), _1178607)), _1178609) = _1178609)], (7408 ^ _781215) ^ [_905915, _905917, _905919] : [class_Orderings_Oorder(_905915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905915), _905917), _905919)), _905917 = _905919], (592 ^ _781215) ^ [_790431, _790433, _790435, _790437, _790439, _790441, _790443, _790445] : [-(c_List_Olistrelp(_790443, _790439, _790435, _790431)), c_List_Olistrelp(_790445, _790441, _790437, _790433), _790445 = _790443, _790441 = _790439, _790437 = _790435, _790433 = _790431], (51636 ^ _781215) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (15652 ^ _781215) ^ [_1056392, _1056394, _1056396, _1056398] : [c_Map_Odom(_1056392, _1056394, _1056396) = hAPP(hAPP(c_Set_Oinsert(_1056392), _1056398), c_Orderings_Obot__class_Obot(tc_fun(_1056392, tc_HOL_Obool))), -(_1056396 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1056392, tc_Option_Ooption(_1056394)), hAPP(c_COMBK(tc_Option_Ooption(_1056394), _1056392), c_Option_Ooption_ONone(_1056394))), _1056398), hAPP(c_Option_Ooption_OSome(_1056394), 15655 ^ [_1056392, _1056394, _1056396, _1056398])))], (20118 ^ _781215) ^ [_1142343, _1142345, _1142347] : [class_Lattices_Olattice(_1142343), hAPP(_1142345, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1142343), 20123 ^ [_1142343, _1142345, _1142347]), 20124 ^ [_1142343, _1142345, _1142347])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1142343), hAPP(_1142345, 20123 ^ [_1142343, _1142345, _1142347])), hAPP(_1142345, 20124 ^ [_1142343, _1142345, _1142347])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1142343), _1142347)), -(_1142347 = c_Orderings_Obot__class_Obot(tc_fun(_1142343, tc_HOL_Obool))), -(hAPP(_1142345, c_Big__Operators_Olattice__class_OSup__fin(_1142343, _1142347)) = c_Big__Operators_Olattice__class_OSup__fin(_1142343, hAPP(c_Set_Oimage(_1142343, _1142343, _1142345), _1142347)))], (45568 ^ _781215) ^ [_1695906, _1695908] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1695906, _1695908)))], (25845 ^ _781215) ^ [_1249814, _1249816, _1249818, _1249820] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1249814, tc_fun(_1249816, tc_HOL_Obool))), _1249818), _1249820)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1249814, _1249816)), hAPP(hAPP(c_Product__Type_OPair(_1249814, _1249816), _1249818), _1249820)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1249814, _1249816), tc_HOL_Obool)))))], (16641 ^ _781215) ^ [_1078057, _1078059, _1078061, _1078063, _1078065, _1078067] : [c_Finite__Set_Ofun__left__comm(_1078057, _1078059, _1078061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078057), _1078063)), -(hBOOL(hAPP(hAPP(c_member(_1078057), _1078065), _1078063))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1078057, _1078059, _1078061), _1078067), hAPP(hAPP(c_Set_Oinsert(_1078057), _1078065), _1078063)) = hAPP(hAPP(_1078061, _1078065), hAPP(hAPP(c_Finite__Set_Ofold(_1078057, _1078059, _1078061), _1078067), _1078063)))], (198 ^ _781215) ^ [_784182, _784184, _784186, _784188, _784190, _784192] : [-(c_Finite__Set_Ofolding__one(_784190, _784186, _784182)), c_Finite__Set_Ofolding__one(_784192, _784188, _784184), _784192 = _784190, _784188 = _784186, _784184 = _784182], (22695 ^ _781215) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (46369 ^ _781215) ^ [_1712930, _1712932, _1712934, _1712936] : [class_Orderings_Olinorder(_1712930), c_List_Olinorder__class_Osorted(_1712930, hAPP(c_List_Orev(_1712930), _1712932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712934), _1712936)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712936), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712930)), _1712932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712930), hAPP(hAPP(c_List_Onth(_1712930), _1712932), _1712936)), hAPP(hAPP(c_List_Onth(_1712930), _1712932), _1712934))))], (16579 ^ _781215) ^ [_1076917, _1076919, _1076921, _1076923, _1076925, _1076927] : [c_Finite__Set_Ofun__left__comm(_1076917, _1076919, _1076921), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1076917, _1076919, _1076921, _1076923, _1076925), _1076927)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1076917, _1076919, _1076921), _1076923), _1076925) = _1076927)], (23640 ^ _781215) ^ [_1207323, _1207325, _1207327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207323), _1207325)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1207323), _1207327)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1207325), _1207327))))], (778 ^ _781215) ^ [_793210, _793212, _793214, _793216, _793218, _793220, _793222, _793224] : [-(c_Fun_Oinj__on(_793222, _793218, _793214, _793210)), c_Fun_Oinj__on(_793224, _793220, _793216, _793212), _793224 = _793222, _793220 = _793218, _793216 = _793214, _793212 = _793210], (22516 ^ _781215) ^ [_1187987, _1187989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187989)), -(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), _1187987), _1187989))))], (17617 ^ _781215) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6978 ^ _781215) ^ [_896888, _896890] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _896888), _896890), _896888)))], (32541 ^ _781215) ^ [_1383726, _1383728, _1383730, _1383732, _1383734, _1383736] : [c_Equiv__Relations_Oequiv(_1383726, _1383728, _1383730), hBOOL(hAPP(hAPP(c_member(_1383726), _1383732), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383726, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1383726, _1383726, _1383730), hAPP(hAPP(c_Set_Oinsert(_1383726), _1383734), c_Orderings_Obot__class_Obot(tc_fun(_1383726, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1383726, _1383726, _1383730), hAPP(hAPP(c_Set_Oinsert(_1383726), _1383736), c_Orderings_Obot__class_Obot(tc_fun(_1383726, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1383726, _1383726)), hAPP(hAPP(c_Product__Type_OPair(_1383726, _1383726), _1383734), _1383736)), _1383730)))], (5436 ^ _781215) ^ [_864231, _864233] : [_864233 = _864231, -(tc_List_Olist(_864233) = tc_List_Olist(_864231))], (20701 ^ _781215) ^ [_1152562, _1152564] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1152562), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1152564)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152562), _1152564)))], (41229 ^ _781215) ^ [_1590790, _1590792] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1590790, _1590792) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1590790), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1590792)))], (25198 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (39216 ^ _781215) ^ [_1534531, _1534533] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534531), hAPP(c_Set_OCollect(_1534531), _1534533))), 39219 ^ _781215 : [(39226 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534531), c_Orderings_Otop__class_Otop(tc_fun(_1534531, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1534531), hAPP(c_Set_OCollect(_1534531), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534531), c_fNot), _1534533)))))], (39220 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534531), hAPP(c_Set_OCollect(_1534531), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534531), c_fNot), _1534533)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1534531), c_Orderings_Otop__class_Otop(tc_fun(_1534531, tc_HOL_Obool)))))]]], (39653 ^ _781215) ^ [_1551868, _1551870, _1551872] : [c_Predicate_Oreflp(_1551868, _1551870), -(hBOOL(hAPP(hAPP(_1551870, _1551872), _1551872)))], (18159 ^ _781215) ^ [_1106344, _1106346, _1106348, _1106350] : [class_Orderings_Olinorder(_1106344), 18162 ^ _781215 : [(18163 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106344), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106344), _1106346), _1106348)), _1106350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106344), _1106346), _1106350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106344), _1106348), _1106350)))], (18173 ^ _781215) ^ [] : [18174 ^ _781215 : [(18177 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106344), _1106348), _1106350))], (18175 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106344), _1106346), _1106350))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106344), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106344), _1106346), _1106348)), _1106350)))]]], (16019 ^ _781215) ^ [_1063995, _1063997, _1063999, _1064001, _1064003, _1064005] : [c_Finite__Set_Ofun__left__comm(_1063995, _1063997, _1063999), -(hAPP(hAPP(_1063999, _1064001), hAPP(hAPP(_1063999, _1064003), _1064005)) = hAPP(hAPP(_1063999, _1064003), hAPP(hAPP(_1063999, _1064001), _1064005)))], (13470 ^ _781215) ^ [_1015368, _1015370, _1015372, _1015374] : [class_Groups_Oordered__comm__monoid__add(_1015368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015368), c_Groups_Ozero__class_Ozero(_1015368)), _1015370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015368), _1015372), _1015374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015368), _1015372), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015368), _1015370), _1015374))))], (26536 ^ _781215) ^ [_1262641] : [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), _1262641))), 26539 ^ _781215 : [(26546 ^ _781215) ^ [] : [-(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), _1262641)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1262641)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1262641)), 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), _1262641)))))], (26540 ^ _781215) ^ [] : [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), _1262641))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1262641)) = 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)))]]], (36207 ^ _781215) ^ [_1461873, _1461875] : [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), _1461873)), _1461875))), _1461873 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1461875 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13512 ^ _781215) ^ [_1016129, _1016131, _1016133] : [class_Groups_Oordered__comm__monoid__add(_1016129), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016129), c_Groups_Ozero__class_Ozero(_1016129)), _1016131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016129), c_Groups_Ozero__class_Ozero(_1016129)), _1016133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1016129), c_Groups_Ozero__class_Ozero(_1016129)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016129), _1016131), _1016133))))], (652 ^ _781215) ^ [_791303, _791305, _791307, _791309, _791311, _791313] : [-(c_Finite__Set_Ofun__left__comm(_791311, _791307, _791303)), c_Finite__Set_Ofun__left__comm(_791313, _791309, _791305), _791313 = _791311, _791309 = _791307, _791305 = _791303], (4608 ^ _781215) ^ [_851097, _851099] : [_851099 = _851097, -(c_Rings_Oinverse__class_Odivide(_851099) = c_Rings_Oinverse__class_Odivide(_851097))], (9841 ^ _781215) ^ [_948494, _948496, _948498] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _948494)), _948496) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _948494)), _948498), -(_948496 = _948498)], (31565 ^ _781215) ^ [_1361643, _1361645, _1361647, _1361649] : [class_Groups_Oab__group__add(_1361643), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361645, _1361643), hAPP(hAPP(c_COMBB(_1361643, _1361643, _1361645), c_Groups_Ouminus__class_Ouminus(_1361643)), _1361647)), _1361649) = hAPP(c_Groups_Ouminus__class_Ouminus(_1361643), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361645, _1361643), _1361647), _1361649)))], (9251 ^ _781215) ^ [_938653, _938655, _938657] : [class_Groups_Oordered__ab__group__add(_938653), 9254 ^ _781215 : [(9261 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938653), hAPP(c_Groups_Ouminus__class_Ouminus(_938653), _938657)), _938655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938653), hAPP(c_Groups_Ouminus__class_Ouminus(_938653), _938655)), _938657)))], (9255 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938653), hAPP(c_Groups_Ouminus__class_Ouminus(_938653), _938655)), _938657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938653), hAPP(c_Groups_Ouminus__class_Ouminus(_938653), _938657)), _938655)))]]], (36033 ^ _781215) ^ [_1458729, _1458731] : [-(_1458729 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1458731, _1458729) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458731), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1458729)))], (18818 ^ _781215) ^ [_1118627, _1118629, _1118631, _1118633] : [class_Orderings_Olinorder(_1118627), 18821 ^ _781215 : [(18830 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118627), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1118627), _1118629), _1118631)), _1118633))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118627), _1118629), _1118633)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118627), _1118631), _1118633))], (18822 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118627), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1118627), _1118629), _1118631)), _1118633)), 18825 ^ _781215 : [(18828 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118627), _1118631), _1118633)))], (18826 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118627), _1118629), _1118633)))]]]]], (6365 ^ _781215) ^ [_884672, _884674, _884676, _884678] : [hBOOL(hAPP(hAPP(c_member(_884672), _884674), _884676)), -(hBOOL(hAPP(hAPP(c_member(_884672), _884674), _884678))), -(hBOOL(hAPP(hAPP(c_member(_884672), _884674), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_884672, tc_HOL_Obool)), _884676), _884678))))], (18379 ^ _781215) ^ [_1110123, _1110125, _1110127, _1110129] : [class_Orderings_Olinorder(_1110123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110123), _1110125), _1110127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110123), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1110123), _1110125), _1110129)), _1110127)))], (22844 ^ _781215) ^ [_1193373, _1193375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193373)), 22847 ^ _781215 : [(22854 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193375)), -(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), _1193375), _1193373))))], (22848 ^ _781215) ^ [] : [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), _1193375), _1193373))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193375)))]]], (44120 ^ _781215) ^ [_1663430, _1663432, _1663434] : [_1663430 = hAPP(hAPP(c_List_Oappend(_1663432), _1663430), _1663434), -(_1663434 = c_List_Olist_ONil(_1663432))], (22172 ^ _781215) ^ [_1180925, _1180927, _1180929, _1180931] : [class_Divides_Osemiring__div(_1180925), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180925), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180925), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1180925), _1180927), _1180929)), _1180929)), c_Divides_Odiv__class_Omod(_1180925, _1180927, _1180929))), _1180931) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180925), _1180927), _1180931))], (38019 ^ _781215) ^ [_1504483, _1504485] : [class_Complete__Lattice_Ocomplete__lattice(_1504483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1504483), _1504485)), -(_1504485 = c_Orderings_Obot__class_Obot(tc_fun(_1504483, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1504483, _1504485) = c_Complete__Lattice_OSup__class_OSup(_1504483, _1504485))], (40376 ^ _781215) ^ [_1571008, _1571010] : [c_Wellfounded_OwfP(_1571008, _1571010), 40379 ^ _781215 : [(40380 ^ _781215) ^ [_1571072] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1571008, _1571010), _1571072)))]]], (15306 ^ _781215) ^ [_1049723, _1049725, _1049727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049723), _1049725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049723), _1049727)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049725), _1049727))))], (14588 ^ _781215) ^ [_1036466, _1036468, _1036470] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1036466, _1036468, _1036470))), 14591 ^ _781215 : [(14594 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1036470)))], (14592 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1036468)))]]], (5742 ^ _781215) ^ [_872072, _872074] : [-(hAPP(c_Option_Othe(_872072), hAPP(c_Option_Ooption_OSome(_872072), _872074)) = _872074)], (15620 ^ _781215) ^ [_1055577, _1055579, _1055581] : [hBOOL(hAPP(c_Com_OWT, _1055581)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1055577, _1055579, _1055581))))], (40067 ^ _781215) ^ [_1563350] : [-(c_Wellfounded_Owf(tc_fun(_1563350, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1563350)))], (46815 ^ _781215) ^ [_1722589, _1722591, _1722593, _1722595, _1722597] : [class_Groups_Omonoid__add(_1722589), 46821 ^ _781215 : [(46826 ^ _781215) ^ [] : [hAPP(_1722597, 46820 ^ [_1722589, _1722591, _1722593, _1722595, _1722597]) = c_Groups_Ozero__class_Ozero(_1722589)], (46824 ^ _781215) ^ [] : [hBOOL(hAPP(_1722595, 46820 ^ [_1722589, _1722591, _1722593, _1722595, _1722597]))], (46822 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1722591), 46820 ^ [_1722589, _1722591, _1722593, _1722595, _1722597]), hAPP(c_List_Oset(_1722591), _1722593))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1722589), hAPP(hAPP(c_List_Omap(_1722591, _1722589), _1722597), hAPP(c_List_Ofilter(_1722591, _1722595), _1722593))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1722589), hAPP(hAPP(c_List_Omap(_1722591, _1722589), _1722597), _1722593)))], (46101 ^ _781215) ^ [_1706251, _1706253] : [-(c_List_Oconcat(_1706251, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1706251), tc_List_Olist(_1706251)), c_List_Olist_Olist__case(tc_List_Olist(_1706251), _1706251, c_List_Olist_ONil(_1706251), hAPP(hAPP(c_COMBB(tc_List_Olist(_1706251), tc_fun(tc_List_Olist(_1706251), tc_List_Olist(_1706251)), _1706251), c_COMBK(tc_List_Olist(_1706251), tc_List_Olist(_1706251))), hAPP(hAPP(c_COMBC(_1706251, tc_List_Olist(_1706251), tc_List_Olist(_1706251)), c_List_Olist_OCons(_1706251)), c_List_Olist_ONil(_1706251))))), _1706253)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1706251), _1706251), c_List_Ohd(_1706251)), hAPP(c_List_Ofilter(tc_List_Olist(_1706251), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1706251)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1706251), tc_List_Olist(_1706251), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1706251)))), _1706253)))], (11864 ^ _781215) ^ [_987709] : [hAPP(c_Nat_OSuc, _987709) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20573 ^ _781215) ^ [_1150458] : [class_Rings_Osemiring__1(_1150458), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150458), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1150458))], (14258 ^ _781215) ^ [_1030461, _1030463] : [class_Rings_Olinordered__idom(_1030461), hBOOL(hAPP(hAPP(c_member(_1030461), _1030463), c_Int_Oring__1__class_OInts(_1030461))), 14265 ^ _781215 : [(14272 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030461), _1030463), c_Groups_Ozero__class_Ozero(_1030461))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030461), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030461), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030461), c_Groups_Oone__class_Oone(_1030461)), _1030463)), _1030463)), c_Groups_Ozero__class_Ozero(_1030461))))], (14266 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030461), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030461), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030461), c_Groups_Oone__class_Oone(_1030461)), _1030463)), _1030463)), c_Groups_Ozero__class_Ozero(_1030461))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030461), _1030463), c_Groups_Ozero__class_Ozero(_1030461))))]]], (42911 ^ _781215) ^ [_1634774, _1634776, _1634778, _1634780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634774), _1634776)), -(hAPP(hAPP(c_List_Onth(_1634778), hAPP(hAPP(c_List_Otake(_1634778), _1634776), _1634780)), _1634774) = hAPP(hAPP(c_List_Onth(_1634778), _1634780), _1634774))], (38069 ^ _781215) ^ [_1505362, _1505364] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1505362, tc_HOL_Obool)), _1505364)), 38075 ^ _781215 : [(38078 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1505362), 38074 ^ [_1505362, _1505364]))], (38076 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1505362, tc_HOL_Obool)), 38074 ^ [_1505362, _1505364]), _1505364)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505362), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1505362, tc_HOL_Obool), _1505364))))], (6772 ^ _781215) ^ [_892303, _892305, _892307, _892309] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892303, tc_HOL_Obool)), _892305), hAPP(hAPP(c_Set_Oinsert(_892303), _892307), _892309)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892303, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892303, tc_HOL_Obool)), _892305), hAPP(hAPP(c_Set_Oinsert(_892303), _892307), c_Orderings_Obot__class_Obot(tc_fun(_892303, tc_HOL_Obool))))), _892309))], (22314 ^ _781215) ^ [_1183955, _1183957, _1183959, _1183961] : [class_Divides_Osemiring__div(_1183955), -(c_Divides_Odiv__class_Omod(_1183955, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183955), _1183957), _1183959), _1183961) = c_Divides_Odiv__class_Omod(_1183955, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183955), c_Divides_Odiv__class_Omod(_1183955, _1183957, _1183961)), _1183959), _1183961))], (23114 ^ _781215) ^ [_1197720] : [c_Nat__Transfer_Onat__set(_1197720), 23117 ^ _781215 : [(23124 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197720))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1197720)))], (23118 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1197720)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1197720))))]]], (18105 ^ _781215) ^ [_1105213, _1105215, _1105217, _1105219] : [class_Orderings_Olinorder(_1105213), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105213), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105213), _1105215), _1105217)), _1105219) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105213), _1105215), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105213), _1105217), _1105219)))], (18135 ^ _781215) ^ [_1105910, _1105912, _1105914] : [class_Orderings_Olinorder(_1105910), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105910), _1105912), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105910), _1105912), _1105914)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105910), _1105912), _1105914))], (23981 ^ _781215) ^ [_1213570, _1213572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213572)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1213570)), hAPP(c_Int_Onat, _1213572)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213570), _1213572)))], (15156 ^ _781215) ^ [_1047252, _1047254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047252)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1047252), _1047254)))], (14377 ^ _781215) ^ [_1032704, _1032706] : [class_Rings_Oring__1(_1032704), hBOOL(hAPP(hAPP(c_member(_1032704), _1032706), c_Int_Oring__1__class_OInts(_1032704))), -(hBOOL(hAPP(hAPP(c_member(_1032704), hAPP(c_Groups_Ouminus__class_Ouminus(_1032704), _1032706)), c_Int_Oring__1__class_OInts(_1032704))))], (22769 ^ _781215) ^ [_1192239, _1192241] : [c_Nat__Transfer_Onat__set(_1192239), c_Nat__Transfer_Onat__set(_1192241), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1192239), _1192241)))], (27255 ^ _781215) ^ [_1276462, _1276464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276462), 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)), _1276464)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1276462, _1276464), c_Divides_OnegDivAlg(_1276462, _1276464))))], (38048 ^ _781215) ^ [_1504943, _1504945, _1504947] : [38050 ^ _781215 : [(38053 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1504943, tc_HOL_Obool)), 38049 ^ [_1504943, _1504945, _1504947]), _1504947))], (38051 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1504943, tc_HOL_Obool)), 38049 ^ [_1504943, _1504945, _1504947]), _1504945)))]], -(_1504945 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1504943, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1504943, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1504943, tc_HOL_Obool), _1504945)), _1504947)))], (18111 ^ _781215) ^ [_1105356, _1105358, _1105360, _1105362] : [class_Orderings_Olinorder(_1105356), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105356), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105356), _1105358), _1105360)), _1105362) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105356), _1105358), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105356), _1105360), _1105362)))], (7072 ^ _781215) ^ [_898948, _898950] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _898948), _898950), _898948)))], (24778 ^ _781215) ^ [_1228436, _1228438, _1228440, _1228442] : [class_Rings_Olinordered__semidom(_1228436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228436), _1228438), _1228440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228436), c_Groups_Ozero__class_Ozero(_1228436)), _1228438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228436), hAPP(hAPP(c_Power_Opower__class_Opower(_1228436), _1228438), _1228442)), hAPP(hAPP(c_Power_Opower__class_Opower(_1228436), _1228440), _1228442))))], (51582 ^ _781215) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (15134 ^ _781215) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42499 ^ _781215) ^ [_1623556, _1623558, _1623560] : [-(c_List_Oset__Cons(_1623556, _1623558, _1623560) = hAPP(c_Set_OCollect(tc_List_Olist(_1623556)), hAPP(hAPP(c_COMBB(tc_fun(_1623556, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1623556)), c_HOL_OEx(_1623556)), hAPP(hAPP(c_COMBB(tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool)), tc_fun(_1623556, tc_HOL_Obool), tc_List_Olist(_1623556)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), tc_HOL_Obool, _1623556), c_HOL_OEx(tc_List_Olist(_1623556)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623556), tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool)), tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1623556, tc_fun(tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool))), tc_fun(tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool)), tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool))), tc_List_Olist(_1623556)), c_COMBS(_1623556, tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1623556, tc_fun(tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool))), tc_List_Olist(_1623556)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1623556), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool)), _1623556), c_COMBS(tc_List_Olist(_1623556), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool)), tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1623556)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), tc_fun(tc_List_Olist(_1623556), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1623556), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1623556)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623556), tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_List_Olist(_1623556))), tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1623556), tc_List_Olist(_1623556)), tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool)), tc_fun(tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_List_Olist(_1623556))), tc_fun(_1623556, tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool))), tc_List_Olist(_1623556)), c_COMBB(tc_fun(tc_List_Olist(_1623556), tc_List_Olist(_1623556)), tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), _1623556)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1623556), tc_List_Olist(_1623556)), tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool)), tc_List_Olist(_1623556)), c_COMBB(tc_List_Olist(_1623556), tc_HOL_Obool, tc_List_Olist(_1623556))), c_fequal))), c_List_Olist_OCons(_1623556)))))), hAPP(hAPP(c_COMBC(_1623556, tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool)), _1623556), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1623556))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1623556), c_fconj), hAPP(hAPP(c_COMBC(_1623556, tc_fun(_1623556, tc_HOL_Obool), tc_HOL_Obool), c_member(_1623556)), _1623558)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623556), tc_fun(tc_List_Olist(_1623556), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1623556))), _1623560)))))))], (22084 ^ _781215) ^ [_1179012, _1179014, _1179016, _1179018, _1179020] : [-(_1179012 = c_Orderings_Obot__class_Obot(tc_fun(_1179014, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1179016, tc_HOL_Obool)), _1179018), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179014, tc_fun(_1179016, tc_HOL_Obool)), _1179012), _1179020)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179014, tc_fun(_1179016, tc_HOL_Obool)), _1179012), hAPP(hAPP(c_COMBB(tc_fun(_1179016, tc_HOL_Obool), tc_fun(_1179016, tc_HOL_Obool), _1179014), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1179016, tc_HOL_Obool)), _1179018)), _1179020)))], (46181 ^ _781215) ^ [_1708010, _1708012, _1708014, _1708016, _1708018] : [-(hAPP(c_List_Ofoldl(_1708010, _1708012, _1708014, _1708016), _1708018) = c_List_Ofoldr(_1708012, _1708010, hAPP(c_COMBC(_1708010, _1708012, _1708010), _1708014), hAPP(c_List_Orev(_1708012), _1708018), _1708016))], (51250 ^ _781215) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (35885 ^ _781215) ^ [_1455818, _1455820, _1455822] : [class_Groups_Oordered__ab__group__add__abs(_1455818), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455818), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1455818), hAPP(c_Groups_Oabs__class_Oabs(_1455818), _1455820)), hAPP(c_Groups_Oabs__class_Oabs(_1455818), _1455822))), hAPP(c_Groups_Oabs__class_Oabs(_1455818), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1455818), _1455822), _1455820)))))], (8934 ^ _781215) ^ [_932717, _932719, _932721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932717, tc_HOL_Obool)), _932721), _932719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932717, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_932717, tc_HOL_Obool)), _932719)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_932717, tc_HOL_Obool)), _932721))))], (16025 ^ _781215) ^ [_1064130, _1064132, _1064134, _1064136, _1064138] : [class_Lattices_Olattice(_1064130), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1064132, _1064130)), _1064134), _1064136), _1064138) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064130), hAPP(_1064134, _1064138)), hAPP(_1064136, _1064138)))], (40665 ^ _781215) ^ [_1578030, _1578032, _1578034, _1578036, _1578038] : [c_Com_Ocom_OWhile(_1578030, _1578032) = c_Com_Ocom_OLocal(_1578034, _1578036, _1578038)], (6455 ^ _781215) ^ [_886365, _886367, _886369, _886371] : [_886365 = _886367, 6458 ^ _781215 : [(6465 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886369), _886367), _886371)), -(hBOOL(hAPP(hAPP(c_member(_886369), _886365), _886371)))], (6459 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886369), _886365), _886371)), -(hBOOL(hAPP(hAPP(c_member(_886369), _886367), _886371)))]]], (44222 ^ _781215) ^ [_1665368, _1665370, _1665372] : [-(hAPP(c_List_Oset(_1665368), hAPP(hAPP(c_List_Oappend(_1665368), _1665370), _1665372)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665368, tc_HOL_Obool)), hAPP(c_List_Oset(_1665368), _1665370)), hAPP(c_List_Oset(_1665368), _1665372)))], (8269 ^ _781215) ^ [_920675, _920677, _920679, _920681] : [class_Groups_Ocancel__semigroup__add(_920675), 8272 ^ _781215 : [(8279 ^ _781215) ^ [] : [_920677 = _920681, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920675), _920677), _920679) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920675), _920681), _920679))], (8273 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920675), _920677), _920679) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920675), _920681), _920679), -(_920677 = _920681)]]], (27852 ^ _781215) ^ [_1288945, _1288947, _1288949] : [class_Rings_Odivision__ring(_1288945), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1288945), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288945), _1288947), _1288949)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288945), hAPP(c_Groups_Ouminus__class_Ouminus(_1288945), _1288947)), _1288949))], (46115 ^ _781215) ^ [_1706669, _1706671, _1706673] : [_1706671 = hAPP(hAPP(c_List_Olist_OCons(_1706669), _1706673), c_List_Olist_ONil(_1706669)), -(hAPP(c_List_Orev(_1706669), _1706671) = hAPP(hAPP(c_List_Olist_OCons(_1706669), _1706673), c_List_Olist_ONil(_1706669)))], (7594 ^ _781215) ^ [_908791, _908793, _908795, _908797, _908799] : [-(hBOOL(hAPP(hAPP(c_member(_908791), _908793), _908795))), -(hAPP(c_Map_Orestrict__map(_908791, _908797, _908799, _908795), _908793) = c_Option_Ooption_ONone(_908797))], (38810 ^ _781215) ^ [_1525294, _1525296, _1525298, _1525300, _1525302, _1525304, _1525306, _1525308, _1525310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1525294, _1525296)), hAPP(hAPP(c_Product__Type_OPair(_1525294, _1525296), _1525298), _1525300)), _1525302)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1525304, _1525306)), hAPP(hAPP(c_Product__Type_OPair(_1525304, _1525306), hAPP(_1525308, _1525298)), hAPP(_1525310, _1525300))), hAPP(c_Set_Oimage(tc_prod(_1525294, _1525296), tc_prod(_1525304, _1525306), c_Product__Type_Omap__pair(_1525294, _1525304, _1525296, _1525306, _1525308, _1525310)), _1525302))))], (20966 ^ _781215) ^ [_1156828, _1156830] : [hBOOL(hAPP(_1156828, hAPP(c_Int_Onat, _1156830))), 20969 ^ _781215 : [(20976 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1156830), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1156828, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20970 ^ _781215) ^ [_1156928] : [_1156830 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1156928), -(hBOOL(hAPP(_1156828, _1156928)))]]], (37243 ^ _781215) ^ [_1486899, _1486901, _1486903, _1486905, _1486907] : [_1486899 = c_Orderings_Obot__class_Obot(tc_fun(_1486901, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486903, tc_HOL_Obool)), _1486905), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486901, tc_fun(_1486903, tc_HOL_Obool)), _1486899), _1486907)) = _1486905)], (44138 ^ _781215) ^ [_1663739, _1663741, _1663743] : [_1663743 = c_List_Olist_ONil(_1663741), -(_1663739 = hAPP(hAPP(c_List_Oappend(_1663741), _1663743), _1663739))], (17375 ^ _781215) ^ [_1092400] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092400) = 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(_1092400)))))], (30722 ^ _781215) ^ [_1343558, _1343560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1343558)), 30731 ^ _781215 : [(30734 ^ _781215) ^ [] : [hBOOL(hAPP(_1343560, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30727 ^ [_1343558, _1343560]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 30728 ^ [_1343558, _1343560]), _1343558))))], (30732 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1343560, 30727 ^ [_1343558, _1343560])))]], 30735 ^ _781215 : [(30738 ^ _781215) ^ [] : [hBOOL(hAPP(_1343560, 30727 ^ [_1343558, _1343560]))], (30736 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1343560, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30727 ^ [_1343558, _1343560]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 30728 ^ [_1343558, _1343560]), _1343558)))))]], 30739 ^ _781215 : [(30749 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1343560, 30756 ^ [_1343558, _1343560]))), 30750 ^ _781215 : [(30751 ^ _781215) ^ [_1344105] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1344105), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1343558))), hBOOL(hAPP(_1343560, _1344105))]]], (30740 ^ _781215) ^ [] : [30741 ^ _781215 : [(30742 ^ _781215) ^ [_1343990] : [hBOOL(hAPP(_1343560, _1343990))]], 30744 ^ _781215 : [(30747 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1343560, 30743 ^ [_1343558, _1343560])))], (30745 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30743 ^ [_1343558, _1343560]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1343558))))]]]]], (35723 ^ _781215) ^ [_1452985, _1452987] : [class_Rings_Olinordered__idom(_1452985), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452985), hAPP(c_Groups_Oabs__class_Oabs(_1452985), _1452987)), hAPP(c_Groups_Oabs__class_Oabs(_1452985), _1452987)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452985), _1452987), _1452987))], (8053 ^ _781215) ^ [_917001, _917003] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917001), _917003))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917001), hAPP(c_Nat_OSuc, _917003))), -(_917003 = _917001)], (32184 ^ _781215) ^ [_1375471, _1375473] : [-(c_Relation_OId__on(_1375471, _1375473) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1375471, tc_fun(tc_prod(_1375471, _1375471), tc_HOL_Obool)), _1375473), hAPP(hAPP(c_COMBC(_1375471, tc_fun(tc_prod(_1375471, _1375471), tc_HOL_Obool), tc_fun(tc_prod(_1375471, _1375471), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1375471, _1375471), tc_fun(tc_fun(tc_prod(_1375471, _1375471), tc_HOL_Obool), tc_fun(tc_prod(_1375471, _1375471), tc_HOL_Obool)), _1375471), c_Set_Oinsert(tc_prod(_1375471, _1375471))), hAPP(hAPP(c_COMBS(_1375471, _1375471, tc_prod(_1375471, _1375471)), c_Product__Type_OPair(_1375471, _1375471)), c_COMBI(_1375471)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1375471, _1375471), tc_HOL_Obool)))))], (17197 ^ _781215) ^ [_1089333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1089333)), -(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), _1089333))))], (31481 ^ _781215) ^ [_1358830, _1358832, _1358834, _1358836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1358830), _1358836)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1358834), _1358832))), -(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), _1358830), _1358832)), 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), _1358834), _1358836)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (4222 ^ _781215) ^ [_845284, _845286, _845288, _845290, _845292, _845294, _845296, _845298] : [-(c_Product__Type_Oscomp(_845298, _845294, _845290, _845286) = c_Product__Type_Oscomp(_845296, _845292, _845288, _845284)), _845298 = _845296, _845294 = _845292, _845290 = _845288, _845286 = _845284], (7849 ^ _781215) ^ [_913770, _913772] : [7850 ^ _781215 : [(7851 ^ _781215) ^ [_913823] : [_913772 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913770), _913823))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913770), _913772)))], (39957 ^ _781215) ^ [_1561409, _1561411, _1561413, _1561415] : [c_Wellfounded_Owf(_1561409, _1561411), c_Wellfounded_Owf(_1561413, _1561415), -(c_Wellfounded_Owf(tc_prod(_1561409, _1561413), c_Wellfounded_Olex__prod(_1561409, _1561413, _1561411, _1561415)))], (18635 ^ _781215) ^ [_1114999, _1115001] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114999)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115001)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1115001))), 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), _1114999)), c_Int_Onat)))))], (46103 ^ _781215) ^ [_1706394, _1706396] : [-(c_Fun_Oinj__on(tc_List_Olist(_1706394), tc_List_Olist(_1706394), c_List_Orev(_1706394), _1706396))], (48830 ^ _781215) ^ [_1767038, _1767040, _1767042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1767038), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1767040), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1767040)), _1767042)))), -(hBOOL(hAPP(hAPP(c_member(_1767040), hAPP(c_Random_Opick(_1767040, _1767042), _1767038)), hAPP(c_List_Oset(_1767040), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1767040), _1767040), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1767040)), _1767042)))))], (29894 ^ _781215) ^ [_1326374] : [-(_1326374 = 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)), _1326374), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (49960 ^ _781215) ^ [_1794292, _1794294, _1794296] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1794292, _1794292)), hAPP(hAPP(c_Product__Type_OPair(_1794292, _1794292), _1794294), _1794294)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794292, _1794292), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1794296))))], (17063 ^ _781215) ^ [_1087224, _1087226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087224)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087226))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1087224), _1087226))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1087224), c_Int_OPls)))], (33422 ^ _781215) ^ [_1403390, _1403392, _1403394] : [class_Orderings_Oorder(_1403390), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1403390, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1403390), _1403392)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1403390, _1403392, _1403394)) = c_Orderings_Obot__class_Obot(tc_fun(_1403390, tc_HOL_Obool)))], (40496 ^ _781215) ^ [_1574192] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574192, tc_HOL_Obool) = c_Set_OBall(_1574192))], (42122 ^ _781215) ^ [_1612279, _1612281, _1612283] : [hBOOL(hAPP(hAPP(c_member(_1612279), _1612281), hAPP(c_List_Oset(_1612279), _1612283))), -(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(_1612279)), _1612283))))], (33368 ^ _781215) ^ [_1402125, _1402127, _1402129, _1402131] : [class_Orderings_Oorder(_1402125), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402125, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1402125, _1402127, _1402129)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1402125, _1402129, _1402131)) = c_Orderings_Obot__class_Obot(tc_fun(_1402125, tc_HOL_Obool)))], (41381 ^ _781215) ^ [_1594417, _1594419, _1594421, _1594423, _1594425] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1594417), tc_List_Olist(_1594419), tc_List_Olist(_1594421), hAPP(c_List_Omap(_1594417, _1594419), _1594423)), hAPP(c_List_Omap(_1594421, _1594417), _1594425)) = hAPP(c_List_Omap(_1594421, _1594419), hAPP(c_Fun_Ocomp(_1594417, _1594419, _1594421, _1594423), _1594425)))], (39622 ^ _781215) ^ [_1549822, _1549824, _1549826, _1549828, _1549830, _1549832, _1549834] : [class_Rings_Osemiring__0(_1549822), c_Fun_Oinj__on(tc_prod(_1549824, _1549826), _1549822, hAPP(c_Product__Type_Oprod_Oprod__case(_1549824, _1549826, _1549822), hAPP(hAPP(c_COMBC(_1549824, tc_fun(_1549826, _1549822), tc_fun(_1549826, _1549822)), hAPP(hAPP(c_COMBB(tc_fun(_1549822, _1549822), tc_fun(tc_fun(_1549826, _1549822), tc_fun(_1549826, _1549822)), _1549824), c_COMBB(_1549822, _1549822, _1549826)), hAPP(hAPP(c_COMBB(_1549822, tc_fun(_1549822, _1549822), _1549824), c_Groups_Otimes__class_Otimes(_1549822)), _1549828))), _1549830)), hAPP(hAPP(c_Product__Type_OSigma(_1549824, _1549826), _1549832), hAPP(c_COMBK(tc_fun(_1549826, tc_HOL_Obool), _1549824), _1549834))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1549822), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1549824, _1549822), _1549828), _1549832)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1549826, _1549822), _1549830), _1549834)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1549822, _1549822), c_Fun_Oid(_1549822)), hAPP(c_Set_OCollect(_1549822), hAPP(hAPP(c_COMBB(tc_fun(_1549824, tc_HOL_Obool), tc_HOL_Obool, _1549822), c_HOL_OEx(_1549824)), hAPP(hAPP(c_COMBB(tc_fun(_1549824, tc_fun(_1549826, tc_HOL_Obool)), tc_fun(_1549824, tc_HOL_Obool), _1549822), hAPP(c_COMBB(tc_fun(_1549826, tc_HOL_Obool), tc_HOL_Obool, _1549824), c_HOL_OEx(_1549826))), hAPP(hAPP(c_COMBC(_1549822, tc_fun(_1549824, tc_fun(_1549826, tc_HOL_Obool)), tc_fun(_1549824, tc_fun(_1549826, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1549824, tc_fun(tc_fun(_1549826, tc_HOL_Obool), tc_fun(_1549826, tc_HOL_Obool))), tc_fun(tc_fun(_1549824, tc_fun(_1549826, tc_HOL_Obool)), tc_fun(_1549824, tc_fun(_1549826, tc_HOL_Obool))), _1549822), c_COMBS(_1549824, tc_fun(_1549826, tc_HOL_Obool), tc_fun(_1549826, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1549824, tc_fun(_1549826, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1549824, tc_fun(tc_fun(_1549826, tc_HOL_Obool), tc_fun(_1549826, tc_HOL_Obool))), _1549822), hAPP(c_COMBB(tc_fun(_1549826, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1549826, tc_HOL_Obool), tc_fun(_1549826, tc_HOL_Obool)), _1549824), c_COMBS(_1549826, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1549824, tc_fun(_1549826, tc_HOL_Obool)), tc_fun(_1549824, tc_fun(_1549826, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1549822), hAPP(c_COMBB(tc_fun(_1549826, tc_HOL_Obool), tc_fun(_1549826, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1549824), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549826), c_fconj))), hAPP(hAPP(c_COMBC(_1549822, tc_fun(_1549824, tc_fun(_1549826, _1549822)), tc_fun(_1549824, tc_fun(_1549826, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1549826, _1549822), tc_fun(_1549826, tc_HOL_Obool)), tc_fun(tc_fun(_1549824, tc_fun(_1549826, _1549822)), tc_fun(_1549824, tc_fun(_1549826, tc_HOL_Obool))), _1549822), c_COMBB(tc_fun(_1549826, _1549822), tc_fun(_1549826, tc_HOL_Obool), _1549824)), hAPP(hAPP(c_COMBB(tc_fun(_1549822, tc_HOL_Obool), tc_fun(tc_fun(_1549826, _1549822), tc_fun(_1549826, tc_HOL_Obool)), _1549822), c_COMBB(_1549822, tc_HOL_Obool, _1549826)), c_fequal))), hAPP(hAPP(c_COMBC(_1549824, tc_fun(_1549826, _1549822), tc_fun(_1549826, _1549822)), hAPP(hAPP(c_COMBB(tc_fun(_1549822, _1549822), tc_fun(tc_fun(_1549826, _1549822), tc_fun(_1549826, _1549822)), _1549824), c_COMBB(_1549822, _1549822, _1549826)), hAPP(hAPP(c_COMBB(_1549822, tc_fun(_1549822, _1549822), _1549824), c_Groups_Otimes__class_Otimes(_1549822)), _1549828))), _1549830)))))), hAPP(hAPP(c_COMBC(_1549824, tc_fun(_1549826, tc_HOL_Obool), tc_fun(_1549826, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1549826, tc_HOL_Obool), tc_fun(_1549826, tc_HOL_Obool)), _1549824), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1549826)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549824), c_fconj), hAPP(hAPP(c_COMBC(_1549824, tc_fun(_1549824, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549824)), _1549832)))), hAPP(hAPP(c_COMBC(_1549826, tc_fun(_1549826, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549826)), _1549834))))))))], (12692 ^ _781215) ^ [_1002159, _1002161, _1002163] : [class_Rings_Olinordered__semiring__strict(_1002159), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002159), c_Groups_Ozero__class_Ozero(_1002159)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002159), _1002161), _1002163))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002159), c_Groups_Ozero__class_Ozero(_1002159)), _1002163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002159), c_Groups_Ozero__class_Ozero(_1002159)), _1002161)))], (27281 ^ _781215) ^ [_1276827, _1276829, _1276831, _1276833, _1276835, _1276837, _1276839] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1276827, _1276829), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1276831), _1276833))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1276835, _1276829), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1276837), _1276839))), -(_1276829 = 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), _1276827), _1276835), _1276829), 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), _1276831), _1276837)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1276833), _1276839)), _1276829))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1276833), _1276839), _1276829)))))], (35497 ^ _781215) ^ [_1448360] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1448360)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1448360))], (15150 ^ _781215) ^ [_1047107, _1047109] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047107)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047109)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1047107), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1047109))))], (30261 ^ _781215) ^ [_1334757, _1334759, _1334761] : [class_Orderings_Oorder(_1334757), _1334759 = _1334761, -(c_SetInterval_Oord__class_OatLeastAtMost(_1334757, _1334759, _1334761) = hAPP(hAPP(c_Set_Oinsert(_1334757), _1334759), c_Orderings_Obot__class_Obot(tc_fun(_1334757, tc_HOL_Obool))))], (31475 ^ _781215) ^ [_1358637, _1358639, _1358641, _1358643] : [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), _1358637), _1358639)), 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), _1358641), _1358643)), 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), _1358637), _1358643)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1358641), _1358639))))], (51348 ^ _781215) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (36776 ^ _781215) ^ [_1473126] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1473126), c_Orderings_Otop__class_Otop(tc_fun(_1473126, 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(_1473126), c_Orderings_Otop__class_Otop(tc_fun(_1473126, tc_HOL_Obool))))))], (1688 ^ _781215) ^ [_805285, _805287] : [-(class_Rings_Ocomm__semiring(_805285)), _805287 = _805285, class_Rings_Ocomm__semiring(_805287)], (11236 ^ _781215) ^ [_976437, _976439, _976441, _976443] : [class_Rings_Ocomm__semiring__1(_976437), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976437), _976439), _976441)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976437), _976443), _976441)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976437), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976437), _976439), _976443)), _976441))], (49381 ^ _781215) ^ [_1779777, _1779779] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1779777, _1779777, _1779777), c_Transitive__Closure_Ortrancl(_1779777, _1779779)), c_Transitive__Closure_Ortrancl(_1779777, _1779779)) = c_Transitive__Closure_Ortrancl(_1779777, _1779779))], (25839 ^ _781215) ^ [_1249186, _1249188, _1249190, _1249192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool)), _1249190), _1249192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1249186, tc_fun(_1249188, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1249186, tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_fun(_1249188, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1249188, tc_fun(tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_fun(_1249188, tc_HOL_Obool)), _1249186), c_COMBC(_1249188, tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1249188, tc_prod(_1249186, _1249188)), tc_fun(_1249188, tc_fun(tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_HOL_Obool)), _1249186), hAPP(c_COMBB(tc_prod(_1249186, _1249188), tc_fun(tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_HOL_Obool), _1249188), c_member(tc_prod(_1249186, _1249188)))), c_Product__Type_OPair(_1249186, _1249188)))), _1249190)), hAPP(hAPP(c_COMBC(_1249186, tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_fun(_1249188, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1249188, tc_fun(tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_fun(_1249188, tc_HOL_Obool)), _1249186), c_COMBC(_1249188, tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1249188, tc_prod(_1249186, _1249188)), tc_fun(_1249188, tc_fun(tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_HOL_Obool)), _1249186), hAPP(c_COMBB(tc_prod(_1249186, _1249188), tc_fun(tc_fun(tc_prod(_1249186, _1249188), tc_HOL_Obool), tc_HOL_Obool), _1249188), c_member(tc_prod(_1249186, _1249188)))), c_Product__Type_OPair(_1249186, _1249188)))), _1249192))))], (4384 ^ _781215) ^ [_847721, _847723] : [_847723 = _847721, -(c_Fun_Oid(_847723) = c_Fun_Oid(_847721))], (5408 ^ _781215) ^ [_863827, _863829, _863831, _863833] : [-(c_Product__Type_OPair(_863833, _863829) = c_Product__Type_OPair(_863831, _863827)), _863833 = _863831, _863829 = _863827], (41094 ^ _781215) ^ [_1587454, _1587456, _1587458, _1587460, _1587462] : [hAPP(hAPP(c_Map_Omap__of(_1587454, _1587456), _1587458), _1587460) = hAPP(c_Option_Ooption_OSome(_1587456), _1587462), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587454, _1587456)), hAPP(hAPP(c_Product__Type_OPair(_1587454, _1587456), _1587460), _1587462)), hAPP(c_List_Oset(tc_prod(_1587454, _1587456)), _1587458))))], (51646 ^ _781215) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (5909 ^ _781215) ^ [_875320, _875322] : [hAPP(c_Option_Ooption_OSome(_875320), _875322) = c_Option_Ooption_ONone(_875320)], (22218 ^ _781215) ^ [_1182101] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182101, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1182101)], (41343 ^ _781215) ^ [_1593608, _1593610, _1593612, _1593614, _1593616, _1593618] : [c_Fun_Oinj__on(_1593608, _1593610, _1593612, _1593614), c_Fun_Oinj__on(_1593610, _1593616, _1593618, hAPP(c_Set_Oimage(_1593608, _1593610, _1593612), _1593614)), -(c_Fun_Oinj__on(_1593608, _1593616, hAPP(c_Fun_Ocomp(_1593610, _1593616, _1593608, _1593618), _1593612), _1593614))], (16407 ^ _781215) ^ [_1071278, _1071280, _1071282] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1071278), _1071280)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071278), _1071282)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1071278), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071278, tc_HOL_Obool)), _1071280), _1071282))))], (15384 ^ _781215) ^ [_1050888, _1050890, _1050892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050888), _1050890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1050892), _1050888)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1050892), _1050890))))], (20038 ^ _781215) ^ [_1140678, _1140680] : [class_Orderings_Olinorder(_1140678), hBOOL(hAPP(c_Finite__Set_Ofinite(_1140678), _1140680)), -(_1140680 = c_Orderings_Obot__class_Obot(tc_fun(_1140678, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1140678), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1140678), 20051 ^ [_1140678, _1140680]), 20052 ^ [_1140678, _1140680])), hAPP(hAPP(c_Set_Oinsert(_1140678), 20051 ^ [_1140678, _1140680]), hAPP(hAPP(c_Set_Oinsert(_1140678), 20052 ^ [_1140678, _1140680]), c_Orderings_Obot__class_Obot(tc_fun(_1140678, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1140678), c_Big__Operators_Olinorder__class_OMax(_1140678, _1140680)), _1140680)))], (38205 ^ _781215) ^ [_1508992, _1508994, _1508996, _1508998, _1509000, _1509002] : [hAPP(_1508992, _1508994) = _1508996, hBOOL(hAPP(hAPP(c_member(_1508998), _1508996), _1509000)), -(hBOOL(hAPP(hAPP(c_member(_1509002), _1508994), hAPP(c_Set_Ovimage(_1509002, _1508998, _1508992), _1509000))))], (25929 ^ _781215) ^ [_1251560, _1251562, _1251564, _1251566] : [class_Rings_Ocomm__semiring__1(_1251560), class_Rings_Ono__zero__divisors(_1251560), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251562), _1251564)), 25940 ^ _781215 : [(25950 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1251562, _1251560), _1251566), _1251564) = c_Groups_Ozero__class_Ozero(_1251560)), 25951 ^ _781215 : [(25952 ^ _781215) ^ [_1251938] : [hBOOL(hAPP(hAPP(c_member(_1251562), _1251938), _1251564)), hAPP(_1251566, _1251938) = c_Groups_Ozero__class_Ozero(_1251560)]]], (25941 ^ _781215) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1251562, _1251560), _1251566), _1251564) = c_Groups_Ozero__class_Ozero(_1251560), 25945 ^ _781215 : [(25948 ^ _781215) ^ [] : [-(hAPP(_1251566, 25944 ^ [_1251560, _1251562, _1251564, _1251566]) = c_Groups_Ozero__class_Ozero(_1251560))], (25946 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1251562), 25944 ^ [_1251560, _1251562, _1251564, _1251566]), _1251564)))]]]]], (9893 ^ _781215) ^ [_949558, _949560] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949558), _949560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _949560)), _949558)))], (14254 ^ _781215) ^ [_1030392, _1030394] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1030392)), hAPP(c_Option_Ooption_OSome(_1030392), _1030394)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1588 ^ _781215) ^ [_804035, _804037] : [-(class_Rings_Olinordered__semidom(_804035)), _804037 = _804035, class_Rings_Olinordered__semidom(_804037)], (43605 ^ _781215) ^ [_1652086] : [class_Orderings_Oord(_1652086), -(c_Hilbert__Choice_OGreatest(_1652086) = c_Hilbert__Choice_OGreatestM(_1652086, _1652086, c_COMBI(_1652086)))], (34952 ^ _781215) ^ [_1436395, _1436397, _1436399, _1436401] : [class_Groups_Ocomm__monoid__mult(_1436395), hBOOL(hAPP(c_Finite__Set_Ofinite(_1436397), _1436399)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1436397, _1436395), _1436401), _1436399) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1436395, _1436397, c_Groups_Otimes__class_Otimes(_1436395)), _1436401), c_Groups_Oone__class_Oone(_1436395)), _1436399))], (42955 ^ _781215) ^ [_1635820, _1635822, _1635824, _1635826, _1635828, _1635830, _1635832] : [-(hAPP(hAPP(c_List_Ozip(_1635820, _1635822), hAPP(hAPP(c_List_Olist__update(_1635820, _1635824), _1635826), _1635828)), hAPP(hAPP(c_List_Olist__update(_1635822, _1635830), _1635826), _1635832)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1635820, _1635822), hAPP(hAPP(c_List_Ozip(_1635820, _1635822), _1635824), _1635830)), _1635826), hAPP(hAPP(c_Product__Type_OPair(_1635820, _1635822), _1635828), _1635832)))], (42973 ^ _781215) ^ [_1636338, _1636340, _1636342, _1636344, _1636346] : [-(hAPP(hAPP(c_List_Olist__update(_1636338, hAPP(hAPP(c_List_Olist_OCons(_1636338), _1636340), _1636342)), _1636344), _1636346) = c_Nat_Onat_Onat__case(tc_List_Olist(_1636338), hAPP(hAPP(c_List_Olist_OCons(_1636338), _1636346), _1636342), hAPP(hAPP(c_COMBB(tc_List_Olist(_1636338), tc_List_Olist(_1636338), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1636338), _1636340)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1636338, tc_List_Olist(_1636338)), c_List_Olist__update(_1636338, _1636342)), _1636346)), _1636344))], (1678 ^ _781215) ^ [_805160, _805162] : [-(class_Divides_Osemiring__div(_805160)), _805162 = _805160, class_Divides_Osemiring__div(_805162)], (2570 ^ _781215) ^ [_819420, _819422] : [_819422 = _819420, -(c_SetInterval_Oord__class_OatLeast(_819422) = c_SetInterval_Oord__class_OatLeast(_819420))], (36392 ^ _781215) ^ [_1465296, _1465298] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465296, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1465296, tc_HOL_Obool))), _1465298) = _1465298)], (38534 ^ _781215) ^ [_1517700, _1517702, _1517704, _1517706] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1517700), _1517702)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517704), _1517706)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1517700, _1517704)), hAPP(hAPP(c_Product__Type_OSigma(_1517700, _1517704), _1517702), hAPP(c_COMBK(tc_fun(_1517704, tc_HOL_Obool), _1517700), _1517706)))))], (36634 ^ _781215) ^ [] : [-(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)))], (47024 ^ _781215) ^ [_1727039, _1727041, _1727043, _1727045] : [class_Orderings_Olinorder(_1727039), -(c_List_Olinorder__class_Osorted(_1727039, hAPP(hAPP(c_List_Omap(_1727041, _1727039), _1727043), c_List_Olinorder__class_Osort__key(_1727041, _1727039, _1727043, _1727045))))], (17209 ^ _781215) ^ [_1089545, _1089547] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089545), c_Int_OPls))), 17212 ^ _781215 : [(17219 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089547), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089545)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1089545), _1089547)))], (17213 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089547), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089545)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089545))]]], (4936 ^ _781215) ^ [_856181, _856183, _856185, _856187, _856189, _856191] : [-(c_Lazy__Sequence_Oanamorph(_856191, _856187, _856183) = c_Lazy__Sequence_Oanamorph(_856189, _856185, _856181)), _856191 = _856189, _856187 = _856185, _856183 = _856181], (2364 ^ _781215) ^ [_816159, _816161] : [_816161 = _816159, -(c_Int_Oring__1__class_OInts(_816161) = c_Int_Oring__1__class_OInts(_816159))], (50912 ^ _781215) ^ [_1816036, _1816038, _1816040, _1816042] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1816036, _1816038), c_Lazy__Sequence_Olazy__sequence_OInsert(_1816036, _1816040, _1816042)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1816038, _1816040)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1816036, _1816038), _1816042))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17731 ^ _781215) ^ [_1098044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098044), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1098044) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34600 ^ _781215) ^ [_1429480, _1429482, _1429484, _1429486, _1429488, _1429490] : [c_Fun_Oinj__on(_1429480, _1429482, _1429484, _1429486), hAPP(_1429484, _1429488) = hAPP(_1429484, _1429490), hBOOL(hAPP(hAPP(c_member(_1429480), _1429488), _1429486)), hBOOL(hAPP(hAPP(c_member(_1429480), _1429490), _1429486)), -(_1429488 = _1429490)], (7724 ^ _781215) ^ [_911280, _911282] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911280), _911282) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911282), _911280))], (11334 ^ _781215) ^ [_978518, _978520, _978522, _978524] : [11335 ^ _781215 : [(11338 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_978522), _978524)))], (11336 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_978518), _978520)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_978518, _978522)), c_Sum__Type_OPlus(_978518, _978522, _978520, _978524)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39238 ^ _781215) ^ [_1535036, _1535038, _1535040] : [-(hAPP(c_Set_OCollect(_1535036), hAPP(hAPP(c_COMBS(_1535036, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535036), c_fimplies), _1535038)), _1535040)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1535036, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1535036, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1535036), _1535038))), hAPP(c_Set_OCollect(_1535036), _1535040)))], (32519 ^ _781215) ^ [_1383143, _1383145, _1383147, _1383149, _1383151, _1383153, _1383155, _1383157, _1383159, _1383161] : [c_Equiv__Relations_Oequiv(_1383143, _1383145, _1383147), c_Equiv__Relations_Oequiv(_1383149, _1383151, _1383153), c_Equiv__Relations_Ocongruent2(_1383143, _1383149, tc_fun(_1383155, tc_HOL_Obool), _1383147, _1383153, _1383157), hBOOL(hAPP(hAPP(c_member(_1383143), _1383159), _1383145)), hBOOL(hAPP(hAPP(c_member(_1383149), _1383161), _1383151)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383143, tc_fun(_1383155, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1383143, _1383143, _1383147), hAPP(hAPP(c_Set_Oinsert(_1383143), _1383159), c_Orderings_Obot__class_Obot(tc_fun(_1383143, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1383149, tc_fun(_1383155, tc_HOL_Obool)), tc_fun(_1383155, tc_HOL_Obool), _1383143), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383149, tc_fun(_1383155, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1383149, _1383149, _1383153), hAPP(hAPP(c_Set_Oinsert(_1383149), _1383161), c_Orderings_Obot__class_Obot(tc_fun(_1383149, tc_HOL_Obool)))))), _1383157)) = hAPP(hAPP(_1383157, _1383159), _1383161))], (13123 ^ _781215) ^ [_1009745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009745), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1009745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13772 ^ _781215) ^ [_1021135, _1021137, _1021139] : [class_Rings_Olinordered__ring__strict(_1021135), 13775 ^ _781215 : [(13776 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021135), c_Groups_Ozero__class_Ozero(_1021135)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1021135), _1021137), _1021137)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1021135), _1021139), _1021139)))), _1021137 = c_Groups_Ozero__class_Ozero(_1021135), _1021139 = c_Groups_Ozero__class_Ozero(_1021135)], (13786 ^ _781215) ^ [] : [13787 ^ _781215 : [(13790 ^ _781215) ^ [] : [-(_1021139 = c_Groups_Ozero__class_Ozero(_1021135))], (13788 ^ _781215) ^ [] : [-(_1021137 = c_Groups_Ozero__class_Ozero(_1021135))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021135), c_Groups_Ozero__class_Ozero(_1021135)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1021135), _1021137), _1021137)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1021135), _1021139), _1021139)))))]]], (47418 ^ _781215) ^ [_1735059, _1735061, _1735063, _1735065] : [47420 ^ _781215 : [(47425 ^ _781215) ^ [] : [hBOOL(hAPP(_1735065, hAPP(hAPP(c_List_Onth(_1735061), _1735063), 47419 ^ [_1735059, _1735061, _1735063, _1735065])))], (47423 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47419 ^ [_1735059, _1735061, _1735063, _1735065]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735061)), _1735063))))], (47421 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47419 ^ [_1735059, _1735061, _1735063, _1735065]), _1735059)))]], 47428 ^ _781215 : [(47431 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1735065, hAPP(hAPP(c_List_Onth(_1735061), _1735063), _1735059))))], (47429 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735059), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735061)), _1735063))))]], -(c_List_OtakeWhile(_1735061, _1735065, _1735063) = hAPP(hAPP(c_List_Otake(_1735061), _1735059), _1735063))], (43990 ^ _781215) ^ [_1660345, _1660347, _1660349, _1660351, _1660353] : [-(hAPP(hAPP(c_List_Ozip(_1660345, _1660347), hAPP(hAPP(c_List_Olist_OCons(_1660345), _1660349), _1660351)), _1660353) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1660345, _1660347)), _1660347, c_List_Olist_ONil(tc_prod(_1660345, _1660347)), hAPP(hAPP(c_COMBC(_1660347, tc_fun(tc_List_Olist(_1660347), tc_List_Olist(tc_prod(_1660345, _1660347))), tc_fun(tc_List_Olist(_1660347), tc_List_Olist(tc_prod(_1660345, _1660347)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1660345, _1660347)), tc_List_Olist(tc_prod(_1660345, _1660347))), tc_fun(tc_fun(tc_List_Olist(_1660347), tc_List_Olist(tc_prod(_1660345, _1660347))), tc_fun(tc_List_Olist(_1660347), tc_List_Olist(tc_prod(_1660345, _1660347)))), _1660347), c_COMBB(tc_List_Olist(tc_prod(_1660345, _1660347)), tc_List_Olist(tc_prod(_1660345, _1660347)), tc_List_Olist(_1660347))), hAPP(hAPP(c_COMBB(tc_prod(_1660345, _1660347), tc_fun(tc_List_Olist(tc_prod(_1660345, _1660347)), tc_List_Olist(tc_prod(_1660345, _1660347))), _1660347), c_List_Olist_OCons(tc_prod(_1660345, _1660347))), hAPP(c_Product__Type_OPair(_1660345, _1660347), _1660349)))), hAPP(c_List_Ozip(_1660345, _1660347), _1660351))), _1660353))], (12232 ^ _781215) ^ [_993775, _993777, _993779, _993781, _993783] : [class_Rings_Oordered__semiring(_993775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993775), _993777), _993779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993775), _993781), _993783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993775), c_Groups_Ozero__class_Ozero(_993775)), _993777)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993775), c_Groups_Ozero__class_Ozero(_993775)), _993781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993775), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993775), _993777), _993781)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993775), _993779), _993783))))], (51240 ^ _781215) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (26888 ^ _781215) ^ [_1269820, _1269822, _1269824] : [hBOOL(hAPP(_1269820, hAPP(hAPP(c_Product__Type_OPair(_1269822, _1269824), 26889 ^ [_1269820, _1269822, _1269824]), 26890 ^ [_1269820, _1269822, _1269824]))), 26893 ^ _781215 : [(26894 ^ _781215) ^ [_1269967] : [-(hBOOL(hAPP(_1269820, _1269967)))]]], (43563 ^ _781215) ^ [_1651185, _1651187, _1651189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651185), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651187)), _1651189))), -(c_List_Obutlast(_1651187, hAPP(hAPP(c_List_Otake(_1651187), _1651185), _1651189)) = hAPP(hAPP(c_List_Otake(_1651187), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1651185), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1651189))], (14714 ^ _781215) ^ [_1038553, _1038555, _1038557, _1038559] : [class_Int_Onumber__ring(_1038553), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038553), hAPP(c_Int_Onumber__class_Onumber__of(_1038553), _1038555)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038553), hAPP(c_Int_Onumber__class_Onumber__of(_1038553), _1038557)), _1038559)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038553), hAPP(c_Int_Onumber__class_Onumber__of(_1038553), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1038555), _1038557))), _1038559))], (38490 ^ _781215) ^ [_1516183, _1516185, _1516187, _1516189, _1516191, _1516193] : [class_Groups_Ocomm__monoid__add(_1516183), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1516185, _1516183), hAPP(hAPP(c_COMBC(_1516185, tc_fun(_1516187, tc_HOL_Obool), _1516183), hAPP(hAPP(c_COMBB(tc_fun(_1516187, _1516183), tc_fun(tc_fun(_1516187, tc_HOL_Obool), _1516183), _1516185), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1516187, _1516183)), _1516189)), _1516191)), _1516193) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1516185, _1516187), _1516183), hAPP(c_Product__Type_Oprod_Oprod__case(_1516185, _1516187, _1516183), _1516189)), hAPP(hAPP(c_Product__Type_OSigma(_1516185, _1516187), _1516193), hAPP(c_COMBK(tc_fun(_1516187, tc_HOL_Obool), _1516185), _1516191))))], (15026 ^ _781215) ^ [_1045059, _1045061, _1045063] : [class_Int_Onumber__ring(_1045059), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045059), hAPP(c_Groups_Ouminus__class_Ouminus(_1045059), hAPP(c_Int_Onumber__class_Onumber__of(_1045059), _1045061))), _1045063) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045059), hAPP(c_Int_Onumber__class_Onumber__of(_1045059), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1045061))), _1045063))], (29992 ^ _781215) ^ [_1328770, _1328772, _1328774, _1328776] : [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), _1328770), _1328772)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1328774), _1328776))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1328770), _1328776) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1328774), _1328772))], (51120 ^ _781215) ^ [_1820063, _1820065] : [class_Orderings_Otop(_1820063), -(class_Orderings_Otop(tc_fun(_1820065, _1820063)))], (38983 ^ _781215) ^ [_1529548] : [-(c_Finite__Set_Ofun__left__comm__idem(_1529548, tc_fun(_1529548, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1529548, tc_HOL_Obool), tc_fun(tc_fun(_1529548, tc_HOL_Obool), tc_fun(_1529548, tc_HOL_Obool)), _1529548), hAPP(c_COMBC(tc_fun(_1529548, tc_HOL_Obool), tc_fun(_1529548, tc_HOL_Obool), tc_fun(_1529548, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1529548, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1529548, tc_fun(_1529548, tc_HOL_Obool), tc_fun(_1529548, tc_HOL_Obool)), c_Set_Oinsert(_1529548)), c_Orderings_Obot__class_Obot(tc_fun(_1529548, tc_HOL_Obool))))))], (38414 ^ _781215) ^ [_1514009, _1514011, _1514013, _1514015, _1514017, _1514019] : [-(hBOOL(hAPP(hAPP(c_member(_1514009), _1514011), _1514013))), 38417 ^ _781215 : [(38424 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514009), _1514015), _1514013))), -(hAPP(c_Set_Ovimage(_1514017, _1514009, hAPP(hAPP(c_COMBC(_1514017, _1514009, _1514009), hAPP(hAPP(c_COMBC(_1514017, _1514009, tc_fun(_1514009, _1514009)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1514009, tc_fun(_1514009, _1514009)), _1514017), c_If(_1514009)), hAPP(hAPP(c_COMBC(_1514017, tc_fun(_1514017, tc_HOL_Obool), tc_HOL_Obool), c_member(_1514017)), _1514019))), _1514011)), _1514015)), _1514013) = c_Orderings_Obot__class_Obot(tc_fun(_1514017, tc_HOL_Obool)))], (38418 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1514009), _1514015), _1514013)), -(hAPP(c_Set_Ovimage(_1514017, _1514009, hAPP(hAPP(c_COMBC(_1514017, _1514009, _1514009), hAPP(hAPP(c_COMBC(_1514017, _1514009, tc_fun(_1514009, _1514009)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1514009, tc_fun(_1514009, _1514009)), _1514017), c_If(_1514009)), hAPP(hAPP(c_COMBC(_1514017, tc_fun(_1514017, tc_HOL_Obool), tc_HOL_Obool), c_member(_1514017)), _1514019))), _1514011)), _1514015)), _1514013) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1514017, tc_HOL_Obool)), _1514019))]]], (26224 ^ _781215) ^ [_1256831, _1256833, _1256835] : [class_Orderings_Oorder(_1256831), 26227 ^ _781215 : [(26234 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256831), _1256833), _1256835))), -(c_Orderings_Obot__class_Obot(tc_fun(_1256831, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1256831, _1256833, _1256835))], (26228 ^ _781215) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1256831, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1256831, _1256833, _1256835), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256831), _1256833), _1256835))]]], (22733 ^ _781215) ^ [_1191506, _1191508, _1191510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191506), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22736 ^ _781215 : [(22737 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1191508, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1191510), _1191506)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1191510, _1191506))), 22740 ^ _781215 : [(22741 ^ _781215) ^ [_1191716, _1191718] : [-(hBOOL(hAPP(hAPP(_1191508, _1191718), _1191716))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191506), _1191716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1191716), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1191510 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1191506), _1191718)), _1191716)]]], (22755 ^ _781215) ^ [] : [22758 ^ _781215 : [(22761 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 22757 ^ [_1191506, _1191508, _1191510]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22763 ^ _781215) ^ [] : [-(_1191510 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1191506), 22756 ^ [_1191506, _1191508, _1191510])), 22757 ^ [_1191506, _1191508, _1191510]))], (22765 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1191508, 22756 ^ [_1191506, _1191508, _1191510]), 22757 ^ [_1191506, _1191508, _1191510]))], (22759 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191506), 22757 ^ [_1191506, _1191508, _1191510])))]], -(hBOOL(hAPP(hAPP(_1191508, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1191510), _1191506)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1191510, _1191506))))]]], (37225 ^ _781215) ^ [_1486396, _1486398, _1486400, _1486402, _1486404, _1486406] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1486396, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1486398, _1486396, _1486400), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486402, tc_fun(_1486398, tc_HOL_Obool)), _1486404), _1486406))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486402, tc_fun(_1486396, tc_HOL_Obool)), _1486404), hAPP(hAPP(c_COMBB(tc_fun(_1486398, tc_HOL_Obool), tc_fun(_1486396, tc_HOL_Obool), _1486402), c_Relation_OImage(_1486398, _1486396, _1486400)), _1486406)))))], (7177 ^ _781215) ^ [_901337, _901339, _901341, _901343, _901345, _901347, _901349] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_901337, _901339, _901341, _901343, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901337, tc_HOL_Obool)), _901345), hAPP(hAPP(c_Set_Oinsert(_901337), _901347), c_Orderings_Obot__class_Obot(tc_fun(_901337, tc_HOL_Obool))))), _901349)), hBOOL(hAPP(hAPP(c_member(_901337), _901347), _901345)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_901337, _901339, _901341, _901343, _901345), hAPP(hAPP(_901341, _901347), _901349))))], (12664 ^ _781215) ^ [_1001649, _1001651, _1001653] : [class_Rings_Olinordered__semiring__strict(_1001649), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001649), c_Groups_Ozero__class_Ozero(_1001649)), _1001651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001649), _1001653), c_Groups_Ozero__class_Ozero(_1001649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001649), _1001653), _1001651)), c_Groups_Ozero__class_Ozero(_1001649))))], (24514 ^ _781215) ^ [_1223478, _1223480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1223478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223480)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1223480), _1223478)), _1223480) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1223480), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223478), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (8239 ^ _781215) ^ [_920174, _920176, _920178, _920180] : [class_Groups_Ocancel__semigroup__add(_920174), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920174), _920176), _920178) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920174), _920180), _920178), -(_920176 = _920180)], (39383 ^ _781215) ^ [_1540878, _1540880] : [-(hAPP(c_Set_OPow(_1540878), _1540880) = hAPP(c_Set_OCollect(tc_fun(_1540878, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1540878, tc_HOL_Obool), tc_fun(_1540878, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1540878, tc_HOL_Obool))), _1540880)))], (14124 ^ _781215) ^ [_1027529, _1027531, _1027533, _1027535] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_1027529)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1027529), _1027531), _1027533), _1027535)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1778 ^ _781215) ^ [_806410, _806412] : [-(class_Rings_Omult__zero(_806410)), _806412 = _806410, class_Rings_Omult__zero(_806412)], (35635 ^ _781215) ^ [_1450969, _1450971, _1450973, _1450975] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1450969, _1450971, _1450973, c_Code__Numeral_OSuc__code__numeral(_1450975)) = hAPP(_1450973, _1450975))], (49285 ^ _781215) ^ [_1777374, _1777376, _1777378, _1777380] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777374, _1777374)), hAPP(hAPP(c_Product__Type_OPair(_1777374, _1777374), _1777376), _1777378)), c_Transitive__Closure_Ortrancl(_1777374, _1777380)))), 49286 ^ _781215 : [(49289 ^ _781215) ^ [] : [-(_1777376 = _1777378), hBOOL(hAPP(hAPP(c_member(tc_prod(_1777374, _1777374)), hAPP(hAPP(c_Product__Type_OPair(_1777374, _1777374), _1777376), _1777378)), c_Transitive__Closure_Otrancl(_1777374, _1777380)))], (49287 ^ _781215) ^ [] : [_1777376 = _1777378]]], (24756 ^ _781215) ^ [_1228023, _1228025, _1228027, _1228029] : [class_Groups_Omonoid__mult(_1228023), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1228023), _1228025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1228027), _1228029)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1228023), hAPP(hAPP(c_Power_Opower__class_Opower(_1228023), _1228025), _1228027)), _1228029))], (22860 ^ _781215) ^ [_1193614, _1193616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193614)), 22863 ^ _781215 : [(22870 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193614), _1193616)), -(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), _1193616), _1193614))))], (22864 ^ _781215) ^ [] : [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), _1193616), _1193614))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193614), _1193616)))]]], (50866 ^ _781215) ^ [_1814812, _1814814] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1814812), _1814814)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1814812)), c_Int_OBit0(_1814814))))], (18752 ^ _781215) ^ [_1117389, _1117391, _1117393, _1117395] : [class_Orderings_Olinorder(_1117389), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117389), _1117391), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117389), _1117393), _1117395)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117389), _1117393), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117389), _1117391), _1117395)))], (5366 ^ _781215) ^ [_863210, _863212] : [_863212 = _863210, -(c_Lazy__Sequence_Osingle(_863212) = c_Lazy__Sequence_Osingle(_863210))], (1148 ^ _781215) ^ [_798535, _798537] : [-(class_Rings_Oordered__ring__abs(_798535)), _798537 = _798535, class_Rings_Oordered__ring__abs(_798537)], (29998 ^ _781215) ^ [_1328917, _1328919, _1328921, _1328923] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1328917), _1328923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1328921), _1328919), -(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), _1328917), _1328919)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1328921), _1328923))), c_Int_Ointrel)))], (19924 ^ _781215) ^ [_1138687, _1138689, _1138691] : [class_Orderings_Olinorder(_1138687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1138687), _1138689)), -(hBOOL(hAPP(hAPP(c_member(_1138687), _1138691), _1138689))), -(c_Big__Operators_Olattice_OSup__fin(_1138687, c_Orderings_Oord__class_Omax(_1138687), hAPP(hAPP(c_Set_Oinsert(_1138687), _1138691), _1138689)) = hAPP(hAPP(c_Finite__Set_Ofold(_1138687, _1138687, c_Orderings_Oord__class_Omax(_1138687)), _1138691), _1138689))], (29946 ^ _781215) ^ [] : [-(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)))))], (20888 ^ _781215) ^ [_1155679] : [class_Int_Onumber__ring(_1155679), c_Int_Oiszero(_1155679, hAPP(c_Int_Onumber__class_Onumber__of(_1155679), c_Int_OBit1(c_Int_OPls)))], (47799 ^ _781215) ^ [_1743582, _1743584, _1743586, _1743588, _1743590] : [-(c_List_Olist__all2(_1743582, _1743584, _1743586, _1743588, _1743590)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743582)), _1743588) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743584)), _1743590), 47805 ^ _781215 : [(47808 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1743586, hAPP(hAPP(c_List_Onth(_1743582), _1743588), 47804 ^ [_1743582, _1743584, _1743586, _1743588, _1743590])), hAPP(hAPP(c_List_Onth(_1743584), _1743590), 47804 ^ [_1743582, _1743584, _1743586, _1743588, _1743590])))], (47806 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47804 ^ [_1743582, _1743584, _1743586, _1743588, _1743590]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743582)), _1743588))))]]], (45660 ^ _781215) ^ [_1697380, _1697382] : [class_Orderings_Olinorder(_1697380), -(_1697382 = c_List_Olist_ONil(_1697380)), c_List_Olinorder__class_Osorted(_1697380, _1697382), -(c_List_Olinorder__class_Osorted(_1697380, c_List_Obutlast(_1697380, _1697382)))], (17479 ^ _781215) ^ [_1094130, _1094132, _1094134] : [class_Lattices_Olattice(_1094130), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094130), _1094132)), -(hBOOL(hAPP(hAPP(c_member(_1094130), _1094134), _1094132))), -(c_Big__Operators_Olattice__class_OSup__fin(_1094130, hAPP(hAPP(c_Set_Oinsert(_1094130), _1094134), _1094132)) = hAPP(hAPP(c_Finite__Set_Ofold(_1094130, _1094130, c_Lattices_Osemilattice__sup__class_Osup(_1094130)), _1094134), _1094132))], (44886 ^ _781215) ^ [_1681397, _1681399, _1681401] : [-(hAPP(c_List_Orotate(_1681397, _1681399), _1681401) = hAPP(c_List_Orotate(_1681397, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1681399, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681397)), _1681401))), _1681401))], (47986 ^ _781215) ^ [_1747458, _1747460] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1747458)), _1747460)), 47992 ^ _781215 : [(47995 ^ _781215) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1747458), 47991 ^ [_1747458, _1747460]))], (47993 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1747458)), 47991 ^ [_1747458, _1747460]), hAPP(c_List_Oset(tc_List_Olist(_1747458)), _1747460))))]], 47999 ^ _781215 : [(48003 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1747458)), 48001 ^ [_1747458, _1747460]), hAPP(c_List_Oset(tc_List_Olist(_1747458)), _1747460))))], (48005 ^ _781215) ^ [] : [47998 ^ [_1747458, _1747460] = 48001 ^ [_1747458, _1747460]], (48007 ^ _781215) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1747458, tc_HOL_Obool)), hAPP(c_List_Oset(_1747458), 47998 ^ [_1747458, _1747460])), hAPP(c_List_Oset(_1747458), 48001 ^ [_1747458, _1747460])) = c_Orderings_Obot__class_Obot(tc_fun(_1747458, tc_HOL_Obool))], (48000 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1747458)), 47998 ^ [_1747458, _1747460]), hAPP(c_List_Oset(tc_List_Olist(_1747458)), _1747460))))]], -(hBOOL(hAPP(c_List_Odistinct(_1747458), c_List_Oconcat(_1747458, _1747460))))], (10208 ^ _781215) ^ [_955146] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _955146) = _955146)], (7758 ^ _781215) ^ [_911949, _911951] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _911949)), _911951) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911949), hAPP(c_Nat_OSuc, _911951)))], (1498 ^ _781215) ^ [_802910, _802912] : [-(class_Groups_Olinordered__ab__semigroup__add(_802910)), _802912 = _802910, class_Groups_Olinordered__ab__semigroup__add(_802912)], (21690 ^ _781215) ^ [_1170341] : [-(c_Int_Opred(c_Int_OBit0(_1170341)) = c_Int_OBit1(c_Int_Opred(_1170341)))], (41010 ^ _781215) ^ [_1585703, _1585705, _1585707, _1585709, _1585711] : [hAPP(hAPP(c_List_Omap(_1585703, _1585705), _1585707), _1585709) = hAPP(hAPP(c_List_Omap(_1585703, _1585705), _1585711), _1585709), 41013 ^ _781215 : [(41014 ^ _781215) ^ [_1585826] : [hBOOL(hAPP(hAPP(c_member(_1585703), _1585826), hAPP(c_List_Oset(_1585703), _1585709))), -(hAPP(_1585707, _1585826) = hAPP(_1585711, _1585826))]]], (30169 ^ _781215) ^ [_1333219, _1333221, _1333223] : [-(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)), _1333219)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1333221, _1333223)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1333221), _1333219), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1333223), _1333219)))], (24240 ^ _781215) ^ [_1218436, _1218438, _1218440] : [class_Rings_Olinordered__semidom(_1218436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218436), hAPP(hAPP(c_Power_Opower__class_Opower(_1218436), _1218438), 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(_1218436), _1218440), 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(_1218436), c_Groups_Ozero__class_Ozero(_1218436)), _1218440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218436), _1218438), _1218440)))], (24882 ^ _781215) ^ [_1230188, _1230190, _1230192] : [class_Power_Opower(_1230188), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1230188), _1230190), hAPP(c_Nat_OSuc, _1230192)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230188), _1230190), hAPP(hAPP(c_Power_Opower__class_Opower(_1230188), _1230190), _1230192)))], (22246 ^ _781215) ^ [_1182545, _1182547] : [class_Divides_Osemiring__div(_1182545), -(c_Divides_Odiv__class_Omod(_1182545, c_Groups_Ozero__class_Ozero(_1182545), _1182547) = c_Groups_Ozero__class_Ozero(_1182545))], (44329 ^ _781215) ^ [_1667934, _1667936, _1667938, _1667940, _1667942, _1667944] : [hAPP(hAPP(c_List_Olist_OCons(_1667934), _1667936), _1667938) = _1667940, _1667942 = hAPP(hAPP(c_List_Oappend(_1667934), _1667938), _1667944), -(hAPP(hAPP(c_List_Olist_OCons(_1667934), _1667936), _1667942) = hAPP(hAPP(c_List_Oappend(_1667934), _1667940), _1667944))], (51670 ^ _781215) ^ [_1825663, _1825665, _1825667, _1825669, _1825671, _1825673] : [-(hAPP(hAPP(hAPP(c_COMBC(_1825663, _1825665, _1825667), _1825669), _1825671), _1825673) = hAPP(hAPP(_1825669, _1825673), _1825671))], (10730 ^ _781215) ^ [_965010, _965012, _965014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965010), _965012)), 10733 ^ _781215 : [(10740 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965014), _965010)), _965012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965014), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965012), _965010))))], (10734 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965014), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965012), _965010))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965014), _965010)), _965012)))]]], (17925 ^ _781215) ^ [_1101248, _1101250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101248)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1101248), _1101250)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1101248)), hAPP(c_Int_Onat, _1101250)))], (40907 ^ _781215) ^ [_1583103, _1583105, _1583107, _1583109] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1583103)), hAPP(c_Set_Oimage(_1583105, tc_Option_Ooption(_1583103), _1583107), c_Orderings_Otop__class_Otop(tc_fun(_1583105, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1583103)), hAPP(c_Set_Oimage(_1583105, tc_Option_Ooption(_1583103), c_Map_Omap__add(_1583105, _1583103, _1583107, hAPP(c_Map_Omap__of(_1583105, _1583103), _1583109))), c_Orderings_Otop__class_Otop(tc_fun(_1583105, tc_HOL_Obool))))))], (19032 ^ _781215) ^ [_1122375, _1122377, _1122379, _1122381] : [class_Groups_Oordered__ab__group__add(_1122375), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1122375), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122375), _1122377), _1122379)), _1122381) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122375), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1122375), _1122377), _1122381)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1122375), _1122379), _1122381)))], (39815 ^ _781215) ^ [_1556333, _1556335, _1556337] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1556333, _1556335)), _1556337)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1556335), hAPP(c_Relation_ORange(_1556333, _1556335), _1556337))))], (22234 ^ _781215) ^ [_1182371, _1182373] : [class_Divides_Osemiring__div(_1182371), -(c_Divides_Odiv__class_Omod(_1182371, _1182373, _1182373) = c_Groups_Ozero__class_Ozero(_1182371))], (39975 ^ _781215) ^ [_1561754, _1561756] : [c_Wellfounded_Owf(_1561754, _1561756), -(c_Wellfounded_Owf(_1561754, hAPP(hAPP(c_Relation_Orel__comp(_1561754, _1561754, _1561754), _1561756), _1561756)))], (25292 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (20460 ^ _781215) ^ [_1148405, _1148407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148405)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1148405), _1148407)))], (37227 ^ _781215) ^ [_1486490, _1486492, _1486494, _1486496] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1486490, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486492, tc_fun(_1486490, tc_HOL_Obool)), _1486494), _1486496)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486492, tc_fun(_1486490, tc_HOL_Obool)), _1486494), hAPP(hAPP(c_COMBB(tc_fun(_1486490, tc_HOL_Obool), tc_fun(_1486490, tc_HOL_Obool), _1486492), c_Groups_Ouminus__class_Ouminus(tc_fun(_1486490, tc_HOL_Obool))), _1486496)))], (31405 ^ _781215) ^ [_1356703, _1356705] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1356703), _1356705)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1356705), _1356703)))], (15857 ^ _781215) ^ [] : [-(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))))], (23214 ^ _781215) ^ [_1199249, _1199251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199249), _1199251)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199249, _1199251) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199249), _1199251))], (26795 ^ _781215) ^ [_1268057, _1268059, _1268061, _1268063, _1268065, _1268067, _1268069] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1268057, _1268059, tc_fun(_1268061, tc_HOL_Obool)), _1268063), hAPP(hAPP(c_Product__Type_OPair(_1268057, _1268059), _1268065), _1268067)), _1268069)), -(hBOOL(hAPP(hAPP(hAPP(_1268063, _1268065), _1268067), _1268069)))], (39823 ^ _781215) ^ [_1556513, _1556515, _1556517, _1556519] : [hBOOL(hAPP(hAPP(c_member(_1556513), _1556515), hAPP(c_Relation_ORange(_1556517, _1556513), _1556519))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556517, _1556513)), hAPP(hAPP(c_Product__Type_OPair(_1556517, _1556513), 39826 ^ [_1556513, _1556515, _1556517, _1556519]), _1556515)), _1556519)))], (36642 ^ _781215) ^ [_1470147] : [class_Lattices_Oboolean__algebra(_1470147), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1470147), c_Orderings_Obot__class_Obot(_1470147)) = c_Orderings_Otop__class_Otop(_1470147))], (3830 ^ _781215) ^ [_839280, _839282, _839284, _839286] : [-(c_List_Oconcat(_839286, _839282) = c_List_Oconcat(_839284, _839280)), _839286 = _839284, _839282 = _839280], (25796 ^ _781215) ^ [_1245837, _1245839, _1245841] : [-(hAPP(c_Divides_Oadjust(_1245837), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1245839), _1245841)) = 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), _1245841), _1245837)), 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)))), _1245839)), 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)))), _1245839)), _1245841))))], (3738 ^ _781215) ^ [_837856, _837858, _837860, _837862] : [-(c_List_Olists(_837862, _837858) = c_List_Olists(_837860, _837856)), _837862 = _837860, _837858 = _837856], (36760 ^ _781215) ^ [_1472578, _1472580, _1472582, _1472584] : [hAPP(c_Set_Oimage(_1472578, _1472580, _1472582), c_Orderings_Otop__class_Otop(tc_fun(_1472578, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1472580, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472580, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1472580, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1472578, _1472580, _1472582), _1472584))), hAPP(c_Set_Oimage(_1472578, _1472580, _1472582), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1472578, tc_HOL_Obool)), _1472584)))))], (13092 ^ _781215) ^ [_1009211, _1009213] : [class_Groups_Ogroup__add(_1009211), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1009211), c_Groups_Ozero__class_Ozero(_1009211)), _1009213) = hAPP(c_Groups_Ouminus__class_Ouminus(_1009211), _1009213))], (21776 ^ _781215) ^ [_1171875, _1171877, _1171879] : [class_Rings_Osemiring__1(_1171875), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1171875, _1171877, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1171879) = _1171879)], (10058 ^ _781215) ^ [_952228, _952230, _952232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952228), _952230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952232), _952230))))], (22932 ^ _781215) ^ [_1194751, _1194753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194751), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22935 ^ _781215 : [(22942 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194753), 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), _1194753), _1194751))))], (22936 ^ _781215) ^ [] : [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), _1194753), _1194751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194753), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (20922 ^ _781215) ^ [_1156158, _1156160] : [-(_1156158 = hAPP(c_Int_Onat, _1156160)), 20925 ^ _781215 : [(20928 ^ _781215) ^ [] : [_1156160 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1156158)], (20926 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156160)))]], 20929 ^ _781215 : [(20932 ^ _781215) ^ [] : [_1156158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20930 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156160))]]], (51408 ^ _781215) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (25544 ^ _781215) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (30776 ^ _781215) ^ [_1344614, _1344616, _1344618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1344614)), 30779 ^ _781215 : [(30780 ^ _781215) ^ [_1344748] : [30782 ^ _781215 : [(30788 ^ _781215) ^ [] : [-(_1344748 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30784 ^ [_1344614, _1344616, _1344618, _1344748]), 30781 ^ [_1344614, _1344616, _1344618, _1344748]))], (30786 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30784 ^ [_1344614, _1344616, _1344618, _1344748]), _1344616)))], (30783 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30781 ^ [_1344614, _1344616, _1344618, _1344748]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1344614))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1344748), _1344618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1344748), _1344614)), _1344618)))]]], (45546 ^ _781215) ^ [_1695527, _1695529, _1695531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1695527), _1695529)), _1695531)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1695529), c_List_Oupt(_1695527, _1695531)) = c_List_Oupt(_1695527, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1695527), _1695529)))], (51630 ^ _781215) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (39234 ^ _781215) ^ [_1534901, _1534903] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1534901, tc_HOL_Obool)), _1534903) = hAPP(c_Set_OCollect(_1534901), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534901), c_fNot), hAPP(hAPP(c_COMBC(_1534901, tc_fun(_1534901, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534901)), _1534903))))], (36782 ^ _781215) ^ [] : [-(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))))], (42497 ^ _781215) ^ [_1623433, _1623435, _1623437, _1623439] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1623433), tc_List_Olist(_1623433), c_List_Olistrel(_1623433, _1623435)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1623433)), hAPP(hAPP(c_List_Olist_OCons(_1623433), _1623437), _1623439)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1623433), tc_HOL_Obool)))) = c_List_Oset__Cons(_1623433, hAPP(c_Relation_OImage(_1623433, _1623433, _1623435), hAPP(hAPP(c_Set_Oinsert(_1623433), _1623437), c_Orderings_Obot__class_Obot(tc_fun(_1623433, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1623433), tc_List_Olist(_1623433), c_List_Olistrel(_1623433, _1623435)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1623433)), _1623439), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1623433), tc_HOL_Obool))))))], (49451 ^ _781215) ^ [_1781532, _1781534, _1781536, _1781538] : [-(hBOOL(hAPP(hAPP(c_member(_1781532), _1781534), hAPP(c_Relation_ODomain(_1781532, _1781532), _1781536)))), 49454 ^ _781215 : [(49461 ^ _781215) ^ [] : [_1781534 = _1781538, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1781532, _1781532)), hAPP(hAPP(c_Product__Type_OPair(_1781532, _1781532), _1781534), _1781538)), c_Transitive__Closure_Ortrancl(_1781532, _1781536))))], (49455 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1781532, _1781532)), hAPP(hAPP(c_Product__Type_OPair(_1781532, _1781532), _1781534), _1781538)), c_Transitive__Closure_Ortrancl(_1781532, _1781536))), -(_1781534 = _1781538)]]], (40536 ^ _781215) ^ [_1575272, _1575274, _1575276, _1575278] : [40538 ^ _781215 : [(40541 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1575272, _1575272, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1575272, tc_fun(_1575272, _1575274), tc_fun(_1575272, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1575274, tc_HOL_Obool), tc_fun(tc_fun(_1575272, _1575274), tc_fun(_1575272, tc_HOL_Obool)), _1575272), c_COMBB(_1575274, tc_HOL_Obool, _1575272)), hAPP(hAPP(c_COMBB(_1575274, tc_fun(_1575274, tc_HOL_Obool), _1575272), c_fequal), _1575278))), _1575278)), 40537 ^ [_1575272, _1575274, _1575276, _1575278]))], (40539 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575272, _1575272)), 40537 ^ [_1575272, _1575274, _1575276, _1575278]), _1575276)))]], -(c_Equiv__Relations_Ocongruent(_1575272, _1575274, _1575276, _1575278))], (25426 ^ _781215) ^ [_1239192, _1239194] : [class_Int_Onumber__ring(_1239192), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239192), _1239194), hAPP(c_Int_Onumber__class_Onumber__of(_1239192), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1239192), _1239194))], (36259 ^ _781215) ^ [_1462791, _1462793] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1462791), _1462793) = 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), _1462791)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1462793)))))], (25718 ^ _781215) ^ [_1244155, _1244157, _1244159, _1244161, _1244163] : [hBOOL(hAPP(hAPP(c_member(_1244155), _1244157), c_SetInterval_Oord_OatLeastAtMost(_1244155, _1244159, _1244161, _1244163))), 25721 ^ _781215 : [(25724 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1244159, _1244157), _1244163)))], (25722 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1244159, _1244161), _1244157)))]]], (35045 ^ _781215) ^ [_1438517, _1438519, _1438521, _1438523] : [c_Fun_Oinj__on(_1438517, tc_fun(tc_fun(_1438517, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1438517, tc_fun(tc_prod(_1438517, _1438517), tc_HOL_Obool), tc_fun(tc_fun(_1438517, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438517, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1438517, _1438517), tc_HOL_Obool), tc_fun(tc_fun(_1438517, tc_HOL_Obool), tc_HOL_Obool)), _1438517), c_Equiv__Relations_Oquotient(_1438517)), hAPP(hAPP(c_COMBC(_1438517, tc_fun(_1438517, tc_HOL_Obool), tc_fun(_1438517, tc_HOL_Obool)), c_Set_Oinsert(_1438517)), c_Orderings_Obot__class_Obot(tc_fun(_1438517, tc_HOL_Obool))))), _1438519), _1438521), hBOOL(hAPP(hAPP(c_member(_1438517), _1438523), _1438521)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1438517), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1438517, tc_HOL_Obool)), _1438521), hAPP(hAPP(c_Set_Oinsert(_1438517), _1438523), c_Orderings_Obot__class_Obot(tc_fun(_1438517, tc_HOL_Obool))))), _1438519) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1438517, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1438517), _1438521), _1438519)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1438517), hAPP(hAPP(c_Set_Oinsert(_1438517), _1438523), c_Orderings_Obot__class_Obot(tc_fun(_1438517, tc_HOL_Obool)))), _1438519)))], (3490 ^ _781215) ^ [_834000, _834002, _834004, _834006, _834008, _834010, _834012, _834014] : [-(c_List_Olist_Olist__case(_834014, _834010, _834006, _834002) = c_List_Olist_Olist__case(_834012, _834008, _834004, _834000)), _834014 = _834012, _834010 = _834008, _834006 = _834004, _834002 = _834000], (39910 ^ _781215) ^ [_1560479, _1560481, _1560483, _1560485, _1560487, _1560489, _1560491] : [-(c_Predicate_Opred__comp(_1560479, _1560481, _1560483, _1560485, _1560487, _1560489, _1560491)), 39911 ^ _781215 : [(39912 ^ _781215) ^ [_1560544] : [hBOOL(hAPP(hAPP(_1560485, _1560489), _1560544)), hBOOL(hAPP(hAPP(_1560487, _1560544), _1560491))]]], (6562 ^ _781215) ^ [_888362, _888364, _888366, _888368] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_888362, _888364)), _888366), _888368))), 6563 ^ _781215 : [(6564 ^ _781215) ^ [_888430] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888362), _888366), _888430)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888364), _888430), _888368))]]], (45893 ^ _781215) ^ [_1701537, _1701539] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1701537, _1701539) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701537, hAPP(c_Nat_OSuc, _1701539))))], (37012 ^ _781215) ^ [_1480382, _1480384, _1480386, _1480388, _1480390] : [hBOOL(hAPP(hAPP(c_member(_1480382), _1480384), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1480386, tc_fun(_1480382, tc_HOL_Obool)), _1480388), _1480390))), 37015 ^ _781215 : [(37016 ^ _781215) ^ [_1480506] : [hBOOL(hAPP(hAPP(c_member(_1480386), _1480506), _1480388)), -(hBOOL(hAPP(hAPP(c_member(_1480382), _1480384), hAPP(_1480390, _1480506))))]]], (42345 ^ _781215) ^ [_1619871, _1619873, _1619875, _1619877, _1619879] : [hAPP(hAPP(c_List_Olist_OCons(_1619871), _1619873), _1619875) = hAPP(hAPP(c_List_Olist_OCons(_1619871), _1619877), _1619879), 42348 ^ _781215 : [(42351 ^ _781215) ^ [] : [-(_1619875 = _1619879)], (42349 ^ _781215) ^ [] : [-(_1619873 = _1619877)]]], (46720 ^ _781215) ^ [_1720671, _1720673, _1720675] : [hBOOL(hAPP(c_List_Odistinct(_1720671), _1720673)), -(hBOOL(hAPP(c_List_Odistinct(_1720671), c_List_OdropWhile(_1720671, _1720675, _1720673))))], (31832 ^ _781215) ^ [_1367481, _1367483, _1367485] : [class_Groups_Ocomm__monoid__add(_1367481), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1367481), _1367483), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1367485))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1367481), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1367481), _1367483), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1367485))), hAPP(_1367483, hAPP(c_Nat_OSuc, _1367485))))], (46191 ^ _781215) ^ [_1708253, _1708255, _1708257] : [hAPP(c_List_Orev(_1708253), _1708255) = _1708257, -(_1708255 = hAPP(c_List_Orev(_1708253), _1708257))], (7428 ^ _781215) ^ [_906221, _906223, _906225] : [class_Orderings_Opreorder(_906221), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906221), _906223), _906225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906221), _906225), _906223))], (11638 ^ _781215) ^ [_984365, _984367] : [class_Rings_Ocomm__semiring__1(_984365), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984365), _984367), c_Groups_Ozero__class_Ozero(_984365)) = _984367)], (42819 ^ _781215) ^ [_1632011, _1632013, _1632015, _1632017, _1632019] : [hBOOL(hAPP(hAPP(c_member(_1632011), _1632013), hAPP(c_List_Oset(_1632011), _1632015))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1632017), hAPP(_1632019, _1632013))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1632017), c_List_Olist_Olist__size(_1632011, _1632019, _1632015))))], (24348 ^ _781215) ^ [_1220218, _1220220] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220218))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220218)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220220)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32834 ^ _781215) ^ [_1389663, _1389665, _1389667, _1389669] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389663, tc_HOL_Obool)), _1389665), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389663, tc_HOL_Obool)), _1389667), _1389669)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389663, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389663, tc_HOL_Obool)), _1389665), _1389667)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389663, tc_HOL_Obool)), _1389665), _1389669)))], (36444 ^ _781215) ^ [_1466146, _1466148] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466146, tc_HOL_Obool)), _1466148), c_Orderings_Otop__class_Otop(tc_fun(_1466146, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1466146, tc_HOL_Obool)))], (15322 ^ _781215) ^ [_1049979, _1049981] : [15323 ^ _781215 : [(15326 ^ _781215) ^ [] : [_1049979 = _1049981], (15324 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049979), _1049981))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049981), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50169 ^ _781215) ^ [_1800316, _1800318] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1800316, _1800316)), _1800318), c_Relation_OId(_1800316))), -(_1800318 = hAPP(hAPP(c_Product__Type_OPair(_1800316, _1800316), 50172 ^ [_1800316, _1800318]), 50172 ^ [_1800316, _1800318]))], (49822 ^ _781215) ^ [_1790889, _1790891, _1790893, _1790895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1790889, _1790891), tc_HOL_Obool)), _1790893), _1790895)), c_Relation_Osingle__valued(_1790889, _1790891, _1790895), -(c_Relation_Osingle__valued(_1790889, _1790891, _1790893))], (39420 ^ _781215) ^ [_1542005, _1542007, _1542009, _1542011, _1542013, _1542015] : [hBOOL(hAPP(hAPP(c_member(_1542005), _1542007), _1542009)), -(hAPP(c_Fun_Ooverride__on(_1542005, _1542011, _1542013, _1542015, _1542009), _1542007) = hAPP(_1542015, _1542007))], (49095 ^ _781215) ^ [_1771851, _1771853] : [-(hAPP(c_Relation_ORange(_1771851, _1771851), c_Transitive__Closure_Otrancl(_1771851, _1771853)) = hAPP(c_Relation_ORange(_1771851, _1771851), _1771853))], (28194 ^ _781215) ^ [_1294628, _1294630] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294628), _1294630), hAPP(c_Int_Onumber__class_Onumber__of(_1294628), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1294628)), class_Fields_Ofield__inverse__zero(_1294628), class_Int_Onumber__ring(_1294628)], (39008 ^ _781215) ^ [_1530046, _1530048, _1530050] : [hBOOL(hAPP(_1530046, _1530048)), -(hBOOL(hAPP(hAPP(c_member(_1530050), _1530048), hAPP(c_Set_OCollect(_1530050), _1530046))))], (7448 ^ _781215) ^ [_906527, _906529, _906531] : [class_Orderings_Oorder(_906527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906527), _906529), _906531)), _906531 = _906529], (43247 ^ _781215) ^ [_1643182, _1643184, _1643186, _1643188] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643182), tc_List_Olist(_1643182))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643182), tc_List_Olist(_1643182)), _1643184), _1643186)), c_List_Olistrel1(_1643182, _1643188))), 43252 ^ _781215 : [(43257 ^ _781215) ^ [] : [-(_1643186 = hAPP(hAPP(c_List_Olist__update(_1643182, _1643184), 43251 ^ [_1643182, _1643184, _1643186, _1643188]), 43250 ^ [_1643182, _1643184, _1643186, _1643188]))], (43255 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43251 ^ [_1643182, _1643184, _1643186, _1643188]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643182)), _1643184))))], (43253 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643182, _1643182)), hAPP(hAPP(c_Product__Type_OPair(_1643182, _1643182), hAPP(hAPP(c_List_Onth(_1643182), _1643184), 43251 ^ [_1643182, _1643184, _1643186, _1643188])), 43250 ^ [_1643182, _1643184, _1643186, _1643188])), _1643188)))]]], (26666 ^ _781215) ^ [_1265055, _1265057] : [26667 ^ _781215 : [(26670 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1265057), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (26668 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265055), _1265057))]], -(c_Divides_OposDivAlg(_1265055, _1265057) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265055))], (17151 ^ _781215) ^ [_1088617, _1088619] : [class_Int_Onumber__ring(_1088617), class_Rings_Olinordered__idom(_1088617), 17158 ^ _781215 : [(17165 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1088619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088617), c_Groups_Ozero__class_Ozero(_1088617)), hAPP(c_Int_Onumber__class_Onumber__of(_1088617), _1088619))))], (17159 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088617), c_Groups_Ozero__class_Ozero(_1088617)), hAPP(c_Int_Onumber__class_Onumber__of(_1088617), _1088619))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1088619)))]]], (37937 ^ _781215) ^ [_1502620, _1502622, _1502624] : [c_Equiv__Relations_Oequiv(_1502620, _1502622, _1502624), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502620, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1502620), _1502622), _1502624)) = _1502622)], (17793 ^ _781215) ^ [_1099044] : [class_Int_Onumber__ring(_1099044), -(c_Int_Oiszero(_1099044, hAPP(c_Int_Onumber__class_Onumber__of(_1099044), c_Int_OPls)))], (1108 ^ _781215) ^ [_798035, _798037] : [-(class_Rings_Olinordered__ring__strict(_798035)), _798037 = _798035, class_Rings_Olinordered__ring__strict(_798037)], (1068 ^ _781215) ^ [_797535, _797537] : [-(class_Rings_Olinordered__semiring__1__strict(_797535)), _797537 = _797535, class_Rings_Olinordered__semiring__1__strict(_797537)], (30494 ^ _781215) ^ [_1339022, _1339024] : [30502 ^ _781215 : [(30505 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1339024, 30501 ^ [_1339022, _1339024])))], (30503 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30501 ^ [_1339022, _1339024]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1339022))))]], 30495 ^ _781215 : [(30496 ^ _781215) ^ [_1339091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1339091), _1339022)), hBOOL(hAPP(_1339024, _1339091))]]], (20810 ^ _781215) ^ [_1154360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1154360))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1154360)))], (32686 ^ _781215) ^ [_1386503, _1386505, _1386507] : [class_Lattices_Osemilattice__inf(_1386503), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386503), _1386505), _1386507)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1386503), _1386505), _1386507) = _1386505)], (37848 ^ _781215) ^ [_1500695, _1500697, _1500699] : [class_Complete__Lattice_Ocomplete__lattice(_1500695), class_Orderings_Olinorder(_1500695), 37855 ^ _781215 : [(37865 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500695), _1500697), c_Complete__Lattice_OSup__class_OSup(_1500695, _1500699)))), 37866 ^ _781215 : [(37867 ^ _781215) ^ [_1501001] : [hBOOL(hAPP(hAPP(c_member(_1500695), _1501001), _1500699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500695), _1500697), _1501001))]]], (37856 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500695), _1500697), c_Complete__Lattice_OSup__class_OSup(_1500695, _1500699))), 37860 ^ _781215 : [(37863 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500695), _1500697), 37859 ^ [_1500695, _1500697, _1500699])))], (37861 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1500695), 37859 ^ [_1500695, _1500697, _1500699]), _1500699)))]]]]], (10990 ^ _781215) ^ [_970609, _970611, _970613] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_970609), _970611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970609, tc_HOL_Obool)), _970613), _970611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_970609), _970613)), hAPP(c_Finite__Set_Ocard(_970609), _970611))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_970609, tc_HOL_Obool)), _970613), _970611)))], (40579 ^ _781215) ^ [_1576417, _1576419] : [class_Complete__Lattice_Ocomplete__lattice(_1576417), -(c_Complete__Lattice_OInf__class_OInf(_1576417, _1576419) = c_Complete__Lattice_OSup__class_OSup(_1576417, hAPP(c_Set_OCollect(_1576417), hAPP(hAPP(c_COMBB(tc_fun(_1576417, tc_HOL_Obool), tc_HOL_Obool, _1576417), c_HOL_OAll(_1576417)), hAPP(hAPP(c_COMBB(tc_fun(_1576417, tc_HOL_Obool), tc_fun(_1576417, tc_HOL_Obool), _1576417), hAPP(c_COMBS(_1576417, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1576417), c_fimplies), hAPP(hAPP(c_COMBC(_1576417, tc_fun(_1576417, tc_HOL_Obool), tc_HOL_Obool), c_member(_1576417)), _1576419)))), c_Orderings_Oord__class_Oless__eq(_1576417))))))], (24051 ^ _781215) ^ [_1214937, _1214939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1214937)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214937), _1214939)), _1214937) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (3748 ^ _781215) ^ [_838005, _838007] : [_838007 = _838005, -(c_List_Odrop(_838007) = c_List_Odrop(_838005))], (13274 ^ _781215) ^ [_1011953, _1011955, _1011957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1011953), _1011955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011957), _1011953)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011957), _1011955))))], (36913 ^ _781215) ^ [_1476987, _1476989, _1476991, _1476993] : [c_Orderings_Otop__class_Otop(tc_fun(_1476987, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1476989, tc_fun(_1476987, tc_HOL_Obool)), _1476991), _1476993), 36916 ^ _781215 : [(36917 ^ _781215) ^ [_1477103] : [hBOOL(hAPP(hAPP(c_member(_1476989), _1477103), _1476991)), -(hAPP(_1476993, _1477103) = c_Orderings_Otop__class_Otop(tc_fun(_1476987, tc_HOL_Obool)))]]], (1128 ^ _781215) ^ [_798285, _798287] : [-(class_Rings_Olinordered__semiring__1(_798285)), _798287 = _798285, class_Rings_Olinordered__semiring__1(_798287)], (10112 ^ _781215) ^ [_953248, _953250, _953252] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _953250), _953252)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953248), _953250)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953248), _953252)))], (37440 ^ _781215) ^ [_1491761, _1491763] : [class_Complete__Lattice_Ocomplete__lattice(_1491761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491761), _1491763)), -(c_Complete__Lattice_OInf__class_OInf(_1491761, _1491763) = hAPP(hAPP(c_Finite__Set_Ofold(_1491761, _1491761, c_Lattices_Osemilattice__inf__class_Oinf(_1491761)), c_Orderings_Otop__class_Otop(_1491761)), _1491763))], (49241 ^ _781215) ^ [_1776299, _1776301, _1776303, _1776305, _1776307] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776299, _1776299)), hAPP(hAPP(c_Product__Type_OPair(_1776299, _1776299), _1776301), _1776303)), c_Transitive__Closure_Ortrancl(_1776299, _1776305))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1776299, _1776299)), hAPP(hAPP(c_Product__Type_OPair(_1776299, _1776299), _1776303), _1776307)), _1776305)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776299, _1776299)), hAPP(hAPP(c_Product__Type_OPair(_1776299, _1776299), _1776301), _1776307)), c_Transitive__Closure_Otrancl(_1776299, _1776305))))], (40657 ^ _781215) ^ [_1577806, _1577808, _1577810, _1577812, _1577814] : [c_Com_Ocom_OWhile(_1577806, _1577808) = c_Com_Ocom_OCall(_1577810, _1577812, _1577814)], (46682 ^ _781215) ^ [_1719720, _1719722, _1719724] : [-(hBOOL(hAPP(hAPP(c_member(_1719720), _1719722), hAPP(c_List_Oset(_1719720), _1719724)))), -(c_List_Oremdups(_1719720, hAPP(hAPP(c_List_Olist_OCons(_1719720), _1719722), _1719724)) = hAPP(hAPP(c_List_Olist_OCons(_1719720), _1719722), c_List_Oremdups(_1719720, _1719724)))], (38560 ^ _781215) ^ [_1518474, _1518476, _1518478, _1518480, _1518482, _1518484] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1518474, _1518476)), hAPP(hAPP(c_Product__Type_OPair(_1518474, _1518476), _1518478), _1518480)), hAPP(hAPP(c_Product__Type_OSigma(_1518474, _1518476), _1518482), _1518484))), 38563 ^ _781215 : [(38566 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1518476), _1518480), hAPP(_1518484, _1518478))))], (38564 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1518474), _1518478), _1518482)))]]], (48774 ^ _781215) ^ [_1766222, _1766224] : [-(c_Random_Olog(_1766222, _1766224) = 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(_1766222, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1766224), _1766222)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1766222), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1766224), _1766222)))], (47659 ^ _781215) ^ [_1740563, _1740565, _1740567, _1740569, _1740571, _1740573, _1740575] : [c_List_Olist__all2(_1740569, _1740565, hAPP(hAPP(c_COMBB(_1740563, tc_fun(_1740565, tc_HOL_Obool), _1740569), _1740567), _1740571), _1740573, _1740575), -(c_List_Olist__all2(_1740563, _1740565, _1740567, hAPP(hAPP(c_List_Omap(_1740569, _1740563), _1740571), _1740573), _1740575))], (1318 ^ _781215) ^ [_800660, _800662] : [-(class_Complete__Lattice_Ocomplete__lattice(_800660)), _800662 = _800660, class_Complete__Lattice_Ocomplete__lattice(_800662)], (26382 ^ _781215) ^ [_1259943, _1259945] : [class_Rings_Olinordered__idom(_1259943), 26385 ^ _781215 : [(26392 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259943), c_Groups_Ozero__class_Ozero(_1259943)), hAPP(c_Int_Oring__1__class_Oof__int(_1259943), _1259945))))], (26386 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259943), c_Groups_Ozero__class_Ozero(_1259943)), hAPP(c_Int_Oring__1__class_Oof__int(_1259943), _1259945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259945)))]]], (27303 ^ _781215) ^ [_1277479, _1277481, _1277483, _1277485] : [_1277479 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1277481), _1277483)), _1277485), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1277479, _1277481), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1277483), _1277485)))), 27310 ^ _781215 : [(27313 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1277485), _1277481))], (27311 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277481)))]], 27318 ^ _781215 : [(27321 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1277481), _1277485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1277485), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (27319 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277481))]]], (43858 ^ _781215) ^ [_1656813, _1656815] : [-(_1656815 = c_List_Olist_ONil(_1656813)), -(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(_1656813)), _1656815))))], (13456 ^ _781215) ^ [_1015113, _1015115, _1015117] : [class_Groups_Oordered__comm__monoid__add(_1015113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015113), _1015115), c_Groups_Ozero__class_Ozero(_1015113))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015113), _1015117), c_Groups_Ozero__class_Ozero(_1015113))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015113), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015113), _1015115), _1015117)), c_Groups_Ozero__class_Ozero(_1015113))))], (1238 ^ _781215) ^ [_799660, _799662] : [-(class_Int_Onumber__ring(_799660)), _799662 = _799660, class_Int_Onumber__ring(_799662)], (51214 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (13178 ^ _781215) ^ [_1010556, _1010558] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1010556), _1010558), 13183 ^ _781215 : [(13186 ^ _781215) ^ [] : [-(_1010558 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13184 ^ _781215) ^ [] : [-(_1010556 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 13187 ^ _781215 : [(13190 ^ _781215) ^ [] : [-(_1010558 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13188 ^ _781215) ^ [] : [-(_1010556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (51620 ^ _781215) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (33727 ^ _781215) ^ [_1410155, _1410157, _1410159] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1410155), _1410157)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410155), _1410159)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410155, tc_HOL_Obool)), _1410157), _1410159) = c_Orderings_Obot__class_Obot(tc_fun(_1410155, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1410155), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410155, tc_HOL_Obool)), _1410157), _1410159)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1410155), _1410157)), hAPP(c_Finite__Set_Ocard(_1410155), _1410159)))], (47926 ^ _781215) ^ [_1746337, _1746339, _1746341, _1746343] : [-(hBOOL(hAPP(_1746337, _1746339))), -(hAPP(c_List_OremoveAll(_1746341, _1746339), hAPP(c_List_Ofilter(_1746341, _1746337), _1746343)) = hAPP(c_List_Ofilter(_1746341, _1746337), _1746343))], (11838 ^ _781215) ^ [_987307, _987309] : [class_Groups_Ogroup__add(_987307), 11841 ^ _781215 : [(11848 ^ _781215) ^ [] : [c_Groups_Ozero__class_Ozero(_987307) = _987309, -(c_Groups_Ozero__class_Ozero(_987307) = hAPP(c_Groups_Ouminus__class_Ouminus(_987307), _987309))], (11842 ^ _781215) ^ [] : [c_Groups_Ozero__class_Ozero(_987307) = hAPP(c_Groups_Ouminus__class_Ouminus(_987307), _987309), -(c_Groups_Ozero__class_Ozero(_987307) = _987309)]]], (44664 ^ _781215) ^ [_1676677, _1676679, _1676681, _1676683] : [-(_1676677 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1676679), _1676677), hAPP(hAPP(c_List_Olist_OCons(_1676679), _1676681), _1676683)) = hAPP(hAPP(c_List_Odrop(_1676679), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1676677), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1676683))], (9319 ^ _781215) ^ [_940001, _940003, _940005] : [hBOOL(hAPP(hAPP(c_member(_940001), _940003), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_940001, tc_HOL_Obool)), _940005))), hBOOL(hAPP(hAPP(c_member(_940001), _940003), _940005))], (504 ^ _781215) ^ [_789011, _789013, _789015, _789017, _789019, _789021, _789023, _789025, _789027, _789029] : [-(c_Finite__Set_Ofolding__image(_789027, _789023, _789019, _789015, _789011)), c_Finite__Set_Ofolding__image(_789029, _789025, _789021, _789017, _789013), _789029 = _789027, _789025 = _789023, _789021 = _789019, _789017 = _789015, _789013 = _789011], (4888 ^ _781215) ^ [_855409, _855411] : [_855411 = _855409, -(c_New__DSequence_Opos__empty(_855411) = c_New__DSequence_Opos__empty(_855409))], (4524 ^ _781215) ^ [_849817, _849819, _849821, _849823] : [-(c_Relation_Oconverse(_849823, _849819) = c_Relation_Oconverse(_849821, _849817)), _849823 = _849821, _849819 = _849817], (49383 ^ _781215) ^ [_1779821, _1779823] : [-(hAPP(c_Relation_ORange(_1779821, _1779821), c_Transitive__Closure_Ortrancl(_1779821, _1779823)) = c_Orderings_Otop__class_Otop(tc_fun(_1779821, tc_HOL_Obool)))], (43968 ^ _781215) ^ [_1659507, _1659509, _1659511, _1659513, _1659515] : [_1659507 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1659509, _1659511, _1659513), _1659507), _1659515) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659511), _1659509), c_List_Olist_ONil(_1659511)), _1659515))], (13760 ^ _781215) ^ [_1020848, _1020850, _1020852] : [class_Rings_Olinordered__ring(_1020848), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020848), c_Groups_Ozero__class_Ozero(_1020848)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020848), _1020850), _1020850)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020848), _1020852), _1020852)))))], (968 ^ _781215) ^ [_796057, _796059, _796061, _796063, _796065, _796067] : [-(c_Nitpick_Oless__eq__frac(_796065, _796061, _796057)), c_Nitpick_Oless__eq__frac(_796067, _796063, _796059), _796067 = _796065, _796063 = _796061, _796059 = _796057], (6814 ^ _781215) ^ [_893337, _893339, _893341, _893343] : [hBOOL(hAPP(hAPP(c_member(_893337), _893339), c_Map_Odom(_893337, _893341, _893343))), hAPP(_893343, _893339) = c_Option_Ooption_ONone(_893341)], (6261 ^ _781215) ^ [_882253, _882255, _882257, _882259, _882261] : [hAPP(_882253, _882255) = c_Option_Ooption_ONone(_882257), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_882259, tc_HOL_Obool)), c_Map_Odom(_882259, _882257, _882253)), hAPP(hAPP(c_Set_Oinsert(_882259), _882255), _882261)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_882259, tc_HOL_Obool)), c_Map_Odom(_882259, _882257, _882253)), _882261))], (38588 ^ _781215) ^ [_1519219, _1519221, _1519223, _1519225, _1519227, _1519229] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1519219, _1519221)), hAPP(hAPP(c_Product__Type_OPair(_1519219, _1519221), _1519223), _1519225)), hAPP(hAPP(c_Product__Type_OSigma(_1519219, _1519221), _1519227), _1519229)))), hBOOL(hAPP(hAPP(c_member(_1519219), _1519223), _1519227)), hBOOL(hAPP(hAPP(c_member(_1519221), _1519225), hAPP(_1519229, _1519223)))], (51192 ^ _781215) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (46892 ^ _781215) ^ [_1724553, _1724555, _1724557, _1724559, _1724561] : [-(c_Enum_Oproduct(_1724553, _1724555, hAPP(hAPP(c_List_Olist_OCons(_1724553), _1724557), _1724559), _1724561) = hAPP(hAPP(c_List_Oappend(tc_prod(_1724553, _1724555)), hAPP(hAPP(c_List_Omap(_1724555, tc_prod(_1724553, _1724555)), hAPP(c_Product__Type_OPair(_1724553, _1724555), _1724557)), _1724561)), c_Enum_Oproduct(_1724553, _1724555, _1724559, _1724561)))], (33837 ^ _781215) ^ [_1412263, _1412265, _1412267] : [class_Orderings_Olinorder(_1412263), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412263), _1412265)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412263), _1412267)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412263, tc_HOL_Obool)), _1412265), _1412267) = c_Orderings_Obot__class_Obot(tc_fun(_1412263, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1412263), c_Big__Operators_Olinorder__class_OMin(_1412263, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412263, tc_HOL_Obool)), _1412265), _1412267))), c_Big__Operators_Olinorder__class_OMin(_1412263, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412263, tc_HOL_Obool)), _1412265), _1412267))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1412263), c_Big__Operators_Olinorder__class_OMin(_1412263, _1412265)), c_Big__Operators_Olinorder__class_OMin(_1412263, _1412267)))], (51144 ^ _781215) ^ [_1820379, _1820381] : [class_Groups_Ominus(_1820379), -(class_Groups_Ominus(tc_fun(_1820381, _1820379)))], (43591 ^ _781215) ^ [_1651812, _1651814] : [-(c_List_Obutlast(_1651812, _1651814) = hAPP(hAPP(c_List_Otake(_1651812), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651812)), _1651814)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1651814))], (11525 ^ _781215) ^ [_982125, _982127, _982129, _982131, _982133] : [-(hBOOL(hAPP(hAPP(c_member(_982125), _982127), hAPP(c_Set_Oimage(_982129, _982125, _982131), _982133)))), 11526 ^ _781215 : [(11527 ^ _781215) ^ [_982195] : [hBOOL(hAPP(hAPP(c_member(_982129), _982195), _982133)), _982127 = hAPP(_982131, _982195)]]], (34001 ^ _781215) ^ [_1415507, _1415509, _1415511, _1415513] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1415507), _1415509)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415507), _1415511)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1415507, tc_Nat_Onat), _1415513), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415507, tc_HOL_Obool)), _1415509), _1415511)) = 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(_1415507, tc_Nat_Onat), _1415513), _1415509)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1415507, tc_Nat_Onat), _1415513), _1415511))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1415507, tc_Nat_Onat), _1415513), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415507, tc_HOL_Obool)), _1415509), _1415511))))], (26552 ^ _781215) ^ [_1262901, _1262903, _1262905, _1262907, _1262909, _1262911] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262901, tc_fun(_1262903, tc_HOL_Obool))), _1262905), _1262907), _1262909), _1262911)), -(hBOOL(hAPP(hAPP(_1262905, _1262909), _1262911))), -(hBOOL(hAPP(hAPP(_1262907, _1262909), _1262911)))], (23530 ^ _781215) ^ [_1205161, _1205163] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205161))), -(c_SMT_Oz3div(_1205163, _1205161) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205163), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205161))))], (44922 ^ _781215) ^ [_1682206, _1682208] : [class_Lattices_Oab__semigroup__idem__mult(_1682206), -(_1682208 = c_List_Olist_ONil(_1682206)), -(hAPP(c_Finite__Set_Ofold1(_1682206, c_Groups_Otimes__class_Otimes(_1682206)), hAPP(c_List_Oset(_1682206), _1682208)) = hAPP(c_List_Ofoldl(_1682206, _1682206, c_Groups_Otimes__class_Otimes(_1682206), hAPP(c_List_Ohd(_1682206), _1682208)), hAPP(c_List_Otl(_1682206), _1682208)))], (7776 ^ _781215) ^ [_912350, _912352, _912354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912350), _912352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912350), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912352), _912354))))], (45267 ^ _781215) ^ [_1689305, _1689307, _1689309] : [hBOOL(hAPP(c_List_Odistinct(_1689305), _1689307)), -(hBOOL(hAPP(c_List_Odistinct(_1689305), hAPP(c_List_Ofilter(_1689305, _1689309), _1689307))))], (39677 ^ _781215) ^ [_1552265, _1552267] : [-(hAPP(c_Set_Oimage(_1552265, _1552265, c_Fun_Oid(_1552265)), _1552267) = _1552267)], (13218 ^ _781215) ^ [_1011091, _1011093] : [13219 ^ _781215 : [(13222 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011093))], (13220 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011091))]], -(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), _1011091), _1011093))))], (3462 ^ _781215) ^ [_833526, _833528, _833530, _833532, _833534, _833536, _833538, _833540, _833542, _833544] : [-(c_List_Ofoldr(_833544, _833540, _833536, _833532, _833528) = c_List_Ofoldr(_833542, _833538, _833534, _833530, _833526)), _833544 = _833542, _833540 = _833538, _833536 = _833534, _833532 = _833530, _833528 = _833526], (32706 ^ _781215) ^ [_1386825, _1386827, _1386829, _1386831] : [class_Lattices_Osemilattice__inf(_1386825), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386825), _1386827), _1386829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386825), _1386827), _1386831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386825), _1386827), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1386825), _1386829), _1386831))))], (22178 ^ _781215) ^ [_1181092, _1181094, _1181096, _1181098] : [class_Divides_Osemiring__div(_1181092), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181092), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181092), _1181094), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1181092), _1181096), _1181094))), c_Divides_Odiv__class_Omod(_1181092, _1181096, _1181094))), _1181098) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181092), _1181096), _1181098))], (32135 ^ _781215) ^ [_1374491, _1374493, _1374495, _1374497, _1374499] : [class_Groups_Ocomm__monoid__add(_1374491), class_Groups_Oordered__ab__semigroup__add(_1374491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374493), _1374495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1374493, tc_HOL_Obool)), _1374497), _1374495)), 32153 ^ _781215 : [(32156 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374491), c_Groups_Ozero__class_Ozero(_1374491)), hAPP(_1374499, 32152 ^ [_1374491, _1374493, _1374495, _1374497, _1374499])))], (32154 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1374493), 32152 ^ [_1374491, _1374493, _1374495, _1374497, _1374499]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374493, tc_HOL_Obool)), _1374495), _1374497))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374491), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1374493, _1374491), _1374499), _1374497)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1374493, _1374491), _1374499), _1374495))))], (4142 ^ _781215) ^ [_844084, _844086, _844088, _844090, _844092, _844094] : [-(c_Random_Ominus__shift(_844094, _844090, _844086) = c_Random_Ominus__shift(_844092, _844088, _844084)), _844094 = _844092, _844090 = _844088, _844086 = _844084], (46441 ^ _781215) ^ [_1714885, _1714887, _1714889, _1714891] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714885), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1714885))), _1714887))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714889), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714885))), c_List_Otranspose(_1714885, _1714887)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714891), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714885))), hAPP(c_List_Ofilter(tc_List_Olist(_1714885), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714885)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714889)), c_Nat_Osize__class_Osize(tc_List_Olist(_1714885)))), _1714887)))), -(hAPP(hAPP(c_List_Onth(_1714885), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714885)), c_List_Otranspose(_1714885, _1714887)), _1714889)), _1714891) = hAPP(hAPP(c_List_Onth(_1714885), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714885)), _1714887), _1714891)), _1714889))], (49018 ^ _781215) ^ [_1770446, _1770448] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1770446), _1770448) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1770446)), hAPP(c_Code__Numeral_Onat__of, _1770448))))], (42734 ^ _781215) ^ [_1630257, _1630259, _1630261, _1630263] : [hBOOL(hAPP(c_List_Odistinct(_1630257), _1630259)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630261), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630257)), _1630259))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630263), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630257)), _1630259))), 42745 ^ _781215 : [(42752 ^ _781215) ^ [] : [_1630261 = _1630263, -(hAPP(hAPP(c_List_Onth(_1630257), _1630259), _1630261) = hAPP(hAPP(c_List_Onth(_1630257), _1630259), _1630263))], (42746 ^ _781215) ^ [] : [hAPP(hAPP(c_List_Onth(_1630257), _1630259), _1630261) = hAPP(hAPP(c_List_Onth(_1630257), _1630259), _1630263), -(_1630261 = _1630263)]]], (49179 ^ _781215) ^ [_1774212, _1774214, _1774216, _1774218] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1774212, tc_fun(_1774212, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1774212, tc_fun(tc_prod(_1774212, _1774212), tc_HOL_Obool), tc_fun(_1774212, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774212, tc_fun(tc_fun(tc_prod(_1774212, _1774212), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1774212, _1774212), tc_HOL_Obool), tc_fun(_1774212, tc_HOL_Obool)), _1774212), c_COMBC(_1774212, tc_fun(tc_prod(_1774212, _1774212), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774212, tc_prod(_1774212, _1774212)), tc_fun(_1774212, tc_fun(tc_fun(tc_prod(_1774212, _1774212), tc_HOL_Obool), tc_HOL_Obool)), _1774212), hAPP(c_COMBB(tc_prod(_1774212, _1774212), tc_fun(tc_fun(tc_prod(_1774212, _1774212), tc_HOL_Obool), tc_HOL_Obool), _1774212), c_member(tc_prod(_1774212, _1774212)))), c_Product__Type_OPair(_1774212, _1774212)))), _1774214)), c_fequal), _1774216), _1774218)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774212, _1774212)), hAPP(hAPP(c_Product__Type_OPair(_1774212, _1774212), _1774216), _1774218)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774212, _1774212), tc_HOL_Obool)), _1774214), c_Relation_OId(_1774212)))))], (18880 ^ _781215) ^ [_1119687, _1119689, _1119691, _1119693] : [class_Orderings_Olinorder(_1119687), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119687), _1119689), _1119691)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119687), _1119693), _1119691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119687), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1119687), _1119689), _1119693)), _1119691)))], (42441 ^ _781215) ^ [_1621848, _1621850, _1621852, _1621854, _1621856, _1621858] : [_1621848 = _1621850, -(hAPP(hAPP(c_Map_Omap__of(_1621852, _1621854), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1621852, _1621854)), hAPP(hAPP(c_Product__Type_OPair(_1621852, _1621854), _1621848), _1621856)), _1621858)), _1621850) = hAPP(c_Option_Ooption_OSome(_1621854), _1621856))], (13992 ^ _781215) ^ [_1025039, _1025041, _1025043] : [13993 ^ _781215 : [(13996 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1025039), _1025043))], (13994 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1025041)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025039), _1025041)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1025043), _1025041))))], (51494 ^ _781215) ^ [_1823752, _1823754] : [-(class_Nat_Osize(tc_sum(_1823752, _1823754)))], (51272 ^ _781215) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (26690 ^ _781215) ^ [_1265424, _1265426, _1265428, _1265430, _1265432] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1265424, _1265426)), hAPP(hAPP(c_Product__Type_OPair(_1265424, _1265426), _1265430), _1265432)), _1265428)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1265424, _1265426, _1265428), _1265430), _1265432)))], (17239 ^ _781215) ^ [_1090026, _1090028, _1090030] : [class_Lattices_Olattice(_1090026), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090026), _1090028)), -(_1090030 = c_Orderings_Obot__class_Obot(tc_fun(_1090026, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1090026, tc_HOL_Obool)), _1090030), _1090028)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1090026), c_Big__Operators_Olattice__class_OSup__fin(_1090026, _1090030)), c_Big__Operators_Olattice__class_OSup__fin(_1090026, _1090028)) = c_Big__Operators_Olattice__class_OSup__fin(_1090026, _1090028))], (26827 ^ _781215) ^ [_1268708, _1268710, _1268712] : [26829 ^ _781215 : [(26832 ^ _781215) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1268708, _1268710), 26828 ^ [_1268708, _1268710, _1268712]))], (26830 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1268710, 26828 ^ [_1268708, _1268710, _1268712]), _1268712)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1268708, _1268710), _1268712)))], (32826 ^ _781215) ^ [_1389272, _1389274, _1389276, _1389278] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389272, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389272, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389272, tc_HOL_Obool)), _1389274), _1389276)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389272, tc_HOL_Obool)), _1389276), _1389278))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389272, tc_HOL_Obool)), _1389278), _1389274)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389272, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389272, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389272, tc_HOL_Obool)), _1389274), _1389276)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389272, tc_HOL_Obool)), _1389276), _1389278))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389272, tc_HOL_Obool)), _1389278), _1389274)))], (16933 ^ _781215) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5570 ^ _781215) ^ [_866230, _866232] : [_866232 = _866230, -(tc_Hoare__Mirabelle_Otriple(_866232) = tc_Hoare__Mirabelle_Otriple(_866230))], (3186 ^ _781215) ^ [_829184, _829186, _829188, _829190, _829192, _829194] : [-(c_List_Olist_Olist__size(_829194, _829190, _829186) = c_List_Olist_Olist__size(_829192, _829188, _829184)), _829194 = _829192, _829190 = _829188, _829186 = _829184], (51608 ^ _781215) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (44548 ^ _781215) ^ [_1673957, _1673959] : [_1673959 = c_List_Olist_ONil(_1673957), -(hAPP(c_List_Orotate1(_1673957), _1673959) = c_List_Olist_ONil(_1673957))], (47932 ^ _781215) ^ [_1746397, _1746399] : [-(hAPP(c_List_OremoveAll(_1746397, _1746399), c_List_Olist_ONil(_1746397)) = c_List_Olist_ONil(_1746397))], (40166 ^ _781215) ^ [_1565546, _1565548, _1565550] : [c_Wellfounded_Owf(_1565546, _1565548), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1565546, tc_HOL_Obool)), _1565550), hAPP(c_Relation_OImage(_1565546, _1565546, _1565548), _1565550))), -(_1565550 = c_Orderings_Obot__class_Obot(tc_fun(_1565546, tc_HOL_Obool)))], (15921 ^ _781215) ^ [_1061814, _1061816, _1061818, _1061820] : [hBOOL(hAPP(hAPP(c_member(_1061814), _1061816), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061814, tc_HOL_Obool)), _1061818), _1061820))), -(hBOOL(hAPP(hAPP(c_member(_1061814), _1061816), _1061818))), -(hBOOL(hAPP(hAPP(c_member(_1061814), _1061816), _1061820)))], (9391 ^ _781215) ^ [_941351, _941353, _941355, _941357] : [class_Orderings_Opreorder(_941351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941351), _941353), _941355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941351), _941355), _941357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941351), _941353), _941357)))], (4574 ^ _781215) ^ [_850570, _850572, _850574, _850576, _850578, _850580] : [-(c_Nitpick_Otimes__frac(_850580, _850576, _850572) = c_Nitpick_Otimes__frac(_850578, _850574, _850570)), _850580 = _850578, _850576 = _850574, _850572 = _850570], (16533 ^ _781215) ^ [_1076040, _1076042, _1076044, _1076046, _1076048, _1076050, _1076052, _1076054] : [c_Finite__Set_Ofolding__image__simple__idem(_1076040, _1076042, _1076044, _1076046, _1076048, _1076050), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076042), _1076052)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076042), _1076054)), -(hAPP(_1076050, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1076042, tc_HOL_Obool)), _1076052), _1076054)) = hAPP(hAPP(_1076044, hAPP(_1076050, _1076052)), hAPP(_1076050, _1076054)))], (19108 ^ _781215) ^ [_1123949, _1123951, _1123953] : [class_Int_Onumber(_1123949), class_Orderings_Oord(_1123949), 19115 ^ _781215 : [(19122 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123949), hAPP(c_Int_Onumber__class_Onumber__of(_1123949), _1123951)), hAPP(c_Int_Onumber__class_Onumber__of(_1123949), _1123953)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123949), hAPP(c_Int_Onumber__class_Onumber__of(_1123949), _1123951)), hAPP(c_Int_Onumber__class_Onumber__of(_1123949), _1123953)) = hAPP(c_Int_Onumber__class_Onumber__of(_1123949), _1123951))], (19116 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123949), hAPP(c_Int_Onumber__class_Onumber__of(_1123949), _1123951)), hAPP(c_Int_Onumber__class_Onumber__of(_1123949), _1123953))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123949), hAPP(c_Int_Onumber__class_Onumber__of(_1123949), _1123951)), hAPP(c_Int_Onumber__class_Onumber__of(_1123949), _1123953)) = hAPP(c_Int_Onumber__class_Onumber__of(_1123949), _1123953))]]], (12840 ^ _781215) ^ [_1004933, _1004935, _1004937] : [class_Groups_Oordered__ab__group__add(_1004933), 12843 ^ _781215 : [(12850 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004933), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1004933), _1004935), _1004937)), c_Groups_Ozero__class_Ozero(_1004933))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004933), _1004935), _1004937)))], (12844 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004933), _1004935), _1004937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004933), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1004933), _1004935), _1004937)), c_Groups_Ozero__class_Ozero(_1004933))))]]], (33326 ^ _781215) ^ [_1401152, _1401154, _1401156, _1401158] : [class_Orderings_Oorder(_1401152), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401152, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1401152, _1401154), _1401156)), c_SetInterval_Oord__class_OatLeastAtMost(_1401152, _1401156, _1401158)) = c_Orderings_Obot__class_Obot(tc_fun(_1401152, tc_HOL_Obool)))], (32938 ^ _781215) ^ [_1391995, _1391997, _1391999, _1392001, _1392003] : [class_Lattices_Olattice(_1391995), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1391997, _1391995)), _1391999), _1392001), _1392003) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1391995), hAPP(_1391999, _1392003)), hAPP(_1392001, _1392003)))], (26584 ^ _781215) ^ [_1263568, _1263570, _1263572] : [_1263568 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1263570, _1263570), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1263570, _1263570), tc_HOL_Obool)), _1263568), _1263572)))], (27846 ^ _781215) ^ [_1288854, _1288856] : [_1288854 = _1288856, -(hAPP(c_Int_ORep__Integ, _1288854) = hAPP(c_Int_ORep__Integ, _1288856))], (22876 ^ _781215) ^ [_1193864, _1193866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193864)), 22879 ^ _781215 : [(22888 ^ _781215) ^ [] : [-(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), _1193864), _1193866)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193866), _1193864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193866))], (22880 ^ _781215) ^ [] : [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), _1193864), _1193866))), 22883 ^ _781215 : [(22886 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193866)))], (22884 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193866), _1193864)))]]]]], (21055 ^ _781215) ^ [_1158306] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158306))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158306)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7534 ^ _781215) ^ [_907869, _907871, _907873, _907875] : [class_Orderings_Opreorder(_907869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907869), _907871), _907873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907869), _907873), _907875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907869), _907871), _907875)))], (9683 ^ _781215) ^ [_945551, _945553, _945555, _945557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945551, tc_HOL_Obool)), _945553), _945555)), hBOOL(hAPP(hAPP(c_member(_945551), _945557), _945553)), -(hBOOL(hAPP(hAPP(c_member(_945551), _945557), _945555)))], (48715 ^ _781215) ^ [_1764825, _1764827, _1764829, _1764831, _1764833, _1764835, _1764837] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1764825, _1764827, _1764829, _1764831), _1764833), _1764835), _1764837) = hAPP(hAPP(_1764835, hAPP(c_Product__Type_Ofst(_1764827, _1764829), hAPP(_1764833, _1764837))), hAPP(c_Product__Type_Osnd(_1764827, _1764829), hAPP(_1764833, _1764837))))], (16343 ^ _781215) ^ [_1070001, _1070003, _1070005, _1070007] : [hBOOL(hAPP(hAPP(c_member(_1070001), _1070003), _1070005)), -(hBOOL(hAPP(hAPP(c_member(_1070001), _1070003), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1070001, tc_HOL_Obool)), _1070005), _1070007))))], (28942 ^ _781215) ^ [_1308864, _1308866, _1308868] : [class_Fields_Olinordered__field__inverse__zero(_1308864), 28945 ^ _781215 : [(28960 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308864), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308864), _1308866), _1308868)), c_Groups_Ozero__class_Ozero(_1308864)))), 28961 ^ _781215 : [(28968 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308864), _1308866), c_Groups_Ozero__class_Ozero(_1308864))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308864), c_Groups_Ozero__class_Ozero(_1308864)), _1308868))], (28962 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308864), c_Groups_Ozero__class_Ozero(_1308864)), _1308866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308864), _1308868), c_Groups_Ozero__class_Ozero(_1308864)))]]], (28946 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308864), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308864), _1308866), _1308868)), c_Groups_Ozero__class_Ozero(_1308864))), 28951 ^ _781215 : [(28954 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308864), _1308868), c_Groups_Ozero__class_Ozero(_1308864))))], (28952 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308864), c_Groups_Ozero__class_Ozero(_1308864)), _1308866)))]], 28955 ^ _781215 : [(28958 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308864), c_Groups_Ozero__class_Ozero(_1308864)), _1308868)))], (28956 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308864), _1308866), c_Groups_Ozero__class_Ozero(_1308864))))]]]]], (20659 ^ _781215) ^ [_1151959] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1151959))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1151959)) = _1151959)], (49710 ^ _781215) ^ [_1788269, _1788271, _1788273, _1788275, _1788277] : [-(hAPP(c_Relation_Oconverse(_1788269, _1788271), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1788273, tc_fun(tc_prod(_1788269, _1788271), tc_HOL_Obool)), _1788275), _1788277)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1788273, tc_fun(tc_prod(_1788271, _1788269), tc_HOL_Obool)), _1788275), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1788269, _1788271), tc_HOL_Obool), tc_fun(tc_prod(_1788271, _1788269), tc_HOL_Obool), _1788273), c_Relation_Oconverse(_1788269, _1788271)), _1788277)))], (47954 ^ _781215) ^ [_1746765, _1746767, _1746769] : [-(hAPP(c_List_Oset(_1746765), c_List_Oinsert(_1746765, _1746767, _1746769)) = hAPP(hAPP(c_Set_Oinsert(_1746765), _1746767), hAPP(c_List_Oset(_1746765), _1746769)))], (51558 ^ _781215) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (9363 ^ _781215) ^ [_940885, _940887, _940889, _940891] : [class_Orderings_Opreorder(_940885), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940885), _940887), _940889)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940885), _940889), _940891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940885), _940887), _940891)))], (24496 ^ _781215) ^ [_1223175] : [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, _1223175, 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, _1223175, 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))], (16243 ^ _781215) ^ [_1068311, _1068313, _1068315] : [class_Lattices_Osemilattice__sup(_1068311), 16246 ^ _781215 : [(16253 ^ _781215) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068311), _1068313), _1068315) = _1068315, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068311), _1068313), _1068315)))], (16247 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068311), _1068313), _1068315)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068311), _1068313), _1068315) = _1068315)]]], (30311 ^ _781215) ^ [_1335703, _1335705] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1335703), _1335705) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1335703, _1335705))], (5985 ^ _781215) ^ [_876536] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_876536), c_Orderings_Obot__class_Obot(tc_fun(_876536, tc_HOL_Obool)))))], (42789 ^ _781215) ^ [_1631399, _1631401, _1631403, _1631405] : [-(_1631399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1631401), hAPP(hAPP(c_List_Olist_OCons(_1631401), _1631403), _1631405)), _1631399) = hAPP(hAPP(c_List_Onth(_1631401), _1631405), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1631399), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (51448 ^ _781215) ^ [] : [-(class_HOL_Oequal(tc_HOL_Obool))], (41321 ^ _781215) ^ [_1593056, _1593058, _1593060, _1593062, _1593064, _1593066, _1593068, _1593070] : [hAPP(c_Fun_Ocomp(_1593056, _1593058, _1593060, _1593062), _1593064) = hAPP(c_Fun_Ocomp(_1593066, _1593058, _1593060, _1593068), _1593070), 41324 ^ _781215 : [(41325 ^ _781215) ^ [_1593171] : [-(hAPP(_1593062, hAPP(_1593064, _1593171)) = hAPP(_1593068, hAPP(_1593070, _1593171)))]]], (2512 ^ _781215) ^ [_818523, _818525, _818527, _818529] : [-(c_Groups_Osgn__class_Osgn(_818529, _818525) = c_Groups_Osgn__class_Osgn(_818527, _818523)), _818529 = _818527, _818525 = _818523], (5532 ^ _781215) ^ [_865681, _865683] : [_865683 = _865681, -(c_Option_Ooption_OSome(_865683) = c_Option_Ooption_OSome(_865681))], (47846 ^ _781215) ^ [_1744675, _1744677, _1744679, _1744681, _1744683, _1744685, _1744687, _1744689] : [c_List_Olist__all2(_1744675, _1744677, _1744679, _1744681, _1744683), hBOOL(hAPP(hAPP(_1744679, _1744685), _1744687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744689), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744677)), _1744683))), -(c_List_Olist__all2(_1744675, _1744677, _1744679, hAPP(hAPP(c_List_Olist__update(_1744675, _1744681), _1744689), _1744685), hAPP(hAPP(c_List_Olist__update(_1744677, _1744683), _1744689), _1744687)))], (32088 ^ _781215) ^ [_1373385, _1373387, _1373389] : [32090 ^ _781215 : [(32093 ^ _781215) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1373389, 32089 ^ [_1373385, _1373387, _1373389]))], (32091 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373385), 32089 ^ [_1373385, _1373387, _1373389]), _1373387)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1373385, tc_Int_Oint), _1373389), _1373387) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1373385, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1373385), c_Int_Onat), _1373389)), _1373387)))], (22808 ^ _781215) ^ [_1192847, _1192849] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1192847), _1192849) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1192849 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22817 ^ _781215 : [(22820 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192847), _1192849)))], (22818 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192847)))]], 22821 ^ _781215 : [(22824 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192849), _1192847)))], (22822 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192847), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (48615 ^ _781215) ^ [_1762947, _1762949, _1762951] : [-(c_List_Olist__ex(_1762947, _1762949, _1762951)), 48616 ^ _781215 : [(48617 ^ _781215) ^ [_1763012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763012), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762947)), _1762951))), hBOOL(hAPP(_1762949, hAPP(hAPP(c_List_Onth(_1762947), _1762951), _1763012)))]]], (6594 ^ _781215) ^ [_888958, _888960, _888962] : [hBOOL(hAPP(hAPP(c_member(_888958), _888960), _888962)), -(hAPP(hAPP(c_Set_Oinsert(_888958), _888960), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888958, tc_HOL_Obool)), _888962), hAPP(hAPP(c_Set_Oinsert(_888958), _888960), c_Orderings_Obot__class_Obot(tc_fun(_888958, tc_HOL_Obool))))) = _888962)], (5997 ^ _781215) ^ [_876809, _876811, _876813] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_876809), _876813)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_876809), hAPP(hAPP(c_Set_Oinsert(_876809), _876811), _876813))))], (29046 ^ _781215) ^ [_1310785, _1310787, _1310789] : [class_Fields_Olinordered__field(_1310785), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310785), _1310787), c_Groups_Ozero__class_Ozero(_1310785))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310785), c_Groups_Ozero__class_Ozero(_1310785)), _1310789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310785), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310785), _1310787), _1310789)), c_Groups_Ozero__class_Ozero(_1310785))))], (10890 ^ _781215) ^ [_968383, _968385, _968387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968383), _968385)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968387), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968385), _968383))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _968387), _968383)), hAPP(c_Nat_OSuc, _968385)))], (36524 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (15378 ^ _781215) ^ [_1050776, _1050778, _1050780] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050776), _1050778)), _1050780) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050776), _1050780)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050778), _1050780)))], (11134 ^ _781215) ^ [_974061, _974063, _974065, _974067] : [class_Rings_Ocomm__semiring__1(_974061), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974061), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974061), _974063), _974065)), _974067) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974061), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974061), _974063), _974067)), _974065))], (13294 ^ _781215) ^ [_1012333, _1012335, _1012337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012333), _1012335)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012337), _1012335))), 13297 ^ _781215 : [(13300 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012333), _1012337)))], (13298 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1012335)))]]], (1348 ^ _781215) ^ [_801035, _801037] : [-(class_Lattices_Osemilattice__sup(_801035)), _801037 = _801035, class_Lattices_Osemilattice__sup(_801037)], (11962 ^ _781215) ^ [_989079, _989081] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989079), _989081) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_989079 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_989081 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2886 ^ _781215) ^ [_824338, _824340, _824342, _824344, _824346, _824348] : [-(c_Map_Oran(_824348, _824344, _824340) = c_Map_Oran(_824346, _824342, _824338)), _824348 = _824346, _824344 = _824342, _824340 = _824338], (24077 ^ _781215) ^ [_1215395, _1215397] : [_1215395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1215397), _1215395) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11470 ^ _781215) ^ [_981157, _981159, _981161, _981163] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981157), _981159)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981161), hAPP(c_Set_Oimage(_981157, _981161, _981163), _981159))))], (51604 ^ _781215) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (50517 ^ _781215) ^ [_1808416, _1808418, _1808420] : [50519 ^ _781215 : [(50522 ^ _781215) ^ [] : [hBOOL(hAPP(_1808418, 50518 ^ [_1808416, _1808418, _1808420]))], (50520 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808416), 50518 ^ [_1808416, _1808418, _1808420]), hAPP(c_List_Oset(_1808416), _1808420))))]], -(c_List_Olist__all(_1808416, _1808418, _1808420))], (158 ^ _781215) ^ [_783682, _783684] : [-(class_Rings_Odivision__ring__inverse__zero(_783682)), _783684 = _783682, class_Rings_Odivision__ring__inverse__zero(_783684)], (28214 ^ _781215) ^ [_1294934, _1294936] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294934), _1294936), hAPP(c_Int_Onumber__class_Onumber__of(_1294934), c_Int_OBit1(c_Int_OPls))) = _1294936), class_Fields_Ofield(_1294934), class_Int_Onumber__ring(_1294934)], (25750 ^ _781215) ^ [_1244754, _1244756, _1244758] : [class_Orderings_Olinorder(_1244754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244754), _1244756), _1244758)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1244754, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1244754, _1244756, _1244758)), hAPP(hAPP(c_Set_Oinsert(_1244754), _1244758), c_Orderings_Obot__class_Obot(tc_fun(_1244754, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1244754, _1244756, _1244758))], (47539 ^ _781215) ^ [_1737821, _1737823, _1737825, _1737827] : [-(hBOOL(hAPP(c_List_Olistsp(_1737821, _1737823), hAPP(hAPP(c_List_Olist_OCons(_1737821), _1737825), _1737827)))), hBOOL(hAPP(_1737823, _1737825)), hBOOL(hAPP(c_List_Olistsp(_1737821, _1737823), _1737827))], (26777 ^ _781215) ^ [_1267628, _1267630, _1267632, _1267634, _1267636] : [hBOOL(hAPP(hAPP(_1267628, _1267630), _1267632)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1267634, _1267636, tc_HOL_Obool), _1267628), hAPP(hAPP(c_Product__Type_OPair(_1267634, _1267636), _1267630), _1267632))))], (17459 ^ _781215) ^ [_1093660, _1093662, _1093664] : [class_Lattices_Olattice(_1093660), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093660), _1093662)), 17466 ^ _781215 : [(17473 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1093660, tc_HOL_Obool)), _1093662), hAPP(hAPP(c_Set_Oinsert(_1093660), _1093664), c_Orderings_Obot__class_Obot(tc_fun(_1093660, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1093660, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1093660, hAPP(hAPP(c_Set_Oinsert(_1093660), _1093664), _1093662)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1093660), _1093664), c_Big__Operators_Olattice__class_OSup__fin(_1093660, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1093660, tc_HOL_Obool)), _1093662), hAPP(hAPP(c_Set_Oinsert(_1093660), _1093664), c_Orderings_Obot__class_Obot(tc_fun(_1093660, tc_HOL_Obool)))))))], (17467 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1093660, tc_HOL_Obool)), _1093662), hAPP(hAPP(c_Set_Oinsert(_1093660), _1093664), c_Orderings_Obot__class_Obot(tc_fun(_1093660, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1093660, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1093660, hAPP(hAPP(c_Set_Oinsert(_1093660), _1093664), _1093662)) = _1093664)]]], (31553 ^ _781215) ^ [_1361279, _1361281, _1361283, _1361285, _1361287] : [class_Rings_Osemiring__0(_1361279), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361279), _1361281), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361283, _1361279), _1361285), _1361287)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361283, _1361279), hAPP(hAPP(c_COMBB(_1361279, _1361279, _1361283), hAPP(c_Groups_Otimes__class_Otimes(_1361279), _1361281)), _1361285)), _1361287))], (25913 ^ _781215) ^ [_1251254, _1251256, _1251258] : [class_Groups_Ocomm__monoid__mult(_1251254), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1251256, _1251254), hAPP(c_COMBK(_1251254, _1251256), c_Groups_Oone__class_Oone(_1251254))), _1251258) = c_Groups_Oone__class_Oone(_1251254))], (44473 ^ _781215) ^ [_1671787, _1671789, _1671791, _1671793, _1671795, _1671797] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671787), tc_List_Olist(_1671787))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671787), tc_List_Olist(_1671787)), hAPP(hAPP(c_List_Oappend(_1671787), _1671789), hAPP(hAPP(c_List_Olist_OCons(_1671787), _1671791), c_List_Olist_ONil(_1671787)))), hAPP(hAPP(c_List_Oappend(_1671787), _1671793), hAPP(hAPP(c_List_Olist_OCons(_1671787), _1671795), c_List_Olist_ONil(_1671787))))), c_List_Olistrel1(_1671787, _1671797))), 44478 ^ _781215 : [(44481 ^ _781215) ^ [] : [-(_1671791 = _1671795)], (44479 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671787), tc_List_Olist(_1671787))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671787), tc_List_Olist(_1671787)), _1671789), _1671793)), c_List_Olistrel1(_1671787, _1671797))))]], 44482 ^ _781215 : [(44485 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1671787, _1671787)), hAPP(hAPP(c_Product__Type_OPair(_1671787, _1671787), _1671791), _1671795)), _1671797)))], (44483 ^ _781215) ^ [] : [-(_1671789 = _1671793)]]], (50888 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34238 ^ _781215) ^ [_1422480, _1422482, _1422484, _1422486, _1422488, _1422490] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422480, tc_fun(_1422482, tc_HOL_Obool))), _1422484), _1422486), _1422488), _1422490)), -(hBOOL(hAPP(hAPP(_1422486, _1422488), _1422490)))], (51672 ^ _781215) ^ [_1825715, _1825717, _1825719, _1825721, _1825723, _1825725] : [-(hAPP(hAPP(hAPP(c_COMBS(_1825715, _1825717, _1825719), _1825721), _1825723), _1825725) = hAPP(hAPP(_1825721, _1825725), hAPP(_1825723, _1825725)))], (18451 ^ _781215) ^ [_1111641, _1111643, _1111645, _1111647] : [class_Orderings_Olinorder(_1111641), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111641), _1111643)), hBOOL(hAPP(hAPP(c_member(_1111641), _1111645), _1111643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111641), hAPP(hAPP(c_Finite__Set_Ofold(_1111641, _1111641, c_Orderings_Oord__class_Omin(_1111641)), _1111647), _1111643)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1111641), _1111645), _1111647))))], (31507 ^ _781215) ^ [_1359754, _1359756, _1359758, _1359760, _1359762] : [class_Groups_Oab__group__add(_1359754), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359756, _1359754), hAPP(hAPP(c_COMBS(_1359756, _1359754, _1359754), hAPP(hAPP(c_COMBB(_1359754, tc_fun(_1359754, _1359754), _1359756), c_Groups_Ominus__class_Ominus(_1359754)), _1359758)), _1359760)), _1359762) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1359754), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359756, _1359754), _1359758), _1359762)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359756, _1359754), _1359760), _1359762)))], (36492 ^ _781215) ^ [_1467095, _1467097] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1467095, _1467097)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1467095, _1467097), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467095), c_Orderings_Otop__class_Otop(tc_fun(_1467095, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467097), c_Orderings_Otop__class_Otop(tc_fun(_1467097, tc_HOL_Obool))))], (38368 ^ _781215) ^ [_1512853, _1512855, _1512857, _1512859] : [c_Fun_Oinj__on(_1512853, _1512855, _1512857, c_Orderings_Otop__class_Otop(tc_fun(_1512853, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1512853, _1512855, _1512857), hAPP(c_Set_Oimage(_1512853, _1512855, _1512857), _1512859)) = _1512859)], (42327 ^ _781215) ^ [_1619481, _1619483, _1619485, _1619487] : [hBOOL(hAPP(hAPP(c_member(_1619481), _1619483), hAPP(c_List_Oset(_1619481), hAPP(hAPP(c_List_Olist_OCons(_1619481), _1619485), _1619487)))), -(_1619483 = _1619485), -(hBOOL(hAPP(hAPP(c_member(_1619481), _1619483), hAPP(c_List_Oset(_1619481), _1619487))))], (30546 ^ _781215) ^ [_1340035, _1340037, _1340039] : [hBOOL(hAPP(c_Predicate_OPowp(_1340035, hAPP(hAPP(c_COMBC(_1340035, tc_fun(_1340035, tc_HOL_Obool), tc_HOL_Obool), c_member(_1340035)), _1340037)), _1340039)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1340035, tc_HOL_Obool)), _1340039), hAPP(c_Set_OPow(_1340035), _1340037))))], (12496 ^ _781215) ^ [_998615, _998617, _998619] : [class_Groups_Oordered__comm__monoid__add(_998615), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998615), c_Groups_Ozero__class_Ozero(_998615)), _998617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998615), c_Groups_Ozero__class_Ozero(_998615)), _998619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998615), c_Groups_Ozero__class_Ozero(_998615)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998615), _998617), _998619))))], (31074 ^ _781215) ^ [_1349960] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1349960)) = hAPP(c_Nat_OSuc, _1349960))], (2998 ^ _781215) ^ [_826138, _826140, _826142, _826144] : [-(c_Com_Ocom_OWhile(_826144, _826140) = c_Com_Ocom_OWhile(_826142, _826138)), _826144 = _826142, _826140 = _826138], (2152 ^ _781215) ^ [_812743, _812745, _812747, _812749] : [-(c_Nat__Transfer_Otsub(_812749, _812745) = c_Nat__Transfer_Otsub(_812747, _812743)), _812749 = _812747, _812745 = _812743], (37550 ^ _781215) ^ [_1494330, _1494332, _1494334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1494330, tc_HOL_Obool), tc_HOL_Obool)), _1494332), _1494334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494330, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494330, tc_HOL_Obool), _1494334)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494330, tc_HOL_Obool), _1494332))))], (20478 ^ _781215) ^ [_1148741, _1148743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1148741), _1148743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148741)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148743))))], (42070 ^ _781215) ^ [_1611182, _1611184, _1611186, _1611188, _1611190] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611182)), _1611184) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611186)), _1611188), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611182)), _1611190) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611186)), _1611188), hBOOL(hAPP(c_List_Odistinct(_1611186), _1611188)), hAPP(c_Map_Omap__of(_1611186, _1611182), hAPP(hAPP(c_List_Ozip(_1611186, _1611182), _1611188), _1611184)) = hAPP(c_Map_Omap__of(_1611186, _1611182), hAPP(hAPP(c_List_Ozip(_1611186, _1611182), _1611188), _1611190)), -(_1611184 = _1611190)], (32748 ^ _781215) ^ [_1387594, _1387596, _1387598, _1387600] : [class_Lattices_Osemilattice__inf(_1387594), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387594), _1387596), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1387594), _1387598), _1387600))), 32755 ^ _781215 : [(32758 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387594), _1387596), _1387600)))], (32756 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387594), _1387596), _1387598)))]]], (10392 ^ _781215) ^ [_958424, _958426, _958428, _958430] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_958424, _958426)), c_Sum__Type_OPlus(_958424, _958426, _958428, _958430))), 10395 ^ _781215 : [(10398 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_958426), _958430)))], (10396 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_958424), _958428)))]]], (41749 ^ _781215) ^ [_1603405, _1603407, _1603409, _1603411, _1603413, _1603415] : [c_Finite__Set_Ofolding__idem(_1603405, _1603407, _1603409, _1603411), hBOOL(hAPP(c_Finite__Set_Ofinite(_1603405), _1603413)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1603405), _1603415)), -(hAPP(_1603411, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1603405, tc_HOL_Obool)), _1603413), _1603415)) = hAPP(c_Fun_Ocomp(_1603407, _1603407, _1603407, hAPP(_1603411, _1603413)), hAPP(_1603411, _1603415)))], (35239 ^ _781215) ^ [_1442937, _1442939, _1442941, _1442943, _1442945] : [c_Fun_Oinj__on(_1442937, _1442939, _1442941, _1442943), hBOOL(hAPP(hAPP(c_member(_1442937), _1442945), _1442943)), -(hAPP(c_Fun_Othe__inv__into(_1442937, _1442939, _1442943, _1442941), hAPP(_1442941, _1442945)) = _1442945)], (35963 ^ _781215) ^ [_1457430, _1457432, _1457434, _1457436, _1457438, _1457440] : [hAPP(_1457436, hAPP(c_Product__Type_Osnd(_1457434, _1457430), _1457438)) = hAPP(_1457440, hAPP(c_Product__Type_Osnd(_1457434, _1457430), _1457438)), -(hAPP(c_Product__Type_Oapsnd(_1457430, _1457432, _1457434, _1457436), _1457438) = hAPP(c_Product__Type_Oapsnd(_1457430, _1457432, _1457434, _1457440), _1457438))], (2594 ^ _781215) ^ [_819760, _819762, _819764, _819766] : [-(c_Nitpick_Onumber__of__frac(_819766, _819762) = c_Nitpick_Onumber__of__frac(_819764, _819760)), _819766 = _819764, _819762 = _819760], (38065 ^ _781215) ^ [_1505284, _1505286] : [-(c_Nitpick_Onumber__of__frac(_1505284, _1505286) = c_Nitpick_OAbs__Frac(_1505284, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1505286), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (18643 ^ _781215) ^ [_1115163] : [class_Orderings_Oord(_1115163), -(c_Orderings_Oord__class_Omin(_1115163) = c_Orderings_Oord_Omin(_1115163, c_Orderings_Oord__class_Oless__eq(_1115163)))], (316 ^ _781215) ^ [_786009, _786011, _786013, _786015, _786017, _786019, _786021, _786023] : [-(c_Wellfounded_Omax__extp(_786021, _786017, _786013, _786009)), c_Wellfounded_Omax__extp(_786023, _786019, _786015, _786011), _786023 = _786021, _786019 = _786017, _786015 = _786013, _786011 = _786009], (51580 ^ _781215) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (20858 ^ _781215) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (9791 ^ _781215) ^ [_947591, _947593] : [class_Groups_Omonoid__mult(_947591), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947591), _947593), c_Groups_Oone__class_Oone(_947591)) = _947593)], (48353 ^ _781215) ^ [_1757272, _1757274, _1757276, _1757278] : [class_Groups_Ocomm__monoid__mult(_1757272), hBOOL(hAPP(c_Finite__Set_Ofinite(_1757274), _1757276)), 48363 ^ _781215 : [(48366 ^ _781215) ^ [] : [hAPP(_1757278, 48362 ^ [_1757272, _1757274, _1757276, _1757278]) = c_Groups_Oone__class_Oone(_1757272)], (48364 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757274), 48362 ^ [_1757272, _1757274, _1757276, _1757278]), _1757276)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1757272, _1757274, c_Groups_Otimes__class_Otimes(_1757272)), _1757278), c_Groups_Oone__class_Oone(_1757272)), _1757276) = c_Groups_Oone__class_Oone(_1757272))], (20792 ^ _781215) ^ [_1154073] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154073))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1154073)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15628 ^ _781215) ^ [_1055763, _1055765, _1055767, _1055769, _1055771, _1055773] : [c_Com_Ocom_OCond(_1055763, _1055765, _1055767) = c_Com_Ocom_OLocal(_1055769, _1055771, _1055773)], (39721 ^ _781215) ^ [_1553138, _1553140, _1553142, _1553144, _1553146] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1553138, _1553140, _1553142), _1553144), _1553146) = hAPP(c_Set_OCollect(tc_prod(_1553138, _1553142)), hAPP(c_Product__Type_Oprod_Oprod__case(_1553138, _1553142, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1553142, tc_fun(_1553140, tc_HOL_Obool)), tc_fun(_1553142, tc_HOL_Obool), _1553138), hAPP(c_COMBB(tc_fun(_1553140, tc_HOL_Obool), tc_HOL_Obool, _1553142), c_HOL_OEx(_1553140))), hAPP(hAPP(c_COMBC(_1553138, tc_fun(_1553142, tc_fun(_1553140, tc_HOL_Obool)), tc_fun(_1553142, tc_fun(_1553140, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1553140, tc_HOL_Obool), tc_fun(_1553140, tc_HOL_Obool)), tc_fun(tc_fun(_1553142, tc_fun(_1553140, tc_HOL_Obool)), tc_fun(_1553142, tc_fun(_1553140, tc_HOL_Obool))), _1553138), c_COMBB(tc_fun(_1553140, tc_HOL_Obool), tc_fun(_1553140, tc_HOL_Obool), _1553142)), hAPP(hAPP(c_COMBB(tc_fun(_1553140, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1553140, tc_HOL_Obool), tc_fun(_1553140, tc_HOL_Obool)), _1553138), c_COMBS(_1553140, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553140, tc_HOL_Obool), tc_fun(_1553140, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1553138), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1553140), c_fconj)), hAPP(hAPP(c_COMBC(_1553138, tc_fun(tc_prod(_1553138, _1553140), tc_HOL_Obool), tc_fun(_1553140, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553140, tc_fun(tc_fun(tc_prod(_1553138, _1553140), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1553138, _1553140), tc_HOL_Obool), tc_fun(_1553140, tc_HOL_Obool)), _1553138), c_COMBC(_1553140, tc_fun(tc_prod(_1553138, _1553140), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553140, tc_prod(_1553138, _1553140)), tc_fun(_1553140, tc_fun(tc_fun(tc_prod(_1553138, _1553140), tc_HOL_Obool), tc_HOL_Obool)), _1553138), hAPP(c_COMBB(tc_prod(_1553138, _1553140), tc_fun(tc_fun(tc_prod(_1553138, _1553140), tc_HOL_Obool), tc_HOL_Obool), _1553140), c_member(tc_prod(_1553138, _1553140)))), c_Product__Type_OPair(_1553138, _1553140)))), _1553144))))), hAPP(hAPP(c_COMBC(_1553142, tc_fun(tc_prod(_1553140, _1553142), tc_HOL_Obool), tc_fun(_1553140, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553140, tc_fun(tc_fun(tc_prod(_1553140, _1553142), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1553140, _1553142), tc_HOL_Obool), tc_fun(_1553140, tc_HOL_Obool)), _1553142), c_COMBC(_1553140, tc_fun(tc_prod(_1553140, _1553142), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553140, tc_prod(_1553140, _1553142)), tc_fun(_1553140, tc_fun(tc_fun(tc_prod(_1553140, _1553142), tc_HOL_Obool), tc_HOL_Obool)), _1553142), hAPP(c_COMBB(tc_prod(_1553140, _1553142), tc_fun(tc_fun(tc_prod(_1553140, _1553142), tc_HOL_Obool), tc_HOL_Obool), _1553140), c_member(tc_prod(_1553140, _1553142)))), hAPP(c_COMBC(_1553140, _1553142, tc_prod(_1553140, _1553142)), c_Product__Type_OPair(_1553140, _1553142))))), _1553146))))))], (32596 ^ _781215) ^ [_1384918, _1384920, _1384922] : [32597 ^ _781215 : [(32600 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1384918), _1384922))], (32598 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1384918), _1384920))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1384918), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384918, tc_HOL_Obool)), _1384920), _1384922))))], (28234 ^ _781215) ^ [_1295246, _1295248, _1295250, _1295252] : [class_Fields_Olinordered__field__inverse__zero(_1295246), class_Int_Onumber(_1295246), 28241 ^ _781215 : [(28242 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), _1295248), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295246), _1295250), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252)))), 28245 ^ _781215 : [(28252 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), c_Groups_Ozero__class_Ozero(_1295246)), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252)))), 28255 ^ _781215 : [(28262 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252)), c_Groups_Ozero__class_Ozero(_1295246)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), _1295248), c_Groups_Ozero__class_Ozero(_1295246))))], (28256 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252)), c_Groups_Ozero__class_Ozero(_1295246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), _1295250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295246), _1295248), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252)))))]]], (28246 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), c_Groups_Ozero__class_Ozero(_1295246)), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295246), _1295248), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252))), _1295250)))]]], (28268 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), _1295248), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295246), _1295250), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252))))), 28271 ^ _781215 : [(28274 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295246), _1295248), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252))), _1295250))], (28272 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), c_Groups_Ozero__class_Ozero(_1295246)), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252))))]], 28275 ^ _781215 : [(28278 ^ _781215) ^ [] : [28279 ^ _781215 : [(28282 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), _1295250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295246), _1295248), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252))))], (28280 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252)), c_Groups_Ozero__class_Ozero(_1295246))))]], 28283 ^ _781215 : [(28286 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), _1295248), c_Groups_Ozero__class_Ozero(_1295246)))], (28284 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252)), c_Groups_Ozero__class_Ozero(_1295246)))]]], (28276 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295246), c_Groups_Ozero__class_Ozero(_1295246)), hAPP(c_Int_Onumber__class_Onumber__of(_1295246), _1295252)))]]]]], (6207 ^ _781215) ^ [_881195, _881197, _881199, _881201, _881203, _881205, _881207, _881209] : [c_Finite__Set_Ofolding__image__simple__idem(_881195, _881197, _881199, _881201, _881203, _881205), hBOOL(hAPP(c_Finite__Set_Ofinite(_881197), _881207)), -(hAPP(_881205, hAPP(hAPP(c_Set_Oinsert(_881197), _881209), _881207)) = hAPP(hAPP(_881199, hAPP(_881203, _881209)), hAPP(_881205, _881207)))], (45141 ^ _781215) ^ [_1687085, _1687087, _1687089] : [_1687085 = c_List_Olist_ONil(_1687087), -(c_List_Olast(_1687087, hAPP(hAPP(c_List_Olist_OCons(_1687087), _1687089), _1687085)) = _1687089)], (18479 ^ _781215) ^ [_1112145, _1112147, _1112149] : [class_Orderings_Olinorder(_1112145), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112145), _1112147)), -(_1112147 = c_Orderings_Obot__class_Obot(tc_fun(_1112145, tc_HOL_Obool))), 18490 ^ _781215 : [(18491 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112145), _1112149), hAPP(c_Finite__Set_Ofold1(_1112145, c_Orderings_Oord__class_Omin(_1112145)), _1112147))), 18494 ^ _781215 : [(18495 ^ _781215) ^ [_1112438] : [hBOOL(hAPP(hAPP(c_member(_1112145), _1112438), _1112147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112145), _1112149), _1112438)))]]], (18501 ^ _781215) ^ [] : [18503 ^ _781215 : [(18506 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112145), _1112149), 18502 ^ [_1112145, _1112147, _1112149]))], (18504 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112145), 18502 ^ [_1112145, _1112147, _1112149]), _1112147)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112145), _1112149), hAPP(c_Finite__Set_Ofold1(_1112145, c_Orderings_Oord__class_Omin(_1112145)), _1112147))))]]], (21942 ^ _781215) ^ [] : [-(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))))], (13234 ^ _781215) ^ [_1011321, _1011323] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011321), _1011323) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 13237 ^ _781215 : [(13240 ^ _781215) ^ [] : [-(_1011323 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13238 ^ _781215) ^ [] : [-(_1011321 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (40051 ^ _781215) ^ [_1563102, _1563104, _1563106] : [c_Wellfounded_Owf(_1563102, _1563104), -(c_Wellfounded_Owf(_1563102, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1563102, _1563102), tc_HOL_Obool)), _1563104), _1563106)))], (23616 ^ _781215) ^ [_1206675, _1206677, _1206679] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1206675, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206677), _1206679)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206677), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1206675), _1206677), _1206679))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1206675, _1206677)))], (39777 ^ _781215) ^ [_1555272, _1555274, _1555276, _1555278] : [hAPP(hAPP(c_Relation_Orel__comp(_1555272, _1555272, _1555272), _1555274), _1555276) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1555272, _1555272), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1555272, _1555272, _1555272), _1555278), _1555276) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1555272, _1555272), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1555272, _1555272, _1555272), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1555272, _1555272), tc_HOL_Obool)), _1555274), _1555278)), _1555276) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1555272, _1555272), tc_HOL_Obool)))], (26817 ^ _781215) ^ [_1268522, _1268524, _1268526] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1268522, _1268524), _1268526)), 26820 ^ _781215 : [(26821 ^ _781215) ^ [_1268607] : [hBOOL(hAPP(hAPP(_1268524, _1268607), _1268526)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1268522, _1268524), _1268607)))]]], (18407 ^ _781215) ^ [_1110721, _1110723, _1110725] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110721), _1110723)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110725), _1110723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1110721), _1110725)), _1110723))], (30842 ^ _781215) ^ [_1345932] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1345932))))], (39426 ^ _781215) ^ [_1542128, _1542130, _1542132, _1542134] : [-(c_Fun_Ooverride__on(_1542128, _1542130, _1542132, _1542134, c_Orderings_Obot__class_Obot(tc_fun(_1542128, tc_HOL_Obool))) = _1542132)], (4112 ^ _781215) ^ [_843637, _843639, _843641, _843643] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_843643, _843639) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_843641, _843637)), _843643 = _843641, _843639 = _843637], (9735 ^ _781215) ^ [_946545, _946547, _946549, _946551] : [class_Groups_Oordered__ab__semigroup__add(_946545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946545), _946547), _946549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946545), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946545), _946551), _946547)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946545), _946551), _946549))))], (4754 ^ _781215) ^ [_853240, _853242] : [_853242 = _853240, -(c_member(_853242) = c_member(_853240))], (16447 ^ _781215) ^ [_1072176, _1072178, _1072180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072176, tc_HOL_Obool)), _1072178), _1072180)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072176, tc_HOL_Obool)), _1072178), _1072180) = _1072180)], (4706 ^ _781215) ^ [_852530, _852532, _852534, _852536, _852538, _852540] : [-(c_Product__Type_Ointernal__split(_852540, _852536, _852532) = c_Product__Type_Ointernal__split(_852538, _852534, _852530)), _852540 = _852538, _852536 = _852534, _852532 = _852530], (15889 ^ _781215) ^ [_1060769, _1060771, _1060773, _1060775, _1060777, _1060779] : [c_Hoare__Mirabelle_Ohoare__derivs(_1060769, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1060769), tc_HOL_Obool)), _1060771), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1060769), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1060769, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1060769)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1060769, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1060769))), hAPP(hAPP(c_COMBB(tc_fun(_1060769, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1060769, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1060769))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1060769)), _1060773)), c_Com_Ocom_OBODY)), _1060775)), _1060777)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1060769), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1060769, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1060769)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1060769, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1060769))), hAPP(hAPP(c_COMBB(tc_fun(_1060769, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1060769, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1060769))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1060769)), _1060773)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1060775)), _1060777)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _1060779), _1060777)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1060769, _1060771, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1060769)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1060769), hAPP(_1060773, _1060779)), hAPP(c_Com_Ocom_OBODY, _1060779)), hAPP(_1060775, _1060779))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1060769), tc_HOL_Obool)))))], (31910 ^ _781215) ^ [_1369132, _1369134, _1369136, _1369138] : [class_Groups_Ocomm__monoid__add(_1369132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1369134), _1369136)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369132), _1369138), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1369134, _1369136)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369132), hAPP(_1369138, _1369134)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369132), _1369138), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1369134), _1369136))))], (12810 ^ _781215) ^ [_1004381, _1004383, _1004385, _1004387] : [class_Rings_Olinordered__ring__strict(_1004381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004381), _1004383), _1004385)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004381), _1004387), c_Groups_Ozero__class_Ozero(_1004381))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004381), _1004387), _1004385)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004381), _1004387), _1004383))))], (29376 ^ _781215) ^ [_1316525, _1316527, _1316529] : [class_Fields_Olinordered__field(_1316525), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316525), c_Groups_Ozero__class_Ozero(_1316525)), _1316527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316525), c_Groups_Ozero__class_Ozero(_1316525)), _1316529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316525), c_Groups_Ozero__class_Ozero(_1316525)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1316525), _1316527), _1316529))))], (46149 ^ _781215) ^ [_1707407, _1707409] : [c_List_Olist_ONil(_1707407) = hAPP(c_List_Orev(_1707407), _1707409), -(_1707409 = c_List_Olist_ONil(_1707407))], (49986 ^ _781215) ^ [_1795016, _1795018, _1795020, _1795022, _1795024, _1795026] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1795016, _1795016)), hAPP(hAPP(c_Product__Type_OPair(_1795016, _1795016), _1795018), _1795020)), _1795022)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1795016, _1795016)), hAPP(hAPP(c_Product__Type_OPair(_1795016, _1795016), _1795020), _1795024)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1795016, _1795016), tc_HOL_Obool), _1795026), _1795022))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1795016, _1795016)), hAPP(hAPP(c_Product__Type_OPair(_1795016, _1795016), _1795018), _1795024)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1795016, _1795016), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1795026)), _1795022))))], (43481 ^ _781215) ^ [_1649040, _1649042] : [43482 ^ _781215 : [(43483 ^ _781215) ^ [_1649086] : [hBOOL(hAPP(_1649040, _1649086))]], -(hBOOL(hAPP(_1649040, c_Hilbert__Choice_OEps(_1649042, _1649040))))], (35559 ^ _781215) ^ [_1449415, _1449417, _1449419] : [class_Orderings_Oorder(_1449415), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449415, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1449415, _1449417, _1449419)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1449415), _1449419)) = c_Orderings_Obot__class_Obot(tc_fun(_1449415, tc_HOL_Obool)))], (21061 ^ _781215) ^ [_1158397] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158397)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158397)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158397))], (37368 ^ _781215) ^ [_1490276, _1490278] : [c_Equiv__Relations_Oequivp(_1490276, hAPP(hAPP(c_COMBC(_1490276, tc_fun(tc_prod(_1490276, _1490276), tc_HOL_Obool), tc_fun(_1490276, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490276, tc_fun(tc_fun(tc_prod(_1490276, _1490276), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1490276, _1490276), tc_HOL_Obool), tc_fun(_1490276, tc_HOL_Obool)), _1490276), c_COMBC(_1490276, tc_fun(tc_prod(_1490276, _1490276), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490276, tc_prod(_1490276, _1490276)), tc_fun(_1490276, tc_fun(tc_fun(tc_prod(_1490276, _1490276), tc_HOL_Obool), tc_HOL_Obool)), _1490276), hAPP(c_COMBB(tc_prod(_1490276, _1490276), tc_fun(tc_fun(tc_prod(_1490276, _1490276), tc_HOL_Obool), tc_HOL_Obool), _1490276), c_member(tc_prod(_1490276, _1490276)))), c_Product__Type_OPair(_1490276, _1490276)))), _1490278)), -(c_Equiv__Relations_Oequiv(_1490276, c_Orderings_Otop__class_Otop(tc_fun(_1490276, tc_HOL_Obool)), _1490278))], (51772 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, v_c)))], (40150 ^ _781215) ^ [_1565181, _1565183, _1565185] : [-(hAPP(c_Set_Oimage(tc_prod(_1565181, _1565183), _1565181, c_Product__Type_Ofst(_1565181, _1565183)), _1565185) = hAPP(c_Relation_ODomain(_1565181, _1565183), _1565185))], (16852 ^ _781215) ^ [_1083831, _1083833, _1083835, _1083837, _1083839, _1083841, _1083843] : [c_Finite__Set_Ofun__left__comm(_1083831, _1083833, _1083835), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1083831, _1083833, _1083835, _1083837, _1083839), _1083841)), hBOOL(hAPP(hAPP(c_member(_1083831), _1083843), _1083839)), 16864 ^ _781215 : [(16867 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1083831, _1083833, _1083835, _1083837, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1083831, tc_HOL_Obool)), _1083839), hAPP(hAPP(c_Set_Oinsert(_1083831), _1083843), c_Orderings_Obot__class_Obot(tc_fun(_1083831, tc_HOL_Obool))))), 16863 ^ [_1083831, _1083833, _1083835, _1083837, _1083839, _1083841, _1083843])))], (16865 ^ _781215) ^ [] : [-(_1083841 = hAPP(hAPP(_1083835, _1083843), 16863 ^ [_1083831, _1083833, _1083835, _1083837, _1083839, _1083841, _1083843]))]]], (26783 ^ _781215) ^ [_1267757, _1267759, _1267761, _1267763, _1267765] : [hBOOL(hAPP(hAPP(_1267757, _1267759), _1267761)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1267763, _1267765, tc_HOL_Obool), _1267757), hAPP(hAPP(c_Product__Type_OPair(_1267763, _1267765), _1267759), _1267761))))], (8842 ^ _781215) ^ [_931135, _931137, _931139, _931141] : [class_Orderings_Oorder(_931135), _931137 = _931139, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931135), _931141), _931139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931135), _931141), _931137)))], (11476 ^ _781215) ^ [_981277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981277), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14974 ^ _781215) ^ [_1043743, _1043745, _1043747, _1043749] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043743), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043743), _1043745), _1043747)), hAPP(c_Int_Onumber__class_Onumber__of(_1043743), _1043749)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043743), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043743), _1043745), hAPP(c_Int_Onumber__class_Onumber__of(_1043743), _1043749))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043743), _1043747), hAPP(c_Int_Onumber__class_Onumber__of(_1043743), _1043749)))), class_Int_Onumber(_1043743), class_Rings_Osemiring(_1043743)], (7506 ^ _781215) ^ [_907431, _907433, _907435, _907437] : [class_Orderings_Oord(_907431), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907431), _907433), _907435)), _907435 = _907437, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907431), _907433), _907437)))], (41517 ^ _781215) ^ [_1597615, _1597617, _1597619, _1597621, _1597623, _1597625] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1597615, _1597617), _1597615, tc_prod(_1597619, _1597621), c_Product__Type_Ofst(_1597615, _1597617)), c_Product__Type_Omap__pair(_1597619, _1597615, _1597621, _1597617, _1597623, _1597625)) = hAPP(c_Fun_Ocomp(_1597619, _1597615, tc_prod(_1597619, _1597621), _1597623), c_Product__Type_Ofst(_1597619, _1597621)))], (31465 ^ _781215) ^ [] : [-(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))))))], (41833 ^ _781215) ^ [_1605189, _1605191, _1605193, _1605195] : [hBOOL(hAPP(c_List_Odistinct(_1605189), _1605191)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1605189, _1605193)), hAPP(hAPP(c_List_Ozip(_1605189, _1605193), _1605191), _1605195))))], (8720 ^ _781215) ^ [_929154, _929156, _929158] : [class_Orderings_Olinorder(_929154), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929154), _929156), _929158))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929154), _929158), _929156)))], (39186 ^ _781215) ^ [_1533816, _1533818] : [-(hAPP(c_Set_OCollect(_1533816), hAPP(c_fequal, _1533818)) = hAPP(hAPP(c_Set_Oinsert(_1533816), _1533818), c_Orderings_Obot__class_Obot(tc_fun(_1533816, tc_HOL_Obool))))], (46938 ^ _781215) ^ [_1725578, _1725580] : [-(c_Enum_Oenum__class_Oenum(tc_prod(_1725578, _1725580)) = c_Enum_Oproduct(_1725578, _1725580, c_Enum_Oenum__class_Oenum(_1725578), c_Enum_Oenum__class_Oenum(_1725580))), class_Enum_Oenum(_1725578), class_Enum_Oenum(_1725580)], (25760 ^ _781215) ^ [_1244963, _1244965] : [class_Rings_Oring__1(_1244963), 25763 ^ _781215 : [(25770 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244965), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1244963), _1244965) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1244963), hAPP(c_Int_Onat, _1244965)))], (25764 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244965), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1244963), _1244965) = hAPP(c_Groups_Ouminus__class_Ouminus(_1244963), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1244963), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1244965)))))]]], (2522 ^ _781215) ^ [_818672, _818674, _818676, _818678] : [-(c_Divides_Opdivmod(_818678, _818674) = c_Divides_Opdivmod(_818676, _818672)), _818678 = _818676, _818674 = _818672], (35955 ^ _781215) ^ [_1457200, _1457202, _1457204, _1457206, _1457208] : [-(hAPP(c_Product__Type_Osnd(_1457200, _1457202), hAPP(c_Product__Type_Oapsnd(_1457204, _1457202, _1457200, _1457206), _1457208)) = hAPP(_1457206, hAPP(c_Product__Type_Osnd(_1457200, _1457204), _1457208)))], (31593 ^ _781215) ^ [_1362134, _1362136, _1362138, _1362140] : [class_Groups_Ocomm__monoid__add(_1362134), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1362136), _1362138))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362136, _1362134), _1362140), _1362138) = c_Groups_Ozero__class_Ozero(_1362134))], (26578 ^ _781215) ^ [_1263435, _1263437, _1263439, _1263441, _1263443, _1263445] : [hBOOL(hAPP(hAPP(_1263435, _1263437), _1263439)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263441, tc_fun(_1263443, tc_HOL_Obool))), _1263445), _1263435), _1263437), _1263439)))], (34456 ^ _781215) ^ [_1426449, _1426451, _1426453] : [class_Lattices_Olattice(_1426449), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426449), _1426451)), 34463 ^ _781215 : [(34470 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1426449, tc_HOL_Obool)), _1426451), hAPP(hAPP(c_Set_Oinsert(_1426449), _1426453), c_Orderings_Obot__class_Obot(tc_fun(_1426449, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1426449, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1426449, hAPP(hAPP(c_Set_Oinsert(_1426449), _1426453), _1426451)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426449), _1426453), c_Big__Operators_Olattice__class_OInf__fin(_1426449, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1426449, tc_HOL_Obool)), _1426451), hAPP(hAPP(c_Set_Oinsert(_1426449), _1426453), c_Orderings_Obot__class_Obot(tc_fun(_1426449, tc_HOL_Obool)))))))], (34464 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1426449, tc_HOL_Obool)), _1426451), hAPP(hAPP(c_Set_Oinsert(_1426449), _1426453), c_Orderings_Obot__class_Obot(tc_fun(_1426449, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1426449, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1426449, hAPP(hAPP(c_Set_Oinsert(_1426449), _1426453), _1426451)) = _1426453)]]], (27452 ^ _781215) ^ [_1280895, _1280897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1280895), 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)), _1280897)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1280895), _1280897) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1280895, _1280897)))], (9693 ^ _781215) ^ [_945736, _945738, _945740, _945742] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_945736), 9696 ^ _781215 : [(9703 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945736), _945738), _945742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945736), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945736), _945738), _945740)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945736), _945742), _945740))))], (9697 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945736), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945736), _945738), _945740)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945736), _945742), _945740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945736), _945738), _945742)))]]], (45700 ^ _781215) ^ [_1697925, _1697927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1697925), _1697927)), -(c_List_Oupt(_1697927, _1697925) = c_List_Olist_ONil(tc_Nat_Onat))], (4620 ^ _781215) ^ [_851267, _851269, _851271, _851273] : [-(c_Nitpick_Oinverse__frac(_851273, _851269) = c_Nitpick_Oinverse__frac(_851271, _851267)), _851273 = _851271, _851269 = _851267], (16925 ^ _781215) ^ [_1085207] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085207), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085207)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1085207)))], (15552 ^ _781215) ^ [_1054091, _1054093, _1054095, _1054097, _1054099, _1054101] : [-(c_Map_Omap__comp(_1054091, _1054093, _1054095, _1054097, _1054099, _1054101) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1054093), _1054091, c_Option_Ooption_ONone(_1054093), _1054097), hAPP(_1054099, _1054101)))], (44212 ^ _781215) ^ [_1665059, _1665061, _1665063, _1665065, _1665067, _1665069] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665059)), _1665061) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665063)), _1665065), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665059)), _1665067) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665063)), _1665069), -(hAPP(hAPP(c_List_Ozip(_1665059, _1665063), hAPP(hAPP(c_List_Oappend(_1665059), _1665061), _1665067)), hAPP(hAPP(c_List_Oappend(_1665063), _1665065), _1665069)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1665059, _1665063)), hAPP(hAPP(c_List_Ozip(_1665059, _1665063), _1665061), _1665065)), hAPP(hAPP(c_List_Ozip(_1665059, _1665063), _1665067), _1665069)))], (46698 ^ _781215) ^ [_1720033, _1720035, _1720037] : [hBOOL(hAPP(c_List_Odistinct(_1720033), _1720035)), hBOOL(hAPP(hAPP(c_member(_1720033), _1720037), hAPP(c_List_Oset(_1720033), _1720035))), -(c_List_OtakeWhile(_1720033, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1720033), c_fNot), hAPP(hAPP(c_COMBC(_1720033, _1720033, tc_HOL_Obool), c_fequal), _1720037)), hAPP(c_List_Orev(_1720033), _1720035)) = hAPP(c_List_Orev(_1720033), hAPP(c_List_Otl(_1720033), c_List_OdropWhile(_1720033, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1720033), c_fNot), hAPP(hAPP(c_COMBC(_1720033, _1720033, tc_HOL_Obool), c_fequal), _1720037)), _1720035))))], (21428 ^ _781215) ^ [_1165777, _1165779] : [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)), _1165777)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1165779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1165777), _1165779)))], (46215 ^ _781215) ^ [_1708663, _1708665] : [class_Groups_Ocomm__monoid__add(_1708663), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1708663), hAPP(c_List_Orev(_1708663), _1708665)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1708663), _1708665))], (40752 ^ _781215) ^ [_1579938, _1579940, _1579942, _1579944] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1579938, _1579940)), _1579942), _1579944))), 40753 ^ _781215 : [(40760 ^ _781215) ^ [] : [hBOOL(hAPP(_1579938, _1579942)), 40763 ^ _781215 : [(40764 ^ _781215) ^ [_1580157] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1579940), _1579942), _1580157)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1579938, _1579940)), _1580157), _1579944))]]], (40754 ^ _781215) ^ [] : [_1579944 = _1579942, -(hBOOL(hAPP(_1579938, _1579942)))]]], (33250 ^ _781215) ^ [_1399557, _1399559, _1399561] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1399557, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399557, tc_HOL_Obool)), _1399559), _1399561)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399557, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1399557, tc_HOL_Obool)), _1399559)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1399557, tc_HOL_Obool)), _1399561)))], (11563 ^ _781215) ^ [_982949, _982951, _982953, _982955, _982957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_982949, tc_HOL_Obool)), _982951), _982953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_982955, tc_HOL_Obool)), hAPP(c_Set_Oimage(_982949, _982955, _982957), _982951)), hAPP(c_Set_Oimage(_982949, _982955, _982957), _982953))))], (42224 ^ _781215) ^ [_1615304, _1615306, _1615308] : [-(hBOOL(hAPP(hAPP(c_member(_1615304), _1615306), hAPP(c_List_Oset(_1615304), _1615308)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615304)), c_List_Oremove1(_1615304, _1615306, _1615308)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615304)), _1615308))], (4080 ^ _781215) ^ [_843115, _843117, _843119, _843121, _843123, _843125] : [-(c_Set_Oimage(_843125, _843121, _843117) = c_Set_Oimage(_843123, _843119, _843115)), _843125 = _843123, _843121 = _843119, _843117 = _843115], (25120 ^ _781215) ^ [_1234670, _1234672, _1234674, _1234676] : [class_Rings_Olinordered__semidom(_1234670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1234672), _1234674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234670), c_Groups_Ozero__class_Ozero(_1234670)), _1234676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234670), _1234676), c_Groups_Oone__class_Oone(_1234670))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234670), hAPP(hAPP(c_Power_Opower__class_Opower(_1234670), _1234676), _1234674)), hAPP(hAPP(c_Power_Opower__class_Opower(_1234670), _1234676), _1234672))))], (46233 ^ _781215) ^ [_1709104, _1709106] : [c_List_Oconcat(_1709104, _1709106) = c_List_Olist_ONil(_1709104), 46236 ^ _781215 : [(46237 ^ _781215) ^ [_1709195] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709104)), _1709195), hAPP(c_List_Oset(tc_List_Olist(_1709104)), _1709106))), -(_1709195 = c_List_Olist_ONil(_1709104))]]], (25572 ^ _781215) ^ [_1241427, _1241429, _1241431, _1241433, _1241435, _1241437] : [hBOOL(hAPP(hAPP(c_member(_1241427), _1241429), c_SetInterval_Oord_OgreaterThanAtMost(_1241427, _1241431, _1241433, _1241435, _1241437))), 25575 ^ _781215 : [(25578 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1241431, _1241429), _1241437)))], (25576 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1241433, _1241435), _1241429)))]]], (19758 ^ _781215) ^ [_1135795, _1135797, _1135799] : [class_Orderings_Olinorder(_1135795), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135795), _1135797)), hBOOL(hAPP(hAPP(c_member(_1135795), _1135799), _1135797)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1135795), _1135799), c_Big__Operators_Olattice_OSup__fin(_1135795, c_Orderings_Oord__class_Omax(_1135795), _1135797)) = _1135799)], (37031 ^ _781215) ^ [_1480873, _1480875, _1480877, _1480879, _1480881] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1480873, tc_fun(_1480875, tc_HOL_Obool)), _1480877), hAPP(hAPP(c_COMBB(tc_fun(_1480875, tc_HOL_Obool), tc_fun(_1480875, tc_HOL_Obool), _1480873), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480875, tc_HOL_Obool)), _1480879)), _1480881)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480875, tc_HOL_Obool)), _1480879), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1480873, tc_fun(_1480875, tc_HOL_Obool)), _1480877), _1480881)))], (35863 ^ _781215) ^ [_1455303, _1455305, _1455307] : [class_Groups_Oordered__ab__group__add__abs(_1455303), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455303), hAPP(c_Groups_Oabs__class_Oabs(_1455303), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1455303), _1455305), _1455307))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1455303), hAPP(c_Groups_Oabs__class_Oabs(_1455303), _1455305)), hAPP(c_Groups_Oabs__class_Oabs(_1455303), _1455307)))))], (38648 ^ _781215) ^ [_1520632, _1520634, _1520636, _1520638] : [-(_1520632 = c_Orderings_Obot__class_Obot(tc_fun(_1520634, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1520636, _1520634), _1520636, c_Product__Type_Ofst(_1520636, _1520634)), hAPP(hAPP(c_Product__Type_OSigma(_1520636, _1520634), _1520638), hAPP(c_COMBK(tc_fun(_1520634, tc_HOL_Obool), _1520636), _1520632))) = _1520638)], (41029 ^ _781215) ^ [_1586213] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1586213)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1586213), tc_HOL_Obool))))], (36127 ^ _781215) ^ [_1460553, _1460555, _1460557] : [class_Fields_Olinordered__field__inverse__zero(_1460553), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460553), c_Groups_Ozero__class_Ozero(_1460553)), _1460555)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1460553), hAPP(c_Groups_Oabs__class_Oabs(_1460553), _1460557)), _1460555) = hAPP(c_Groups_Oabs__class_Oabs(_1460553), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1460553), _1460557), _1460555)))], (43599 ^ _781215) ^ [_1652007, _1652009, _1652011, _1652013] : [-(_1652007 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652009)), _1652011)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1652009, hAPP(hAPP(c_List_Olist__update(_1652009, _1652011), _1652007), _1652013)) = hAPP(hAPP(c_List_Olist__update(_1652009, c_List_Obutlast(_1652009, _1652011)), _1652007), _1652013))], (17003 ^ _781215) ^ [_1086221] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1086221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086221), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (4694 ^ _781215) ^ [_852360, _852362] : [_852362 = _852360, -(c_List_Oappend(_852362) = c_List_Oappend(_852360))], (40229 ^ _781215) ^ [_1567125, _1567127, _1567129, _1567131] : [c_FunDef_Oreduction__pair(_1567125, _1567127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1567125, _1567125), tc_HOL_Obool)), _1567129), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1567125, _1567125), tc_HOL_Obool), tc_fun(tc_prod(_1567125, _1567125), tc_HOL_Obool)), _1567127))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1567125, _1567125), tc_HOL_Obool)), _1567131), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1567125, _1567125), tc_HOL_Obool), tc_fun(tc_prod(_1567125, _1567125), tc_HOL_Obool)), _1567127))), c_Wellfounded_Owf(_1567125, _1567131), -(c_Wellfounded_Owf(_1567125, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567125, _1567125), tc_HOL_Obool)), _1567129), _1567131)))], (21251 ^ _781215) ^ [_1161712, _1161714, _1161716, _1161718, _1161720, _1161722] : [hBOOL(hAPP(hAPP(c_member(_1161712), _1161714), _1161716)), hBOOL(hAPP(hAPP(c_member(_1161718), _1161720), hAPP(_1161722, _1161714))), -(hBOOL(hAPP(hAPP(c_member(_1161718), _1161720), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1161712, tc_fun(_1161718, tc_HOL_Obool)), _1161716), _1161722))))], (9889 ^ _781215) ^ [_949452, _949454, _949456] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949452), _949454)), _949456) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949452), _949456)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949454), _949456)))], (23801 ^ _781215) ^ [_1210208, _1210210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1210208), _1210210)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1210210, _1210208) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1210210), _1210208), _1210208))], (35417 ^ _781215) ^ [_1446683, _1446685] : [class_Orderings_Olinorder(_1446683), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1446683, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1446683), _1446685)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1446683), _1446685))], (37803 ^ _781215) ^ [_1499476, _1499478, _1499480, _1499482] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1499476), _1499478)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499476), _1499480)), -(_1499480 = c_Orderings_Obot__class_Obot(tc_fun(_1499476, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1499476, tc_HOL_Obool), tc_fun(_1499476, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1499476, tc_HOL_Obool), tc_fun(_1499476, tc_HOL_Obool)), _1499478), _1499480)), c_Wellfounded_Omax__ext(_1499476, _1499482)))), 37817 ^ _781215 : [(37820 ^ _781215) ^ [_1499881] : [hBOOL(hAPP(hAPP(c_member(_1499476), _1499881), _1499480)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1499476, _1499476)), hAPP(hAPP(c_Product__Type_OPair(_1499476, _1499476), 37816 ^ [_1499476, _1499478, _1499480, _1499482]), _1499881)), _1499482))], (37818 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1499476), 37816 ^ [_1499476, _1499478, _1499480, _1499482]), _1499478)))]]], (48964 ^ _781215) ^ [_1769541, _1769543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1769541)), hAPP(c_Code__Numeral_Onat__of, _1769543))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1769541), _1769543)))], (44940 ^ _781215) ^ [_1682625, _1682627, _1682629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1682625), _1682627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1682625), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1682627), _1682629))))], (6858 ^ _781215) ^ [_894215, _894217, _894219, _894221, _894223, _894225, _894227, _894229] : [c_Finite__Set_Ofolding__image__simple(_894215, _894217, _894219, _894221, _894223, _894225), hBOOL(hAPP(c_Finite__Set_Ofinite(_894217), _894227)), -(hAPP(_894225, hAPP(hAPP(c_Set_Oinsert(_894217), _894229), _894227)) = hAPP(hAPP(_894219, hAPP(_894223, _894229)), hAPP(_894225, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894217, tc_HOL_Obool)), _894227), hAPP(hAPP(c_Set_Oinsert(_894217), _894229), c_Orderings_Obot__class_Obot(tc_fun(_894217, tc_HOL_Obool)))))))], (20768 ^ _781215) ^ [_1153720, _1153722] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1153720) = _1153722, 20771 ^ _781215 : [(20774 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153722)))], (20772 ^ _781215) ^ [] : [-(_1153720 = hAPP(c_Int_Onat, _1153722))]]], (45316 ^ _781215) ^ [_1690283, _1690285, _1690287] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1690283, tc_HOL_Obool)), hAPP(c_List_Oset(_1690283), hAPP(c_List_Ofilter(_1690283, _1690285), _1690287))), hAPP(c_List_Oset(_1690283), _1690287))))], (14184 ^ _781215) ^ [_1028888, _1028890, _1028892] : [-(c_Option_Ooption_Ooption__size(_1028888, _1028890, hAPP(c_Option_Ooption_OSome(_1028888), _1028892)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1028890, _1028892)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43714 ^ _781215) ^ [_1654334, _1654336, _1654338] : [hAPP(hAPP(c_List_Otake(_1654334), _1654336), _1654338) = c_List_Olist_ONil(_1654334), -(_1654336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1654338 = c_List_Olist_ONil(_1654334))], (27450 ^ _781215) ^ [_1280860, _1280862] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1280860, _1280862) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1280860, _1280862)))], (46091 ^ _781215) ^ [_1705924, _1705926, _1705928] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1705924), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1705924))), _1705926))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1705928), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705924))), _1705926))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1705924), _1705924), hAPP(hAPP(c_COMBC(tc_List_Olist(_1705924), tc_Nat_Onat, _1705924), c_List_Onth(_1705924)), _1705928)), hAPP(c_List_Ofilter(tc_List_Olist(_1705924), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1705924)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1705928)), c_Nat_Osize__class_Osize(tc_List_Olist(_1705924)))), c_List_Otranspose(_1705924, _1705926))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1705924)), _1705926), _1705928))], (51346 ^ _781215) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (4988 ^ _781215) ^ [_857025, _857027] : [_857027 = _857025, -(c_Nat_Osize__class_Osize(_857027) = c_Nat_Osize__class_Osize(_857025))], (23839 ^ _781215) ^ [_1210926, _1210928] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1210926))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1210926)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1210928)) = 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), _1210928)))], (49343 ^ _781215) ^ [_1778793, _1778795, _1778797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778793, _1778793), tc_HOL_Obool)), _1778795), c_Transitive__Closure_Ortrancl(_1778793, _1778797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778793, _1778793), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1778793, _1778795)), c_Transitive__Closure_Ortrancl(_1778793, _1778797))))], (37875 ^ _781215) ^ [_1501155, _1501157] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1501155, tc_HOL_Obool), hAPP(c_Set_OPow(_1501155), _1501157)) = _1501157)], (49159 ^ _781215) ^ [_1773409, _1773411] : [-(c_Transitive__Closure_Otrancl(_1773409, _1773411) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1773409, _1773409), tc_HOL_Obool)), _1773411), hAPP(hAPP(c_Relation_Orel__comp(_1773409, _1773409, _1773409), c_Transitive__Closure_Otrancl(_1773409, _1773411)), _1773411)))], (40429 ^ _781215) ^ [_1572315, _1572317, _1572319] : [c_Relation_Orefl__on(_1572315, _1572317, _1572319), 40432 ^ _781215 : [(40439 ^ _781215) ^ [_1572799] : [hBOOL(hAPP(hAPP(c_member(_1572315), _1572799), _1572317)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572315, _1572315)), hAPP(hAPP(c_Product__Type_OPair(_1572315, _1572315), _1572799), _1572799)), _1572319)))], (40433 ^ _781215) ^ [_1572526] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572315, _1572315)), _1572526), _1572319)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1572315, _1572315, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1572315, tc_fun(_1572315, tc_HOL_Obool), tc_fun(_1572315, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1572315, tc_HOL_Obool), tc_fun(_1572315, tc_HOL_Obool)), _1572315), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1572315)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572315), c_fconj), hAPP(hAPP(c_COMBC(_1572315, tc_fun(_1572315, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572315)), _1572317)))), hAPP(hAPP(c_COMBC(_1572315, tc_fun(_1572315, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572315)), _1572317))), _1572526)))]]], (33529 ^ _781215) ^ [_1405654, _1405656, _1405658, _1405660, _1405662] : [class_Groups_Ocomm__monoid__mult(_1405654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405656), _1405658)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405656), _1405660)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1405654), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405656, _1405654), _1405662), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405656, tc_HOL_Obool)), _1405658), _1405660))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405656, _1405654), _1405662), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1405656, tc_HOL_Obool)), _1405658), _1405660))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1405654), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405656, _1405654), _1405662), _1405658)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405656, _1405654), _1405662), _1405660)))], (5736 ^ _781215) ^ [_871981, _871983] : [_871981 = _871983, -(hAPP(c_Com_Ocom_OBODY, _871981) = hAPP(c_Com_Ocom_OBODY, _871983))], (41587 ^ _781215) ^ [_1599402, _1599404, _1599406, _1599408, _1599410, _1599412, _1599414, _1599416] : [c_Finite__Set_Ofolding(_1599402, _1599404, _1599406, _1599408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599402), _1599410)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599402), _1599412)), -(hAPP(c_Fun_Ocomp(_1599404, _1599404, _1599414, hAPP(_1599408, _1599412)), hAPP(c_Fun_Ocomp(_1599404, _1599404, _1599414, hAPP(_1599408, _1599410)), _1599416)) = hAPP(c_Fun_Ocomp(_1599404, _1599404, _1599414, hAPP(_1599408, _1599410)), hAPP(c_Fun_Ocomp(_1599404, _1599404, _1599414, hAPP(_1599408, _1599412)), _1599416)))], (40176 ^ _781215) ^ [_1565723, _1565725, _1565727] : [c_Wellfounded_Owf(_1565723, _1565725), c_Wellfounded_Owf(_1565723, _1565727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565723, _1565723), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1565723, _1565723, _1565723), _1565725), _1565727)), _1565725)), -(c_Wellfounded_Owf(_1565723, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565723, _1565723), tc_HOL_Obool)), _1565725), _1565727)))], (41539 ^ _781215) ^ [_1598250, _1598252, _1598254, _1598256, _1598258, _1598260, _1598262] : [-(c_List_Ofoldr(_1598250, _1598252, _1598254, hAPP(hAPP(c_List_Omap(_1598256, _1598250), _1598258), _1598260), _1598262) = c_List_Ofoldr(_1598256, _1598252, hAPP(c_Fun_Ocomp(_1598250, tc_fun(_1598252, _1598252), _1598256, _1598254), _1598258), _1598260, _1598262))], (22320 ^ _781215) ^ [_1184090, _1184092, _1184094, _1184096] : [class_Divides_Osemiring__div(_1184090), -(c_Divides_Odiv__class_Omod(_1184090, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184090), _1184092), _1184094), _1184096) = c_Divides_Odiv__class_Omod(_1184090, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184090), c_Divides_Odiv__class_Omod(_1184090, _1184092, _1184096)), c_Divides_Odiv__class_Omod(_1184090, _1184094, _1184096)), _1184096))], (25960 ^ _781215) ^ [_1252093, _1252095, _1252097, _1252099] : [class_Rings_Ocomm__semiring__1(_1252093), hBOOL(hAPP(c_Finite__Set_Ofinite(_1252095), _1252097)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1252095, _1252093), _1252099), _1252097) = c_Groups_Ozero__class_Ozero(_1252093)), 25969 ^ _781215 : [(25970 ^ _781215) ^ [_1252274] : [hBOOL(hAPP(hAPP(c_member(_1252095), _1252274), _1252097)), hAPP(_1252099, _1252274) = c_Groups_Ozero__class_Ozero(_1252093)]]], (8690 ^ _781215) ^ [_928701, _928703] : [class_Groups_Ogroup__add(_928701), -(hAPP(c_Groups_Ouminus__class_Ouminus(_928701), hAPP(c_Groups_Ouminus__class_Ouminus(_928701), _928703)) = _928703)], (13098 ^ _781215) ^ [_1009331, _1009333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009331), hAPP(c_Nat_OSuc, _1009333))), -(_1009331 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 13106 ^ _781215 : [(13109 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13105 ^ [_1009331, _1009333]), _1009333)))], (13107 ^ _781215) ^ [] : [-(_1009331 = hAPP(c_Nat_OSuc, 13105 ^ [_1009331, _1009333]))]]], (38506 ^ _781215) ^ [_1516611, _1516613, _1516615, _1516617] : [38507 ^ _781215 : [(38510 ^ _781215) ^ [] : [_1516617 = c_Orderings_Obot__class_Obot(tc_fun(_1516613, tc_HOL_Obool))], (38508 ^ _781215) ^ [] : [_1516615 = c_Orderings_Obot__class_Obot(tc_fun(_1516611, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1516611, _1516613), _1516615), hAPP(c_COMBK(tc_fun(_1516613, tc_HOL_Obool), _1516611), _1516617)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516611, _1516613), tc_HOL_Obool)))], (12428 ^ _781215) ^ [_997408, _997410, _997412] : [class_Rings_Olinordered__ring__strict(_997408), 12431 ^ _781215 : [(12446 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997408), c_Groups_Ozero__class_Ozero(_997408)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997408), _997410), _997412)))), 12447 ^ _781215 : [(12454 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997408), _997410), c_Groups_Ozero__class_Ozero(_997408))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997408), _997412), c_Groups_Ozero__class_Ozero(_997408)))], (12448 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997408), c_Groups_Ozero__class_Ozero(_997408)), _997410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997408), c_Groups_Ozero__class_Ozero(_997408)), _997412))]]], (12432 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997408), c_Groups_Ozero__class_Ozero(_997408)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997408), _997410), _997412))), 12437 ^ _781215 : [(12440 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997408), c_Groups_Ozero__class_Ozero(_997408)), _997412)))], (12438 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997408), c_Groups_Ozero__class_Ozero(_997408)), _997410)))]], 12441 ^ _781215 : [(12444 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997408), _997412), c_Groups_Ozero__class_Ozero(_997408))))], (12442 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997408), _997410), c_Groups_Ozero__class_Ozero(_997408))))]]]]], (49357 ^ _781215) ^ [_1779152, _1779154, _1779156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1779152, _1779152), tc_HOL_Obool)), c_Relation_OId(_1779152)), _1779154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1779152, _1779152), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1779152, _1779152, _1779152), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1779152, _1779152), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1779152, _1779156)), _1779154)), _1779156)), _1779154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1779152, _1779152), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1779152, _1779156)), _1779154)))], (21452 ^ _781215) ^ [_1166219, _1166221] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1166219) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1166221), -(_1166219 = _1166221)], (51666 ^ _781215) ^ [_1825573, _1825575, _1825577, _1825579] : [-(hAPP(hAPP(c_COMBK(_1825573, _1825575), _1825577), _1825579) = _1825577)], (51114 ^ _781215) ^ [_1819984, _1819986] : [class_Orderings_Oorder(_1819984), -(class_Orderings_Oorder(tc_fun(_1819986, _1819984)))], (26938 ^ _781215) ^ [_1270814, _1270816, _1270818, _1270820, _1270822, _1270824] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1270814, _1270816, _1270818), _1270820), hAPP(hAPP(c_Product__Type_OPair(_1270814, _1270816), _1270822), _1270824)) = hAPP(hAPP(_1270820, _1270822), _1270824))], (38484 ^ _781215) ^ [_1515948, _1515950, _1515952, _1515954, _1515956] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1515948, _1515950), _1515952), hAPP(hAPP(c_COMBS(_1515948, tc_fun(_1515950, tc_HOL_Obool), tc_fun(_1515950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515950, tc_HOL_Obool), tc_fun(tc_fun(_1515950, tc_HOL_Obool), tc_fun(_1515950, tc_HOL_Obool)), _1515948), c_Groups_Ominus__class_Ominus(tc_fun(_1515950, tc_HOL_Obool))), _1515954)), _1515956)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1515948, _1515950), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1515948, _1515950), _1515952), _1515954)), hAPP(hAPP(c_Product__Type_OSigma(_1515948, _1515950), _1515952), _1515956)))], (21632 ^ _781215) ^ [_1169310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1169310))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1169310)))], (13086 ^ _781215) ^ [_1009106, _1009108] : [class_Groups_Ogroup__add(_1009106), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009106), _1009108), hAPP(c_Groups_Ouminus__class_Ouminus(_1009106), _1009108)) = c_Groups_Ozero__class_Ozero(_1009106))], (48944 ^ _781215) ^ [_1769136, _1769138] : [-(c_Random_Oselect(_1769136, _1769138) = 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(_1769136, 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(_1769136)), _1769138)))), hAPP(hAPP(c_COMBB(_1769136, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1769136, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1769136, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1769136, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1769136), _1769138)), c_Code__Numeral_Onat__of))))], (31399 ^ _781215) ^ [_1356580, _1356582] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1356580), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1356582), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1356580, _1356582))], (2700 ^ _781215) ^ [_821421, _821423, _821425, _821427, _821429, _821431, _821433, _821435, _821437, _821439] : [-(c_Fun_Ooverride__on(_821439, _821435, _821431, _821427, _821423) = c_Fun_Ooverride__on(_821437, _821433, _821429, _821425, _821421)), _821439 = _821437, _821435 = _821433, _821431 = _821429, _821427 = _821425, _821423 = _821421], (18572 ^ _781215) ^ [_1113851, _1113853, _1113855] : [class_Orderings_Olinorder(_1113851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113851), _1113853)), -(_1113853 = c_Orderings_Obot__class_Obot(tc_fun(_1113851, tc_HOL_Obool))), 18583 ^ _781215 : [(18593 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113851), hAPP(c_Finite__Set_Ofold1(_1113851, c_Orderings_Oord__class_Omin(_1113851)), _1113853)), _1113855))), 18594 ^ _781215 : [(18595 ^ _781215) ^ [_1114240] : [hBOOL(hAPP(hAPP(c_member(_1113851), _1114240), _1113853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113851), _1114240), _1113855))]]], (18584 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113851), hAPP(c_Finite__Set_Ofold1(_1113851, c_Orderings_Oord__class_Omin(_1113851)), _1113853)), _1113855)), 18588 ^ _781215 : [(18591 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113851), 18587 ^ [_1113851, _1113853, _1113855]), _1113855)))], (18589 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1113851), 18587 ^ [_1113851, _1113853, _1113855]), _1113853)))]]]]], (29980 ^ _781215) ^ [_1328533, _1328535] : [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), _1328533), _1328535)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1328533), _1328535)))], (51468 ^ _781215) ^ [_1823419] : [-(class_HOL_Oequal(tc_List_Olist(_1823419)))], (1278 ^ _781215) ^ [_800160, _800162] : [-(class_Rings_Oring(_800160)), _800162 = _800160, class_Rings_Oring(_800162)], (8776 ^ _781215) ^ [_930054, _930056, _930058, _930060] : [class_Orderings_Opreorder(_930054), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930054), _930056), _930058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930054), _930058), _930060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930054), _930056), _930060)))], (31461 ^ _781215) ^ [_1358270] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1358270)) = _1358270)], (44566 ^ _781215) ^ [_1674352, _1674354, _1674356] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674352)), hAPP(hAPP(c_List_Odrop(_1674352), _1674354), _1674356)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674352)), _1674356)), _1674354))], (42963 ^ _781215) ^ [_1636061, _1636063, _1636065, _1636067] : [hBOOL(hAPP(hAPP(c_member(_1636061), _1636063), hAPP(c_List_Oset(_1636061), hAPP(hAPP(c_List_Otake(_1636061), _1636065), _1636067)))), -(hBOOL(hAPP(hAPP(c_member(_1636061), _1636063), hAPP(c_List_Oset(_1636061), _1636067))))], (38822 ^ _781215) ^ [_1525704, _1525706, _1525708] : [-(hAPP(c_Product__Type_Omap__pair(_1525704, _1525704, _1525706, _1525706, c_COMBI(_1525704), c_COMBI(_1525706)), _1525708) = _1525708)], (50982 ^ _781215) ^ [_1817912, _1817914, _1817916, _1817918] : [-(c_Lazy__Sequence_Oappend(_1817912, c_Lazy__Sequence_Olazy__sequence_OInsert(_1817912, _1817914, _1817916), _1817918) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1817912, _1817914, c_Lazy__Sequence_Oappend(_1817912, _1817916, _1817918)))], (24180 ^ _781215) ^ [_1217393, _1217395] : [class_Rings_Oring__1__no__zero__divisors(_1217393), 24183 ^ _781215 : [(24190 ^ _781215) ^ [] : [_1217395 = c_Groups_Ozero__class_Ozero(_1217393), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1217393), _1217395), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1217393))], (24184 ^ _781215) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1217393), _1217395), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1217393), -(_1217395 = c_Groups_Ozero__class_Ozero(_1217393))]]], (31409 ^ _781215) ^ [_1356787, _1356789] : [class_Orderings_Oorder(_1356787), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356787, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1356787), _1356789), c_Orderings_Obot__class_Obot(tc_fun(_1356787, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1356787), _1356789)) = hAPP(hAPP(c_Set_Oinsert(_1356787), _1356789), c_Orderings_Obot__class_Obot(tc_fun(_1356787, tc_HOL_Obool))))], (38985 ^ _781215) ^ [_1529641, _1529643, _1529645, _1529647, _1529649, _1529651, _1529653] : [c_Finite__Set_Ofun__left__comm(_1529641, _1529643, _1529645), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1529641, _1529643, _1529645, _1529647, hAPP(hAPP(c_Set_Oinsert(_1529641), _1529649), _1529651)), _1529653)), -(hBOOL(hAPP(hAPP(c_member(_1529641), _1529649), _1529651))), 38997 ^ _781215 : [(39000 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1529641, _1529643, _1529645, _1529647, _1529651), 38996 ^ [_1529641, _1529643, _1529645, _1529647, _1529649, _1529651, _1529653])))], (38998 ^ _781215) ^ [] : [-(_1529653 = hAPP(hAPP(_1529645, _1529649), 38996 ^ [_1529641, _1529643, _1529645, _1529647, _1529649, _1529651, _1529653]))]]], (23634 ^ _781215) ^ [_1207164, _1207166, _1207168, _1207170] : [class_Rings_Ocomm__semiring__1(_1207164), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1207164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207164), _1207166), _1207168)), _1207170) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207164), hAPP(hAPP(c_Power_Opower__class_Opower(_1207164), _1207166), _1207170)), hAPP(hAPP(c_Power_Opower__class_Opower(_1207164), _1207168), _1207170)))], (27146 ^ _781215) ^ [_1274838, _1274840, _1274842, _1274844, _1274846] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1274838, _1274840), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1274842), _1274844))), -(_1274840 = 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)), _1274846)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1274838, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1274840), _1274846)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1274842), _1274846)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1274840), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1274842, _1274846))), _1274844)))))], (37679 ^ _781215) ^ [_1497144, _1497146, _1497148, _1497150, _1497152] : [c_Typedef_Otype__definition(_1497144, _1497146, _1497148, _1497150, _1497152), -(hAPP(c_Set_Oimage(_1497146, _1497144, _1497150), _1497152) = c_Orderings_Otop__class_Otop(tc_fun(_1497144, tc_HOL_Obool)))], (37175 ^ _781215) ^ [_1484928, _1484930, _1484932, _1484934, _1484936] : [-(_1484928 = c_Orderings_Obot__class_Obot(tc_fun(_1484930, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484930, tc_fun(_1484932, tc_HOL_Obool)), _1484928), hAPP(hAPP(c_COMBB(tc_fun(_1484932, tc_HOL_Obool), tc_fun(_1484932, tc_HOL_Obool), _1484930), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484932, tc_HOL_Obool)), _1484934)), _1484936)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484932, tc_HOL_Obool)), _1484934), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484930, tc_fun(_1484932, tc_HOL_Obool)), _1484928), _1484936)))], (5973 ^ _781215) ^ [_876342, _876344, _876346] : [c_Hoare__Mirabelle_Ohoare__derivs(_876342, _876344, _876346), -(c_Hoare__Mirabelle_Ohoare__valids(_876342, _876344, _876346))], (35363 ^ _781215) ^ [_1445771, _1445773, _1445775] : [class_Orderings_Olinorder(_1445771), 35366 ^ _781215 : [(35373 ^ _781215) ^ [] : [_1445773 = _1445775, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1445771), _1445773) = hAPP(c_SetInterval_Oord__class_OatLeast(_1445771), _1445775))], (35367 ^ _781215) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1445771), _1445773) = hAPP(c_SetInterval_Oord__class_OatLeast(_1445771), _1445775), -(_1445773 = _1445775)]]], (35117 ^ _781215) ^ [_1440421, _1440423, _1440425, _1440427, _1440429, _1440431, _1440433] : [c_Big__Operators_Ocomm__monoid__big(_1440421, _1440423, _1440425, _1440427, _1440429), 35120 ^ _781215 : [(35127 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1440423), _1440431))), -(hAPP(hAPP(_1440429, _1440433), _1440431) = _1440427)], (35121 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1440423), _1440431)), -(hAPP(hAPP(_1440429, _1440433), _1440431) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1440421, _1440423, _1440425), _1440433), _1440427), _1440431))]]], (24750 ^ _781215) ^ [_1227898, _1227900, _1227902] : [class_Rings_Osemiring__1(_1227898), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1227898), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1227900), _1227902)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1227898), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1227898), _1227900)), _1227902))], (10280 ^ _781215) ^ [_956326, _956328, _956330, _956332] : [c_Hoare__Mirabelle_Ohoare__derivs(_956326, _956328, _956330), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_956326), tc_HOL_Obool)), _956328), _956332)), -(c_Hoare__Mirabelle_Ohoare__derivs(_956326, _956332, _956330))], (21808 ^ _781215) ^ [_1172483, _1172485, _1172487, _1172489, _1172491] : [hBOOL(hAPP(hAPP(c_member(_1172483), _1172485), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1172487, tc_fun(_1172483, tc_HOL_Obool)), _1172489), _1172491))), 21812 ^ _781215 : [(21815 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1172483), _1172485), hAPP(_1172491, 21811 ^ [_1172483, _1172485, _1172487, _1172489, _1172491]))))], (21813 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1172487), 21811 ^ [_1172483, _1172485, _1172487, _1172489, _1172491]), _1172489)))]]], (38886 ^ _781215) ^ [_1527434, _1527436, _1527438, _1527440, _1527442] : [c_Relation_Orefl__on(_1527434, _1527436, _1527438), c_Relation_Orefl__on(_1527434, _1527440, _1527442), -(c_Relation_Orefl__on(_1527434, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1527434, tc_HOL_Obool)), _1527436), _1527440), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1527434, _1527434), tc_HOL_Obool)), _1527438), _1527442)))], (15394 ^ _781215) ^ [_1051125, _1051127] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1051125), _1051127)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1051125)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1051127)))], (46884 ^ _781215) ^ [_1724182, _1724184] : [-(c_Enum_On__lists(_1724182, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1724184) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1724182)), c_List_Olist_ONil(_1724182)), c_List_Olist_ONil(tc_List_Olist(_1724182))))], (4166 ^ _781215) ^ [_844454, _844456, _844458, _844460] : [-(c_List_Ofilter(_844460, _844456) = c_List_Ofilter(_844458, _844454)), _844460 = _844458, _844456 = _844454], (43914 ^ _781215) ^ [_1658124, _1658126, _1658128] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1658124))), -(c_List_Osublist(_1658126, hAPP(hAPP(c_List_Olist_OCons(_1658126), _1658128), c_List_Olist_ONil(_1658126)), _1658124) = c_List_Olist_ONil(_1658126))], (6600 ^ _781215) ^ [_889115, _889117, _889119, _889121, _889123] : [c_Finite__Set_Ofolding__one(_889115, _889117, _889119), hBOOL(hAPP(c_Finite__Set_Ofinite(_889115), _889121)), hBOOL(hAPP(hAPP(c_member(_889115), _889123), _889121)), 6611 ^ _781215 : [(6618 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889115, tc_HOL_Obool)), _889121), hAPP(hAPP(c_Set_Oinsert(_889115), _889123), c_Orderings_Obot__class_Obot(tc_fun(_889115, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_889115, tc_HOL_Obool))), -(hAPP(_889119, _889121) = hAPP(hAPP(_889117, _889123), hAPP(_889119, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889115, tc_HOL_Obool)), _889121), hAPP(hAPP(c_Set_Oinsert(_889115), _889123), c_Orderings_Obot__class_Obot(tc_fun(_889115, tc_HOL_Obool)))))))], (6612 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889115, tc_HOL_Obool)), _889121), hAPP(hAPP(c_Set_Oinsert(_889115), _889123), c_Orderings_Obot__class_Obot(tc_fun(_889115, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_889115, tc_HOL_Obool)), -(hAPP(_889119, _889121) = _889123)]]], (25590 ^ _781215) ^ [_1241773, _1241775] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1241773, _1241775))))], (51304 ^ _781215) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (8532 ^ _781215) ^ [_925972, _925974, _925976] : [class_Groups_Oordered__ab__group__add(_925972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925972), _925974), _925976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925972), hAPP(c_Groups_Ouminus__class_Ouminus(_925972), _925976)), hAPP(c_Groups_Ouminus__class_Ouminus(_925972), _925974))))], (48652 ^ _781215) ^ [_1763682, _1763684, _1763686] : [c_List_Olist__ex(_1763682, _1763684, _1763686), -(c_List_Olist__ex(_1763682, _1763684, hAPP(c_List_Orev(_1763682), _1763686)))], (33320 ^ _781215) ^ [_1401003, _1401005, _1401007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401003, tc_HOL_Obool)), _1401005), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1401003, tc_HOL_Obool)), _1401007))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401003, tc_HOL_Obool)), _1401005), _1401007) = c_Orderings_Obot__class_Obot(tc_fun(_1401003, tc_HOL_Obool)))], (36993 ^ _781215) ^ [_1479837, _1479839, _1479841, _1479843, _1479845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479837, tc_HOL_Obool)), _1479839), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479841, tc_fun(_1479837, tc_HOL_Obool)), _1479843), _1479845))), 36996 ^ _781215 : [(36997 ^ _781215) ^ [_1479970] : [hBOOL(hAPP(hAPP(c_member(_1479841), _1479970), _1479843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479837, tc_HOL_Obool)), _1479839), hAPP(_1479845, _1479970))))]]], (21522 ^ _781215) ^ [_1167447] : [c_Int_OPls = c_Int_OBit0(_1167447), -(c_Int_OPls = _1167447)], (31535 ^ _781215) ^ [_1360608, _1360610, _1360612, _1360614] : [class_Rings_Oring__1(_1360608), -(hAPP(c_Int_Oring__1__class_Oof__int(_1360608), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360610, tc_Int_Oint), _1360612), _1360614)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360610, _1360608), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1360608, _1360610), c_Int_Oring__1__class_Oof__int(_1360608)), _1360612)), _1360614))], (42783 ^ _781215) ^ [_1631292, _1631294, _1631296, _1631298] : [_1631292 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1631294), hAPP(hAPP(c_List_Olist_OCons(_1631294), _1631296), _1631298)), _1631292) = _1631296)], (40305 ^ _781215) ^ [_1569257, _1569259, _1569261, _1569263] : [40306 ^ _781215 : [(40307 ^ _781215) ^ [_1569311] : [hBOOL(hAPP(hAPP(_1569261, _1569263), _1569311))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1569257, _1569259, _1569261), _1569263)))], (13882 ^ _781215) ^ [_1023043, _1023045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1023043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1023045)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1023043), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023043), _1023045))))], (14948 ^ _781215) ^ [_1043289, _1043291, _1043293] : [class_Rings_Olinordered__idom(_1043289), -(c_Groups_Osgn__class_Osgn(_1043289, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043289), _1043291), _1043293)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043289), c_Groups_Osgn__class_Osgn(_1043289, _1043291)), c_Groups_Osgn__class_Osgn(_1043289, _1043293)))], (2678 ^ _781215) ^ [_821032, _821034, _821036, _821038, _821040, _821042, _821044, _821046, _821048, _821050] : [-(c_Finite__Set_Ofold__graph(_821050, _821046, _821042, _821038, _821034) = c_Finite__Set_Ofold__graph(_821048, _821044, _821040, _821036, _821032)), _821050 = _821048, _821046 = _821044, _821042 = _821040, _821038 = _821036, _821034 = _821032], (2658 ^ _781215) ^ [_820726, _820728, _820730, _820732, _820734, _820736] : [-(c_Partial__Function_Oflat__lub(_820736, _820732, _820728) = c_Partial__Function_Oflat__lub(_820734, _820730, _820726)), _820736 = _820734, _820732 = _820730, _820728 = _820726], (17941 ^ _781215) ^ [_1101550, _1101552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1101550), _1101552)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1101552), _1101550)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1101552)), hAPP(c_Int_Onat, _1101550)))], (44828 ^ _781215) ^ [_1680244, _1680246, _1680248] : [-(hAPP(hAPP(c_List_Odrop(_1680244), _1680246), hAPP(c_List_Otl(_1680244), _1680248)) = hAPP(c_List_Otl(_1680244), hAPP(hAPP(c_List_Odrop(_1680244), _1680246), _1680248)))], (38684 ^ _781215) ^ [_1521694, _1521696, _1521698, _1521700] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1521694, _1521696), _1521698), _1521700) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1521694, tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool)), _1521698), hAPP(hAPP(c_COMBS(_1521694, tc_fun(_1521696, tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool)), tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1521696, tc_HOL_Obool), tc_fun(tc_fun(_1521696, tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool)), tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool)), _1521694), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1521696, tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool))), _1521700)), hAPP(hAPP(c_COMBC(_1521694, tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool), tc_fun(_1521696, tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1521696, tc_fun(tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool), tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool), tc_fun(_1521696, tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool))), _1521694), c_COMBC(_1521696, tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool), tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1521696, tc_prod(_1521694, _1521696)), tc_fun(_1521696, tc_fun(tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool), tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool))), _1521694), hAPP(c_COMBB(tc_prod(_1521694, _1521696), tc_fun(tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool), tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool)), _1521696), c_Set_Oinsert(tc_prod(_1521694, _1521696)))), c_Product__Type_OPair(_1521694, _1521696)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521694, _1521696), tc_HOL_Obool))))))], (6802 ^ _781215) ^ [_893076, _893078, _893080] : [_893078 = _893080, -(hBOOL(hAPP(hAPP(c_member(_893076), _893078), hAPP(hAPP(c_Set_Oinsert(_893076), _893080), c_Orderings_Obot__class_Obot(tc_fun(_893076, tc_HOL_Obool))))))], (42028 ^ _781215) ^ [_1610245, _1610247, _1610249, _1610251, _1610253] : [class_Orderings_Olinorder(_1610245), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610247)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1610247, _1610245, _1610249), _1610251), _1610253)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610247)), _1610253)))], (51184 ^ _781215) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (35205 ^ _781215) ^ [_1442289, _1442291, _1442293] : [class_Lattices_Olattice(_1442289), hAPP(_1442291, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1442289), 35210 ^ [_1442289, _1442291, _1442293]), 35211 ^ [_1442289, _1442291, _1442293])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1442289), hAPP(_1442291, 35210 ^ [_1442289, _1442291, _1442293])), hAPP(_1442291, 35211 ^ [_1442289, _1442291, _1442293])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442289), _1442293)), -(_1442293 = c_Orderings_Obot__class_Obot(tc_fun(_1442289, tc_HOL_Obool))), -(hAPP(_1442291, c_Big__Operators_Olattice__class_OInf__fin(_1442289, _1442293)) = c_Big__Operators_Olattice__class_OInf__fin(_1442289, hAPP(c_Set_Oimage(_1442289, _1442289, _1442291), _1442293)))], (31495 ^ _781215) ^ [_1359248, _1359250, _1359252, _1359254] : [class_Rings_Ocomm__semiring__1(_1359248), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1359248), c_Groups_Oone__class_Oone(_1359248)), c_Groups_Oone__class_Oone(_1359248))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1359248), hAPP(hAPP(c_COMBB(_1359248, _1359248, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1359248), _1359250)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1359248, _1359248), hAPP(hAPP(c_COMBB(_1359248, tc_fun(_1359248, _1359248), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1359248)), c_Nat_Osemiring__1__class_Oof__nat(_1359248))), _1359252))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1359254))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359248), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1359248), _1359254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1359248), _1359250), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1359248), _1359250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359248), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1359248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1359254), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1359252)))))], (50878 ^ _781215) ^ [_1815039, _1815041] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1815039), _1815041)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1815039)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1815041))))], (37332 ^ _781215) ^ [_1489123, _1489125, _1489127, _1489129, _1489131, _1489133, _1489135] : [37334 ^ _781215 : [(37337 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1489131, 37333 ^ [_1489123, _1489125, _1489127, _1489129, _1489131, _1489133, _1489135]), _1489133), _1489135))], (37335 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1489123), 37333 ^ [_1489123, _1489125, _1489127, _1489129, _1489131, _1489133, _1489135]), _1489129)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1489123, tc_fun(_1489125, tc_fun(_1489127, tc_HOL_Obool))), _1489129), _1489131), _1489133), _1489135)))], (39715 ^ _781215) ^ [_1553002, _1553004] : [39716 ^ _781215 : [(39717 ^ _781215) ^ [_1553066, _1553068] : [_1553004 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1553002, _1553066), 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)), _1553068)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1553002), _1553004)))], (28850 ^ _781215) ^ [_1307077, _1307079, _1307081, _1307083] : [class_Fields_Olinordered__field(_1307077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307077), c_Groups_Ozero__class_Ozero(_1307077)), _1307079)), 28857 ^ _781215 : [(28864 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307077), _1307081), _1307079)), _1307083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307077), _1307081), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307077), _1307083), _1307079))))], (28858 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307077), _1307081), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307077), _1307083), _1307079))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307077), _1307081), _1307079)), _1307083)))]]], (17833 ^ _781215) ^ [_1099732] : [class_Rings_Osemiring__1(_1099732), -(hBOOL(hAPP(hAPP(c_member(_1099732), c_Groups_Oone__class_Oone(_1099732)), c_Nat_Osemiring__1__class_ONats(_1099732))))], (21490 ^ _781215) ^ [_1166864, _1166866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1166864), _1166866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1166864)), c_Int_OBit0(_1166866))))], (40097 ^ _781215) ^ [_1563883, _1563885] : [hBOOL(hAPP(hAPP(c_member(_1563883), 40098 ^ [_1563883, _1563885]), c_Wellfounded_Oacc(_1563883, _1563885))), -(c_Wellfounded_Owf(_1563883, _1563885))], (50758 ^ _781215) ^ [] : [-(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)))], (40057 ^ _781215) ^ [_1563209, _1563211] : [c_Wellfounded_Owf(_1563209, _1563211), -(c_Wellfounded_Owf(tc_fun(_1563209, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1563209, _1563211)))], (37592 ^ _781215) ^ [_1495196] : [class_Complete__Lattice_Ocomplete__lattice(_1495196), -(c_Complete__Lattice_OInf__class_OInf(_1495196, c_Orderings_Otop__class_Otop(tc_fun(_1495196, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1495196))], (41443 ^ _781215) ^ [_1595850, _1595852, _1595854, _1595856, _1595858] : [class_Groups_Ocomm__monoid__mult(_1595850), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595852), _1595854)), c_Fun_Oinj__on(_1595852, _1595852, _1595856, _1595854), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1595852, _1595850), _1595858), hAPP(c_Set_Oimage(_1595852, _1595852, _1595856), _1595854)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1595852, _1595850), hAPP(c_Fun_Ocomp(_1595852, _1595850, _1595852, _1595858), _1595856)), _1595854))], (21846 ^ _781215) ^ [_1173420, _1173422, _1173424] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1173420, tc_fun(_1173422, tc_HOL_Obool)), _1173424), hAPP(c_COMBK(tc_fun(_1173422, tc_HOL_Obool), _1173420), c_Orderings_Obot__class_Obot(tc_fun(_1173422, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1173422, tc_HOL_Obool)))], (49911 ^ _781215) ^ [_1793190, _1793192, _1793194, _1793196, _1793198] : [c_Relation_Osingle__valued(_1793190, _1793190, _1793192), hBOOL(hAPP(hAPP(c_member(tc_prod(_1793190, _1793190)), hAPP(hAPP(c_Product__Type_OPair(_1793190, _1793190), _1793194), _1793196)), c_Transitive__Closure_Ortrancl(_1793190, _1793192))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1793190, _1793190)), hAPP(hAPP(c_Product__Type_OPair(_1793190, _1793190), _1793194), _1793198)), c_Transitive__Closure_Ortrancl(_1793190, _1793192))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1793190, _1793190)), hAPP(hAPP(c_Product__Type_OPair(_1793190, _1793190), _1793196), _1793198)), c_Transitive__Closure_Ortrancl(_1793190, _1793192)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1793190, _1793190)), hAPP(hAPP(c_Product__Type_OPair(_1793190, _1793190), _1793198), _1793196)), c_Transitive__Closure_Ortrancl(_1793190, _1793192))))], (3568 ^ _781215) ^ [_835289, _835291, _835293, _835295] : [-(c_List_Obutlast(_835295, _835291) = c_List_Obutlast(_835293, _835289)), _835295 = _835293, _835291 = _835289], (2552 ^ _781215) ^ [_819119, _819121, _819123, _819125, _819127, _819129, _819131, _819133] : [-(c_Sum__Type_OPlus(_819133, _819129, _819125, _819121) = c_Sum__Type_OPlus(_819131, _819127, _819123, _819119)), _819133 = _819131, _819129 = _819127, _819125 = _819123, _819121 = _819119], (50906 ^ _781215) ^ [_1815744, _1815746, _1815748] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1815744, _1815746), _1815748) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1815744, tc_Lazy__Sequence_Olazy__sequence(_1815744)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1815744, tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1815744, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_Nat_Onat)), _1815744), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1815744), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1815744)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1815744, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1815744), tc_Nat_Onat)), _1815744), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1815744))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1815744), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1815746))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1815744, _1815746))))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1815744), _1815748)))], (21458 ^ _781215) ^ [_1166310] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1166310) = 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)), _1166310)))], (27524 ^ _781215) ^ [_1282141, _1282143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1282141), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1282143), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1282141), _1282143) = 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), _1282141), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1282143)))))], (1638 ^ _781215) ^ [_804660, _804662] : [-(class_Rings_Ono__zero__divisors(_804660)), _804662 = _804660, class_Rings_Ono__zero__divisors(_804662)], (34073 ^ _781215) ^ [_1417396, _1417398, _1417400, _1417402, _1417404, _1417406, _1417408, _1417410, _1417412, _1417414, _1417416] : [c_Equiv__Relations_Oequiv(_1417396, _1417398, _1417400), c_Equiv__Relations_Oequiv(_1417402, _1417404, _1417406), c_Equiv__Relations_Ocongruent2(_1417396, _1417402, tc_fun(_1417408, tc_HOL_Obool), _1417400, _1417406, _1417410), hBOOL(hAPP(hAPP(c_member(tc_fun(_1417396, tc_HOL_Obool)), _1417412), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1417396), _1417398), _1417400))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1417402, tc_HOL_Obool)), _1417414), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1417402), _1417404), _1417406))), 34095 ^ _781215 : [(34101 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1417408, tc_HOL_Obool)), hAPP(hAPP(_1417410, 34094 ^ [_1417396, _1417398, _1417400, _1417402, _1417404, _1417406, _1417408, _1417410, _1417412, _1417414, _1417416]), 34097 ^ [_1417396, _1417398, _1417400, _1417402, _1417404, _1417406, _1417408, _1417410, _1417412, _1417414, _1417416])), _1417416))], (34099 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417402), 34097 ^ [_1417396, _1417398, _1417400, _1417402, _1417404, _1417406, _1417408, _1417410, _1417412, _1417414, _1417416]), _1417404)))], (34096 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417396), 34094 ^ [_1417396, _1417398, _1417400, _1417402, _1417404, _1417406, _1417408, _1417410, _1417412, _1417414, _1417416]), _1417398)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1417408, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417396, tc_fun(_1417408, tc_HOL_Obool)), _1417412), hAPP(hAPP(c_COMBB(tc_fun(_1417402, tc_fun(_1417408, tc_HOL_Obool)), tc_fun(_1417408, tc_HOL_Obool), _1417396), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417402, tc_fun(_1417408, tc_HOL_Obool)), _1417414)), _1417410))), _1417416)))], (49511 ^ _781215) ^ [_1782967, _1782969, _1782971, _1782973] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1782967), tc_List_Olist(_1782967))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1782967), tc_List_Olist(_1782967)), _1782969), _1782971)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1782967), c_List_Olistrel1(_1782967, _1782973)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782967)), _1782969) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782967)), _1782971))], (33056 ^ _781215) ^ [_1394524, _1394526] : [class_Lattices_Osemilattice__inf(_1394524), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1394524), _1394526), _1394526) = _1394526)], (43766 ^ _781215) ^ [_1655268, _1655270, _1655272, _1655274] : [hAPP(hAPP(c_List_Omap(_1655268, _1655270), _1655272), _1655274) = c_List_Olist_ONil(_1655270), -(_1655274 = c_List_Olist_ONil(_1655268))], (51360 ^ _781215) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (27828 ^ _781215) ^ [_1288500, _1288502] : [class_Rings_Odivision__ring(_1288500), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288500), _1288502), c_Groups_Oone__class_Oone(_1288500)) = _1288502)], (39616 ^ _781215) ^ [_1549701, _1549703] : [c_Relation_Orefl__on(_1549701, c_Orderings_Otop__class_Otop(tc_fun(_1549701, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1549701, _1549701)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549701, _1549701, tc_HOL_Obool), _1549703))), -(c_Predicate_Oreflp(_1549701, _1549703))], (6419 ^ _781215) ^ [_885663, _885665, _885667, _885669] : [hBOOL(hAPP(hAPP(c_member(_885663), _885665), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_885663, tc_HOL_Obool)), _885667), _885669))), 6422 ^ _781215 : [(6425 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_885663), _885665), _885669))], (6423 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885663), _885665), _885667)))]]], (22596 ^ _781215) ^ [_1189203, _1189205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189203), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189203), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189205, _1189203))))], (13064 ^ _781215) ^ [_1008745, _1008747] : [class_Groups_Ogroup__add(_1008745), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008745), hAPP(c_Groups_Ouminus__class_Ouminus(_1008745), _1008747)), _1008747) = c_Groups_Ozero__class_Ozero(_1008745))], (33741 ^ _781215) ^ [_1410454, _1410456, _1410458] : [class_Groups_Oab__semigroup__mult(_1410454), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410454), _1410456)), -(_1410456 = c_Orderings_Obot__class_Obot(tc_fun(_1410454, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410454), _1410458)), -(_1410458 = c_Orderings_Obot__class_Obot(tc_fun(_1410454, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410454, tc_HOL_Obool)), _1410456), _1410458) = c_Orderings_Obot__class_Obot(tc_fun(_1410454, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1410454, c_Groups_Otimes__class_Otimes(_1410454)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410454, tc_HOL_Obool)), _1410456), _1410458)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1410454), hAPP(c_Finite__Set_Ofold1(_1410454, c_Groups_Otimes__class_Otimes(_1410454)), _1410456)), hAPP(c_Finite__Set_Ofold1(_1410454, c_Groups_Otimes__class_Otimes(_1410454)), _1410458)))], (8301 ^ _781215) ^ [_921205, _921207, _921209, _921211] : [class_Groups_Oab__semigroup__add(_921205), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921205), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921205), _921207), _921209)), _921211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921205), _921207), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921205), _921209), _921211)))], (38374 ^ _781215) ^ [_1512991, _1512993, _1512995, _1512997] : [hBOOL(hAPP(hAPP(c_member(_1512991), _1512993), _1512995)), -(hAPP(c_Set_Ovimage(_1512997, _1512991, hAPP(c_COMBK(_1512991, _1512997), _1512993)), _1512995) = c_Orderings_Otop__class_Otop(tc_fun(_1512997, tc_HOL_Obool)))], (45984 ^ _781215) ^ [_1703289, _1703291] : [class_Orderings_Olinorder(_1703289), 45987 ^ _781215 : [(45988 ^ _781215) ^ [] : [c_List_Olinorder__class_Osorted(_1703289, _1703291), 45991 ^ _781215 : [(45992 ^ _781215) ^ [_1703460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703460), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703289)), _1703291))), 45995 ^ _781215 : [(45996 ^ _781215) ^ [_1703577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1703577), _1703460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1703289), hAPP(hAPP(c_List_Onth(_1703289), _1703291), _1703577)), hAPP(hAPP(c_List_Onth(_1703289), _1703291), _1703460))))]]]]], (46002 ^ _781215) ^ [] : [46004 ^ _781215 : [(46010 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1703289), hAPP(hAPP(c_List_Onth(_1703289), _1703291), 46006 ^ [_1703289, _1703291])), hAPP(hAPP(c_List_Onth(_1703289), _1703291), 46003 ^ [_1703289, _1703291])))], (46008 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46006 ^ [_1703289, _1703291]), 46003 ^ [_1703289, _1703291])))], (46005 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46003 ^ [_1703289, _1703291]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703289)), _1703291))))]], -(c_List_Olinorder__class_Osorted(_1703289, _1703291))]]], (39767 ^ _781215) ^ [_1554999, _1555001, _1555003, _1555005] : [hAPP(hAPP(c_Relation_Orel__comp(_1554999, _1554999, _1554999), _1555001), _1555003) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1554999, _1554999), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1554999, _1554999, _1554999), _1555001), _1555005) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1554999, _1554999), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1554999, _1554999, _1554999), _1555001), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554999, _1554999), tc_HOL_Obool)), _1555003), _1555005)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1554999, _1554999), tc_HOL_Obool)))], (31252 ^ _781215) ^ [_1353529, _1353531] : [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)), _1353529), _1353531)), 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)), _1353529), 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)), _1353531), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (16806 ^ _781215) ^ [_1082907, _1082909, _1082911, _1082913] : [hBOOL(hAPP(_1082907, _1082909)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1082911, tc_HOL_Obool)), _1082913), _1082907), _1082909)))], (12908 ^ _781215) ^ [_1006120] : [class_Rings_Olinordered__semidom(_1006120), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006120), c_Groups_Oone__class_Oone(_1006120)), c_Groups_Ozero__class_Ozero(_1006120)))], (40144 ^ _781215) ^ [_1565068, _1565070, _1565072] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1565068, _1565070)), _1565072)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1565068), hAPP(c_Relation_ODomain(_1565068, _1565070), _1565072))))], (43569 ^ _781215) ^ [_1651338, _1651340, _1651342, _1651344] : [hBOOL(hAPP(_1651338, _1651340)), -(hBOOL(hAPP(_1651338, c_Hilbert__Choice_OLeastM(_1651342, tc_Nat_Onat, _1651344, _1651338))))], (7648 ^ _781215) ^ [_909734, _909736, _909738, _909740, _909742] : [hAPP(_909734, _909736) = hAPP(c_Option_Ooption_OSome(_909738), _909740), -(hBOOL(hAPP(hAPP(c_member(_909738), _909740), c_Map_Oran(_909742, _909738, _909734))))], (13812 ^ _781215) ^ [_1021833, _1021835, _1021837] : [class_Rings_Olinordered__idom(_1021833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021833), c_Groups_Ozero__class_Ozero(_1021833)), _1021835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021833), c_Groups_Ozero__class_Ozero(_1021833)), _1021837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021833), _1021837), c_Groups_Oone__class_Oone(_1021833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1021833), _1021837), _1021835)), _1021835)))], (47006 ^ _781215) ^ [_1726742] : [class_Enum_Oenum(_1726742), -(hAPP(c_List_Oset(_1726742), c_Enum_Oenum__class_Oenum(_1726742)) = c_Orderings_Otop__class_Otop(tc_fun(_1726742, tc_HOL_Obool)))], (14497 ^ _781215) ^ [_1034732, _1034734, _1034736] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_1034732, _1034734, _1034736)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1034734)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1034736))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (40651 ^ _781215) ^ [_1577694, _1577696] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_1577694, _1577696))), -(hBOOL(hAPP(c_Com_OWT, _1577696)))], (6003 ^ _781215) ^ [_876922] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_876922), c_Orderings_Obot__class_Obot(tc_fun(_876922, tc_HOL_Obool)))))], (10025 ^ _781215) ^ [_951583, _951585] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951583), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951583), _951585))))], (48954 ^ _781215) ^ [_1769346] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1769346)) = _1769346)], (21067 ^ _781215) ^ [_1158447, _1158449] : [class_Int_Onumber__ring(_1158447), class_Rings_Olinordered__idom(_1158447), 21074 ^ _781215 : [(21081 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158449), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158447), hAPP(c_Int_Onumber__class_Onumber__of(_1158447), _1158449)), c_Groups_Oone__class_Oone(_1158447))))], (21075 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158447), hAPP(c_Int_Onumber__class_Onumber__of(_1158447), _1158449)), c_Groups_Oone__class_Oone(_1158447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158449), c_Int_OBit1(c_Int_OPls))))]]], (20936 ^ _781215) ^ [_1156397, _1156399] : [hAPP(c_Int_Onat, _1156397) = _1156399, 20939 ^ _781215 : [(20946 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156397))), -(_1156399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20940 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156397)), -(_1156397 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1156399))]]], (48858 ^ _781215) ^ [_1767795, _1767797] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1767795), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1767797), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 48865 ^ _781215 : [(48872 ^ _781215) ^ [] : [_1767795 = _1767797, -(hAPP(c_Code__Numeral_Oof__nat, _1767795) = hAPP(c_Code__Numeral_Oof__nat, _1767797))], (48866 ^ _781215) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1767795) = hAPP(c_Code__Numeral_Oof__nat, _1767797), -(_1767795 = _1767797)]]], (39860 ^ _781215) ^ [_1558179, _1558181, _1558183, _1558185] : [hBOOL(hAPP(hAPP(c_member(_1558181), _1558185), hAPP(c_Relation_ORange(_1558179, _1558181), _1558183))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1558179, _1558181, hAPP(hAPP(c_COMBC(_1558179, tc_fun(tc_prod(_1558179, _1558181), tc_HOL_Obool), tc_fun(_1558181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558181, tc_fun(tc_fun(tc_prod(_1558179, _1558181), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1558179, _1558181), tc_HOL_Obool), tc_fun(_1558181, tc_HOL_Obool)), _1558179), c_COMBC(_1558181, tc_fun(tc_prod(_1558179, _1558181), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558181, tc_prod(_1558179, _1558181)), tc_fun(_1558181, tc_fun(tc_fun(tc_prod(_1558179, _1558181), tc_HOL_Obool), tc_HOL_Obool)), _1558179), hAPP(c_COMBB(tc_prod(_1558179, _1558181), tc_fun(tc_fun(tc_prod(_1558179, _1558181), tc_HOL_Obool), tc_HOL_Obool), _1558181), c_member(tc_prod(_1558179, _1558181)))), c_Product__Type_OPair(_1558179, _1558181)))), _1558183)), _1558185)))], (10764 ^ _781215) ^ [_965688, _965690, _965692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965688), _965690)), _965692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965692), _965690))))], (16477 ^ _781215) ^ [_1072947, _1072949, _1072951] : [c_Hoare__Mirabelle_Otriple__valid(_1072947, _1072949, _1072951), -(hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(_1072947, tc_HOL_Obool, hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_HOL_Obool))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_HOL_Obool)), tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1072947, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_HOL_OAll(_1072947)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_HOL_Obool))), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_HOL_Obool)), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_HOL_Obool), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, _1072947), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBC(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(_1072947, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBS(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1072947, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1072947), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1072947), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1072947), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1072947, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_Com_Ocom), c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1072947)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))), hAPP(hAPP(c_COMBC(tc_Com_Ocom, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_Natural_Oevaln)), _1072949))))))))), _1072951)))], (15340 ^ _781215) ^ [_1050177, _1050179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050177), _1050179)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050179), _1050177)), -(_1050177 = _1050179)], (21416 ^ _781215) ^ [_1165566] : [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)), _1165566))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1165566)))], (40563 ^ _781215) ^ [_1576033, _1576035] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576033, _1576033)), _1576035)), c_Wellfounded_Oacyclic(_1576033, _1576035), -(c_Wellfounded_Owf(_1576033, _1576035))], (41931 ^ _781215) ^ [_1607810, _1607812, _1607814, _1607816, _1607818, _1607820, _1607822, _1607824] : [-(hAPP(hAPP(c_List_Ozip(_1607810, _1607812), hAPP(hAPP(c_List_Omap(_1607814, _1607810), _1607816), _1607818)), hAPP(hAPP(c_List_Omap(_1607820, _1607812), _1607822), _1607824)) = hAPP(hAPP(c_List_Omap(tc_prod(_1607814, _1607820), tc_prod(_1607810, _1607812)), hAPP(c_Product__Type_Oprod_Oprod__case(_1607814, _1607820, tc_prod(_1607810, _1607812)), hAPP(hAPP(c_COMBC(_1607814, tc_fun(_1607820, _1607812), tc_fun(_1607820, tc_prod(_1607810, _1607812))), hAPP(hAPP(c_COMBB(tc_fun(_1607812, tc_prod(_1607810, _1607812)), tc_fun(tc_fun(_1607820, _1607812), tc_fun(_1607820, tc_prod(_1607810, _1607812))), _1607814), c_COMBB(_1607812, tc_prod(_1607810, _1607812), _1607820)), hAPP(hAPP(c_COMBB(_1607810, tc_fun(_1607812, tc_prod(_1607810, _1607812)), _1607814), c_Product__Type_OPair(_1607810, _1607812)), _1607816))), _1607822))), hAPP(hAPP(c_List_Ozip(_1607814, _1607820), _1607818), _1607824)))], (28080 ^ _781215) ^ [_1292828, _1292830, _1292832, _1292834] : [class_Fields_Ofield__inverse__zero(_1292828), class_Int_Onumber(_1292828), 28087 ^ _781215 : [(28088 ^ _781215) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292828), _1292830), _1292832) = hAPP(c_Int_Onumber__class_Onumber__of(_1292828), _1292834), 28091 ^ _781215 : [(28098 ^ _781215) ^ [] : [_1292832 = c_Groups_Ozero__class_Ozero(_1292828), -(hAPP(c_Int_Onumber__class_Onumber__of(_1292828), _1292834) = c_Groups_Ozero__class_Ozero(_1292828))], (28092 ^ _781215) ^ [] : [-(_1292832 = c_Groups_Ozero__class_Ozero(_1292828)), -(_1292830 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292828), hAPP(c_Int_Onumber__class_Onumber__of(_1292828), _1292834)), _1292832))]]], (28104 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292828), _1292830), _1292832) = hAPP(c_Int_Onumber__class_Onumber__of(_1292828), _1292834)), 28107 ^ _781215 : [(28110 ^ _781215) ^ [] : [_1292830 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1292828), hAPP(c_Int_Onumber__class_Onumber__of(_1292828), _1292834)), _1292832)], (28108 ^ _781215) ^ [] : [_1292832 = c_Groups_Ozero__class_Ozero(_1292828)]], 28111 ^ _781215 : [(28114 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1292828), _1292834) = c_Groups_Ozero__class_Ozero(_1292828)], (28112 ^ _781215) ^ [] : [-(_1292832 = c_Groups_Ozero__class_Ozero(_1292828))]]]]], (51654 ^ _781215) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (1768 ^ _781215) ^ [_806285, _806287] : [-(class_Rings_Osemiring__0(_806285)), _806287 = _806285, class_Rings_Osemiring__0(_806287)], (7995 ^ _781215) ^ [_916117, _916119] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916117), _916119))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916119), hAPP(c_Nat_OSuc, _916117))))], (20619 ^ _781215) ^ [_1151208, _1151210, _1151212] : [class_Rings_Olinordered__semidom(_1151208), 20622 ^ _781215 : [(20629 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1151210), _1151212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151208), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151208), _1151210)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151208), _1151212))))], (20623 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151208), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151208), _1151210)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151208), _1151212))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1151210), _1151212)))]]], (23706 ^ _781215) ^ [_1208626, _1208628, _1208630] : [-(_1208626 = 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), _1208626), _1208628)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1208626), _1208630)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1208628), _1208630))], (34860 ^ _781215) ^ [_1434566, _1434568, _1434570, _1434572, _1434574, _1434576] : [c_Fun_Oinj__on(_1434566, _1434568, _1434570, _1434572), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434568, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1434566, _1434568, _1434570), _1434572)), _1434574)), c_Fun_Oinj__on(_1434568, _1434566, _1434576, _1434574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434566, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1434568, _1434566, _1434576), _1434574)), _1434572)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434566), _1434572)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434568), _1434574)), -(hAPP(c_Finite__Set_Ocard(_1434566), _1434572) = hAPP(c_Finite__Set_Ocard(_1434568), _1434574))], (5698 ^ _781215) ^ [_871316, _871318, _871320] : [class_Orderings_Obot(_871316), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_871318, _871316)), _871320) = c_Orderings_Obot__class_Obot(_871316))], (15642 ^ _781215) ^ [_1056157, _1056159, _1056161] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_1056157, _1056159, _1056161)], (11626 ^ _781215) ^ [_984175, _984177] : [class_Groups_Ocomm__monoid__add(_984175), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984175), _984177), c_Groups_Ozero__class_Ozero(_984175)) = _984177)], (50133 ^ _781215) ^ [_1799172, _1799174, _1799176, _1799178, _1799180] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1799172, _1799172)), hAPP(hAPP(c_Product__Type_OPair(_1799172, _1799172), _1799174), _1799176)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1799172, _1799172), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1799178)), _1799180))), 50137 ^ _781215 : [(50140 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1799172, _1799172)), hAPP(hAPP(c_Product__Type_OPair(_1799172, _1799172), 50136 ^ [_1799172, _1799174, _1799176, _1799178, _1799180]), _1799176)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1799172, _1799172), tc_HOL_Obool), _1799178), _1799180))))], (50138 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1799172, _1799172)), hAPP(hAPP(c_Product__Type_OPair(_1799172, _1799172), _1799174), 50136 ^ [_1799172, _1799174, _1799176, _1799178, _1799180])), _1799180)))]]], (24962 ^ _781215) ^ [_1231742, _1231744, _1231746] : [class_Rings_Olinordered__semidom(_1231742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231742), c_Groups_Oone__class_Oone(_1231742)), _1231744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231742), hAPP(hAPP(c_Power_Opower__class_Opower(_1231742), _1231744), _1231746)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231742), _1231744), hAPP(hAPP(c_Power_Opower__class_Opower(_1231742), _1231744), _1231746)))))], (27235 ^ _781215) ^ [_1276206, _1276208, _1276210, _1276212] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1276206, _1276208), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1276210), _1276212))), -(_1276208 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1276206, _1276208) = _1276212)], (31583 ^ _781215) ^ [_1362010, _1362012, _1362014, _1362016] : [class_Groups_Ocomm__monoid__add(_1362010), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1362012), _1362014))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362012, _1362010), _1362016), _1362014) = c_Groups_Ozero__class_Ozero(_1362010))], (13738 ^ _781215) ^ [_1020452, _1020454, _1020456] : [class_Rings_Olinordered__ring__strict(_1020452), 13741 ^ _781215 : [(13750 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020452), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020452), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020452), _1020454), _1020454)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020452), _1020456), _1020456))), c_Groups_Ozero__class_Ozero(_1020452)))), _1020454 = c_Groups_Ozero__class_Ozero(_1020452), _1020456 = c_Groups_Ozero__class_Ozero(_1020452)], (13742 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020452), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020452), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020452), _1020454), _1020454)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020452), _1020456), _1020456))), c_Groups_Ozero__class_Ozero(_1020452))), 13745 ^ _781215 : [(13748 ^ _781215) ^ [] : [-(_1020456 = c_Groups_Ozero__class_Ozero(_1020452))], (13746 ^ _781215) ^ [] : [-(_1020454 = c_Groups_Ozero__class_Ozero(_1020452))]]]]], (46976 ^ _781215) ^ [_1726207, _1726209, _1726211, _1726213, _1726215] : [class_Orderings_Olinorder(_1726207), -(hAPP(c_List_Ofilter(_1726209, _1726211), c_List_Olinorder__class_Osort__key(_1726209, _1726207, _1726213, _1726215)) = c_List_Olinorder__class_Osort__key(_1726209, _1726207, _1726213, hAPP(c_List_Ofilter(_1726209, _1726211), _1726215)))], (50142 ^ _781215) ^ [_1799484, _1799486, _1799488, _1799490, _1799492] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1799484, _1799484)), hAPP(hAPP(c_Product__Type_OPair(_1799484, _1799484), _1799486), _1799488)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1799484, _1799484), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1799490)), _1799492))), 50146 ^ _781215 : [(50149 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1799484, _1799484)), hAPP(hAPP(c_Product__Type_OPair(_1799484, _1799484), 50145 ^ [_1799484, _1799486, _1799488, _1799490, _1799492]), _1799488)), _1799492)))], (50147 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1799484, _1799484)), hAPP(hAPP(c_Product__Type_OPair(_1799484, _1799484), _1799486), 50145 ^ [_1799484, _1799486, _1799488, _1799490, _1799492])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1799484, _1799484), tc_HOL_Obool), _1799490), _1799492))))]]], (18435 ^ _781215) ^ [_1111294, _1111296, _1111298, _1111300] : [-(hAPP(c_Nat_Onat_Onat__rec(_1111294, _1111296, _1111298), hAPP(c_Nat_OSuc, _1111300)) = hAPP(hAPP(_1111298, _1111300), hAPP(c_Nat_Onat_Onat__rec(_1111294, _1111296, _1111298), _1111300)))], (44246 ^ _781215) ^ [_1666021, _1666023, _1666025, _1666027] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1666021)), hAPP(hAPP(c_List_Oappend(_1666021), _1666023), _1666025)), c_List_Olists(_1666021, _1666027)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1666021)), _1666023), c_List_Olists(_1666021, _1666027))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1666021)), _1666025), c_List_Olists(_1666021, _1666027)))], (8285 ^ _781215) ^ [_920940, _920942, _920944, _920946] : [class_Groups_Ocancel__semigroup__add(_920940), 8288 ^ _781215 : [(8295 ^ _781215) ^ [] : [_920944 = _920946, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920940), _920942), _920944) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920940), _920942), _920946))], (8289 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920940), _920942), _920944) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920940), _920942), _920946), -(_920944 = _920946)]]], (31336 ^ _781215) ^ [_1355174, _1355176, _1355178] : [class_Orderings_Olinorder(_1355174), 31339 ^ _781215 : [(31346 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355174), _1355176), _1355178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1355174, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1355174), _1355176)), hAPP(c_SetInterval_Oord__class_OlessThan(_1355174), _1355178))))], (31340 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1355174, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1355174), _1355176)), hAPP(c_SetInterval_Oord__class_OlessThan(_1355174), _1355178))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355174), _1355176), _1355178)))]]], (41563 ^ _781215) ^ [_1598868, _1598870, _1598872, _1598874, _1598876, _1598878, _1598880, _1598882] : [c_Finite__Set_Ofolding(_1598868, _1598870, _1598872, _1598874), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598868), _1598876)), -(hAPP(c_Fun_Ocomp(_1598870, _1598870, _1598878, hAPP(_1598872, _1598880)), hAPP(c_Fun_Ocomp(_1598870, _1598870, _1598878, hAPP(_1598874, _1598876)), _1598882)) = hAPP(c_Fun_Ocomp(_1598870, _1598870, _1598878, hAPP(_1598874, _1598876)), hAPP(c_Fun_Ocomp(_1598870, _1598870, _1598878, hAPP(_1598872, _1598880)), _1598882)))], (38654 ^ _781215) ^ [_1520725, _1520727, _1520729, _1520731] : [_1520725 = c_Orderings_Obot__class_Obot(tc_fun(_1520727, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1520727, _1520729), _1520729, c_Product__Type_Osnd(_1520727, _1520729)), hAPP(hAPP(c_Product__Type_OSigma(_1520727, _1520729), _1520725), hAPP(c_COMBK(tc_fun(_1520729, tc_HOL_Obool), _1520727), _1520731))) = c_Orderings_Obot__class_Obot(tc_fun(_1520729, tc_HOL_Obool)))], (46954 ^ _781215) ^ [_1725816] : [class_Enum_Oenum(_1725816), -(c_Enum_Oenum__class_Oenum(tc_Option_Ooption(_1725816)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(_1725816)), c_Option_Ooption_ONone(_1725816)), hAPP(hAPP(c_List_Omap(_1725816, tc_Option_Ooption(_1725816)), c_Option_Ooption_OSome(_1725816)), c_Enum_Oenum__class_Oenum(_1725816))))], (50700 ^ _781215) ^ [_1812153, _1812155, _1812157] : [c_FunDef_Ois__measure(_1812153, _1812155), -(c_FunDef_Ois__measure(tc_prod(_1812157, _1812153), hAPP(hAPP(c_COMBB(_1812153, tc_Nat_Onat, tc_prod(_1812157, _1812153)), _1812155), c_Product__Type_Osnd(_1812157, _1812153))))], (37902 ^ _781215) ^ [_1501706, _1501708, _1501710] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501706, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1501706, tc_HOL_Obool), _1501708)), _1501710) = c_Orderings_Obot__class_Obot(tc_fun(_1501706, tc_HOL_Obool)), 37905 ^ _781215 : [(37906 ^ _781215) ^ [_1501841] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1501706, tc_HOL_Obool)), _1501841), _1501708)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501706, tc_HOL_Obool)), _1501841), _1501710) = c_Orderings_Obot__class_Obot(tc_fun(_1501706, tc_HOL_Obool)))]]], (9985 ^ _781215) ^ [_950969, _950971] : [9986 ^ _781215 : [(9989 ^ _781215) ^ [] : [_950969 = _950971], (9987 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _950969), _950971))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950969), _950971)))], (14387 ^ _781215) ^ [_1032877] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _1032877)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27810 ^ _781215) ^ [_1288100] : [-(hAPP(c_Int_Onat, _1288100) = 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, _1288100)), 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)))))))], (36285 ^ _781215) ^ [_1463529, _1463531] : [-(c_Nitpick_Onat__lcm(_1463529, _1463531) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1463529), _1463531)), c_Nitpick_Onat__gcd(_1463529, _1463531)))], (26944 ^ _781215) ^ [_1270998, _1271000, _1271002, _1271004, _1271006, _1271008, _1271010, _1271012] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1270998, _1271000, _1271002), _1271004), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1271006, _1271008, tc_prod(_1270998, _1271000)), _1271010), _1271012)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1271006, _1271008, _1271002), hAPP(hAPP(c_COMBB(tc_fun(_1271008, tc_prod(_1270998, _1271000)), tc_fun(_1271008, _1271002), _1271006), hAPP(c_COMBB(tc_prod(_1270998, _1271000), _1271002, _1271008), hAPP(c_Product__Type_Oprod_Oprod__case(_1270998, _1271000, _1271002), _1271004))), _1271010)), _1271012))], (18860 ^ _781215) ^ [_1119365, _1119367, _1119369] : [class_Orderings_Olinorder(_1119365), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119365), _1119367), _1119369)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1119365), _1119367), _1119369) = _1119369)], (35735 ^ _781215) ^ [_1453251, _1453253] : [class_Groups_Oordered__ab__group__add__abs(_1453251), -(hAPP(c_Groups_Oabs__class_Oabs(_1453251), hAPP(c_Groups_Oabs__class_Oabs(_1453251), _1453253)) = hAPP(c_Groups_Oabs__class_Oabs(_1453251), _1453253))], (30375 ^ _781215) ^ [_1336810, _1336812, _1336814, _1336816] : [class_Orderings_Olinorder(_1336810), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336810), _1336812), _1336814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336810), _1336814), _1336816)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1336810, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1336810, _1336812, _1336814)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1336810, _1336814, _1336816)) = c_SetInterval_Oord__class_OatLeastAtMost(_1336810, _1336812, _1336816))], (37213 ^ _781215) ^ [_1486000, _1486002, _1486004, _1486006, _1486008] : [-(_1486000 = c_Orderings_Obot__class_Obot(tc_fun(_1486002, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486004, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486002, tc_fun(_1486004, tc_HOL_Obool)), _1486000), _1486006)), _1486008) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486002, tc_fun(_1486004, tc_HOL_Obool)), _1486000), hAPP(hAPP(c_COMBC(_1486002, tc_fun(_1486004, tc_HOL_Obool), tc_fun(_1486004, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1486004, tc_HOL_Obool), tc_fun(tc_fun(_1486004, tc_HOL_Obool), tc_fun(_1486004, tc_HOL_Obool)), _1486002), c_Groups_Ominus__class_Ominus(tc_fun(_1486004, tc_HOL_Obool))), _1486006)), _1486008)))], (51712 ^ _781215) ^ [_1826240, _1826242] : [hBOOL(hAPP(hAPP(c_fconj, _1826240), _1826242)), -(hBOOL(_1826240))], (51396 ^ _781215) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (31352 ^ _781215) ^ [_1355466, _1355468, _1355470, _1355472, _1355474, _1355476] : [hBOOL(hAPP(hAPP(c_member(_1355466), _1355468), _1355470)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1355466, _1355472)), hAPP(hAPP(c_Product__Type_OPair(_1355466, _1355472), _1355468), _1355474)), _1355476)), -(hBOOL(hAPP(hAPP(c_member(_1355472), _1355474), hAPP(c_Relation_OImage(_1355466, _1355472, _1355476), _1355470))))], (17713 ^ _781215) ^ [_1097767] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1097767)), -(hAPP(c_Int_Onat, _1097767) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11430 ^ _781215) ^ [_980580, _980582, _980584, _980586, _980588, _980590] : [-(hBOOL(hAPP(hAPP(c_member(_980580), _980582), _980584))), -(hAPP(c_Set_Oimage(_980580, _980586, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_980580, _980586), _980588), _980582), _980590)), _980584) = hAPP(c_Set_Oimage(_980580, _980586, _980588), _980584))], (24466 ^ _781215) ^ [_1222365, _1222367, _1222369] : [class_Rings_Olinordered__idom(_1222365), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222365), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1222365), hAPP(hAPP(c_Power_Opower__class_Opower(_1222365), _1222367), 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(_1222365), _1222369), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1222365)))], (37951 ^ _781215) ^ [_1502889] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502889, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1502889, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1502889, tc_HOL_Obool)))], (42629 ^ _781215) ^ [_1627473, _1627475, _1627477, _1627479] : [-(hAPP(hAPP(c_List_Onth(_1627473), hAPP(hAPP(c_List_Olist_OCons(_1627473), _1627475), _1627477)), hAPP(c_Nat_OSuc, _1627479)) = hAPP(hAPP(c_List_Onth(_1627473), _1627477), _1627479))], (45540 ^ _781215) ^ [_1695410, _1695412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695410), _1695412)), -(c_List_Oupt(_1695410, _1695412) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1695410), c_List_Oupt(hAPP(c_Nat_OSuc, _1695410), _1695412)))], (26650 ^ _781215) ^ [_1264806, _1264808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264806)), 26653 ^ _781215 : [(26660 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264808), _1264806))), -(c_Divides_OposDivAlg(_1264808, _1264806) = hAPP(c_Divides_Oadjust(_1264806), c_Divides_OposDivAlg(_1264808, 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)))), _1264806))))], (26654 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264808), _1264806)), -(c_Divides_OposDivAlg(_1264808, _1264806) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264808))]]], (25736 ^ _781215) ^ [_1244512, _1244514, _1244516, _1244518] : [hBOOL(hAPP(hAPP(c_member(_1244512), _1244514), c_SetInterval_Oord_OgreaterThan(_1244512, _1244516, _1244518))), -(hBOOL(hAPP(hAPP(_1244516, _1244518), _1244514)))], (20354 ^ _781215) ^ [_1146616] : [c_Int_OPls = c_Int_OBit1(_1146616)], (7228 ^ _781215) ^ [_902752, _902754, _902756, _902758, _902760, _902762] : [-(hBOOL(hAPP(hAPP(c_member(_902752), _902754), _902756))), -(c_Map_Orestrict__map(_902752, _902758, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_902752, tc_Option_Ooption(_902758)), _902760), _902754), _902762), _902756) = c_Map_Orestrict__map(_902752, _902758, _902760, _902756))], (24992 ^ _781215) ^ [_1232227, _1232229, _1232231] : [class_Rings_Olinordered__semidom(_1232227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232227), c_Groups_Oone__class_Oone(_1232227)), _1232229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232227), c_Groups_Oone__class_Oone(_1232227)), hAPP(hAPP(c_Power_Opower__class_Opower(_1232227), _1232229), hAPP(c_Nat_OSuc, _1232231)))))], (28488 ^ _781215) ^ [_1300214, _1300216, _1300218, _1300220] : [class_Fields_Olinordered__field__inverse__zero(_1300214), class_Int_Onumber(_1300214), 28495 ^ _781215 : [(28496 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300214), _1300216), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1300214), _1300218), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220)))), 28499 ^ _781215 : [(28506 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300214), c_Groups_Ozero__class_Ozero(_1300214)), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220)))), 28509 ^ _781215 : [(28516 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300214), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220)), c_Groups_Ozero__class_Ozero(_1300214)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300214), _1300216), c_Groups_Ozero__class_Ozero(_1300214))))], (28510 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300214), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220)), c_Groups_Ozero__class_Ozero(_1300214))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300214), _1300218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300214), _1300216), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220)))))]]], (28500 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300214), c_Groups_Ozero__class_Ozero(_1300214)), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300214), _1300216), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220))), _1300218)))]]], (28522 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300214), _1300216), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1300214), _1300218), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220))))), 28525 ^ _781215 : [(28528 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300214), _1300216), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220))), _1300218))], (28526 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300214), c_Groups_Ozero__class_Ozero(_1300214)), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220))))]], 28529 ^ _781215 : [(28532 ^ _781215) ^ [] : [28533 ^ _781215 : [(28536 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300214), _1300218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300214), _1300216), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220))))], (28534 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300214), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220)), c_Groups_Ozero__class_Ozero(_1300214))))]], 28537 ^ _781215 : [(28540 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300214), _1300216), c_Groups_Ozero__class_Ozero(_1300214)))], (28538 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300214), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220)), c_Groups_Ozero__class_Ozero(_1300214)))]]], (28530 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300214), c_Groups_Ozero__class_Ozero(_1300214)), hAPP(c_Int_Onumber__class_Onumber__of(_1300214), _1300220)))]]]]], (25646 ^ _781215) ^ [_1242783, _1242785, _1242787, _1242789] : [hBOOL(hAPP(hAPP(c_member(_1242783), _1242785), c_SetInterval_Oord_OlessThan(_1242783, _1242787, _1242789))), -(hBOOL(hAPP(hAPP(_1242787, _1242785), _1242789)))], (1418 ^ _781215) ^ [_801910, _801912] : [-(class_Groups_Ouminus(_801910)), _801912 = _801910, class_Groups_Ouminus(_801912)], (30760 ^ _781215) ^ [_1344252] : [-(hAPP(c_Relation_OField(_1344252), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1344252, _1344252), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1344252, tc_HOL_Obool)))], (50734 ^ _781215) ^ [_1812668] : [class_HOL_Oequal(_1812668), -(c_HOL_Oequal__class_Oequal(_1812668) = c_fequal)], (17979 ^ _781215) ^ [_1102183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1102183)), -(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, _1102183))))], (48723 ^ _781215) ^ [_1765068, _1765070, _1765072, _1765074, _1765076] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1765068, _1765070, _1765068, _1765072), hAPP(c_Product__Type_OPair(_1765070, _1765068), _1765074)), _1765076) = hAPP(_1765076, _1765074))], (64 ^ _781215) ^ [_782213, _782215, _782217, _782219, _782221, _782223, _782225, _782227, _782229, _782231, _782233, _782235] : [-(c_Finite__Set_Ofolding__image__simple__idem(_782233, _782229, _782225, _782221, _782217, _782213)), c_Finite__Set_Ofolding__image__simple__idem(_782235, _782231, _782227, _782223, _782219, _782215), _782235 = _782233, _782231 = _782229, _782227 = _782225, _782223 = _782221, _782219 = _782217, _782215 = _782213], (7041 ^ _781215) ^ [_898215, _898217, _898219] : [7042 ^ _781215 : [(7043 ^ _781215) ^ [_898274] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _898215), _898217), _898274), _898219))]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898215), _898217), _898219)))], (4046 ^ _781215) ^ [_842596, _842598, _842600, _842602] : [-(c_Big__Operators_Olinorder__class_OMin(_842602, _842598) = c_Big__Operators_Olinorder__class_OMin(_842600, _842596)), _842602 = _842600, _842598 = _842596], (22604 ^ _781215) ^ [_1189376, _1189378] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189376, _1189378) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1189376 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1189378), 22607 ^ [_1189376, _1189378]))], (13312 ^ _781215) ^ [_1012683, _1012685, _1012687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012683), _1012685)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012683), _1012687))), 13315 ^ _781215 : [(13318 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012685), _1012687)))], (13316 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1012683)))]]], (44307 ^ _781215) ^ [_1667361, _1667363, _1667365, _1667367, _1667369] : [-(hAPP(hAPP(c_List_Oappend(_1667361), _1667363), _1667365) = hAPP(hAPP(c_List_Oappend(_1667361), _1667367), _1667369)), 44308 ^ _781215 : [(44315 ^ _781215) ^ [_1667585] : [hAPP(hAPP(c_List_Oappend(_1667361), _1667363), _1667585) = _1667367, _1667365 = hAPP(hAPP(c_List_Oappend(_1667361), _1667585), _1667369)], (44309 ^ _781215) ^ [_1667473] : [_1667363 = hAPP(hAPP(c_List_Oappend(_1667361), _1667367), _1667473), hAPP(hAPP(c_List_Oappend(_1667361), _1667473), _1667365) = _1667369]]], (24294 ^ _781215) ^ [_1219340, _1219342, _1219344] : [class_Rings_Olinordered__idom(_1219340), 24297 ^ _781215 : [(24306 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219340), hAPP(hAPP(c_Power_Opower__class_Opower(_1219340), _1219342), 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(_1219340), _1219344), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1219340)), _1219342 = c_Groups_Ozero__class_Ozero(_1219340), _1219344 = c_Groups_Ozero__class_Ozero(_1219340)], (24298 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219340), hAPP(hAPP(c_Power_Opower__class_Opower(_1219340), _1219342), 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(_1219340), _1219344), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1219340), 24301 ^ _781215 : [(24304 ^ _781215) ^ [] : [-(_1219344 = c_Groups_Ozero__class_Ozero(_1219340))], (24302 ^ _781215) ^ [] : [-(_1219342 = c_Groups_Ozero__class_Ozero(_1219340))]]]]], (1658 ^ _781215) ^ [_804910, _804912] : [-(class_Rings_Ocomm__semiring__1(_804910)), _804912 = _804910, class_Rings_Ocomm__semiring__1(_804912)], (11958 ^ _781215) ^ [_989009] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _989009) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50160 ^ _781215) ^ [_1800056, _1800058, _1800060, _1800062] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1800056, _1800056)), hAPP(hAPP(c_Product__Type_OPair(_1800056, _1800056), _1800058), _1800060)), c_Transitive__Closure_Otrancl(_1800056, _1800062))), 50164 ^ _781215 : [(50167 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1800056, _1800056)), hAPP(hAPP(c_Product__Type_OPair(_1800056, _1800056), 50163 ^ [_1800056, _1800058, _1800060, _1800062]), _1800060)), _1800062)))], (50165 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1800056, _1800056)), hAPP(hAPP(c_Product__Type_OPair(_1800056, _1800056), _1800058), 50163 ^ [_1800056, _1800058, _1800060, _1800062])), c_Transitive__Closure_Ortrancl(_1800056, _1800062))))]]], (16517 ^ _781215) ^ [_1075590, _1075592, _1075594, _1075596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1075590, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075590, tc_HOL_Obool)), _1075592), _1075594)), _1075596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1075590, tc_HOL_Obool)), _1075592), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1075590, tc_HOL_Obool)), _1075594), _1075596))))], (30010 ^ _781215) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (37586 ^ _781215) ^ [_1495103] : [class_Complete__Lattice_Ocomplete__lattice(_1495103), -(c_Complete__Lattice_OInf__class_OInf(_1495103, c_Orderings_Obot__class_Obot(tc_fun(_1495103, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1495103))], (51190 ^ _781215) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (5544 ^ _781215) ^ [_865851, _865853, _865855, _865857] : [-(hAPP(_865857, _865853) = hAPP(_865855, _865851)), _865857 = _865855, _865853 = _865851], (22436 ^ _781215) ^ [_1186537, _1186539] : [class_Divides_Osemiring__div(_1186537), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1186537), c_Groups_Ozero__class_Ozero(_1186537)), _1186539) = c_Groups_Ozero__class_Ozero(_1186537))], (33112 ^ _781215) ^ [_1396067, _1396069, _1396071, _1396073, _1396075] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396067, tc_fun(_1396069, tc_HOL_Obool)), _1396071), hAPP(hAPP(c_COMBC(_1396067, tc_fun(_1396069, tc_HOL_Obool), tc_fun(_1396069, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396069, tc_HOL_Obool), tc_fun(tc_fun(_1396069, tc_HOL_Obool), tc_fun(_1396069, tc_HOL_Obool)), _1396067), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396069, tc_HOL_Obool))), _1396073)), _1396075)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396069, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396067, tc_fun(_1396069, tc_HOL_Obool)), _1396071), _1396073)), _1396075))], (17678 ^ _781215) ^ [_1097185] : [17680 ^ _781215 : [(17683 ^ _781215) ^ [] : [hBOOL(hAPP(_1097185, hAPP(c_Int_Onat, 17679 ^ [_1097185])))], (17681 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 17679 ^ [_1097185])))]], 17684 ^ _781215 : [(17685 ^ _781215) ^ [_1097318] : [-(hBOOL(hAPP(_1097185, _1097318)))]]], (29122 ^ _781215) ^ [_1312140, _1312142, _1312144] : [class_Fields_Olinordered__field__inverse__zero(_1312140), 29125 ^ _781215 : [(29140 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312140), c_Groups_Ozero__class_Ozero(_1312140)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312140), _1312142), _1312144)))), 29141 ^ _781215 : [(29148 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312140), _1312142), c_Groups_Ozero__class_Ozero(_1312140))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312140), _1312144), c_Groups_Ozero__class_Ozero(_1312140)))], (29142 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312140), c_Groups_Ozero__class_Ozero(_1312140)), _1312142)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312140), c_Groups_Ozero__class_Ozero(_1312140)), _1312144))]]], (29126 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312140), c_Groups_Ozero__class_Ozero(_1312140)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312140), _1312142), _1312144))), 29131 ^ _781215 : [(29134 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312140), c_Groups_Ozero__class_Ozero(_1312140)), _1312144)))], (29132 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312140), c_Groups_Ozero__class_Ozero(_1312140)), _1312142)))]], 29135 ^ _781215 : [(29138 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312140), _1312144), c_Groups_Ozero__class_Ozero(_1312140))))], (29136 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312140), _1312142), c_Groups_Ozero__class_Ozero(_1312140))))]]]]], (23670 ^ _781215) ^ [_1207950, _1207952, _1207954] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1207950), _1207952)), _1207954) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1207950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1207952), _1207954)))], (27271 ^ _781215) ^ [_1276674, _1276676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1276674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1276676)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1276674, _1276676), c_Divides_OposDivAlg(_1276674, _1276676))))], (48880 ^ _781215) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31704 ^ _781215) ^ [_1364532, _1364534, _1364536] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1364532), _1364534)), 31707 ^ _781215 : [(31727 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364532, tc_Nat_Onat), _1364536), _1364534) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 31728 ^ _781215 : [(31729 ^ _781215) ^ [_1365013] : [hBOOL(hAPP(hAPP(c_member(_1364532), _1365013), _1364534)), hAPP(_1364536, _1365013) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 31737 ^ _781215 : [(31742 ^ _781215) ^ [] : [hAPP(_1364536, 31736 ^ [_1364532, _1364534, _1364536, _1365013]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31740 ^ _781215) ^ [] : [_1365013 = 31736 ^ [_1364532, _1364534, _1364536, _1365013]], (31738 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364532), 31736 ^ [_1364532, _1364534, _1364536, _1365013]), _1364534)))]]]]], (31708 ^ _781215) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364532, tc_Nat_Onat), _1364536), _1364534) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 31712 ^ _781215 : [(31717 ^ _781215) ^ [_1364852] : [hBOOL(hAPP(hAPP(c_member(_1364532), _1364852), _1364534)), -(31711 ^ [_1364532, _1364534, _1364536] = _1364852), -(hAPP(_1364536, _1364852) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31715 ^ _781215) ^ [] : [-(hAPP(_1364536, 31711 ^ [_1364532, _1364534, _1364536]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31713 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364532), 31711 ^ [_1364532, _1364534, _1364536]), _1364534)))]]]]], (18141 ^ _781215) ^ [_1106035, _1106037, _1106039] : [class_Orderings_Olinorder(_1106035), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106035), _1106037), _1106039) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106035), _1106039), _1106037))], (15408 ^ _781215) ^ [_1051401, _1051403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051401), _1051403)), 15411 ^ _781215 : [(15414 ^ _781215) ^ [] : [_1051401 = _1051403], (15412 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051401), _1051403)))]]], (44373 ^ _781215) ^ [_1669070, _1669072, _1669074] : [-(c_List_Obutlast(_1669070, hAPP(hAPP(c_List_Oappend(_1669070), _1669072), hAPP(hAPP(c_List_Olist_OCons(_1669070), _1669074), c_List_Olist_ONil(_1669070)))) = _1669072)], (36430 ^ _781215) ^ [] : [-(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))], (21898 ^ _781215) ^ [_1174723, _1174725, _1174727, _1174729, _1174731, _1174733] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174723, tc_fun(_1174725, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1174727, _1174723, _1174729), _1174731)), _1174733) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174727, tc_fun(_1174725, tc_HOL_Obool)), _1174731), hAPP(hAPP(c_COMBB(_1174723, tc_fun(_1174725, tc_HOL_Obool), _1174727), _1174733), _1174729)))], (17819 ^ _781215) ^ [_1099477, _1099479, _1099481] : [class_Rings_Osemiring__1(_1099477), hBOOL(hAPP(hAPP(c_member(_1099477), _1099479), c_Nat_Osemiring__1__class_ONats(_1099477))), hBOOL(hAPP(hAPP(c_member(_1099477), _1099481), c_Nat_Osemiring__1__class_ONats(_1099477))), -(hBOOL(hAPP(hAPP(c_member(_1099477), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099477), _1099479), _1099481)), c_Nat_Osemiring__1__class_ONats(_1099477))))], (48011 ^ _781215) ^ [_1748175, _1748177, _1748179, _1748181, _1748183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1748175, _1748177)), hAPP(_1748175, _1748179))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1748181, _1748181)), hAPP(hAPP(c_Product__Type_OPair(_1748181, _1748181), _1748177), _1748179)), c_List_Omeasures(_1748181, _1748183))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1748181, _1748181)), hAPP(hAPP(c_Product__Type_OPair(_1748181, _1748181), _1748177), _1748179)), c_List_Omeasures(_1748181, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1748181, tc_Nat_Onat)), _1748175), _1748183)))))], (10188 ^ _781215) ^ [_954793, _954795, _954797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954793), _954795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954793), _954797)), 10195 ^ _781215 : [(10202 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954795), _954797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954795), _954793)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954797), _954793))))], (10196 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954795), _954793)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954797), _954793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954795), _954797)))]]], (13632 ^ _781215) ^ [_1018421, _1018423, _1018425, _1018427, _1018429] : [class_Rings_Olinordered__semiring__strict(_1018421), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018421), _1018423), _1018425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018421), _1018427), _1018429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018421), c_Groups_Ozero__class_Ozero(_1018421)), _1018423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018421), c_Groups_Ozero__class_Ozero(_1018421)), _1018427)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018421), _1018423), _1018427)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018421), _1018425), _1018429))))], (37838 ^ _781215) ^ [_1500304, _1500306, _1500308, _1500310] : [-(hAPP(c_Set_Oimage(_1500304, _1500306, _1500308), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1500304, tc_HOL_Obool), _1500310)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1500304, tc_HOL_Obool), tc_fun(_1500306, tc_HOL_Obool)), _1500310), c_Set_Oimage(_1500304, _1500306, _1500308)))], (302 ^ _781215) ^ [_785816, _785818, _785820, _785822] : [-(c_Equiv__Relations_Oequivp(_785820, _785816)), c_Equiv__Relations_Oequivp(_785822, _785818), _785822 = _785820, _785818 = _785816], (26914 ^ _781215) ^ [_1270351, _1270353, _1270355, _1270357, _1270359, _1270361] : [hAPP(hAPP(c_Product__Type_OPair(_1270351, _1270353), _1270355), _1270357) = hAPP(hAPP(c_Product__Type_OPair(_1270351, _1270353), _1270359), _1270361), 26917 ^ _781215 : [(26920 ^ _781215) ^ [] : [-(_1270357 = _1270361)], (26918 ^ _781215) ^ [] : [-(_1270355 = _1270359)]]], (21446 ^ _781215) ^ [_1166134, _1166136] : [_1166134 = _1166136, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1166134) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1166136))], (38185 ^ _781215) ^ [_1508467, _1508469, _1508471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508467, tc_HOL_Obool)), _1508469), hAPP(hAPP(c_Set_Oinsert(_1508467), _1508471), c_Orderings_Obot__class_Obot(tc_fun(_1508467, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1508467, _1508471, _1508469) = _1508471)], (16489 ^ _781215) ^ [_1075043] : [class_Groups_Oab__semigroup__mult(_1075043), -(c_Finite__Set_Ofun__left__comm(_1075043, _1075043, c_Groups_Otimes__class_Otimes(_1075043)))], (46291 ^ _781215) ^ [_1710472, _1710474] : [-(hAPP(c_List_Oset(_1710472), c_List_Oconcat(_1710472, _1710474)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1710472), tc_fun(_1710472, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1710472)), _1710474)), c_List_Oset(_1710472)))], (6144 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (20617 ^ _781215) ^ [] : [-(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))], (38550 ^ _781215) ^ [_1518046, _1518048, _1518050, _1518052, _1518054] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518046, _1518048), _1518050), hAPP(hAPP(c_COMBS(_1518046, tc_fun(_1518048, tc_HOL_Obool), tc_fun(_1518048, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518048, tc_HOL_Obool), tc_fun(tc_fun(_1518048, tc_HOL_Obool), tc_fun(_1518048, tc_HOL_Obool)), _1518046), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518048, tc_HOL_Obool))), _1518052)), _1518054)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1518046, _1518048), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518046, _1518048), _1518050), _1518052)), hAPP(hAPP(c_Product__Type_OSigma(_1518046, _1518048), _1518050), _1518054)))], (22376 ^ _781215) ^ [_1185350, _1185352, _1185354, _1185356, _1185358, _1185360] : [class_Divides_Oring__div(_1185350), c_Divides_Odiv__class_Omod(_1185350, _1185352, _1185354) = c_Divides_Odiv__class_Omod(_1185350, _1185356, _1185354), c_Divides_Odiv__class_Omod(_1185350, _1185358, _1185354) = c_Divides_Odiv__class_Omod(_1185350, _1185360, _1185354), -(c_Divides_Odiv__class_Omod(_1185350, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185350), _1185352), _1185358), _1185354) = c_Divides_Odiv__class_Omod(_1185350, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185350), _1185356), _1185360), _1185354))], (5424 ^ _781215) ^ [_864061, _864063] : [_864063 = _864061, -(c_Groups_Oplus__class_Oplus(_864063) = c_Groups_Oplus__class_Oplus(_864061))], (44204 ^ _781215) ^ [_1664858, _1664860, _1664862] : [class_Groups_Omonoid__add(_1664858), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1664858), hAPP(hAPP(c_List_Oappend(_1664858), _1664860), _1664862)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1664858), hAPP(c_List_Omonoid__add__class_Olistsum(_1664858), _1664860)), hAPP(c_List_Omonoid__add__class_Olistsum(_1664858), _1664862)))], (25294 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (16015 ^ _781215) ^ [_1063910, _1063912, _1063914] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063910, tc_HOL_Obool)), _1063912), _1063914) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063910, tc_HOL_Obool)), _1063914), _1063912))], (8470 ^ _781215) ^ [_924839, _924841, _924843, _924845, _924847, _924849] : [-(hBOOL(hAPP(hAPP(c_member(_924839), _924841), c_Map_Odom(_924839, _924843, _924845)))), -(c_Map_Omap__add(_924839, _924843, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_924839, tc_Option_Ooption(_924843)), _924847), _924841), hAPP(c_Option_Ooption_OSome(_924843), _924849)), _924845) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_924839, tc_Option_Ooption(_924843)), c_Map_Omap__add(_924839, _924843, _924847, _924845)), _924841), hAPP(c_Option_Ooption_OSome(_924843), _924849)))], (24508 ^ _781215) ^ [_1223363, _1223365] : [class_Rings_Oring__1(_1223363), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1223363), hAPP(c_Groups_Ouminus__class_Ouminus(_1223363), c_Groups_Oone__class_Oone(_1223363))), 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)))), _1223365)) = c_Groups_Oone__class_Oone(_1223363))], (40116 ^ _781215) ^ [_1564346, _1564348, _1564350] : [c_Wellfounded_Owf(_1564346, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564346, _1564346), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564346, _1564346), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1564346, _1564346, _1564346), _1564348), _1564348)), hAPP(hAPP(c_Relation_Orel__comp(_1564346, _1564346, _1564346), _1564350), _1564348))), _1564350)), -(c_Wellfounded_Owf(_1564346, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564346, _1564346), tc_HOL_Obool)), _1564348), _1564350)))], (20906 ^ _781215) ^ [_1155966, _1155968] : [_1155966 = hAPP(c_Int_Onat, _1155968), 20909 ^ _781215 : [(20916 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1155968))), -(_1155966 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20910 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1155968)), -(_1155968 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155966))]]], (49541 ^ _781215) ^ [_1783795, _1783797, _1783799, _1783801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1783795), tc_List_Olist(_1783795))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1783795), tc_List_Olist(_1783795)), _1783797), _1783799)), c_List_Olistrel(_1783795, _1783801))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1783795), tc_List_Olist(_1783795))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1783795), tc_List_Olist(_1783795)), _1783797), _1783799)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1783795), c_List_Olistrel1(_1783795, _1783801)))))], (20735 ^ _781215) ^ [_1153162] : [class_Int_Onumber__ring(_1153162), -(hAPP(c_Int_Onumber__class_Onumber__of(_1153162), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1153162))], (49674 ^ _781215) ^ [_1787454, _1787456] : [-(hAPP(c_Relation_OField(_1787454), hAPP(c_Relation_Oconverse(_1787454, _1787454), _1787456)) = hAPP(c_Relation_OField(_1787454), _1787456))], (44618 ^ _781215) ^ [_1675599, _1675601, _1675603] : [hAPP(hAPP(c_List_Odrop(_1675599), _1675601), _1675603) = c_List_Olist_ONil(_1675599), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675599)), _1675603)), _1675601)))], (31258 ^ _781215) ^ [_1353666, _1353668] : [class_Orderings_Olinorder(_1353666), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353666, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1353666), _1353668)), hAPP(hAPP(c_Set_Oinsert(_1353666), _1353668), c_Orderings_Obot__class_Obot(tc_fun(_1353666, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1353666), _1353668))], (2978 ^ _781215) ^ [_825832, _825834, _825836, _825838, _825840, _825842] : [-(c_Com_Ocom_OCond(_825842, _825838, _825834) = c_Com_Ocom_OCond(_825840, _825836, _825832)), _825842 = _825840, _825838 = _825836, _825834 = _825832], (25676 ^ _781215) ^ [_1243289] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1243289)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1243289)], (21261 ^ _781215) ^ [_1161929, _1161931, _1161933, _1161935, _1161937] : [class_Complete__Lattice_Ocomplete__lattice(_1161929), hBOOL(hAPP(hAPP(c_member(_1161931), _1161933), _1161935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161929), hAPP(_1161937, _1161933)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1161931, _1161929), _1161935), _1161937))))], (7865 ^ _781215) ^ [_914105, _914107, _914109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914105), _914109)), _914107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914105), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _914107), _914109))))], (12066 ^ _781215) ^ [_990802, _990804, _990806, _990808] : [class_Groups_Oordered__comm__monoid__add(_990802), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990802), c_Groups_Ozero__class_Ozero(_990802)), _990804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990802), _990806), _990808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990802), _990806), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_990802), _990808), _990804))))], (32072 ^ _781215) ^ [_1372947, _1372949, _1372951, _1372953] : [class_Groups_Oab__group__add(_1372947), 32075 ^ _781215 : [(32082 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1372949), _1372951))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1372947), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1372947, _1372947), hAPP(hAPP(c_COMBB(_1372947, tc_fun(_1372947, _1372947), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1372947)), _1372953)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1372947, tc_Nat_Onat), _1372953), 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, _1372949, _1372951)) = c_Groups_Ozero__class_Ozero(_1372947))], (32076 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1372949), _1372951)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1372947), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1372947, _1372947), hAPP(hAPP(c_COMBB(_1372947, tc_fun(_1372947, _1372947), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1372947)), _1372953)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1372947, tc_Nat_Onat), _1372953), 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, _1372949, _1372951)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1372947), hAPP(_1372953, _1372949)), hAPP(_1372953, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1372951), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (18790 ^ _781215) ^ [_1118157, _1118159, _1118161] : [class_Orderings_Olinorder(_1118157), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118157), _1118159), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1118157), _1118159), _1118161))))], (31467 ^ _781215) ^ [_1358381] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1358381) = 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), _1358381), 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))))))], (20952 ^ _781215) ^ [_1156589, _1156591] : [-(hAPP(c_Int_Onat, _1156589) = _1156591), 20955 ^ _781215 : [(20958 ^ _781215) ^ [] : [_1156589 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1156591)], (20956 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156589)))]], 20959 ^ _781215 : [(20962 ^ _781215) ^ [] : [_1156591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20960 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156589))]]], (26430 ^ _781215) ^ [_1260711, _1260713] : [class_Rings_Oring__1(_1260711), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260713)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1260711), hAPP(c_Int_Onat, _1260713)) = hAPP(c_Int_Oring__1__class_Oof__int(_1260711), _1260713))], (27498 ^ _781215) ^ [_1281658] : [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), _1281658))), -(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), _1281658)) = 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), _1281658))))], (43790 ^ _781215) ^ [_1655683] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655683)), c_List_Olist_ONil(_1655683)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18037 ^ _781215) ^ [_1103350, _1103352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1103350)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103352))), -(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(_1103352))), 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), _1103350)), c_Int_Onat))))))], (41120 ^ _781215) ^ [_1588098, _1588100, _1588102] : [hBOOL(hAPP(c_List_Odistinct(_1588098), hAPP(hAPP(c_List_Omap(tc_prod(_1588098, _1588100), _1588098), c_Product__Type_Ofst(_1588098, _1588100)), _1588102))), -(c_Map_Oran(_1588098, _1588100, hAPP(c_Map_Omap__of(_1588098, _1588100), _1588102)) = hAPP(c_Set_Oimage(tc_prod(_1588098, _1588100), _1588100, c_Product__Type_Osnd(_1588098, _1588100)), hAPP(c_List_Oset(tc_prod(_1588098, _1588100)), _1588102)))], (35595 ^ _781215) ^ [_1450157, _1450159, _1450161] : [class_Fields_Olinordered__field__inverse__zero(_1450157), 35601 ^ _781215 : [(35606 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1450157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1450157), 35600 ^ [_1450157, _1450159, _1450161]), _1450159)), _1450161))], (35604 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450157), 35600 ^ [_1450157, _1450159, _1450161]), c_Groups_Oone__class_Oone(_1450157))))], (35602 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450157), c_Groups_Ozero__class_Ozero(_1450157)), 35600 ^ [_1450157, _1450159, _1450161])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1450157), _1450159), _1450161)))], (49680 ^ _781215) ^ [_1787607, _1787609, _1787611, _1787613, _1787615] : [-(hAPP(c_Relation_Oconverse(_1787607, _1787609), hAPP(hAPP(c_Relation_Orel__comp(_1787607, _1787611, _1787609), _1787613), _1787615)) = hAPP(hAPP(c_Relation_Orel__comp(_1787609, _1787611, _1787607), hAPP(c_Relation_Oconverse(_1787611, _1787609), _1787615)), hAPP(c_Relation_Oconverse(_1787607, _1787611), _1787613)))], (26470 ^ _781215) ^ [_1261499] : [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), _1261499))), 26473 ^ _781215 : [(26480 ^ _781215) ^ [] : [-(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), _1261499))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261499)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261499)), 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), _1261499)))))], (26474 ^ _781215) ^ [] : [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), _1261499)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1261499)) = 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), _1261499))))]]], (5430 ^ _781215) ^ [_864146, _864148] : [_864148 = _864146, -(c_Groups_Oone__class_Oone(_864148) = c_Groups_Oone__class_Oone(_864146))], (41769 ^ _781215) ^ [_1603843, _1603845, _1603847, _1603849, _1603851] : [c_Finite__Set_Ofolding__idem(_1603843, _1603845, _1603847, _1603849), -(hAPP(c_Fun_Ocomp(_1603845, _1603845, _1603845, hAPP(_1603847, _1603851)), hAPP(_1603847, _1603851)) = hAPP(_1603847, _1603851))], (38682 ^ _781215) ^ [_1521420, _1521422, _1521424, _1521426, _1521428, _1521430, _1521432, _1521434] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1521420, _1521422), tc_fun(tc_prod(_1521424, _1521426), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1521420, _1521422), _1521428), hAPP(c_COMBK(tc_fun(_1521422, tc_HOL_Obool), _1521420), _1521430))), hAPP(c_Product__Type_Oprod_Oprod__case(_1521420, _1521422, tc_fun(tc_prod(_1521424, _1521426), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1521420, tc_fun(_1521422, tc_fun(_1521424, tc_fun(_1521426, tc_HOL_Obool))), tc_fun(_1521422, tc_fun(tc_prod(_1521424, _1521426), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1521424, tc_fun(_1521426, tc_HOL_Obool)), tc_fun(tc_prod(_1521424, _1521426), tc_HOL_Obool)), tc_fun(tc_fun(_1521422, tc_fun(_1521424, tc_fun(_1521426, tc_HOL_Obool))), tc_fun(_1521422, tc_fun(tc_prod(_1521424, _1521426), tc_HOL_Obool))), _1521420), c_COMBB(tc_fun(_1521424, tc_fun(_1521426, tc_HOL_Obool)), tc_fun(tc_prod(_1521424, _1521426), tc_HOL_Obool), _1521422)), hAPP(hAPP(c_COMBB(tc_fun(_1521424, tc_HOL_Obool), tc_fun(tc_fun(_1521424, tc_fun(_1521426, tc_HOL_Obool)), tc_fun(tc_prod(_1521424, _1521426), tc_HOL_Obool)), _1521420), c_Product__Type_OSigma(_1521424, _1521426)), _1521432))), hAPP(hAPP(c_COMBB(tc_fun(_1521426, tc_HOL_Obool), tc_fun(_1521424, tc_fun(_1521426, tc_HOL_Obool)), _1521422), c_COMBK(tc_fun(_1521426, tc_HOL_Obool), _1521424)), _1521434)))) = hAPP(hAPP(c_Product__Type_OSigma(_1521424, _1521426), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1521420, tc_fun(_1521424, tc_HOL_Obool)), _1521428), _1521432)), hAPP(c_COMBK(tc_fun(_1521426, tc_HOL_Obool), _1521424), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1521422, tc_fun(_1521426, tc_HOL_Obool)), _1521430), _1521434))))], (21496 ^ _781215) ^ [_1166986, _1166988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1166986)), c_Int_OBit0(_1166988))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1166986), _1166988)))], (6405 ^ _781215) ^ [_885404] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _885404), _885404)))], (51656 ^ _781215) ^ [] : [-(class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))], (2918 ^ _781215) ^ [_824860, _824862, _824864, _824866, _824868, _824870, _824872, _824874] : [-(c_Product__Type_Oapfst(_824874, _824870, _824866, _824862) = c_Product__Type_Oapfst(_824872, _824868, _824864, _824860)), _824874 = _824872, _824870 = _824868, _824866 = _824864, _824862 = _824860], (5939 ^ _781215) ^ [_875747, _875749, _875751, _875753] : [c_Com_Ocom_OCall(_875747, _875749, _875751) = hAPP(c_Com_Ocom_OBODY, _875753)], (10464 ^ _781215) ^ [_959761, _959763, _959765, _959767, _959769, _959771] : [class_Rings_Oring(_959761), 10467 ^ _781215 : [(10474 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959761), _959763), _959769)), _959765)), _959767) = _959771, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959761), _959763), _959765)), _959767) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959761), _959769), _959765)), _959771))], (10468 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959761), _959763), _959765)), _959767) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959761), _959769), _959765)), _959771), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959761), _959763), _959769)), _959765)), _959767) = _959771)]]], (1808 ^ _781215) ^ [_806785, _806787] : [-(class_Orderings_Oord(_806785)), _806787 = _806785, class_Orderings_Oord(_806787)], (25690 ^ _781215) ^ [_1243578, _1243580, _1243582, _1243584, _1243586, _1243588] : [-(hBOOL(hAPP(hAPP(c_member(_1243578), _1243580), c_SetInterval_Oord_OatLeastLessThan(_1243578, _1243582, _1243584, _1243586, _1243588)))), hBOOL(hAPP(hAPP(_1243582, _1243586), _1243580)), hBOOL(hAPP(hAPP(_1243584, _1243580), _1243588))], (40130 ^ _781215) ^ [_1564726, _1564728, _1564730] : [_1564730 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564726, _1564728), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1564726, _1564728), _1564730) = c_Orderings_Obot__class_Obot(tc_fun(_1564726, tc_HOL_Obool)))], (45177 ^ _781215) ^ [_1687500, _1687502, _1687504] : [-(c_List_Olast(_1687500, hAPP(hAPP(c_List_Oappend(_1687500), _1687502), hAPP(hAPP(c_List_Olist_OCons(_1687500), _1687504), c_List_Olist_ONil(_1687500)))) = _1687504)], (34244 ^ _781215) ^ [_1422613, _1422615, _1422617, _1422619, _1422621, _1422623] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422613, tc_fun(_1422615, tc_HOL_Obool))), _1422617), _1422619), _1422621), _1422623)), -(hBOOL(hAPP(hAPP(_1422617, _1422621), _1422623)))], (32066 ^ _781215) ^ [_1372746, _1372748] : [class_Rings_Ocomm__semiring__1(_1372746), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1372746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1372746), c_Groups_Oone__class_Oone(_1372746)), c_Groups_Oone__class_Oone(_1372746))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1372746), c_Nat_Osemiring__1__class_Oof__nat(_1372746)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1372748))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1372746), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1372746), _1372748)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1372746), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1372746), _1372748)), c_Groups_Oone__class_Oone(_1372746))))], (49732 ^ _781215) ^ [_1788921, _1788923, _1788925, _1788927, _1788929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1788921, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1788923, _1788921, _1788925), _1788927)), _1788929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1788923, tc_HOL_Obool)), _1788927), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1788923, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1788921, _1788923, hAPP(c_Relation_Oconverse(_1788923, _1788921), _1788925)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1788921, tc_HOL_Obool)), _1788929))))))], (49929 ^ _781215) ^ [_1793580, _1793582, _1793584, _1793586, _1793588] : [c_Relation_Osingle__valued(_1793580, _1793582, hAPP(c_Relation_Oconverse(_1793582, _1793580), _1793584)), -(hAPP(c_Relation_OImage(_1793582, _1793580, _1793584), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1793582, tc_HOL_Obool)), _1793586), _1793588)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1793580, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1793582, _1793580, _1793584), _1793586)), hAPP(c_Relation_OImage(_1793582, _1793580, _1793584), _1793588)))], (39353 ^ _781215) ^ [_1539324, _1539326, _1539328] : [class_Orderings_Olinorder(_1539324), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539324), _1539326)), -(_1539326 = c_Orderings_Obot__class_Obot(tc_fun(_1539324, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539324), _1539328)), -(_1539328 = c_Orderings_Obot__class_Obot(tc_fun(_1539324, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1539324), c_Big__Operators_Olattice_OInf__fin(_1539324, c_Orderings_Oord__class_Omin(_1539324), _1539326)), c_Big__Operators_Olattice_OInf__fin(_1539324, c_Orderings_Oord__class_Omin(_1539324), _1539328)) = c_Big__Operators_Olattice_OInf__fin(_1539324, c_Orderings_Oord__class_Omin(_1539324), hAPP(c_Set_OCollect(_1539324), hAPP(hAPP(c_COMBB(tc_fun(_1539324, tc_HOL_Obool), tc_HOL_Obool, _1539324), c_HOL_OEx(_1539324)), hAPP(hAPP(c_COMBB(tc_fun(_1539324, tc_fun(_1539324, tc_HOL_Obool)), tc_fun(_1539324, tc_HOL_Obool), _1539324), hAPP(c_COMBB(tc_fun(_1539324, tc_HOL_Obool), tc_HOL_Obool, _1539324), c_HOL_OEx(_1539324))), hAPP(hAPP(c_COMBC(_1539324, tc_fun(_1539324, tc_fun(_1539324, tc_HOL_Obool)), tc_fun(_1539324, tc_fun(_1539324, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1539324, tc_fun(tc_fun(_1539324, tc_HOL_Obool), tc_fun(_1539324, tc_HOL_Obool))), tc_fun(tc_fun(_1539324, tc_fun(_1539324, tc_HOL_Obool)), tc_fun(_1539324, tc_fun(_1539324, tc_HOL_Obool))), _1539324), c_COMBS(_1539324, tc_fun(_1539324, tc_HOL_Obool), tc_fun(_1539324, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1539324, tc_fun(_1539324, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1539324, tc_fun(tc_fun(_1539324, tc_HOL_Obool), tc_fun(_1539324, tc_HOL_Obool))), _1539324), hAPP(c_COMBB(tc_fun(_1539324, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1539324, tc_HOL_Obool), tc_fun(_1539324, tc_HOL_Obool)), _1539324), c_COMBS(_1539324, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1539324, tc_fun(_1539324, tc_HOL_Obool)), tc_fun(_1539324, tc_fun(_1539324, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1539324), hAPP(c_COMBB(tc_fun(_1539324, tc_HOL_Obool), tc_fun(_1539324, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1539324), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539324), c_fconj))), hAPP(hAPP(c_COMBC(_1539324, tc_fun(_1539324, tc_fun(_1539324, _1539324)), tc_fun(_1539324, tc_fun(_1539324, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1539324, _1539324), tc_fun(_1539324, tc_HOL_Obool)), tc_fun(tc_fun(_1539324, tc_fun(_1539324, _1539324)), tc_fun(_1539324, tc_fun(_1539324, tc_HOL_Obool))), _1539324), c_COMBB(tc_fun(_1539324, _1539324), tc_fun(_1539324, tc_HOL_Obool), _1539324)), hAPP(hAPP(c_COMBB(tc_fun(_1539324, tc_HOL_Obool), tc_fun(tc_fun(_1539324, _1539324), tc_fun(_1539324, tc_HOL_Obool)), _1539324), c_COMBB(_1539324, tc_HOL_Obool, _1539324)), c_fequal))), c_Orderings_Oord__class_Omax(_1539324)))))), hAPP(hAPP(c_COMBC(_1539324, tc_fun(_1539324, tc_HOL_Obool), tc_fun(_1539324, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1539324, tc_HOL_Obool), tc_fun(_1539324, tc_HOL_Obool)), _1539324), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1539324)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539324), c_fconj), hAPP(hAPP(c_COMBC(_1539324, tc_fun(_1539324, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539324)), _1539326)))), hAPP(hAPP(c_COMBC(_1539324, tc_fun(_1539324, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539324)), _1539328))))))))], (6782 ^ _781215) ^ [_892627, _892629, _892631, _892633] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_892627), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892627, tc_HOL_Obool)), _892629), _892633))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_892627), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892627, tc_HOL_Obool)), _892629), hAPP(hAPP(c_Set_Oinsert(_892627), _892631), _892633)))))], (10770 ^ _781215) ^ [_965807, _965809, _965811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965811), _965809))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965807), _965809)), _965811)))], (5829 ^ _781215) ^ [_873892, _873894, _873896] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _873892)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _873894), _873892), _873896)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _873894), _873892), _873896)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (13836 ^ _781215) ^ [_1022286, _1022288] : [hAPP(c_Finite__Set_Ocard(_1022286), _1022288) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1022288 = c_Orderings_Obot__class_Obot(tc_fun(_1022286, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022286), _1022288))], (50038 ^ _781215) ^ [_1796425, _1796427, _1796429] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1796425, _1796425)), _1796427), c_Transitive__Closure_Otrancl(_1796425, _1796429)))), 50039 ^ _781215 : [(50040 ^ _781215) ^ [_1796504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1796504)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1796425, _1796425)), _1796427), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1796425, _1796425), tc_HOL_Obool), _1796504), _1796429)))]]], (48850 ^ _781215) ^ [_1767538, _1767540] : [-(c_Random_Oselect__weight(_1767538, _1767540) = 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(_1767538, 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, _1767538), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1767538)), _1767540)))), hAPP(hAPP(c_COMBB(_1767538, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1767538, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1767538, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1767538, _1767540))))], (35018 ^ _781215) ^ [_1437990, _1437992, _1437994, _1437996] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1437990), _1437992)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1437994), _1437996)), 35025 ^ _781215 : [(35026 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1437990), _1437992)), hAPP(c_Finite__Set_Ocard(_1437994), _1437996)))), 35027 ^ _781215 : [(35028 ^ _781215) ^ [_1438201] : [c_Fun_Oinj__on(_1437990, _1437994, _1438201, _1437992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437994, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1437990, _1437994, _1438201), _1437992)), _1437996))]]], (35036 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1437990), _1437992)), hAPP(c_Finite__Set_Ocard(_1437994), _1437996))), 35040 ^ _781215 : [(35043 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437994, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1437990, _1437994, 35039 ^ [_1437990, _1437992, _1437994, _1437996]), _1437992)), _1437996)))], (35041 ^ _781215) ^ [] : [-(c_Fun_Oinj__on(_1437990, _1437994, 35039 ^ [_1437990, _1437992, _1437994, _1437996], _1437992))]]]]], (24444 ^ _781215) ^ [_1221990, _1221992, _1221994] : [class_Rings_Olinordered__idom(_1221990), 24447 ^ _781215 : [(24448 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221990), c_Groups_Ozero__class_Ozero(_1221990)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221990), hAPP(hAPP(c_Power_Opower__class_Opower(_1221990), _1221992), 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(_1221990), _1221994), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1221992 = c_Groups_Ozero__class_Ozero(_1221990), _1221994 = c_Groups_Ozero__class_Ozero(_1221990)], (24458 ^ _781215) ^ [] : [24459 ^ _781215 : [(24462 ^ _781215) ^ [] : [-(_1221994 = c_Groups_Ozero__class_Ozero(_1221990))], (24460 ^ _781215) ^ [] : [-(_1221992 = c_Groups_Ozero__class_Ozero(_1221990))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221990), c_Groups_Ozero__class_Ozero(_1221990)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221990), hAPP(hAPP(c_Power_Opower__class_Opower(_1221990), _1221992), 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(_1221990), _1221994), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (38530 ^ _781215) ^ [_1517484, _1517486, _1517488, _1517490, _1517492] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1517484, _1517486), _1517488), hAPP(hAPP(c_COMBS(_1517484, tc_fun(_1517486, tc_HOL_Obool), tc_fun(_1517486, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517486, tc_HOL_Obool), tc_fun(tc_fun(_1517486, tc_HOL_Obool), tc_fun(_1517486, tc_HOL_Obool)), _1517484), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517486, tc_HOL_Obool))), _1517490)), _1517492)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517484, _1517486), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517484, _1517486), _1517488), _1517490)), hAPP(hAPP(c_Product__Type_OSigma(_1517484, _1517486), _1517488), _1517492)))], (51432 ^ _781215) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (44734 ^ _781215) ^ [_1678469, _1678471, _1678473, _1678475] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1678469) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1678471), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1678469)), hAPP(hAPP(c_List_Olist_OCons(_1678471), _1678473), _1678475)) = hAPP(hAPP(c_List_Odrop(_1678471), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1678469)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1678475))], (51398 ^ _781215) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (34746 ^ _781215) ^ [_1432303, _1432305, _1432307, _1432309, _1432311] : [c_Fun_Oinj__on(_1432303, _1432305, _1432307, _1432309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1432303, tc_HOL_Obool)), _1432311), _1432309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1432305, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1432303, _1432305, _1432307), _1432311)), hAPP(c_Set_Oimage(_1432303, _1432305, _1432307), _1432309))))], (34820 ^ _781215) ^ [_1433758, _1433760, _1433762, _1433764] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1433758), _1433760)), hAPP(c_Finite__Set_Ocard(_1433762), hAPP(c_Set_Oimage(_1433758, _1433762, _1433764), _1433760)) = hAPP(c_Finite__Set_Ocard(_1433758), _1433760), -(c_Fun_Oinj__on(_1433758, _1433762, _1433764, _1433760))], (49119 ^ _781215) ^ [_1772387, _1772389, _1772391, _1772393, _1772395] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1772387, _1772387)), hAPP(hAPP(c_Product__Type_OPair(_1772387, _1772387), _1772389), _1772391)), _1772393)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772387, _1772387)), hAPP(hAPP(c_Product__Type_OPair(_1772387, _1772387), _1772391), _1772395)), c_Transitive__Closure_Otrancl(_1772387, _1772393))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1772387, _1772387)), hAPP(hAPP(c_Product__Type_OPair(_1772387, _1772387), _1772389), _1772395)), c_Transitive__Closure_Otrancl(_1772387, _1772393))))], (4646 ^ _781215) ^ [_851650, _851652, _851654, _851656, _851658, _851660] : [-(c_Nitpick_Oplus__frac(_851660, _851656, _851652) = c_Nitpick_Oplus__frac(_851658, _851654, _851650)), _851660 = _851658, _851656 = _851654, _851652 = _851650], (13918 ^ _781215) ^ [_1023671, _1023673, _1023675] : [-(hBOOL(hAPP(_1023671, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1023673), _1023675)))), 13921 ^ _781215 : [(13924 ^ _781215) ^ [] : [hBOOL(hAPP(_1023671, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13922 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1023673), _1023675)))]], 13926 ^ _781215 : [(13929 ^ _781215) ^ [] : [hBOOL(hAPP(_1023671, 13925 ^ [_1023671, _1023673, _1023675]))], (13927 ^ _781215) ^ [] : [-(_1023673 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1023675), 13925 ^ [_1023671, _1023673, _1023675]))]]], (41501 ^ _781215) ^ [_1597255, _1597257, _1597259, _1597261, _1597263, _1597265, _1597267, _1597269] : [c_Finite__Set_Ofolding__image(_1597255, _1597257, _1597259, _1597261, _1597263), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597257), _1597265)), c_Fun_Oinj__on(_1597257, _1597257, _1597267, _1597265), -(hAPP(hAPP(_1597263, _1597269), hAPP(c_Set_Oimage(_1597257, _1597257, _1597267), _1597265)) = hAPP(hAPP(_1597263, hAPP(c_Fun_Ocomp(_1597257, _1597255, _1597257, _1597269), _1597267)), _1597265))], (49399 ^ _781215) ^ [_1780194] : [-(hAPP(c_Relation_ORange(_1780194, _1780194), c_Relation_OId(_1780194)) = c_Orderings_Otop__class_Otop(tc_fun(_1780194, tc_HOL_Obool)))], (1088 ^ _781215) ^ [_797785, _797787] : [-(class_Groups_Olinordered__ab__group__add(_797785)), _797787 = _797785, class_Groups_Olinordered__ab__group__add(_797787)], (5652 ^ _781215) ^ [_870314, _870316] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, _870314))), _870316), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _870314)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _870316, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, _870314))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (6986 ^ _781215) ^ [_897016, _897018, _897020, _897022] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _897016), _897018), _897020), _897022)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _897016), _897018), hAPP(c_Nat_OSuc, _897020)), _897022)))], (47132 ^ _781215) ^ [_1729485, _1729487, _1729489] : [class_Enum_Oenum(_1729485), class_Enum_Oenum(_1729487), 47139 ^ _781215 : [(47146 ^ _781215) ^ [] : [c_Enum_Oex__n__lists(_1729485, hAPP(hAPP(c_COMBB(tc_fun(_1729487, _1729485), tc_HOL_Obool, tc_List_Olist(_1729485)), _1729489), hAPP(hAPP(c_COMBB(tc_fun(_1729487, tc_Option_Ooption(_1729485)), tc_fun(_1729487, _1729485), tc_List_Olist(_1729485)), c_Fun_Ocomp(tc_Option_Ooption(_1729485), _1729485, _1729487, c_Option_Othe(_1729485))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1729487, _1729485)), tc_fun(_1729487, tc_Option_Ooption(_1729485)), tc_List_Olist(_1729485)), c_Map_Omap__of(_1729487, _1729485)), hAPP(c_List_Ozip(_1729487, _1729485), c_Enum_Oenum__class_Oenum(_1729487))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729487)), c_Enum_Oenum__class_Oenum(_1729487))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1729487, _1729485)), _1729489)))], (47140 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1729487, _1729485)), _1729489)), -(c_Enum_Oex__n__lists(_1729485, hAPP(hAPP(c_COMBB(tc_fun(_1729487, _1729485), tc_HOL_Obool, tc_List_Olist(_1729485)), _1729489), hAPP(hAPP(c_COMBB(tc_fun(_1729487, tc_Option_Ooption(_1729485)), tc_fun(_1729487, _1729485), tc_List_Olist(_1729485)), c_Fun_Ocomp(tc_Option_Ooption(_1729485), _1729485, _1729487, c_Option_Othe(_1729485))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1729487, _1729485)), tc_fun(_1729487, tc_Option_Ooption(_1729485)), tc_List_Olist(_1729485)), c_Map_Omap__of(_1729487, _1729485)), hAPP(c_List_Ozip(_1729487, _1729485), c_Enum_Oenum__class_Oenum(_1729487))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729487)), c_Enum_Oenum__class_Oenum(_1729487))))]]], (33456 ^ _781215) ^ [_1404117, _1404119, _1404121] : [class_Lattices_Osemilattice__inf(_1404117), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404117), _1404119)), hBOOL(hAPP(hAPP(c_member(_1404117), _1404121), _1404119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404117), hAPP(c_Finite__Set_Ofold1(_1404117, c_Lattices_Osemilattice__inf__class_Oinf(_1404117)), _1404119)), _1404121)))], (1868 ^ _781215) ^ [_807535, _807537] : [-(class_HOL_Oequal(_807535)), _807537 = _807535, class_HOL_Oequal(_807537)], (25897 ^ _781215) ^ [_1250897, _1250899] : [class_Int_Onumber__ring(_1250897), -(hAPP(c_Int_Onumber__class_Onumber__of(_1250897), _1250899) = hAPP(c_Int_Oring__1__class_Oof__int(_1250897), _1250899))], (30862 ^ _781215) ^ [_1346267, _1346269, _1346271, _1346273, _1346275] : [class_Orderings_Olinorder(_1346267), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346267, _1346269), _1346271) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346267, _1346273), _1346275), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346267), _1346269), _1346271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346267), _1346273), _1346275)), -(_1346269 = _1346273)], (12856 ^ _781215) ^ [_1005216, _1005218, _1005220] : [class_Rings_Olinordered__ring__strict(_1005216), 12859 ^ _781215 : [(12868 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1005216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005216), _1005218), _1005218)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005216), _1005220), _1005220)) = c_Groups_Ozero__class_Ozero(_1005216)), _1005218 = c_Groups_Ozero__class_Ozero(_1005216), _1005220 = c_Groups_Ozero__class_Ozero(_1005216)], (12860 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1005216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005216), _1005218), _1005218)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005216), _1005220), _1005220)) = c_Groups_Ozero__class_Ozero(_1005216), 12863 ^ _781215 : [(12866 ^ _781215) ^ [] : [-(_1005220 = c_Groups_Ozero__class_Ozero(_1005216))], (12864 ^ _781215) ^ [] : [-(_1005218 = c_Groups_Ozero__class_Ozero(_1005216))]]]]], (43059 ^ _781215) ^ [_1638473, _1638475, _1638477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1638473, tc_HOL_Obool)), _1638475), _1638477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1638473), tc_HOL_Obool)), c_List_Olists(_1638473, _1638475)), c_List_Olists(_1638473, _1638477))))], (32240 ^ _781215) ^ [_1376833, _1376835, _1376837] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1376833, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1376833), _1376835), _1376837), -(_1376835 = c_Orderings_Obot__class_Obot(tc_fun(_1376833, tc_HOL_Obool)))], (49724 ^ _781215) ^ [_1788747, _1788749] : [-(c_Transitive__Closure_Otrancl(_1788747, hAPP(c_Relation_Oconverse(_1788747, _1788747), _1788749)) = hAPP(c_Relation_Oconverse(_1788747, _1788747), c_Transitive__Closure_Otrancl(_1788747, _1788749)))], (25372 ^ _781215) ^ [] : [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)], (8165 ^ _781215) ^ [_918874, _918876, _918878, _918880] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_918874), 8168 ^ _781215 : [(8175 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918874), _918878), _918880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918874), _918876), _918878)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918874), _918876), _918880))))], (8169 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918874), _918876), _918878)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918874), _918876), _918880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918874), _918878), _918880)))]]], (46646 ^ _781215) ^ [_1719045, _1719047] : [hBOOL(hAPP(c_List_Odistinct(_1719045), _1719047)), -(c_List_Oremdups(_1719045, _1719047) = _1719047)], (40673 ^ _781215) ^ [_1578266, _1578268, _1578270, _1578272] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1578266, _1578268)), _1578270), _1578272), _1578270)), hBOOL(hAPP(_1578266, _1578270)), 40681 ^ _781215 : [(40684 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1578266, _1578268)), 40680 ^ [_1578266, _1578268, _1578270, _1578272]), _1578272), _1578270)))], (40682 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1578268), _1578270), _1578272), 40680 ^ [_1578266, _1578268, _1578270, _1578272])))]]], (32966 ^ _781215) ^ [_1392591, _1392593, _1392595] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392591, tc_HOL_Obool)), _1392593), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392591, tc_HOL_Obool)), _1392593), _1392595)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392591, tc_HOL_Obool)), _1392593), _1392595))], (25366 ^ _781215) ^ [_1238382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1238382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1238382))))], (16786 ^ _781215) ^ [_1082577, _1082579, _1082581, _1082583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1082577, tc_HOL_Obool)), _1082579), _1082581)), hBOOL(hAPP(_1082579, _1082583)), -(hBOOL(hAPP(_1082581, _1082583)))], (16951 ^ _781215) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32258 ^ _781215) ^ [_1377208, _1377210, _1377212] : [_1377210 = c_Orderings_Obot__class_Obot(tc_fun(_1377208, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377208), _1377210), _1377212) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377208, tc_HOL_Obool), tc_HOL_Obool)))], (21560 ^ _781215) ^ [_1168056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1168056)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1168056), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11480 ^ _781215) ^ [_981330] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _981330))))], (45416 ^ _781215) ^ [_1692776, _1692778, _1692780, _1692782] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1692776, tc_Nat_Onat), _1692776), c_Product__Type_Ofst(_1692776, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1692776, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1692776, tc_Nat_Onat)), _1692778), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1692776, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1692776, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1692776, tc_Nat_Onat), _1692780), _1692782))) = hAPP(hAPP(c_List_Omap(tc_prod(_1692776, tc_Nat_Onat), _1692776), c_Product__Type_Ofst(_1692776, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1692776, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1692776, tc_Nat_Onat)), _1692778), c_Product__Type_Osnd(_1692776, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1692776, tc_Nat_Onat), _1692780), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1692782)))))], (49185 ^ _781215) ^ [_1774633, _1774635, _1774637, _1774639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774633, _1774633)), hAPP(hAPP(c_Product__Type_OPair(_1774633, _1774633), _1774637), _1774639)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774633, _1774633), tc_HOL_Obool)), _1774635), c_Relation_OId(_1774633)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1774633, tc_fun(_1774633, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1774633, tc_fun(tc_prod(_1774633, _1774633), tc_HOL_Obool), tc_fun(_1774633, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774633, tc_fun(tc_fun(tc_prod(_1774633, _1774633), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1774633, _1774633), tc_HOL_Obool), tc_fun(_1774633, tc_HOL_Obool)), _1774633), c_COMBC(_1774633, tc_fun(tc_prod(_1774633, _1774633), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774633, tc_prod(_1774633, _1774633)), tc_fun(_1774633, tc_fun(tc_fun(tc_prod(_1774633, _1774633), tc_HOL_Obool), tc_HOL_Obool)), _1774633), hAPP(c_COMBB(tc_prod(_1774633, _1774633), tc_fun(tc_fun(tc_prod(_1774633, _1774633), tc_HOL_Obool), tc_HOL_Obool), _1774633), c_member(tc_prod(_1774633, _1774633)))), c_Product__Type_OPair(_1774633, _1774633)))), _1774635)), c_fequal), _1774637), _1774639)))], (46455 ^ _781215) ^ [_1715308, _1715310] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715308), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1715308))), _1715310))), -(c_List_Otranspose(_1715308, c_List_Otranspose(_1715308, _1715310)) = c_List_OtakeWhile(tc_List_Olist(_1715308), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1715308)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1715308), tc_List_Olist(_1715308), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1715308))), _1715310))], (452 ^ _781215) ^ [_788299, _788301, _788303, _788305] : [-(c_Nitpick_Owf_H(_788303, _788299)), c_Nitpick_Owf_H(_788305, _788301), _788305 = _788303, _788301 = _788299], (29938 ^ _781215) ^ [_1327091] : [-(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)), _1327091), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (51576 ^ _781215) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (46197 ^ _781215) ^ [_1708348, _1708350, _1708352] : [_1708350 = hAPP(c_List_Orev(_1708348), _1708352), -(hAPP(c_List_Orev(_1708348), _1708350) = _1708352)], (23680 ^ _781215) ^ [_1208143, _1208145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1208143)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1208143)), _1208145) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1208143), _1208145)))], (47060 ^ _781215) ^ [_1727967, _1727969] : [class_Orderings_Olinorder(_1727967), -(c_List_Olinorder__class_Osorted__list__of__set(_1727967, hAPP(c_List_Oset(_1727967), _1727969)) = c_List_Olinorder__class_Osort__key(_1727967, _1727967, c_COMBI(_1727967), c_List_Oremdups(_1727967, _1727969)))], (48057 ^ _781215) ^ [_1749439, _1749441, _1749443, _1749445, _1749447, _1749449, _1749451, _1749453] : [48059 ^ _781215 : [(48062 ^ _781215) ^ [] : [hAPP(c_Fun_Ocomp(_1749443, _1749443, _1749445, hAPP(_1749447, 48058 ^ [_1749439, _1749441, _1749443, _1749445, _1749447, _1749449, _1749451, _1749453])), _1749449) = hAPP(c_Fun_Ocomp(_1749445, _1749443, _1749445, _1749449), hAPP(_1749451, 48058 ^ [_1749439, _1749441, _1749443, _1749445, _1749447, _1749449, _1749451, _1749453]))], (48060 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1749439), 48058 ^ [_1749439, _1749441, _1749443, _1749445, _1749447, _1749449, _1749451, _1749453]), hAPP(c_List_Oset(_1749439), _1749441))))]], -(hAPP(c_List_Ofoldl(_1749443, _1749439, hAPP(c_COMBC(_1749439, _1749443, _1749443), _1749447), hAPP(_1749449, _1749453)), _1749441) = hAPP(_1749449, hAPP(c_List_Ofoldl(_1749445, _1749439, hAPP(c_COMBC(_1749439, _1749445, _1749445), _1749451), _1749453), _1749441)))], (44487 ^ _781215) ^ [_1672197, _1672199, _1672201, _1672203, _1672205, _1672207] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1672197), tc_List_Olist(_1672197))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1672197), tc_List_Olist(_1672197)), hAPP(hAPP(c_List_Oappend(_1672197), _1672199), hAPP(hAPP(c_List_Olist_OCons(_1672197), _1672201), c_List_Olist_ONil(_1672197)))), hAPP(hAPP(c_List_Oappend(_1672197), _1672203), hAPP(hAPP(c_List_Olist_OCons(_1672197), _1672205), c_List_Olist_ONil(_1672197))))), c_List_Olistrel1(_1672197, _1672207)))), 44488 ^ _781215 : [(44495 ^ _781215) ^ [] : [_1672199 = _1672203, hBOOL(hAPP(hAPP(c_member(tc_prod(_1672197, _1672197)), hAPP(hAPP(c_Product__Type_OPair(_1672197, _1672197), _1672201), _1672205)), _1672207))], (44489 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1672197), tc_List_Olist(_1672197))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1672197), tc_List_Olist(_1672197)), _1672199), _1672203)), c_List_Olistrel1(_1672197, _1672207))), _1672201 = _1672205]]], (7913 ^ _781215) ^ [_914890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914890), _914890))], (24900 ^ _781215) ^ [_1230511, _1230513, _1230515, _1230517] : [class_Groups_Omonoid__mult(_1230511), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1230511), _1230513), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1230515), _1230517)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230511), hAPP(hAPP(c_Power_Opower__class_Opower(_1230511), _1230513), _1230515)), hAPP(hAPP(c_Power_Opower__class_Opower(_1230511), _1230513), _1230517)))], (11980 ^ _781215) ^ [_989324, _989326, _989328] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989324), _989326) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989324), _989328), -(_989326 = _989328), -(_989324 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38818 ^ _781215) ^ [_1525573, _1525575, _1525577, _1525579, _1525581, _1525583, _1525585] : [-(hAPP(c_Product__Type_Osnd(_1525573, _1525575), hAPP(c_Product__Type_Omap__pair(_1525577, _1525573, _1525579, _1525575, _1525581, _1525583), _1525585)) = hAPP(_1525583, hAPP(c_Product__Type_Osnd(_1525577, _1525579), _1525585)))], (32770 ^ _781215) ^ [_1388034, _1388036, _1388038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388034, tc_HOL_Obool)), _1388036), _1388038)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388034, tc_HOL_Obool)), _1388038), _1388036) = _1388036)], (1798 ^ _781215) ^ [_806660, _806662] : [-(class_Rings_Osemiring(_806660)), _806662 = _806660, class_Rings_Osemiring(_806662)], (21037 ^ _781215) ^ [] : [-(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)))))], (43980 ^ _781215) ^ [_1659926] : [-(c_List_Olistset(_1659926, c_List_Olist_ONil(tc_fun(_1659926, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1659926)), c_List_Olist_ONil(_1659926)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1659926), tc_HOL_Obool))))], (23833 ^ _781215) ^ [_1210853, _1210855] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1210853)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1210853)), _1210855) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1210853)), _1210855)))], (47050 ^ _781215) ^ [_1727650, _1727652] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1727650, _1727652)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1727652), tc_fun(_1727650, _1727652)), hAPP(hAPP(c_COMBB(tc_fun(_1727650, tc_Option_Ooption(_1727652)), tc_fun(_1727650, _1727652), tc_List_Olist(_1727652)), c_Fun_Ocomp(tc_Option_Ooption(_1727652), _1727652, _1727650, c_Option_Othe(_1727652))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1727650, _1727652)), tc_fun(_1727650, tc_Option_Ooption(_1727652)), tc_List_Olist(_1727652)), c_Map_Omap__of(_1727650, _1727652)), hAPP(c_List_Ozip(_1727650, _1727652), c_Enum_Oenum__class_Oenum(_1727650))))), c_Enum_On__lists(_1727652, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727650)), c_Enum_Oenum__class_Oenum(_1727650)), c_Enum_Oenum__class_Oenum(_1727652)))), class_Enum_Oenum(_1727650), class_Enum_Oenum(_1727652)], (14662 ^ _781215) ^ [_1037621, _1037623, _1037625] : [class_Int_Onumber__ring(_1037621), class_Rings_Olinordered__idom(_1037621), 14669 ^ _781215 : [(14676 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1037623), _1037625)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037621), hAPP(c_Int_Onumber__class_Onumber__of(_1037621), _1037623)), hAPP(c_Int_Onumber__class_Onumber__of(_1037621), _1037625))))], (14670 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037621), hAPP(c_Int_Onumber__class_Onumber__of(_1037621), _1037623)), hAPP(c_Int_Onumber__class_Onumber__of(_1037621), _1037625))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1037623), _1037625)))]]], (35081 ^ _781215) ^ [_1439790, _1439792] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1439790), _1439792)), -(hAPP(c_Finite__Set_Ocard(_1439790), _1439792) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1439790, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1439790), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1439792))], (10046 ^ _781215) ^ [_951992, _951994, _951996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951994), _951996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951992), _951994)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951992), _951996))))], (31577 ^ _781215) ^ [_1361901, _1361903, _1361905] : [class_Groups_Ocomm__monoid__add(_1361901), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361903, _1361901), _1361905), c_Orderings_Obot__class_Obot(tc_fun(_1361903, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1361901))], (15214 ^ _781215) ^ [_1048200, _1048202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048200)), 15217 ^ _781215 : [(15226 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1048200), _1048202) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1048200 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1048202 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (15218 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1048200), _1048202) = c_Groups_Oone__class_Oone(tc_Int_Oint), 15221 ^ _781215 : [(15224 ^ _781215) ^ [] : [-(_1048202 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (15222 ^ _781215) ^ [] : [-(_1048200 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (41088 ^ _781215) ^ [_1587265, _1587267, _1587269, _1587271] : [hAPP(c_Map_Omap__of(_1587265, _1587267), _1587269) = hAPP(c_Map_Omap__of(_1587265, _1587267), _1587271), -(hAPP(c_Set_Oimage(tc_prod(_1587265, _1587267), _1587265, c_Product__Type_Ofst(_1587265, _1587267)), hAPP(c_List_Oset(tc_prod(_1587265, _1587267)), _1587269)) = hAPP(c_Set_Oimage(tc_prod(_1587265, _1587267), _1587265, c_Product__Type_Ofst(_1587265, _1587267)), hAPP(c_List_Oset(tc_prod(_1587265, _1587267)), _1587271)))], (7754 ^ _781215) ^ [_911863, _911865] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911863), hAPP(c_Nat_OSuc, _911865)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911863), _911865)))], (6956 ^ _781215) ^ [_896422, _896424, _896426, _896428, _896430] : [_896422 = c_Option_Ooption_ONone(_896424), -(c_Map_Odom(_896426, _896424, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_896426, tc_Option_Ooption(_896424)), _896428), _896430), _896422)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896426, tc_HOL_Obool)), c_Map_Odom(_896426, _896424, _896428)), hAPP(hAPP(c_Set_Oinsert(_896426), _896430), c_Orderings_Obot__class_Obot(tc_fun(_896426, tc_HOL_Obool)))))], (40197 ^ _781215) ^ [_1566162, _1566164, _1566166, _1566168] : [40198 ^ _781215 : [(40199 ^ _781215) ^ [_1566237] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566162, _1566166)), hAPP(hAPP(c_Product__Type_OPair(_1566162, _1566166), _1566164), _1566237)), _1566168))]], -(hBOOL(hAPP(hAPP(c_member(_1566162), _1566164), hAPP(c_Relation_ODomain(_1566162, _1566166), _1566168))))], (41309 ^ _781215) ^ [_1592714, _1592716, _1592718, _1592720, _1592722, _1592724, _1592726] : [-(hAPP(c_Fun_Ocomp(_1592714, _1592716, _1592718, _1592720), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1592718, _1592714), _1592722), _1592724), _1592726)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1592718, _1592716), hAPP(c_Fun_Ocomp(_1592714, _1592716, _1592718, _1592720), _1592722)), _1592724), hAPP(_1592720, _1592726)))], (30081 ^ _781215) ^ [_1331252, _1331254] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331252), _1331254)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1331252, tc_HOL_Obool)), hAPP(c_Set_OPow(_1331252), _1331254)) = 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(_1331252), _1331254)))], (10868 ^ _781215) ^ [_967811, _967813, _967815, _967817, _967819, _967821] : [class_Rings_Oordered__ring(_967811), 10871 ^ _781215 : [(10878 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967811), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967811), _967813), _967819)), _967815)), _967817)), _967821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967811), _967813), _967815)), _967817)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967811), _967819), _967815)), _967821))))], (10872 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967811), _967813), _967815)), _967817)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967811), _967819), _967815)), _967821))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967811), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967811), _967813), _967819)), _967815)), _967817)), _967821)))]]], (18123 ^ _781215) ^ [_1105642, _1105644, _1105646, _1105648] : [class_Orderings_Olinorder(_1105642), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105642), _1105644), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105642), _1105646), _1105648)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105642), _1105646), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1105642), _1105644), _1105648)))], (39385 ^ _781215) ^ [_1540937, _1540939, _1540941, _1540943] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1540937), hAPP(c_Set_OCollect(_1540937), _1540939))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1540941), hAPP(c_Set_OCollect(_1540941), hAPP(hAPP(c_COMBB(tc_fun(_1540937, tc_HOL_Obool), tc_HOL_Obool, _1540941), c_HOL_OEx(_1540937)), hAPP(hAPP(c_COMBC(_1540941, tc_fun(_1540937, tc_HOL_Obool), tc_fun(_1540937, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540937, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1540937, tc_HOL_Obool), tc_fun(_1540937, tc_HOL_Obool)), _1540941), c_COMBS(_1540937, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540937, tc_HOL_Obool), tc_fun(_1540937, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1540941), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540937), c_fconj)), hAPP(hAPP(c_COMBC(_1540941, tc_fun(_1540937, _1540941), tc_fun(_1540937, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540941, tc_HOL_Obool), tc_fun(tc_fun(_1540937, _1540941), tc_fun(_1540937, tc_HOL_Obool)), _1540941), c_COMBB(_1540941, tc_HOL_Obool, _1540937)), c_fequal)), _1540943)))), _1540939))))))], (10606 ^ _781215) ^ [_962703, _962705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962703), _962705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962703)), _962705)))], (40667 ^ _781215) ^ [_1578089, _1578091, _1578093, _1578095, _1578097] : [c_Com_Ocom_OLocal(_1578089, _1578091, _1578093) = c_Com_Ocom_OWhile(_1578095, _1578097)], (10800 ^ _781215) ^ [_966316, _966318, _966320, _966322, _966324, _966326] : [hAPP(c_Map_Omap__add(_966316, _966318, _966320, _966322), _966324) = hAPP(c_Option_Ooption_OSome(_966318), _966326), -(hAPP(_966322, _966324) = hAPP(c_Option_Ooption_OSome(_966318), _966326)), 10807 ^ _781215 : [(10810 ^ _781215) ^ [] : [-(hAPP(_966320, _966324) = hAPP(c_Option_Ooption_OSome(_966318), _966326))], (10808 ^ _781215) ^ [] : [-(hAPP(_966322, _966324) = c_Option_Ooption_ONone(_966318))]]], (8215 ^ _781215) ^ [_919842, _919844, _919846, _919848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_919842, tc_HOL_Obool)), _919844), _919846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_919842, tc_HOL_Obool)), _919846), _919848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_919842, tc_HOL_Obool)), _919844), _919848)))], (9095 ^ _781215) ^ [_935531, _935533, _935535, _935537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935531), _935533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935535), _935537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935531), _935535)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935533), _935537))))], (17493 ^ _781215) ^ [_1094350] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094350))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094350)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9501 ^ _781215) ^ [_942895, _942897, _942899] : [class_Orderings_Oorder(_942895), -(_942897 = _942899), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942895), _942897), _942899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942895), _942897), _942899)))], (26518 ^ _781215) ^ [_1262410, _1262412] : [26519 ^ _781215 : [(26522 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1262412), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (26520 ^ _781215) ^ [] : [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), _1262410), _1262412)))]], -(c_Divides_OnegDivAlg(_1262410, _1262412) = 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), _1262410), _1262412)))], (27970 ^ _781215) ^ [_1290992, _1290994] : [class_Rings_Odivision__ring(_1290992), -(_1290994 = c_Groups_Ozero__class_Ozero(_1290992)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290992), _1290994), _1290994) = c_Groups_Oone__class_Oone(_1290992))], (22972 ^ _781215) ^ [_1195417, _1195419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195417), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195419), _1195417)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195417), _1195419) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31866 ^ _781215) ^ [_1368140, _1368142, _1368144, _1368146, _1368148] : [class_Groups_Oab__group__add(_1368140), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368142), _1368144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1368142, tc_HOL_Obool)), _1368146), _1368144)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1368142, _1368140), _1368148), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368142, tc_HOL_Obool)), _1368144), _1368146)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1368140), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1368142, _1368140), _1368148), _1368144)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1368142, _1368140), _1368148), _1368146)))], (41150 ^ _781215) ^ [_1588949, _1588951, _1588953, _1588955] : [hBOOL(hAPP(c_List_Odistinct(_1588949), hAPP(hAPP(c_List_Omap(tc_prod(_1588949, _1588951), _1588949), c_Product__Type_Ofst(_1588949, _1588951)), _1588953))), hBOOL(hAPP(c_List_Odistinct(_1588949), hAPP(hAPP(c_List_Omap(tc_prod(_1588949, _1588951), _1588949), c_Product__Type_Ofst(_1588949, _1588951)), _1588955))), 41157 ^ _781215 : [(41164 ^ _781215) ^ [] : [hAPP(c_List_Oset(tc_prod(_1588949, _1588951)), _1588953) = hAPP(c_List_Oset(tc_prod(_1588949, _1588951)), _1588955), -(hAPP(c_Map_Omap__of(_1588949, _1588951), _1588953) = hAPP(c_Map_Omap__of(_1588949, _1588951), _1588955))], (41158 ^ _781215) ^ [] : [hAPP(c_Map_Omap__of(_1588949, _1588951), _1588953) = hAPP(c_Map_Omap__of(_1588949, _1588951), _1588955), -(hAPP(c_List_Oset(tc_prod(_1588949, _1588951)), _1588953) = hAPP(c_List_Oset(tc_prod(_1588949, _1588951)), _1588955))]]], (21237 ^ _781215) ^ [_1161368, _1161370] : [class_Int_Onumber__ring(_1161368), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161368), c_Groups_Oone__class_Oone(_1161368)), hAPP(c_Int_Onumber__class_Onumber__of(_1161368), _1161370)) = hAPP(c_Int_Onumber__class_Onumber__of(_1161368), 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), _1161370))))], (39518 ^ _781215) ^ [_1545653, _1545655, _1545657] : [class_Lattices_Odistrib__lattice(_1545653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545653), _1545655)), -(_1545655 = c_Orderings_Obot__class_Obot(tc_fun(_1545653, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1545653), _1545657), c_Big__Operators_Olattice__class_OSup__fin(_1545653, _1545655)) = c_Big__Operators_Olattice__class_OSup__fin(_1545653, hAPP(c_Set_OCollect(_1545653), hAPP(hAPP(c_COMBB(tc_fun(_1545653, tc_HOL_Obool), tc_HOL_Obool, _1545653), c_HOL_OEx(_1545653)), hAPP(hAPP(c_COMBC(_1545653, tc_fun(_1545653, tc_HOL_Obool), tc_fun(_1545653, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545653, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1545653, tc_HOL_Obool), tc_fun(_1545653, tc_HOL_Obool)), _1545653), c_COMBS(_1545653, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545653, tc_HOL_Obool), tc_fun(_1545653, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1545653), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545653), c_fconj)), hAPP(hAPP(c_COMBC(_1545653, tc_fun(_1545653, _1545653), tc_fun(_1545653, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545653, tc_HOL_Obool), tc_fun(tc_fun(_1545653, _1545653), tc_fun(_1545653, tc_HOL_Obool)), _1545653), c_COMBB(_1545653, tc_HOL_Obool, _1545653)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1545653), _1545657))))), hAPP(hAPP(c_COMBC(_1545653, tc_fun(_1545653, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545653)), _1545655))))))], (44874 ^ _781215) ^ [_1681190, _1681192, _1681194] : [-(hAPP(c_List_Otl(_1681190), hAPP(hAPP(c_List_Olist_OCons(_1681190), _1681192), _1681194)) = _1681194)], (24894 ^ _781215) ^ [_1230416, _1230418] : [class_Power_Opower(_1230416), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1230416), _1230418), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1230416))], (47749 ^ _781215) ^ [_1742504, _1742506, _1742508, _1742510, _1742512] : [c_List_Olist__all2(_1742504, _1742506, _1742508, _1742510, hAPP(c_List_Orev(_1742506), _1742512)), -(c_List_Olist__all2(_1742504, _1742506, _1742508, hAPP(c_List_Orev(_1742504), _1742510), _1742512))], (12878 ^ _781215) ^ [_1005591, _1005593, _1005595, _1005597, _1005599, _1005601] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1005591), -(_1005593 = c_Groups_Ozero__class_Ozero(_1005591)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1005591), _1005595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005591), _1005593), _1005599)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1005591), _1005597), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005591), _1005593), _1005601)), _1005595 = _1005597, -(_1005599 = _1005601)], (37343 ^ _781215) ^ [_1489414, _1489416] : [-(hBOOL(hAPP(hAPP(c_member(_1489414), _1489416), c_Orderings_Otop__class_Otop(tc_fun(_1489414, tc_HOL_Obool)))))], (18966 ^ _781215) ^ [_1121207, _1121209, _1121211, _1121213] : [class_Orderings_Olinorder(_1121207), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121207), _1121209), _1121211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121207), _1121209), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1121207), _1121213), _1121211))))], (49608 ^ _781215) ^ [_1785666, _1785668, _1785670, _1785672] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1785666), tc_List_Olist(_1785666))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1785666), tc_List_Olist(_1785666)), _1785668), _1785670)), c_List_Olistrel1(_1785666, hAPP(c_Relation_Oconverse(_1785666, _1785666), _1785672)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1785666), tc_List_Olist(_1785666))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1785666), tc_List_Olist(_1785666)), _1785668), _1785670)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1785666), tc_List_Olist(_1785666)), c_List_Olistrel1(_1785666, _1785672)))))], (2114 ^ _781215) ^ [_812144, _812146, _812148, _812150, _812152, _812154, _812156, _812158] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_812158, _812154, _812150, _812146) = c_Nat_Osemiring__1__class_Oof__nat__aux(_812156, _812152, _812148, _812144)), _812158 = _812156, _812154 = _812152, _812150 = _812148, _812146 = _812144], (23738 ^ _781215) ^ [_1209218, _1209220] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1209218, _1209220)) = _1209220), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1209218), _1209220) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1209218, _1209220)))], (7728 ^ _781215) ^ [_911368, _911370, _911372] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911368), _911370)), _911372) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911368), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911370), _911372)))], (22558 ^ _781215) ^ [_1188655, _1188657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1188655), 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)), _1188657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1188655), _1188657)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15524 ^ _781215) ^ [_1053443, _1053445, _1053447, _1053449, _1053451] : [class_Groups_Ominus(_1053443), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053445, _1053443)), _1053447), _1053449), _1053451) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1053443), hAPP(_1053447, _1053451)), hAPP(_1053449, _1053451)))], (34316 ^ _781215) ^ [_1424242, _1424244] : [class_Lattices_Olattice(_1424242), -(c_Big__Operators_Olattice__class_OInf__fin(_1424242, hAPP(hAPP(c_Set_Oinsert(_1424242), _1424244), c_Orderings_Obot__class_Obot(tc_fun(_1424242, tc_HOL_Obool)))) = _1424244)], (42969 ^ _781215) ^ [_1636206, _1636208, _1636210, _1636212] : [-(hAPP(hAPP(c_List_Otake(_1636206), hAPP(c_Nat_OSuc, _1636208)), hAPP(hAPP(c_List_Olist_OCons(_1636206), _1636210), _1636212)) = hAPP(hAPP(c_List_Olist_OCons(_1636206), _1636210), hAPP(hAPP(c_List_Otake(_1636206), _1636208), _1636212)))], (6279 ^ _781215) ^ [_882696, _882698, _882700, _882702, _882704] : [c_Hoare__Mirabelle_Otriple__valid(_882696, _882698, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_882696), _882700), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _882702))), _882704)), -(c_Hoare__Mirabelle_Otriple__valid(_882696, hAPP(c_Nat_OSuc, _882698), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_882696), _882700), hAPP(c_Com_Ocom_OBODY, _882702)), _882704)))], (48658 ^ _781215) ^ [_1763798, _1763800, _1763802, _1763804] : [c_List_Olist__ex(_1763798, _1763800, hAPP(hAPP(c_List_Oappend(_1763798), _1763802), _1763804)), -(c_List_Olist__ex(_1763798, _1763800, _1763802)), -(c_List_Olist__ex(_1763798, _1763800, _1763804))], (33855 ^ _781215) ^ [_1412611, _1412613, _1412615] : [class_Orderings_Olinorder(_1412611), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412611), _1412613)), -(_1412613 = c_Orderings_Obot__class_Obot(tc_fun(_1412611, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412611), _1412615)), -(_1412615 = c_Orderings_Obot__class_Obot(tc_fun(_1412611, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412611, tc_HOL_Obool)), _1412613), _1412615) = c_Orderings_Obot__class_Obot(tc_fun(_1412611, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1412611, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412611, tc_HOL_Obool)), _1412613), _1412615)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1412611), c_Big__Operators_Olinorder__class_OMax(_1412611, _1412613)), c_Big__Operators_Olinorder__class_OMax(_1412611, _1412615)))], (42465 ^ _781215) ^ [_1622469, _1622471, _1622473, _1622475] : [-(hAPP(c_Map_Omap__of(_1622469, _1622471), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1622469, _1622471)), _1622473), _1622475)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1622469, tc_Option_Ooption(_1622471)), hAPP(c_Map_Omap__of(_1622469, _1622471), _1622475)), hAPP(c_Product__Type_Ofst(_1622469, _1622471), _1622473)), hAPP(c_Option_Ooption_OSome(_1622471), hAPP(c_Product__Type_Osnd(_1622469, _1622471), _1622473))))], (41277 ^ _781215) ^ [_1591720, _1591722, _1591724, _1591726, _1591728, _1591730, _1591732, _1591734, _1591736, _1591738, _1591740] : [-(hAPP(c_Product__Type_Omap__pair(_1591720, _1591722, _1591724, _1591726, _1591728, _1591730), hAPP(c_Product__Type_Omap__pair(_1591732, _1591720, _1591734, _1591724, _1591736, _1591738), _1591740)) = hAPP(c_Product__Type_Omap__pair(_1591732, _1591722, _1591734, _1591726, hAPP(c_Fun_Ocomp(_1591720, _1591722, _1591732, _1591728), _1591736), hAPP(c_Fun_Ocomp(_1591724, _1591726, _1591734, _1591730), _1591738)), _1591740))], (42339 ^ _781215) ^ [_1619692, _1619694, _1619696] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619692, tc_HOL_Obool)), hAPP(c_List_Oset(_1619692), _1619694)), hAPP(c_List_Oset(_1619692), hAPP(hAPP(c_List_Olist_OCons(_1619692), _1619696), _1619694)))))], (37768 ^ _781215) ^ [_1498794, _1498796, _1498798, _1498800] : [-(c_Wellfounded_Omax__extp(_1498794, _1498796, _1498798, _1498800)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1498794), _1498798)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1498794), _1498800)), -(_1498800 = c_Orderings_Obot__class_Obot(tc_fun(_1498794, tc_HOL_Obool))), 37782 ^ _781215 : [(37785 ^ _781215) ^ [_1499139] : [hBOOL(hAPP(hAPP(c_member(_1498794), _1499139), _1498800)), hBOOL(hAPP(hAPP(_1498796, 37781 ^ [_1498794, _1498796, _1498798, _1498800]), _1499139))], (37783 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1498794), 37781 ^ [_1498794, _1498796, _1498798, _1498800]), _1498798)))]]], (3540 ^ _781215) ^ [_834839, _834841, _834843, _834845, _834847, _834849, _834851, _834853] : [-(c_Map_Omap__add(_834853, _834849, _834845, _834841) = c_Map_Omap__add(_834851, _834847, _834843, _834839)), _834853 = _834851, _834849 = _834847, _834845 = _834843, _834841 = _834839], (44846 ^ _781215) ^ [_1680596, _1680598, _1680600] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680596)), hAPP(c_List_Orotate(_1680596, _1680598), _1680600)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680596)), _1680600))], (44768 ^ _781215) ^ [_1679475, _1679477, _1679479] : [-(_1679475 = c_List_Olist_ONil(_1679477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679479), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679477)), _1679475))), -(hAPP(c_List_Ohd(_1679477), hAPP(hAPP(c_List_Odrop(_1679477), _1679479), _1679475)) = hAPP(hAPP(c_List_Onth(_1679477), _1679475), _1679479))], (38380 ^ _781215) ^ [_1513116, _1513118, _1513120, _1513122] : [-(hBOOL(hAPP(hAPP(c_member(_1513116), _1513118), _1513120))), -(hAPP(c_Set_Ovimage(_1513122, _1513116, hAPP(c_COMBK(_1513116, _1513122), _1513118)), _1513120) = c_Orderings_Obot__class_Obot(tc_fun(_1513122, tc_HOL_Obool)))], (14726 ^ _781215) ^ [_1038857, _1038859, _1038861] : [class_Int_Onumber__ring(_1038857), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038857), hAPP(c_Int_Onumber__class_Onumber__of(_1038857), _1038859)), hAPP(c_Int_Onumber__class_Onumber__of(_1038857), _1038861)) = hAPP(c_Int_Onumber__class_Onumber__of(_1038857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1038859), _1038861)))], (7080 ^ _781215) ^ [_899090, _899092, _899094, _899096] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_899090, _899092, _899094, _899096, c_Orderings_Obot__class_Obot(tc_fun(_899090, tc_HOL_Obool))), _899096)))], (21732 ^ _781215) ^ [_1171052, _1171054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171052), _1171054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1171052)), c_Int_OBit0(_1171054))))], (4212 ^ _781215) ^ [_845135, _845137, _845139, _845141] : [-(c_Random_Oselect(_845141, _845137) = c_Random_Oselect(_845139, _845135)), _845141 = _845139, _845137 = _845135], (47886 ^ _781215) ^ [_1745609, _1745611, _1745613, _1745615, _1745617] : [c_Fun_Oinj__on(_1745609, _1745611, _1745613, hAPP(hAPP(c_Set_Oinsert(_1745609), _1745615), hAPP(c_List_Oset(_1745609), _1745617))), -(hAPP(hAPP(c_List_Omap(_1745609, _1745611), _1745613), hAPP(c_List_OremoveAll(_1745609, _1745615), _1745617)) = hAPP(c_List_OremoveAll(_1745611, hAPP(_1745613, _1745615)), hAPP(hAPP(c_List_Omap(_1745609, _1745611), _1745613), _1745617)))], (49161 ^ _781215) ^ [_1773464, _1773466, _1773468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1773464, _1773464), tc_HOL_Obool)), _1773466), hAPP(hAPP(c_Product__Type_OSigma(_1773464, _1773464), _1773468), hAPP(c_COMBK(tc_fun(_1773464, tc_HOL_Obool), _1773464), _1773468)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1773464, _1773464), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1773464, _1773466)), hAPP(hAPP(c_Product__Type_OSigma(_1773464, _1773464), _1773468), hAPP(c_COMBK(tc_fun(_1773464, tc_HOL_Obool), _1773464), _1773468)))))], (42767 ^ _781215) ^ [_1630898, _1630900, _1630902] : [-(hBOOL(hAPP(hAPP(c_member(_1630898), _1630900), hAPP(c_List_Oset(_1630898), _1630902)))), 42768 ^ _781215 : [(42769 ^ _781215) ^ [_1630972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630972), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630898)), _1630902))), hAPP(hAPP(c_List_Onth(_1630898), _1630902), _1630972) = _1630900]]], (7586 ^ _781215) ^ [_908630, _908632] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _908630), hAPP(c_Nat_OSuc, _908632)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _908630), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _908632))], (14932 ^ _781215) ^ [_1043063, _1043065] : [class_Rings_Olinordered__idom(_1043063), 14935 ^ _781215 : [(14942 ^ _781215) ^ [] : [_1043065 = c_Groups_Ozero__class_Ozero(_1043063), -(c_Groups_Osgn__class_Osgn(_1043063, _1043065) = c_Groups_Ozero__class_Ozero(_1043063))], (14936 ^ _781215) ^ [] : [c_Groups_Osgn__class_Osgn(_1043063, _1043065) = c_Groups_Ozero__class_Ozero(_1043063), -(_1043065 = c_Groups_Ozero__class_Ozero(_1043063))]]], (10376 ^ _781215) ^ [_958093, _958095, _958097, _958099, _958101] : [-(hAPP(c_Map_Omap__add(_958093, _958095, _958097, _958099), _958101) = c_Option_Ooption_ONone(_958095)), hAPP(_958099, _958101) = c_Option_Ooption_ONone(_958095), hAPP(_958097, _958101) = c_Option_Ooption_ONone(_958095)], (10092 ^ _781215) ^ [_952875, _952877, _952879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952875), _952877)), _952879)), 10095 ^ _781215 : [(10098 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952877), _952879)))], (10096 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952875), _952879)))]]], (45402 ^ _781215) ^ [_1692407, _1692409] : [-(c_List_Otranspose(_1692407, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1692407)), c_List_Olist_ONil(_1692407)), _1692409)) = c_List_Otranspose(_1692407, _1692409))], (6628 ^ _781215) ^ [_889724, _889726] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889724, tc_HOL_Obool)), _889726), _889726) = c_Orderings_Obot__class_Obot(tc_fun(_889724, tc_HOL_Obool)))], (41387 ^ _781215) ^ [_1594624, _1594626, _1594628, _1594630, _1594632] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1594624), tc_Option_Ooption(_1594626), _1594628, hAPP(c_Option_Omap(_1594624, _1594626), _1594630)), hAPP(c_COMBK(tc_Option_Ooption(_1594624), _1594628), c_Option_Ooption_ONone(_1594624))), _1594632) = c_Option_Ooption_ONone(_1594626))], (21434 ^ _781215) ^ [_1165903, _1165905] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1165903), _1165905)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1165903)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1165905))))], (25378 ^ _781215) ^ [_1238542, _1238544] : [c_Nat__Transfer_Ois__nat(_1238542), c_Nat__Transfer_Ois__nat(_1238544), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1238542, _1238544)))], (168 ^ _781215) ^ [_783807, _783809] : [-(class_Rings_Odivision__ring(_783807)), _783809 = _783807, class_Rings_Odivision__ring(_783809)], (25070 ^ _781215) ^ [_1233751, _1233753, _1233755] : [class_Rings_Olinordered__semidom(_1233751), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1233751), c_Groups_Ozero__class_Ozero(_1233751)), _1233753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1233751), _1233753), c_Groups_Oone__class_Oone(_1233751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1233751), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1233751), _1233753), hAPP(hAPP(c_Power_Opower__class_Opower(_1233751), _1233753), _1233755))), hAPP(hAPP(c_Power_Opower__class_Opower(_1233751), _1233753), _1233755))))], (10776 ^ _781215) ^ [_965932, _965934, _965936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965932), _965934)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965934), _965932)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965936), _965932)), _965934))], (45622 ^ _781215) ^ [_1696774, _1696776, _1696778, _1696780, _1696782] : [class_Orderings_Olinorder(_1696774), c_List_Olinorder__class_Osorted(_1696774, hAPP(hAPP(c_List_Omap(_1696776, _1696774), _1696778), _1696780)), -(c_List_Olinorder__class_Osorted(_1696774, hAPP(hAPP(c_List_Omap(_1696776, _1696774), _1696778), c_List_Oremove1(_1696776, _1696782, _1696780))))], (16887 ^ _781215) ^ [_1084509, _1084511] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084509), _1084511))), -(c_Nat__Transfer_Otsub(_1084511, _1084509) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5480 ^ _781215) ^ [_864869, _864871, _864873, _864875] : [-(c_COMBK(_864875, _864871) = c_COMBK(_864873, _864869)), _864875 = _864873, _864871 = _864869], (51254 ^ _781215) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (4066 ^ _781215) ^ [_842894, _842896, _842898, _842900, _842902, _842904] : [-(c_Finite__Set_Ofold(_842904, _842900, _842896) = c_Finite__Set_Ofold(_842902, _842898, _842894)), _842904 = _842902, _842900 = _842898, _842896 = _842894], (11140 ^ _781215) ^ [_974204, _974206, _974208, _974210] : [class_Rings_Ocomm__semiring__1(_974204), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974204), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974204), _974206), _974208)), _974210) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974204), _974206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974204), _974208), _974210)))], (29638 ^ _781215) ^ [_1321466, _1321468, _1321470, _1321472] : [class_Fields_Ofield__inverse__zero(_1321466), -(_1321468 = c_Groups_Ozero__class_Ozero(_1321466)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1321466), _1321470), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321466), _1321472), _1321468)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321466), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1321466), _1321472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1321466), _1321470), _1321468))), _1321468))], (19822 ^ _781215) ^ [_1136894, _1136896, _1136898] : [class_Orderings_Olinorder(_1136894), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136894), _1136896)), -(_1136896 = c_Orderings_Obot__class_Obot(tc_fun(_1136894, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1136894, hAPP(hAPP(c_Set_Oinsert(_1136894), _1136898), _1136896)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1136894), _1136898), c_Big__Operators_Olinorder__class_OMax(_1136894, _1136896)))], (466 ^ _781215) ^ [_788492, _788494] : [-(c_Nitpick_Ounknown(_788492)), _788494 = _788492, c_Nitpick_Ounknown(_788494)], (50772 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (6832 ^ _781215) ^ [_893642, _893644, _893646] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _893642)), _893644), _893646)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _893642))), _893644), _893646)))], (41353 ^ _781215) ^ [_1593795, _1593797, _1593799, _1593801, _1593803, _1593805] : [c_Fun_Oinj__on(_1593795, _1593797, _1593799, _1593801), 41356 ^ _781215 : [(41363 ^ _781215) ^ [] : [c_Fun_Oinj__on(_1593795, _1593803, hAPP(c_Fun_Ocomp(_1593797, _1593803, _1593795, _1593805), _1593799), _1593801), -(c_Fun_Oinj__on(_1593797, _1593803, _1593805, hAPP(c_Set_Oimage(_1593795, _1593797, _1593799), _1593801)))], (41357 ^ _781215) ^ [] : [c_Fun_Oinj__on(_1593797, _1593803, _1593805, hAPP(c_Set_Oimage(_1593795, _1593797, _1593799), _1593801)), -(c_Fun_Oinj__on(_1593795, _1593803, hAPP(c_Fun_Ocomp(_1593797, _1593803, _1593795, _1593805), _1593799), _1593801))]]], (40247 ^ _781215) ^ [_1567526, _1567528, _1567530, _1567532] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567526, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1567526, _1567528), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1567526, _1567528), tc_HOL_Obool)), _1567530), _1567532))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567526, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1567526, _1567528), _1567530)), hAPP(c_Relation_ODomain(_1567526, _1567528), _1567532)))))], (25522 ^ _781215) ^ [_1240659] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1240659), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1240659))], (50990 ^ _781215) ^ [_1818087, _1818089, _1818091, _1818093, _1818095, _1818097] : [-(c_New__Random__Sequence_Opos__union(_1818087, _1818089, _1818091, _1818093, _1818095, _1818097) = c_New__DSequence_Opos__union(_1818087, hAPP(hAPP(hAPP(_1818089, _1818093), _1818095), _1818097), hAPP(hAPP(hAPP(_1818091, _1818093), _1818095), _1818097)))], (51282 ^ _781215) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (51276 ^ _781215) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (48958 ^ _781215) ^ [_1769436, _1769438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1769436), _1769438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1769436)), hAPP(c_Code__Numeral_Onat__of, _1769438))))], (14280 ^ _781215) ^ [_1030893, _1030895, _1030897] : [class_Lattices_Oab__semigroup__idem__mult(_1030893), hAPP(_1030895, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030893), 14285 ^ [_1030893, _1030895, _1030897]), 14286 ^ [_1030893, _1030895, _1030897])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030893), hAPP(_1030895, 14285 ^ [_1030893, _1030895, _1030897])), hAPP(_1030895, 14286 ^ [_1030893, _1030895, _1030897])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030893), _1030897)), -(_1030897 = c_Orderings_Obot__class_Obot(tc_fun(_1030893, tc_HOL_Obool))), -(hAPP(_1030895, hAPP(c_Finite__Set_Ofold1(_1030893, c_Groups_Otimes__class_Otimes(_1030893)), _1030897)) = hAPP(c_Finite__Set_Ofold1(_1030893, c_Groups_Otimes__class_Otimes(_1030893)), hAPP(c_Set_Oimage(_1030893, _1030893, _1030895), _1030897)))], (38310 ^ _781215) ^ [_1511437, _1511439, _1511441, _1511443, _1511445] : [-(c_Map_Odom(_1511437, _1511439, hAPP(hAPP(c_COMBS(_1511437, tc_Option_Ooption(_1511441), tc_Option_Ooption(_1511439)), hAPP(hAPP(c_COMBB(tc_fun(_1511441, _1511439), tc_fun(tc_Option_Ooption(_1511441), tc_Option_Ooption(_1511439)), _1511437), c_Option_Omap(_1511441, _1511439)), _1511443)), _1511445)) = c_Map_Odom(_1511437, _1511441, _1511445))], (29200 ^ _781215) ^ [_1313503, _1313505, _1313507, _1313509] : [class_Fields_Ofield__inverse__zero(_1313503), 29203 ^ _781215 : [(29204 ^ _781215) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313503), _1313505), _1313507) = _1313509, 29207 ^ _781215 : [(29214 ^ _781215) ^ [] : [_1313507 = c_Groups_Ozero__class_Ozero(_1313503), -(_1313509 = c_Groups_Ozero__class_Ozero(_1313503))], (29208 ^ _781215) ^ [] : [-(_1313507 = c_Groups_Ozero__class_Ozero(_1313503)), -(_1313505 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313503), _1313509), _1313507))]]], (29220 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313503), _1313505), _1313507) = _1313509), 29223 ^ _781215 : [(29226 ^ _781215) ^ [] : [_1313505 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313503), _1313509), _1313507)], (29224 ^ _781215) ^ [] : [_1313507 = c_Groups_Ozero__class_Ozero(_1313503)]], 29227 ^ _781215 : [(29230 ^ _781215) ^ [] : [_1313509 = c_Groups_Ozero__class_Ozero(_1313503)], (29228 ^ _781215) ^ [] : [-(_1313507 = c_Groups_Ozero__class_Ozero(_1313503))]]]]], (42343 ^ _781215) ^ [_1619812, _1619814, _1619816] : [hAPP(hAPP(c_List_Olist_OCons(_1619812), _1619814), _1619816) = _1619816], (20527 ^ _781215) ^ [_1149644, _1149646] : [class_Rings_Olinordered__semidom(_1149644), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149644), c_Groups_Ozero__class_Ozero(_1149644)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1149644), _1149646))))], (9295 ^ _781215) ^ [_939497, _939499, _939501] : [class_Groups_Ogroup__add(_939497), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939497), _939499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939497), hAPP(c_Groups_Ouminus__class_Ouminus(_939497), _939499)), _939501)) = _939501)], (27734 ^ _781215) ^ [_1286112, _1286114, _1286116, _1286118, _1286120, _1286122, _1286124, _1286126] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1286112, _1286114), tc_prod(_1286112, _1286114))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1286112, _1286114), tc_prod(_1286112, _1286114)), hAPP(hAPP(c_Product__Type_OPair(_1286112, _1286114), _1286116), _1286118)), hAPP(hAPP(c_Product__Type_OPair(_1286112, _1286114), _1286120), _1286122))), c_Wellfounded_Olex__prod(_1286112, _1286114, _1286124, _1286126))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1286112, _1286112)), hAPP(hAPP(c_Product__Type_OPair(_1286112, _1286112), _1286116), _1286120)), _1286124))), 27741 ^ _781215 : [(27744 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1286114, _1286114)), hAPP(hAPP(c_Product__Type_OPair(_1286114, _1286114), _1286118), _1286122)), _1286126)))], (27742 ^ _781215) ^ [] : [-(_1286116 = _1286120)]]], (18637 ^ _781215) ^ [_1115062] : [class_Orderings_Olinorder(_1115062), -(c_Orderings_Oord_Omax(_1115062, hAPP(c_COMBC(_1115062, _1115062, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1115062))) = c_Orderings_Oord__class_Omin(_1115062))], (42905 ^ _781215) ^ [_1634707, _1634709, _1634711, _1634713, _1634715] : [-(_1634707 = _1634709), -(hAPP(hAPP(c_List_Onth(_1634711), hAPP(hAPP(c_List_Olist__update(_1634711, _1634713), _1634707), _1634715)), _1634709) = hAPP(hAPP(c_List_Onth(_1634711), _1634713), _1634709))], (16875 ^ _781215) ^ [_1084335, _1084337] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084335)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084335)), _1084337)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1084335))), _1084337))], (1858 ^ _781215) ^ [_807410, _807412] : [-(class_Groups_Oone(_807410)), _807412 = _807410, class_Groups_Oone(_807412)], (39969 ^ _781215) ^ [_1561592, _1561594, _1561596, _1561598, _1561600] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561592, _1561594)), hAPP(hAPP(c_Product__Type_OPair(_1561592, _1561594), _1561596), _1561598)), _1561600)), -(hBOOL(hAPP(hAPP(c_member(_1561592), _1561596), hAPP(c_Relation_ODomain(_1561592, _1561594), _1561600))))], (14327 ^ _781215) ^ [_1031826, _1031828, _1031830] : [class_Rings_Oring__1(_1031826), hBOOL(hAPP(hAPP(c_member(_1031826), _1031828), c_Int_Oring__1__class_OInts(_1031826))), hBOOL(hAPP(hAPP(c_member(_1031826), _1031830), c_Int_Oring__1__class_OInts(_1031826))), -(hBOOL(hAPP(hAPP(c_member(_1031826), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031826), _1031828), _1031830)), c_Int_Oring__1__class_OInts(_1031826))))], (25390 ^ _781215) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (1728 ^ _781215) ^ [_805785, _805787] : [-(class_Orderings_Olinorder(_805785)), _805787 = _805785, class_Orderings_Olinorder(_805787)], (45750 ^ _781215) ^ [_1698831, _1698833, _1698835] : [class_Orderings_Olinorder(_1698831), c_List_Olinorder__class_Osorted(_1698831, _1698833), -(c_List_Olinorder__class_Osorted(_1698831, hAPP(hAPP(c_List_Odrop(_1698831), _1698835), _1698833)))], (27472 ^ _781215) ^ [_1281225, _1281227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281227)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1281225), _1281227) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1281225, _1281227)))], (51532 ^ _781215) ^ [_1824235, _1824237] : [-(class_Smallcheck_Osmall(tc_prod(_1824235, _1824237))), class_Smallcheck_Osmall(_1824235), class_Smallcheck_Osmall(_1824237)], (46307 ^ _781215) ^ [_1710668, _1710670, _1710672] : [-(hAPP(c_List_Orev(_1710668), hAPP(hAPP(c_List_Odrop(_1710668), _1710670), _1710672)) = hAPP(hAPP(c_List_Otake(_1710668), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710668)), _1710672)), _1710670)), hAPP(c_List_Orev(_1710668), _1710672)))], (36001 ^ _781215) ^ [_1458121, _1458123, _1458125] : [class_Rings_Olinordered__idom(_1458121), -(hAPP(c_Groups_Oabs__class_Oabs(_1458121), hAPP(hAPP(c_Power_Opower__class_Opower(_1458121), hAPP(c_Groups_Ouminus__class_Ouminus(_1458121), _1458123)), _1458125)) = hAPP(c_Groups_Oabs__class_Oabs(_1458121), hAPP(hAPP(c_Power_Opower__class_Opower(_1458121), _1458123), _1458125)))], (38452 ^ _781215) ^ [_1515077, _1515079, _1515081, _1515083, _1515085, _1515087] : [hBOOL(hAPP(hAPP(c_member(_1515077), _1515079), _1515081)), hBOOL(hAPP(hAPP(c_member(_1515083), _1515085), hAPP(_1515087, _1515079))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515077, _1515083)), hAPP(hAPP(c_Product__Type_OPair(_1515077, _1515083), _1515079), _1515085)), hAPP(hAPP(c_Product__Type_OSigma(_1515077, _1515083), _1515081), _1515087))))], (35379 ^ _781215) ^ [_1446012, _1446014, _1446016] : [class_Orderings_Oord(_1446012), 35382 ^ _781215 : [(35389 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446012), _1446016), _1446014)), -(hBOOL(hAPP(hAPP(c_member(_1446012), _1446014), hAPP(c_SetInterval_Oord__class_OatLeast(_1446012), _1446016))))], (35383 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1446012), _1446014), hAPP(c_SetInterval_Oord__class_OatLeast(_1446012), _1446016))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446012), _1446016), _1446014)))]]], (21243 ^ _781215) ^ [_1161495, _1161497] : [class_Int_Onumber__ring(_1161495), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161495), hAPP(c_Int_Onumber__class_Onumber__of(_1161495), _1161497)), c_Groups_Oone__class_Oone(_1161495)) = hAPP(c_Int_Onumber__class_Onumber__of(_1161495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1161497), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (8662 ^ _781215) ^ [_928202, _928204, _928206] : [class_Groups_Ogroup__add(_928202), 8665 ^ _781215 : [(8672 ^ _781215) ^ [] : [_928206 = hAPP(c_Groups_Ouminus__class_Ouminus(_928202), _928204), -(_928204 = hAPP(c_Groups_Ouminus__class_Ouminus(_928202), _928206))], (8666 ^ _781215) ^ [] : [_928204 = hAPP(c_Groups_Ouminus__class_Ouminus(_928202), _928206), -(_928206 = hAPP(c_Groups_Ouminus__class_Ouminus(_928202), _928204))]]], (43193 ^ _781215) ^ [_1641668, _1641670, _1641672, _1641674] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641668), tc_List_Olist(_1641668))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641668), tc_List_Olist(_1641668)), _1641670), _1641672)), c_List_Olistrel1(_1641668, _1641674))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641668)), _1641670) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641668)), _1641672))], (10564 ^ _781215) ^ [_961956, _961958, _961960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961958), _961960)), -(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, _961956)), _961958)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961956)), _961960))))], (22078 ^ _781215) ^ [_1178879, _1178881, _1178883, _1178885, _1178887] : [_1178879 = c_Orderings_Obot__class_Obot(tc_fun(_1178881, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1178883, tc_HOL_Obool)), _1178885), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1178881, tc_fun(_1178883, tc_HOL_Obool)), _1178879), _1178887)) = _1178885)], (36175 ^ _781215) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (12138 ^ _781215) ^ [_992034, _992036] : [class_Groups_Olinordered__ab__group__add(_992034), 12141 ^ _781215 : [(12148 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992034), _992036), c_Groups_Ozero__class_Ozero(_992034))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992034), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_992034), _992036), _992036)), c_Groups_Ozero__class_Ozero(_992034))))], (12142 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992034), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_992034), _992036), _992036)), c_Groups_Ozero__class_Ozero(_992034))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992034), _992036), c_Groups_Ozero__class_Ozero(_992034))))]]], (23460 ^ _781215) ^ [_1203975, _1203977, _1203979, _1203981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203977), _1203979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203979), 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), _1203977), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1203981, _1203975))), _1203979)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51344 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (21854 ^ _781215) ^ [_1173630, _1173632, _1173634, _1173636] : [-(_1173630 = c_Orderings_Obot__class_Obot(tc_fun(_1173632, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1173632, tc_fun(_1173634, tc_HOL_Obool)), _1173630), hAPP(c_COMBK(tc_fun(_1173634, tc_HOL_Obool), _1173632), _1173636)) = _1173636)], (16375 ^ _781215) ^ [_1070663, _1070665, _1070667] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1070663, tc_HOL_Obool)), _1070665), _1070667) = c_Orderings_Obot__class_Obot(tc_fun(_1070663, tc_HOL_Obool))), _1070665 = c_Orderings_Obot__class_Obot(tc_fun(_1070663, tc_HOL_Obool)), _1070667 = c_Orderings_Obot__class_Obot(tc_fun(_1070663, tc_HOL_Obool))], (49770 ^ _781215) ^ [_1789782, _1789784, _1789786] : [-(hAPP(c_Relation_Oconverse(_1789782, _1789784), _1789786) = hAPP(c_Set_OCollect(tc_prod(_1789784, _1789782)), hAPP(c_Product__Type_Oprod_Oprod__case(_1789784, _1789782, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1789784, tc_fun(tc_prod(_1789782, _1789784), tc_HOL_Obool), tc_fun(_1789782, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1789782, tc_fun(tc_fun(tc_prod(_1789782, _1789784), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1789782, _1789784), tc_HOL_Obool), tc_fun(_1789782, tc_HOL_Obool)), _1789784), c_COMBC(_1789782, tc_fun(tc_prod(_1789782, _1789784), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1789782, tc_prod(_1789782, _1789784)), tc_fun(_1789782, tc_fun(tc_fun(tc_prod(_1789782, _1789784), tc_HOL_Obool), tc_HOL_Obool)), _1789784), hAPP(c_COMBB(tc_prod(_1789782, _1789784), tc_fun(tc_fun(tc_prod(_1789782, _1789784), tc_HOL_Obool), tc_HOL_Obool), _1789782), c_member(tc_prod(_1789782, _1789784)))), hAPP(c_COMBC(_1789782, _1789784, tc_prod(_1789782, _1789784)), c_Product__Type_OPair(_1789782, _1789784))))), _1789786))))], (44232 ^ _781215) ^ [_1665656, _1665658, _1665660, _1665662, _1665664, _1665666] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665656)), _1665658) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665660)), _1665662), -(c_Map_Omap__upds(_1665656, _1665660, _1665664, hAPP(hAPP(c_List_Oappend(_1665656), _1665658), _1665666), _1665662) = c_Map_Omap__upds(_1665656, _1665660, _1665664, _1665658, _1665662))], (2162 ^ _781215) ^ [_812892, _812894] : [_812894 = _812892, -(c_Int_Opred(_812894) = c_Int_Opred(_812892))], (33398 ^ _781215) ^ [_1402844, _1402846, _1402848, _1402850] : [class_Orderings_Olinorder(_1402844), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402844, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1402844), _1402846)), c_SetInterval_Oord__class_OatLeastAtMost(_1402844, _1402848, _1402850)) = c_SetInterval_Oord__class_OatLeastAtMost(_1402844, _1402848, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1402844), _1402846), _1402850)))], (50908 ^ _781215) ^ [_1815939, _1815941, _1815943, _1815945, _1815947] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1815939, _1815941, _1815943, _1815945, _1815947) = hAPP(c_Option_Ooption_Ooption__case(_1815939, tc_prod(_1815941, tc_Lazy__Sequence_Olazy__sequence(_1815941)), _1815943, hAPP(c_Product__Type_Oprod_Oprod__case(_1815941, tc_Lazy__Sequence_Olazy__sequence(_1815941), _1815939), _1815945)), hAPP(c_Lazy__Sequence_Oyield(_1815941), _1815947)))], (22220 ^ _781215) ^ [_1182130, _1182132, _1182134] : [class_Divides_Osemiring__div(_1182130), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1182130), c_Divides_Odiv__class_Omod(_1182130, _1182132, _1182134)), _1182134) = c_Groups_Ozero__class_Ozero(_1182130))], (47942 ^ _781215) ^ [_1746547, _1746549, _1746551] : [hBOOL(hAPP(c_List_Odistinct(_1746547), _1746549)), -(c_List_Oremove1(_1746547, _1746551, _1746549) = hAPP(c_List_OremoveAll(_1746547, _1746551), _1746549))], (26173 ^ _781215) ^ [_1255893, _1255895] : [class_Rings_Oring__1(_1255893), -(hAPP(c_Int_Oring__1__class_Oof__int(_1255893), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1255895)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1255893), hAPP(c_Int_Oring__1__class_Oof__int(_1255893), _1255895)))], (32734 ^ _781215) ^ [_1387323, _1387325, _1387327, _1387329, _1387331] : [class_Lattices_Osemilattice__inf(_1387323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387323), _1387325), _1387327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387323), _1387329), _1387331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387323), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1387323), _1387325), _1387329)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1387323), _1387327), _1387331))))], (50563 ^ _781215) ^ [_1809313, _1809315, _1809317, _1809319] : [-(c_List_Olist__ex1(_1809313, _1809315, hAPP(hAPP(c_List_Olist_OCons(_1809313), _1809317), _1809319))), 50566 ^ _781215 : [(50569 ^ _781215) ^ [] : [c_List_Olist__all(_1809313, hAPP(hAPP(c_COMBS(_1809313, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1809313), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1809313), c_fNot), _1809315))), hAPP(c_fequal, _1809317)), _1809319)], (50567 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1809315, _1809317)))]], 50570 ^ _781215 : [(50573 ^ _781215) ^ [] : [c_List_Olist__ex1(_1809313, _1809315, _1809319)], (50571 ^ _781215) ^ [] : [hBOOL(hAPP(_1809315, _1809317))]]], (18850 ^ _781215) ^ [_1119186, _1119188, _1119190, _1119192] : [class_Orderings_Olinorder(_1119186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119186), _1119188), _1119190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119186), _1119188), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1119186), _1119192), _1119190))))], (15913 ^ _781215) ^ [_1061629, _1061631, _1061633, _1061635] : [15914 ^ _781215 : [(15917 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1061629), _1061631), _1061635))], (15915 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1061629), _1061631), _1061633))]], -(hBOOL(hAPP(hAPP(c_member(_1061629), _1061631), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061629, tc_HOL_Obool)), _1061635), _1061633))))], (27746 ^ _781215) ^ [_1286437, _1286439, _1286441, _1286443, _1286445, _1286447, _1286449, _1286451] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1286437, _1286439), tc_prod(_1286437, _1286439))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1286437, _1286439), tc_prod(_1286437, _1286439)), hAPP(hAPP(c_Product__Type_OPair(_1286437, _1286439), _1286441), _1286443)), hAPP(hAPP(c_Product__Type_OPair(_1286437, _1286439), _1286445), _1286447))), c_Wellfounded_Olex__prod(_1286437, _1286439, _1286449, _1286451)))), 27747 ^ _781215 : [(27750 ^ _781215) ^ [] : [_1286441 = _1286445, hBOOL(hAPP(hAPP(c_member(tc_prod(_1286439, _1286439)), hAPP(hAPP(c_Product__Type_OPair(_1286439, _1286439), _1286443), _1286447)), _1286451))], (27748 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1286437, _1286437)), hAPP(hAPP(c_Product__Type_OPair(_1286437, _1286437), _1286441), _1286445)), _1286449))]]], (43698 ^ _781215) ^ [_1654043, _1654045, _1654047, _1654049, _1654051] : [class_Orderings_Olinorder(_1654043), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1654045, _1654043, _1654047), _1654049), _1654051) = c_List_Olist_ONil(_1654045)], (32884 ^ _781215) ^ [_1390799, _1390801] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1390799, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1390799, tc_HOL_Obool))), _1390801) = c_Orderings_Obot__class_Obot(tc_fun(_1390799, tc_HOL_Obool)))], (49718 ^ _781215) ^ [_1788554, _1788556, _1788558, _1788560] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1788554, _1788554)), hAPP(hAPP(c_Product__Type_OPair(_1788554, _1788554), _1788556), _1788558)), c_Transitive__Closure_Otrancl(_1788554, hAPP(c_Relation_Oconverse(_1788554, _1788554), _1788560)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788554, _1788554)), hAPP(hAPP(c_Product__Type_OPair(_1788554, _1788554), _1788556), _1788558)), hAPP(c_Relation_Oconverse(_1788554, _1788554), c_Transitive__Closure_Otrancl(_1788554, _1788560)))))], (33709 ^ _781215) ^ [_1409760, _1409762, _1409764, _1409766, _1409768] : [class_Groups_Ocomm__monoid__mult(_1409760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409762), _1409764)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409762), _1409766)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409762, tc_HOL_Obool)), _1409764), _1409766) = c_Orderings_Obot__class_Obot(tc_fun(_1409762, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409762, _1409760), _1409768), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409762, tc_HOL_Obool)), _1409764), _1409766)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409760), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409762, _1409760), _1409768), _1409764)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409762, _1409760), _1409768), _1409766)))], (39076 ^ _781215) ^ [_1531408, _1531410, _1531412] : [hBOOL(hAPP(hAPP(c_member(_1531408), _1531410), hAPP(c_Set_OCollect(_1531408), _1531412))), -(hBOOL(hAPP(_1531412, _1531410)))], (37558 ^ _781215) ^ [_1494521, _1494523, _1494525] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494521, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1494521, tc_HOL_Obool)), _1494523), _1494525)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494521, tc_HOL_Obool)), _1494523), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494521, tc_HOL_Obool), _1494525)))], (36951 ^ _781215) ^ [_1477953, _1477955, _1477957, _1477959, _1477961, _1477963] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477953, tc_fun(_1477955, tc_fun(_1477957, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1477953, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1477955, _1477957), tc_HOL_Obool), tc_fun(_1477955, tc_fun(_1477957, tc_HOL_Obool)), _1477953), hAPP(c_COMBC(_1477955, tc_fun(tc_prod(_1477955, _1477957), tc_HOL_Obool), tc_fun(_1477957, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477957, tc_fun(tc_fun(tc_prod(_1477955, _1477957), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1477955, _1477957), tc_HOL_Obool), tc_fun(_1477957, tc_HOL_Obool)), _1477955), c_COMBC(_1477957, tc_fun(tc_prod(_1477955, _1477957), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477957, tc_prod(_1477955, _1477957)), tc_fun(_1477957, tc_fun(tc_fun(tc_prod(_1477955, _1477957), tc_HOL_Obool), tc_HOL_Obool)), _1477955), hAPP(c_COMBB(tc_prod(_1477955, _1477957), tc_fun(tc_fun(tc_prod(_1477955, _1477957), tc_HOL_Obool), tc_HOL_Obool), _1477957), c_member(tc_prod(_1477955, _1477957)))), c_Product__Type_OPair(_1477955, _1477957))))), _1477959)), _1477961), _1477963)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1477955, _1477957)), hAPP(hAPP(c_Product__Type_OPair(_1477955, _1477957), _1477961), _1477963)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477953, tc_fun(tc_prod(_1477955, _1477957), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1477953, tc_HOL_Obool))), _1477959))))], (12650 ^ _781215) ^ [_1001394, _1001396, _1001398] : [class_Rings_Olinordered__semiring__strict(_1001394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001394), c_Groups_Ozero__class_Ozero(_1001394)), _1001396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001394), _1001398), c_Groups_Ozero__class_Ozero(_1001394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001394), _1001396), _1001398)), c_Groups_Ozero__class_Ozero(_1001394))))], (8906 ^ _781215) ^ [_932209, _932211, _932213] : [class_Orderings_Opreorder(_932209), _932211 = _932213, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932209), _932211), _932213)))], (23873 ^ _781215) ^ [_1211504, _1211506, _1211508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211504)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211504), _1211506)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211504), _1211508)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1211506), _1211508))], (7756 ^ _781215) ^ [_911906, _911908] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _911906)), _911908) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911906), _911908)))], (37598 ^ _781215) ^ [_1495289, _1495291, _1495293] : [class_Complete__Lattice_Ocomplete__lattice(_1495289), -(c_Complete__Lattice_OInf__class_OInf(_1495289, hAPP(hAPP(c_Set_Oinsert(_1495289), _1495291), _1495293)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1495289), _1495291), c_Complete__Lattice_OInf__class_OInf(_1495289, _1495293)))], (21958 ^ _781215) ^ [] : [-(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))))], (25514 ^ _781215) ^ [_1240494] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1240494)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1240494)))], (24214 ^ _781215) ^ [_1217945] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1217945)), 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, _1217945, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (38131 ^ _781215) ^ [_1507066, _1507068, _1507070] : [38133 ^ _781215 : [(38136 ^ _781215) ^ [] : [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(_1507068, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 38132 ^ [_1507066, _1507068, _1507070]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1507068, 38132 ^ [_1507066, _1507068, _1507070])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38134 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 38132 ^ [_1507066, _1507068, _1507070]), _1507066)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1507068, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1507070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1507070), hAPP(_1507068, _1507066))), 38146 ^ _781215 : [(38149 ^ _781215) ^ [] : [-(hAPP(_1507068, 38145 ^ [_1507066, _1507068, _1507070]) = _1507070)], (38147 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 38145 ^ [_1507066, _1507068, _1507070]), _1507066)))]]], (36843 ^ _781215) ^ [_1475452, _1475454, _1475456, _1475458, _1475460, _1475462] : [hBOOL(hAPP(hAPP(c_member(_1475452), _1475454), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1475456, tc_fun(_1475452, tc_HOL_Obool)), _1475458), _1475460))), -(hBOOL(hAPP(hAPP(c_member(_1475452), _1475454), hAPP(_1475460, _1475462)))), hBOOL(hAPP(hAPP(c_member(_1475456), _1475462), _1475458))], (15006 ^ _781215) ^ [_1044573, _1044575, _1044577, _1044579] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044573), hAPP(c_Int_Onumber__class_Onumber__of(_1044573), _1044575)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044573), _1044577), _1044579)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044573), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044573), hAPP(c_Int_Onumber__class_Onumber__of(_1044573), _1044575)), _1044577)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044573), hAPP(c_Int_Onumber__class_Onumber__of(_1044573), _1044575)), _1044579))), class_Int_Onumber(_1044573), class_Rings_Oring(_1044573)], (39943 ^ _781215) ^ [_1561162, _1561164, _1561166] : [-(hAPP(c_Relation_ODomain(_1561162, _1561164), hAPP(c_Set_OCollect(tc_prod(_1561162, _1561164)), hAPP(c_Product__Type_Oprod_Oprod__case(_1561162, _1561164, tc_HOL_Obool), _1561166))) = hAPP(c_Set_OCollect(_1561162), hAPP(hAPP(c_COMBB(tc_fun(_1561164, tc_HOL_Obool), tc_HOL_Obool, _1561162), c_HOL_OEx(_1561164)), _1561166)))], (46109 ^ _781215) ^ [_1706544, _1706546, _1706548] : [hAPP(c_List_Orev(_1706544), _1706546) = hAPP(hAPP(c_List_Olist_OCons(_1706544), _1706548), c_List_Olist_ONil(_1706544)), -(_1706546 = hAPP(hAPP(c_List_Olist_OCons(_1706544), _1706548), c_List_Olist_ONil(_1706544)))], (35831 ^ _781215) ^ [_1454829, _1454831] : [class_Groups_Oordered__ab__group__add__abs(_1454829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454829), c_Groups_Ozero__class_Ozero(_1454829)), _1454831)), -(hAPP(c_Groups_Oabs__class_Oabs(_1454829), _1454831) = _1454831)], (43818 ^ _781215) ^ [_1656180] : [class_Groups_Omonoid__add(_1656180), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1656180), c_List_Olist_ONil(_1656180)) = c_Groups_Ozero__class_Ozero(_1656180))], (38970 ^ _781215) ^ [_1529256, _1529258, _1529260, _1529262, _1529264, _1529266] : [-(_1529256 = c_Orderings_Obot__class_Obot(tc_fun(_1529258, tc_HOL_Obool))), 38976 ^ _781215 : [(38979 ^ _781215) ^ [] : [c_Fun_Oinj__on(_1529260, _1529262, _1529264, hAPP(_1529266, 38975 ^ [_1529256, _1529258, _1529260, _1529262, _1529264, _1529266]))], (38977 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1529258), 38975 ^ [_1529256, _1529258, _1529260, _1529262, _1529264, _1529266]), _1529256)))]], -(c_Fun_Oinj__on(_1529260, _1529262, _1529264, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1529258, tc_fun(_1529260, tc_HOL_Obool)), _1529256), _1529266)))], (40110 ^ _781215) ^ [_1564147, _1564149, _1564151] : [c_Wellfounded_Owf(_1564147, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564147, _1564147), tc_HOL_Obool)), _1564149), _1564151)), -(c_Wellfounded_Owf(_1564147, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564147, _1564147), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564147, _1564147), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1564147, _1564147, _1564147), _1564149), _1564149)), hAPP(hAPP(c_Relation_Orel__comp(_1564147, _1564147, _1564147), _1564151), _1564149))), _1564151)))], (49014 ^ _781215) ^ [_1770375, _1770377] : [-(c_Code__Numeral_Onat__of__aux(_1770375, _1770377) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1770375)), _1770377))], (51430 ^ _781215) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (21644 ^ _781215) ^ [_1169497, _1169499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1169497)), c_Int_OBit0(_1169499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1169497), _1169499)))], (2380 ^ _781215) ^ [_816393, _816395] : [_816395 = _816393, -(c_Divides_Oadjust(_816395) = c_Divides_Oadjust(_816393))], (44646 ^ _781215) ^ [_1676248, _1676250, _1676252, _1676254] : [-(hAPP(hAPP(c_List_Oappend(_1676248), _1676250), _1676252) = _1676254), _1676250 = hAPP(hAPP(c_List_Otake(_1676248), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676248)), _1676250)), _1676254), _1676252 = hAPP(hAPP(c_List_Odrop(_1676248), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676248)), _1676250)), _1676254)], (32036 ^ _781215) ^ [_1372074, _1372076, _1372078, _1372080, _1372082] : [class_Groups_Oab__group__add(_1372074), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372076), _1372078)), 32043 ^ _781215 : [(32050 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372076), _1372080), _1372078))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372076, _1372074), _1372082), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1372076, tc_HOL_Obool)), _1372078), hAPP(hAPP(c_Set_Oinsert(_1372076), _1372080), c_Orderings_Obot__class_Obot(tc_fun(_1372076, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372076, _1372074), _1372082), _1372078))], (32044 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1372076), _1372080), _1372078)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372076, _1372074), _1372082), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1372076, tc_HOL_Obool)), _1372078), hAPP(hAPP(c_Set_Oinsert(_1372076), _1372080), c_Orderings_Obot__class_Obot(tc_fun(_1372076, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1372074), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372076, _1372074), _1372082), _1372078)), hAPP(_1372082, _1372080)))]]], (42000 ^ _781215) ^ [_1609698] : [class_Orderings_Olinorder(_1609698), -(c_Finite__Set_Ofun__left__comm(_1609698, tc_List_Olist(_1609698), c_List_Olinorder__class_Oinsort__key(_1609698, _1609698, c_COMBI(_1609698))))], (25236 ^ _781215) ^ [] : [-(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))], (48202 ^ _781215) ^ [_1753334, _1753336, _1753338] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1753334, _1753336) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1753338, _1753336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1753338), _1753334)), -(_1753334 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1753338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1753336), 48209 ^ [_1753334, _1753336, _1753338])))], (720 ^ _781215) ^ [_792303, _792305, _792307, _792309, _792311, _792313, _792315, _792317, _792319, _792321] : [-(c_List_Olist__all2(_792319, _792315, _792311, _792307, _792303)), c_List_Olist__all2(_792321, _792317, _792313, _792309, _792305), _792321 = _792319, _792317 = _792315, _792313 = _792311, _792309 = _792307, _792305 = _792303], (49954 ^ _781215) ^ [_1794149, _1794151, _1794153, _1794155] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1794149, _1794149)), hAPP(hAPP(c_Product__Type_OPair(_1794149, _1794149), _1794151), _1794153)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794149, _1794149), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1794155))), -(_1794151 = _1794153)], (23724 ^ _781215) ^ [_1208952, _1208954, _1208956] : [class_Rings_Ocomm__semiring__1(_1208952), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208952), hAPP(hAPP(c_Power_Opower__class_Opower(_1208952), _1208954), _1208956)), _1208954) = hAPP(hAPP(c_Power_Opower__class_Opower(_1208952), _1208954), hAPP(c_Nat_OSuc, _1208956)))], (18603 ^ _781215) ^ [_1114401, _1114403, _1114405] : [class_Orderings_Olinorder(_1114401), -(_1114403 = c_Orderings_Obot__class_Obot(tc_fun(_1114401, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1114401, tc_HOL_Obool)), _1114403), _1114405)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1114401), _1114405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114401), hAPP(c_Finite__Set_Ofold1(_1114401, c_Orderings_Oord__class_Omin(_1114401)), _1114405)), hAPP(c_Finite__Set_Ofold1(_1114401, c_Orderings_Oord__class_Omin(_1114401)), _1114403))))], (24792 ^ _781215) ^ [_1228705, _1228707, _1228709] : [class_Rings_Olinordered__semidom(_1228705), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228705), c_Groups_Ozero__class_Ozero(_1228705)), _1228707)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228705), c_Groups_Ozero__class_Ozero(_1228705)), hAPP(hAPP(c_Power_Opower__class_Opower(_1228705), _1228707), _1228709))))], (51248 ^ _781215) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (25851 ^ _781215) ^ [_1249971, _1249973, _1249975, _1249977] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1249971, _1249973)), hAPP(hAPP(c_Product__Type_OPair(_1249971, _1249973), _1249975), _1249977)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1249971, _1249973), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1249971, tc_fun(_1249973, tc_HOL_Obool))), _1249975), _1249977)))], (43593 ^ _781215) ^ [_1651876, _1651878, _1651880, _1651882] : [_1651876 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651878)), _1651880)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1651878, hAPP(hAPP(c_List_Olist__update(_1651878, _1651880), _1651876), _1651882)) = c_List_Obutlast(_1651878, _1651880))], (43045 ^ _781215) ^ [_1638048, _1638050, _1638052, _1638054, _1638056, _1638058, _1638060] : [-(hBOOL(hAPP(hAPP(c_member(_1638048), _1638050), hAPP(c_List_Oset(_1638048), hAPP(hAPP(c_List_Otake(_1638048), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638052)), _1638054)), _1638056))))), -(c_Map_Omap__upds(_1638048, _1638052, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1638048, tc_Option_Ooption(_1638052)), _1638058), _1638050), hAPP(c_Option_Ooption_OSome(_1638052), _1638060)), _1638056, _1638054) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1638048, tc_Option_Ooption(_1638052)), c_Map_Omap__upds(_1638048, _1638052, _1638058, _1638056, _1638054)), _1638050), hAPP(c_Option_Ooption_OSome(_1638052), _1638060)))], (6331 ^ _781215) ^ [_884055, _884057, _884059, _884061] : [_884055 = _884057, 6336 ^ _781215 : [(6339 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_884059), _884061), _884057)))], (6337 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_884059), _884061), _884055)))]], 6340 ^ _781215 : [(6343 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_884059), _884061), _884057))], (6341 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_884059), _884061), _884055))]]], (36137 ^ _781215) ^ [_1460754] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1460754), hAPP(c_Int_Onumber__class_Onumber__of(_1460754), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1460754)), class_Int_Onumber__ring(_1460754), class_Rings_Olinordered__idom(_1460754)], (46512 ^ _781215) ^ [_1716568, _1716570] : [-(c_List_OtakeWhile(_1716568, _1716570, c_List_Olist_ONil(_1716568)) = c_List_Olist_ONil(_1716568))], (43231 ^ _781215) ^ [_1642733, _1642735, _1642737, _1642739, _1642741, _1642743] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642733), tc_List_Olist(_1642733))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642733), tc_List_Olist(_1642733)), hAPP(hAPP(c_List_Olist_OCons(_1642733), _1642735), _1642737)), hAPP(hAPP(c_List_Olist_OCons(_1642733), _1642739), _1642741))), c_List_Olistrel1(_1642733, _1642743)))), 43232 ^ _781215 : [(43239 ^ _781215) ^ [] : [_1642735 = _1642739, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642733), tc_List_Olist(_1642733))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642733), tc_List_Olist(_1642733)), _1642737), _1642741)), c_List_Olistrel1(_1642733, _1642743)))], (43233 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1642733, _1642733)), hAPP(hAPP(c_Product__Type_OPair(_1642733, _1642733), _1642735), _1642739)), _1642743)), _1642737 = _1642741]]], (18031 ^ _781215) ^ [_1103206, _1103208] : [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(_1103206))), 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)), _1103208))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103206) = hAPP(c_Nat_OSuc, _1103208))], (29074 ^ _781215) ^ [_1311295, _1311297, _1311299] : [class_Fields_Olinordered__field(_1311295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311295), c_Groups_Ozero__class_Ozero(_1311295)), _1311297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311295), c_Groups_Ozero__class_Ozero(_1311295)), _1311299)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311295), c_Groups_Ozero__class_Ozero(_1311295)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311295), _1311297), _1311299))))], (46463 ^ _781215) ^ [_1715519, _1715521, _1715523, _1715525, _1715527] : [-(c_List_OtakeWhile(_1715519, _1715521, hAPP(hAPP(c_List_Omap(_1715523, _1715519), _1715525), _1715527)) = hAPP(hAPP(c_List_Omap(_1715523, _1715519), _1715525), c_List_OtakeWhile(_1715523, hAPP(c_Fun_Ocomp(_1715519, tc_HOL_Obool, _1715523, _1715521), _1715525), _1715527)))], (13596 ^ _781215) ^ [_1017729, _1017731, _1017733, _1017735] : [class_Rings_Olinordered__semiring(_1017729), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017729), _1017731), _1017733)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017729), _1017735), _1017733))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017729), c_Groups_Ozero__class_Ozero(_1017729)), _1017733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017729), _1017731), _1017735)))], (39322 ^ _781215) ^ [_1538188, _1538190] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1538188)), -(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)), _1538188))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1538190))))) = 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)), _1538188))), 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, _1538190))))))], (50006 ^ _781215) ^ [_1795660, _1795662, _1795664] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1795660, _1795660)), _1795662), c_Transitive__Closure_Ortrancl(_1795660, _1795664))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1795660, _1795660)), _1795662), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1795660, _1795660), tc_HOL_Obool), 50009 ^ [_1795660, _1795662, _1795664]), _1795664))))], (32972 ^ _781215) ^ [_1392736, _1392738, _1392740, _1392742, _1392744] : [class_Lattices_Olattice(_1392736), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392738, _1392736)), _1392740), _1392742), _1392744) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1392736), hAPP(_1392740, _1392744)), hAPP(_1392742, _1392744)))], (2782 ^ _781215) ^ [_822736, _822738] : [_822738 = _822736, -(c_Wellfounded_Ofinite__psubset(_822738) = c_Wellfounded_Ofinite__psubset(_822736))], (51262 ^ _781215) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (22358 ^ _781215) ^ [_1184937, _1184939, _1184941, _1184943] : [class_Divides_Oring__div(_1184937), -(c_Divides_Odiv__class_Omod(_1184937, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1184937), _1184939), _1184941), _1184943) = c_Divides_Odiv__class_Omod(_1184937, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1184937), _1184939), c_Divides_Odiv__class_Omod(_1184937, _1184941, _1184943)), _1184943))], (2464 ^ _781215) ^ [_817775, _817777, _817779, _817781] : [-(c_FunDef_Orp__inv__image(_817781, _817777) = c_FunDef_Orp__inv__image(_817779, _817775)), _817781 = _817779, _817777 = _817775], (43583 ^ _781215) ^ [_1651623, _1651625, _1651627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651623), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651625)), _1651627))), -(hAPP(hAPP(c_List_Otake(_1651625), _1651623), c_List_Obutlast(_1651625, _1651627)) = hAPP(hAPP(c_List_Otake(_1651625), _1651623), _1651627))], (49796 ^ _781215) ^ [_1790474, _1790476, _1790478] : [c_Relation_Ototal__on(_1790474, _1790476, hAPP(c_Relation_Oconverse(_1790474, _1790474), _1790478)), -(c_Relation_Ototal__on(_1790474, _1790476, _1790478))], (5937 ^ _781215) ^ [_875693, _875695, _875697, _875699] : [hAPP(c_Com_Ocom_OBODY, _875693) = c_Com_Ocom_OCall(_875695, _875697, _875699)], (1648 ^ _781215) ^ [_804785, _804787] : [-(class_Groups_Ocomm__monoid__add(_804785)), _804787 = _804785, class_Groups_Ocomm__monoid__add(_804787)], (48045 ^ _781215) ^ [_1749116, _1749118, _1749120, _1749122, _1749124] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1749116, _1749116)), hAPP(hAPP(c_Product__Type_OPair(_1749116, _1749116), _1749118), _1749120)), c_List_Omeasures(_1749116, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1749116, tc_Nat_Onat)), _1749122), _1749124))))), 48046 ^ _781215 : [(48049 ^ _781215) ^ [] : [hAPP(_1749122, _1749118) = hAPP(_1749122, _1749120), hBOOL(hAPP(hAPP(c_member(tc_prod(_1749116, _1749116)), hAPP(hAPP(c_Product__Type_OPair(_1749116, _1749116), _1749118), _1749120)), c_List_Omeasures(_1749116, _1749124)))], (48047 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1749122, _1749118)), hAPP(_1749122, _1749120)))]]], (50728 ^ _781215) ^ [_1812579, _1812581] : [class_HOL_Oequal(_1812579), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1812579), _1812581), _1812581)))], (44568 ^ _781215) ^ [_1674407, _1674409] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674407)), hAPP(c_List_Orotate1(_1674407), _1674409)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674407)), _1674409))], (9951 ^ _781215) ^ [_950449, _950451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _950449)), _950451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950449), _950451)))], (18413 ^ _781215) ^ [_1110868, _1110870, _1110872] : [class_Int_Onumber(_1110868), class_Orderings_Oord(_1110868), 18420 ^ _781215 : [(18427 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110868), hAPP(c_Int_Onumber__class_Onumber__of(_1110868), _1110870)), hAPP(c_Int_Onumber__class_Onumber__of(_1110868), _1110872)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1110868), hAPP(c_Int_Onumber__class_Onumber__of(_1110868), _1110870)), hAPP(c_Int_Onumber__class_Onumber__of(_1110868), _1110872)) = hAPP(c_Int_Onumber__class_Onumber__of(_1110868), _1110872))], (18421 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110868), hAPP(c_Int_Onumber__class_Onumber__of(_1110868), _1110870)), hAPP(c_Int_Onumber__class_Onumber__of(_1110868), _1110872))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1110868), hAPP(c_Int_Onumber__class_Onumber__of(_1110868), _1110870)), hAPP(c_Int_Onumber__class_Onumber__of(_1110868), _1110872)) = hAPP(c_Int_Onumber__class_Onumber__of(_1110868), _1110870))]]], (5660 ^ _781215) ^ [_870543, _870545, _870547] : [hAPP(hAPP(c_Set_Oinsert(_870543), _870545), _870547) = c_Orderings_Obot__class_Obot(tc_fun(_870543, tc_HOL_Obool))], (42961 ^ _781215) ^ [_1636019, _1636021, _1636023] : [-(c_List_Osublist(_1636019, _1636021, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1636023)) = hAPP(hAPP(c_List_Otake(_1636019), _1636023), _1636021))], (40871 ^ _781215) ^ [_1582266, _1582268, _1582270] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1582266, _1582268, _1582270)), 40873 ^ _781215 : [(40874 ^ _781215) ^ [_1582412] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1582266)), _1582412), _1582268)), -(c_Hoare__Mirabelle_Otriple__valid(_1582266, 40872 ^ [_1582266, _1582268, _1582270], _1582412))], (40883 ^ _781215) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1582266, 40872 ^ [_1582266, _1582268, _1582270], 40879 ^ [_1582266, _1582268, _1582270])], (40881 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1582266)), 40879 ^ [_1582266, _1582268, _1582270]), _1582270)))]]], (16265 ^ _781215) ^ [_1068674, _1068676, _1068678] : [class_Lattices_Olattice(_1068674), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068674), _1068676), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068674), _1068678), _1068676))))], (34790 ^ _781215) ^ [_1433139, _1433141, _1433143, _1433145, _1433147, _1433149] : [c_Fun_Oinj__on(_1433139, _1433141, _1433143, _1433145), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1433139, tc_HOL_Obool)), _1433147), _1433145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1433139, tc_HOL_Obool)), _1433149), _1433145)), -(hAPP(c_Set_Oimage(_1433139, _1433141, _1433143), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433139, tc_HOL_Obool)), _1433147), _1433149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433141, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1433139, _1433141, _1433143), _1433147)), hAPP(c_Set_Oimage(_1433139, _1433141, _1433143), _1433149)))], (5989 ^ _781215) ^ [_876626, _876628, _876630, _876632, _876634, _876636] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_876626, _876628, _876630, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_876626), _876632), _876634), _876636)) = hAPP(hAPP(hAPP(_876630, _876632), _876634), _876636))], (7678 ^ _781215) ^ [_910370] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _910370)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _910370)], (29586 ^ _781215) ^ [_1320513, _1320515, _1320517, _1320519] : [class_Fields_Olinordered__field__inverse__zero(_1320513), 29589 ^ _781215 : [(29590 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), _1320515), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320513), _1320517), _1320519))), 29593 ^ _781215 : [(29600 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), c_Groups_Ozero__class_Ozero(_1320513)), _1320519))), 29603 ^ _781215 : [(29610 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), _1320519), c_Groups_Ozero__class_Ozero(_1320513)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), _1320515), c_Groups_Ozero__class_Ozero(_1320513))))], (29604 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), _1320519), c_Groups_Ozero__class_Ozero(_1320513))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), _1320517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1320513), _1320515), _1320519))))]]], (29594 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), c_Groups_Ozero__class_Ozero(_1320513)), _1320519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1320513), _1320515), _1320519)), _1320517)))]]], (29616 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), _1320515), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320513), _1320517), _1320519)))), 29619 ^ _781215 : [(29622 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1320513), _1320515), _1320519)), _1320517))], (29620 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), c_Groups_Ozero__class_Ozero(_1320513)), _1320519)))]], 29623 ^ _781215 : [(29626 ^ _781215) ^ [] : [29627 ^ _781215 : [(29630 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), _1320517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1320513), _1320515), _1320519)))], (29628 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), _1320519), c_Groups_Ozero__class_Ozero(_1320513))))]], 29631 ^ _781215 : [(29634 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), _1320515), c_Groups_Ozero__class_Ozero(_1320513)))], (29632 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), _1320519), c_Groups_Ozero__class_Ozero(_1320513)))]]], (29624 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320513), c_Groups_Ozero__class_Ozero(_1320513)), _1320519))]]]]], (49626 ^ _781215) ^ [_1786321, _1786323, _1786325, _1786327, _1786329] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1786323, _1786321)), hAPP(hAPP(c_Product__Type_OPair(_1786323, _1786321), _1786327), _1786325)), _1786329)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786321, _1786323)), hAPP(hAPP(c_Product__Type_OPair(_1786321, _1786323), _1786325), _1786327)), hAPP(c_Relation_Oconverse(_1786323, _1786321), _1786329))))], (49379 ^ _781215) ^ [_1779726, _1779728] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1779726, _1779726, _1779726), _1779728), c_Transitive__Closure_Ortrancl(_1779726, _1779728)) = hAPP(hAPP(c_Relation_Orel__comp(_1779726, _1779726, _1779726), c_Transitive__Closure_Ortrancl(_1779726, _1779728)), _1779728))], (26610 ^ _781215) ^ [_1264071] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1264071) = 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)))], (50992 ^ _781215) ^ [_1818158, _1818160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1818158), _1818160)), -(c_Lazy__Sequence_Osmall__lazy_H(_1818158, _1818160) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (51356 ^ _781215) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (43686 ^ _781215) ^ [_1653831, _1653833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1653831), _1653833)), -(c_List_Oupto(_1653833, _1653831) = c_List_Olist_ONil(tc_Int_Oint))], (43085 ^ _781215) ^ [_1638908, _1638910, _1638912, _1638914, _1638916, _1638918, _1638920] : [-(c_Map_Omap__upds(_1638908, _1638910, _1638912, hAPP(hAPP(c_List_Olist_OCons(_1638908), _1638914), _1638916), hAPP(hAPP(c_List_Olist_OCons(_1638910), _1638918), _1638920)) = c_Map_Omap__upds(_1638908, _1638910, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1638908, tc_Option_Ooption(_1638910)), _1638912), _1638914), hAPP(c_Option_Ooption_OSome(_1638910), _1638918)), _1638916, _1638920))], (31838 ^ _781215) ^ [_1367640, _1367642, _1367644, _1367646, _1367648] : [class_Groups_Ocomm__monoid__add(_1367640), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367642), _1367644)), -(hBOOL(hAPP(hAPP(c_member(_1367642), _1367646), _1367644))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1367642, _1367640), _1367648), hAPP(hAPP(c_Set_Oinsert(_1367642), _1367646), _1367644)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1367640), hAPP(_1367648, _1367646)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1367642, _1367640), _1367648), _1367644)))], (40992 ^ _781215) ^ [_1585271, _1585273] : [-(hAPP(hAPP(c_List_Omap(_1585271, _1585271), c_COMBI(_1585271)), _1585273) = _1585273)], (9083 ^ _781215) ^ [_935345, _935347] : [class_Lattices_Oab__semigroup__idem__mult(_935345), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935345), _935347), _935347) = _935347)], (18633 ^ _781215) ^ [_1114954, _1114956] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1114954), hAPP(c_Nat_OSuc, _1114956)) = 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), _1114954), _1114956)))], (14146 ^ _781215) ^ [_1028048, _1028050, _1028052] : [hAPP(c_Finite__Set_Ocard(_1028048), _1028050) = hAPP(c_Nat_OSuc, _1028052), 14151 ^ _781215 : [(14154 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1028048), 14149 ^ [_1028048, _1028050, _1028052]), 14150 ^ [_1028048, _1028050, _1028052]))], (14156 ^ _781215) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1028048), 14150 ^ [_1028048, _1028050, _1028052]) = _1028052)], (14158 ^ _781215) ^ [] : [_1028052 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(14150 ^ [_1028048, _1028050, _1028052] = c_Orderings_Obot__class_Obot(tc_fun(_1028048, tc_HOL_Obool)))], (14152 ^ _781215) ^ [] : [-(_1028050 = hAPP(hAPP(c_Set_Oinsert(_1028048), 14149 ^ [_1028048, _1028050, _1028052]), 14150 ^ [_1028048, _1028050, _1028052]))]]], (39554 ^ _781215) ^ [_1547238, _1547240, _1547242] : [class_Orderings_Olinorder(_1547238), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547238), _1547240)), -(_1547240 = c_Orderings_Obot__class_Obot(tc_fun(_1547238, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1547238), _1547242), c_Big__Operators_Olattice_OSup__fin(_1547238, c_Orderings_Oord__class_Omax(_1547238), _1547240)) = c_Big__Operators_Olattice_OSup__fin(_1547238, c_Orderings_Oord__class_Omax(_1547238), hAPP(c_Set_OCollect(_1547238), hAPP(hAPP(c_COMBB(tc_fun(_1547238, tc_HOL_Obool), tc_HOL_Obool, _1547238), c_HOL_OEx(_1547238)), hAPP(hAPP(c_COMBC(_1547238, tc_fun(_1547238, tc_HOL_Obool), tc_fun(_1547238, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547238, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1547238, tc_HOL_Obool), tc_fun(_1547238, tc_HOL_Obool)), _1547238), c_COMBS(_1547238, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547238, tc_HOL_Obool), tc_fun(_1547238, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1547238), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547238), c_fconj)), hAPP(hAPP(c_COMBC(_1547238, tc_fun(_1547238, _1547238), tc_fun(_1547238, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547238, tc_HOL_Obool), tc_fun(tc_fun(_1547238, _1547238), tc_fun(_1547238, tc_HOL_Obool)), _1547238), c_COMBB(_1547238, tc_HOL_Obool, _1547238)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1547238), _1547242))))), hAPP(hAPP(c_COMBC(_1547238, tc_fun(_1547238, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547238)), _1547240))))))], (47701 ^ _781215) ^ [_1741570, _1741572, _1741574, _1741576, _1741578, _1741580] : [c_List_Olist__all2(_1741570, _1741572, _1741574, _1741576, _1741578), -(c_List_Olist__all2(_1741570, _1741572, _1741574, hAPP(hAPP(c_List_Odrop(_1741570), _1741580), _1741576), hAPP(hAPP(c_List_Odrop(_1741572), _1741580), _1741578)))], (1478 ^ _781215) ^ [_802660, _802662] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_802660)), _802662 = _802660, class_Groups_Oordered__ab__semigroup__add__imp__le(_802662)], (33356 ^ _781215) ^ [_1401871, _1401873, _1401875, _1401877] : [class_Orderings_Oorder(_1401871), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401871, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1401871, _1401873, _1401875)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1401871, _1401875, _1401877)) = c_Orderings_Obot__class_Obot(tc_fun(_1401871, tc_HOL_Obool)))], (48235 ^ _781215) ^ [_1754084, _1754086] : [48237 ^ _781215 : [(48240 ^ _781215) ^ [] : [48236 ^ [_1754084, _1754086] = c_Orderings_Obot__class_Obot(tc_fun(_1754084, tc_HOL_Obool))], (48238 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1754084, tc_HOL_Obool)), 48236 ^ [_1754084, _1754086]), hAPP(c_Relation_OImage(_1754084, _1754084, _1754086), 48236 ^ [_1754084, _1754086]))))]], -(c_Wellfounded_Owf(_1754084, _1754086))], (24484 ^ _781215) ^ [_1222841, _1222843, _1222845] : [class_Groups_Omonoid__mult(_1222841), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1222841), _1222843), 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)))), _1222845))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222841), _1222843), hAPP(hAPP(c_Power_Opower__class_Opower(_1222841), hAPP(hAPP(c_Power_Opower__class_Opower(_1222841), _1222843), _1222845)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (50774 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OPls))], (18347 ^ _781215) ^ [_1109564, _1109566, _1109568, _1109570] : [class_Orderings_Olinorder(_1109564), 18350 ^ _781215 : [(18359 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109564), _1109566), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1109564), _1109568), _1109570)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109564), _1109566), _1109568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109564), _1109566), _1109570))], (18351 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109564), _1109566), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1109564), _1109568), _1109570))), 18354 ^ _781215 : [(18357 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109564), _1109566), _1109570)))], (18355 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109564), _1109566), _1109568)))]]]]], (17805 ^ _781215) ^ [_1099222, _1099224, _1099226] : [class_Rings_Osemiring__1(_1099222), hBOOL(hAPP(hAPP(c_member(_1099222), _1099224), c_Nat_Osemiring__1__class_ONats(_1099222))), hBOOL(hAPP(hAPP(c_member(_1099222), _1099226), c_Nat_Osemiring__1__class_ONats(_1099222))), -(hBOOL(hAPP(hAPP(c_member(_1099222), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099222), _1099224), _1099226)), c_Nat_Osemiring__1__class_ONats(_1099222))))], (18193 ^ _781215) ^ [_1106916, _1106918, _1106920, _1106922, _1106924] : [class_Orderings_Olinorder(_1106916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106916), _1106918), _1106920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106916), _1106922), _1106924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106916), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106916), _1106918), _1106922)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106916), _1106920), _1106924))))], (15482 ^ _781215) ^ [_1052776, _1052778, _1052780, _1052782, _1052784, _1052786] : [_1052776 = _1052778, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1052780, _1052782), _1052784), _1052778), _1052786), _1052776) = _1052786)], (44862 ^ _781215) ^ [_1680978, _1680980, _1680982] : [hBOOL(hAPP(c_List_Odistinct(_1680978), _1680982)), -(hBOOL(hAPP(c_List_Odistinct(_1680978), hAPP(c_List_Orotate(_1680978, _1680980), _1680982))))], (39981 ^ _781215) ^ [_1561847, _1561849] : [c_Wellfounded_Owf(_1561847, hAPP(hAPP(c_Relation_Orel__comp(_1561847, _1561847, _1561847), _1561849), _1561849)), -(c_Wellfounded_Owf(_1561847, _1561849))], (21996 ^ _781215) ^ [_1177136, _1177138, _1177140, _1177142, _1177144] : [-(_1177136 = c_Orderings_Obot__class_Obot(tc_fun(_1177138, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1177138, tc_fun(_1177140, tc_HOL_Obool)), _1177136), hAPP(hAPP(c_COMBB(tc_fun(_1177140, tc_HOL_Obool), tc_fun(_1177140, tc_HOL_Obool), _1177138), hAPP(c_Set_Oinsert(_1177140), _1177142)), _1177144)) = hAPP(hAPP(c_Set_Oinsert(_1177140), _1177142), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1177138, tc_fun(_1177140, tc_HOL_Obool)), _1177136), _1177144)))], (49387 ^ _781215) ^ [_1779899, _1779901, _1779903, _1779905] : [49388 ^ _781215 : [(49391 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779899, _1779899)), _1779901), c_Transitive__Closure_Ortrancl(_1779899, _1779905)))], (49389 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779899, _1779899)), _1779901), c_Transitive__Closure_Ortrancl(_1779899, _1779903)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779899, _1779899)), _1779901), c_Transitive__Closure_Ortrancl(_1779899, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1779899, _1779899), tc_HOL_Obool)), _1779903), _1779905)))))], (39044 ^ _781215) ^ [_1530883, _1530885, _1530887, _1530889] : [-(hAPP(c_Set_Ovimage(_1530883, _1530885, _1530887), hAPP(c_Set_OCollect(_1530885), _1530889)) = hAPP(c_Set_OCollect(_1530883), hAPP(hAPP(c_COMBB(_1530885, tc_HOL_Obool, _1530883), _1530889), _1530887)))], (39681 ^ _781215) ^ [_1552341, _1552343, _1552345, _1552347] : [-(c_Product__Type_Oapfst(_1552341, _1552343, _1552345, _1552347) = c_Product__Type_Omap__pair(_1552341, _1552343, _1552345, _1552345, _1552347, c_Fun_Oid(_1552345)))], (11282 ^ _781215) ^ [_977427, _977429] : [class_Rings_Ocomm__semiring__1(_977427), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977427), c_Groups_Oone__class_Oone(_977427)), _977429) = _977429)], (9975 ^ _781215) ^ [_950863, _950865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950863), _950865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _950863), _950865))), -(_950863 = _950865)], (24366 ^ _781215) ^ [_1220540, _1220542, _1220544] : [class_Rings_Oring__1(_1220540), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1220540), hAPP(c_Groups_Ouminus__class_Ouminus(_1220540), _1220542)), 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)))), _1220544)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1220540), _1220542), 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)))), _1220544)))], (7726 ^ _781215) ^ [_911317, _911319, _911321] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911317), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911319), _911321)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911319), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911317), _911321)))], (26526 ^ _781215) ^ [_1262569, _1262571] : [-(c_Divides_OnegDivAlg(_1262569, _1262571) = hAPP(c_Divides_Oadjust(_1262571), c_Divides_OnegDivAlg(_1262569, 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)))), _1262571)))), -(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), _1262569), _1262571)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1262571), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51186 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (44351 ^ _781215) ^ [_1668526, _1668528, _1668530, _1668532, _1668534] : [-(hAPP(hAPP(c_List_Olist__update(_1668526, hAPP(hAPP(c_List_Oappend(_1668526), _1668528), hAPP(hAPP(c_List_Olist_OCons(_1668526), _1668530), _1668532))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668526)), _1668528)), _1668534) = hAPP(hAPP(c_List_Oappend(_1668526), _1668528), hAPP(hAPP(c_List_Olist_OCons(_1668526), _1668534), _1668532)))], (48625 ^ _781215) ^ [_1763179, _1763181] : [c_List_Olist__ex(_1763179, _1763181, c_List_Olist_ONil(_1763179))], (44914 ^ _781215) ^ [_1682050, _1682052, _1682054] : [-(_1682050 = c_List_Olist_ONil(_1682052)), -(hAPP(hAPP(c_List_Otake(_1682052), hAPP(c_Nat_OSuc, _1682054)), _1682050) = hAPP(hAPP(c_List_Olist_OCons(_1682052), hAPP(c_List_Ohd(_1682052), _1682050)), hAPP(hAPP(c_List_Otake(_1682052), _1682054), hAPP(c_List_Otl(_1682052), _1682050))))], (49808 ^ _781215) ^ [_1790662, _1790664] : [-(c_Relation_Ototal__on(_1790662, c_Orderings_Obot__class_Obot(tc_fun(_1790662, tc_HOL_Obool)), _1790664))], (51200 ^ _781215) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (43850 ^ _781215) ^ [_1656661, _1656663, _1656665] : [-(hAPP(hAPP(c_Map_Omap__of(_1656661, _1656663), c_List_Olist_ONil(tc_prod(_1656661, _1656663))), _1656665) = c_Option_Ooption_ONone(_1656663))], (11482 ^ _781215) ^ [_981358, _981360] : [class_Groups_Ozero(_981358), 11485 ^ _781215 : [(11492 ^ _781215) ^ [] : [_981360 = c_Groups_Ozero__class_Ozero(_981358), -(c_Groups_Ozero__class_Ozero(_981358) = _981360)], (11486 ^ _781215) ^ [] : [c_Groups_Ozero__class_Ozero(_981358) = _981360, -(_981360 = c_Groups_Ozero__class_Ozero(_981358))]]], (46779 ^ _781215) ^ [_1721759, _1721761, _1721763, _1721765, _1721767] : [hBOOL(hAPP(hAPP(c_member(_1721759), _1721761), hAPP(c_List_Oset(_1721759), _1721763))), -(hBOOL(hAPP(_1721765, _1721761))), -(c_List_OdropWhile(_1721759, _1721765, hAPP(hAPP(c_List_Oappend(_1721759), _1721763), _1721767)) = hAPP(hAPP(c_List_Oappend(_1721759), c_List_OdropWhile(_1721759, _1721765, _1721763)), _1721767))], (51234 ^ _781215) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (10017 ^ _781215) ^ [_951450, _951452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _951450), _951452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951450), _951452)))], (36177 ^ _781215) ^ [_1461341, _1461343] : [class_Int_Onumber__ring(_1461341), class_Rings_Olinordered__idom(_1461341), 36184 ^ _781215 : [(36191 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1461341), hAPP(c_Int_Onumber__class_Onumber__of(_1461341), _1461343)), c_Groups_Ozero__class_Ozero(_1461341)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1461341), hAPP(c_Int_Onumber__class_Onumber__of(_1461341), _1461343)) = hAPP(c_Int_Onumber__class_Onumber__of(_1461341), _1461343))], (36185 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1461341), hAPP(c_Int_Onumber__class_Onumber__of(_1461341), _1461343)), c_Groups_Ozero__class_Ozero(_1461341))), -(hAPP(c_Groups_Oabs__class_Oabs(_1461341), hAPP(c_Int_Onumber__class_Onumber__of(_1461341), _1461343)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1461341), hAPP(c_Int_Onumber__class_Onumber__of(_1461341), _1461343)))]]], (41709 ^ _781215) ^ [_1602266, _1602268, _1602270, _1602272, _1602274] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1602266, _1602268, _1602270), _1602272), _1602274))), hBOOL(hAPP(hAPP(_1602268, _1602272), _1602274)), hBOOL(hAPP(_1602270, _1602274))], (31638 ^ _781215) ^ [_1362990, _1362992, _1362994, _1362996] : [class_Groups_Ocomm__monoid__add(_1362990), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1362990), _1362992), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1362994)), hAPP(c_Nat_OSuc, _1362996))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1362990), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1362990, tc_Nat_Onat), _1362992), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1362994), _1362996)))], (22629 ^ _781215) ^ [_1189773, _1189775, _1189777, _1189779] : [class_Divides_Osemiring__div(_1189773), 22632 ^ _781215 : [(22639 ^ _781215) ^ [] : [-(_1189775 = c_Groups_Ozero__class_Ozero(_1189773)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1189773), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189773), _1189775), _1189777)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189773), _1189775), _1189779)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1189773), _1189777), _1189779))], (22633 ^ _781215) ^ [] : [_1189775 = c_Groups_Ozero__class_Ozero(_1189773), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1189773), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189773), _1189775), _1189777)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189773), _1189775), _1189779)) = c_Groups_Ozero__class_Ozero(_1189773))]]], (41627 ^ _781215) ^ [_1600222, _1600224, _1600226, _1600228, _1600230, _1600232] : [-(hAPP(c_Set_Ovimage(_1600222, tc_prod(_1600224, _1600226), _1600228), hAPP(hAPP(c_Product__Type_OSigma(_1600224, _1600226), _1600230), hAPP(c_COMBK(tc_fun(_1600226, tc_HOL_Obool), _1600224), _1600232))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1600222, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1600222, _1600224, hAPP(c_Fun_Ocomp(tc_prod(_1600224, _1600226), _1600224, _1600222, c_Product__Type_Ofst(_1600224, _1600226)), _1600228)), _1600230)), hAPP(c_Set_Ovimage(_1600222, _1600226, hAPP(c_Fun_Ocomp(tc_prod(_1600224, _1600226), _1600226, _1600222, c_Product__Type_Osnd(_1600224, _1600226)), _1600228)), _1600232)))], (21774 ^ _781215) ^ [_1171828, _1171830] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1171828)), _1171830) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1171828), _1171830))), _1171830))], (43154 ^ _781215) ^ [_1640650, _1640652, _1640654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1640650, _1640650), tc_HOL_Obool)), _1640652), _1640654)), c_Relation_Orefl__on(_1640650, c_Orderings_Otop__class_Otop(tc_fun(_1640650, tc_HOL_Obool)), _1640654), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1640650), tc_List_Olist(_1640650)), tc_HOL_Obool)), c_List_Olistrel1(_1640650, _1640652)), c_List_Olistrel(_1640650, _1640654))))], (24558 ^ _781215) ^ [_1224348, _1224350, _1224352] : [class_Int_Onumber__ring(_1224348), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1224348), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1224348), _1224350), _1224352)), 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(_1224348), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224348), hAPP(hAPP(c_Power_Opower__class_Opower(_1224348), _1224350), 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(_1224348), _1224352), 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(_1224348), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224348), hAPP(c_Int_Onumber__class_Onumber__of(_1224348), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1224350)), _1224352)))], (14738 ^ _781215) ^ [_1039161, _1039163, _1039165] : [class_Int_Onumber__ring(_1039161), -(hAPP(c_Int_Onumber__class_Onumber__of(_1039161), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1039163), _1039165)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039161), hAPP(c_Int_Onumber__class_Onumber__of(_1039161), _1039163)), hAPP(c_Int_Onumber__class_Onumber__of(_1039161), _1039165)))], (34228 ^ _781215) ^ [_1422277, _1422279, _1422281, _1422283, _1422285, _1422287] : [hBOOL(hAPP(hAPP(_1422277, _1422279), _1422281)), hBOOL(hAPP(hAPP(_1422283, _1422279), _1422281)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422285, tc_fun(_1422287, tc_HOL_Obool))), _1422277), _1422283), _1422279), _1422281)))], (42933 ^ _781215) ^ [_1635303, _1635305, _1635307, _1635309, _1635311] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1635303, _1635305)), _1635307), hAPP(hAPP(c_List_Ozip(_1635303, _1635305), _1635309), _1635311)) = hAPP(hAPP(c_List_Ozip(_1635303, _1635305), hAPP(hAPP(c_List_Otake(_1635303), _1635307), _1635309)), hAPP(hAPP(c_List_Otake(_1635305), _1635307), _1635311)))], (40487 ^ _781215) ^ [_1574012, _1574014, _1574016] : [40489 ^ _781215 : [(40492 ^ _781215) ^ [] : [hBOOL(hAPP(_1574014, 40488 ^ [_1574012, _1574014, _1574016]))], (40490 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1574012), 40488 ^ [_1574012, _1574014, _1574016]), _1574016)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1574012, _1574014), _1574016)))], (23762 ^ _781215) ^ [_1209641, _1209643] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1209641, _1209643) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1209641 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1209643), 23765 ^ [_1209641, _1209643]))], (46789 ^ _781215) ^ [_1721957, _1721959, _1721961, _1721963, _1721965] : [c_List_OdropWhile(_1721957, _1721959, _1721961) = hAPP(hAPP(c_List_Olist_OCons(_1721957), _1721963), _1721965), 46792 ^ _781215 : [(46795 ^ _781215) ^ [] : [hBOOL(hAPP(_1721959, _1721963))], (46793 ^ _781215) ^ [] : [-(_1721961 = hAPP(hAPP(c_List_Oappend(_1721957), c_List_OtakeWhile(_1721957, _1721959, _1721961)), hAPP(hAPP(c_List_Olist_OCons(_1721957), _1721963), _1721965)))]]], (31164 ^ _781215) ^ [] : [-(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))))], (1980 ^ _781215) ^ [_809993, _809995, _809997, _809999, _810001, _810003] : [-(c_Option_Ooption_Ooption__size(_810003, _809999, _809995) = c_Option_Ooption_Ooption__size(_810001, _809997, _809993)), _810003 = _810001, _809999 = _809997, _809995 = _809993], (14568 ^ _781215) ^ [_1036109, _1036111, _1036113, _1036115, _1036117] : [hBOOL(hAPP(_1036109, _1036111)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1036113), _1036111), _1036115)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1036109, _1036113, _1036117)), _1036111), _1036115)))], (19644 ^ _781215) ^ [_1133921, _1133923, _1133925] : [class_Orderings_Olinorder(_1133921), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133921), _1133923)), hBOOL(hAPP(hAPP(c_member(_1133921), _1133925), _1133923)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1133921), _1133925), c_Big__Operators_Olattice_OSup__fin(_1133921, c_Orderings_Oord__class_Omax(_1133921), _1133923)) = c_Big__Operators_Olattice_OSup__fin(_1133921, c_Orderings_Oord__class_Omax(_1133921), _1133923))], (33314 ^ _781215) ^ [_1400860, _1400862, _1400864] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400860, tc_HOL_Obool)), _1400862), _1400864) = c_Orderings_Obot__class_Obot(tc_fun(_1400860, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1400860, tc_HOL_Obool)), _1400862), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1400860, tc_HOL_Obool)), _1400864))))], (14904 ^ _781215) ^ [_1042483, _1042485, _1042487] : [hBOOL(hAPP(c_Com_OWT, _1042483)), hBOOL(hAPP(c_Com_OWT, _1042485)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1042487, _1042483, _1042485))))], (45135 ^ _781215) ^ [_1687017, _1687019, _1687021] : [-(_1687017 = c_List_Olist_ONil(_1687019)), -(c_List_Olast(_1687019, hAPP(hAPP(c_List_Oappend(_1687019), _1687021), _1687017)) = c_List_Olast(_1687019, _1687017))], (25240 ^ _781215) ^ [_1236529, _1236531] : [c_Nat__Transfer_Ois__nat(_1236529), c_Nat__Transfer_Ois__nat(_1236531), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236529), _1236531)))], (50477 ^ _781215) ^ [_1807720, _1807722, _1807724, _1807726] : [c_List_Olist__all(_1807720, _1807722, hAPP(hAPP(c_List_Oappend(_1807720), _1807724), _1807726)), 50480 ^ _781215 : [(50483 ^ _781215) ^ [] : [-(c_List_Olist__all(_1807720, _1807722, _1807726))], (50481 ^ _781215) ^ [] : [-(c_List_Olist__all(_1807720, _1807722, _1807724))]]], (3878 ^ _781215) ^ [_840028, _840030] : [_840030 = _840028, -(c_List_Otake(_840030) = c_List_Otake(_840028))], (25700 ^ _781215) ^ [_1243795, _1243797, _1243799, _1243801, _1243803] : [hBOOL(hAPP(hAPP(c_member(_1243795), _1243797), c_SetInterval_Oord_OgreaterThanLessThan(_1243795, _1243799, _1243801, _1243803))), 25703 ^ _781215 : [(25706 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1243799, _1243797), _1243803)))], (25704 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1243799, _1243801), _1243797)))]]], (21484 ^ _781215) ^ [_1166763, _1166765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1166763)), c_Int_OBit0(_1166765))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1166763), _1166765)))], (10758 ^ _781215) ^ [_965547, _965549, _965551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965547), _965549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965551), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965549), _965551)), _965547))))], (12094 ^ _781215) ^ [_991308, _991310, _991312] : [class_Groups_Oordered__comm__monoid__add(_991308), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991308), c_Groups_Ozero__class_Ozero(_991308)), _991310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991308), c_Groups_Ozero__class_Ozero(_991308)), _991312)), 12105 ^ _781215 : [(12114 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_991308), _991310), _991312) = c_Groups_Ozero__class_Ozero(_991308)), _991310 = c_Groups_Ozero__class_Ozero(_991308), _991312 = c_Groups_Ozero__class_Ozero(_991308)], (12106 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_991308), _991310), _991312) = c_Groups_Ozero__class_Ozero(_991308), 12109 ^ _781215 : [(12112 ^ _781215) ^ [] : [-(_991312 = c_Groups_Ozero__class_Ozero(_991308))], (12110 ^ _781215) ^ [] : [-(_991310 = c_Groups_Ozero__class_Ozero(_991308))]]]]], (17343 ^ _781215) ^ [_1091825, _1091827, _1091829] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091825)))), 17346 ^ _781215 : [(17353 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091827)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091825)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091827)), _1091829)) = 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), _1091825), _1091827))), _1091829))], (17347 ^ _781215) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091827))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091825)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091827)), _1091829)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091825)), _1091829))]]], (51236 ^ _781215) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (37388 ^ _781215) ^ [_1490832, _1490834, _1490836, _1490838] : [c_Equiv__Relations_Oequivp(_1490832, _1490834), hBOOL(hAPP(hAPP(_1490834, _1490836), _1490838)), -(hBOOL(hAPP(hAPP(_1490834, _1490838), _1490836)))], (22190 ^ _781215) ^ [_1181392, _1181394, _1181396] : [class_Divides_Osemiring__div(_1181392), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181392), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181392), _1181394), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1181392), _1181396), _1181394))), c_Divides_Odiv__class_Omod(_1181392, _1181396, _1181394)) = _1181396)], (50613 ^ _781215) ^ [_1810280, _1810282, _1810284] : [c_List_Olist__ex1(_1810280, _1810282, _1810284), 50617 ^ _781215 : [(50622 ^ _781215) ^ [_1810526] : [-(_1810526 = 50616 ^ [_1810280, _1810282, _1810284]), hBOOL(hAPP(hAPP(c_member(_1810280), _1810526), hAPP(c_List_Oset(_1810280), _1810284))), hBOOL(hAPP(_1810282, _1810526))], (50620 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1810282, 50616 ^ [_1810280, _1810282, _1810284])))], (50618 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810280), 50616 ^ [_1810280, _1810282, _1810284]), hAPP(c_List_Oset(_1810280), _1810284))))]]], (6310 ^ _781215) ^ [_883284, _883286, _883288, _883290, _883292, _883294, _883296] : [c_Hoare__Mirabelle_Ohoare__derivs(_883284, _883286, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883284)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883284), _883288), _883290), _883292)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883284), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_883284, _883286, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883284)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883284), _883294), _883290), _883296)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883284), tc_HOL_Obool))))), 6317 ^ _781215 : [(6321 ^ _781215) ^ [_883758] : [hBOOL(hAPP(hAPP(_883288, _883758), 6316 ^ [_883284, _883286, _883288, _883290, _883292, _883294, _883296])), -(hBOOL(hAPP(hAPP(_883292, _883758), 6319 ^ [_883284, _883286, _883288, _883290, _883292, _883294, _883296])))], (6327 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_883296, 6315 ^ [_883284, _883286, _883288, _883290, _883292, _883294, _883296]), 6319 ^ [_883284, _883286, _883288, _883290, _883292, _883294, _883296]))], (6318 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_883294, 6315 ^ [_883284, _883286, _883288, _883290, _883292, _883294, _883296]), 6316 ^ [_883284, _883286, _883288, _883290, _883292, _883294, _883296])))]]], (46658 ^ _781215) ^ [_1719244, _1719246] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719244)), c_List_Oremdups(_1719244, _1719246)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719244)), _1719246), -(c_List_Oremdups(_1719244, _1719246) = _1719246)], (40785 ^ _781215) ^ [_1580573, _1580575, _1580577] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1580573, _1580575)), _1580577), _1580577))), 40786 ^ _781215 : [(40789 ^ _781215) ^ [_1580673] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1580575), _1580577), _1580673)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1580573, _1580575)), _1580673), _1580577))], (40787 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1580573, _1580577)))]]], (22426 ^ _781215) ^ [_1186354, _1186356] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186354), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186356)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1186354, _1186356)))], (36991 ^ _781215) ^ [_1479736, _1479738, _1479740, _1479742, _1479744, _1479746] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479736, tc_fun(_1479738, tc_HOL_Obool)), _1479740), hAPP(hAPP(c_COMBB(_1479742, tc_fun(_1479738, tc_HOL_Obool), _1479736), _1479744), _1479746)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479742, tc_fun(_1479738, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1479736, _1479742, _1479746), _1479740)), _1479744))], (29986 ^ _781215) ^ [_1328638, _1328640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1328638), _1328640)), -(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), _1328638), _1328640)), c_Wellfounded_Oless__than)))], (22602 ^ _781215) ^ [_1189308, _1189310] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1189308))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1189310))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1189308)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1189310)))], (5504 ^ _781215) ^ [_865239, _865241, _865243, _865245, _865247, _865249] : [-(c_COMBC(_865249, _865245, _865241) = c_COMBC(_865247, _865243, _865239)), _865249 = _865247, _865245 = _865243, _865241 = _865239], (3272 ^ _781215) ^ [_830523, _830525, _830527, _830529, _830531, _830533] : [-(c_Big__Operators_Olattice_OInf__fin(_830533, _830529, _830525) = c_Big__Operators_Olattice_OInf__fin(_830531, _830527, _830523)), _830533 = _830531, _830529 = _830527, _830525 = _830523], (8434 ^ _781215) ^ [_924052, _924054, _924056, _924058] : [-(c_Map_Orestrict__map(_924052, _924054, _924056, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_924052, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_924052), _924058), c_Orderings_Obot__class_Obot(tc_fun(_924052, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_924052, tc_Option_Ooption(_924054)), _924056), _924058), c_Option_Ooption_ONone(_924054)))], (7901 ^ _781215) ^ [_914701, _914703] : [_914701 = _914703, -(hAPP(c_Nat_OSuc, _914701) = hAPP(c_Nat_OSuc, _914703))], (46864 ^ _781215) ^ [_1723831, _1723833, _1723835, _1723837] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1723831)), _1723833), hAPP(c_List_Oset(tc_List_Olist(_1723831)), c_Enum_On__lists(_1723831, _1723835, _1723837)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723831)), _1723833) = _1723835)], (46313 ^ _781215) ^ [_1710873, _1710875, _1710877, _1710879] : [-(c_List_Otranspose(_1710873, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1710873)), hAPP(hAPP(c_List_Olist_OCons(_1710873), _1710875), _1710877)), _1710879)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1710873)), hAPP(hAPP(c_List_Olist_OCons(_1710873), _1710875), c_List_Oconcat(_1710873, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1710873), tc_List_Olist(_1710873)), c_List_Olist_Olist__case(tc_List_Olist(_1710873), _1710873, c_List_Olist_ONil(_1710873), hAPP(hAPP(c_COMBB(tc_List_Olist(_1710873), tc_fun(tc_List_Olist(_1710873), tc_List_Olist(_1710873)), _1710873), c_COMBK(tc_List_Olist(_1710873), tc_List_Olist(_1710873))), hAPP(hAPP(c_COMBC(_1710873, tc_List_Olist(_1710873), tc_List_Olist(_1710873)), c_List_Olist_OCons(_1710873)), c_List_Olist_ONil(_1710873))))), _1710879)))), c_List_Otranspose(_1710873, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1710873)), _1710877), c_List_Oconcat(tc_List_Olist(_1710873), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1710873), tc_List_Olist(tc_List_Olist(_1710873))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1710873)), _1710873, c_List_Olist_ONil(tc_List_Olist(_1710873)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1710873), tc_List_Olist(tc_List_Olist(_1710873))), _1710873), hAPP(hAPP(c_COMBC(tc_List_Olist(_1710873), tc_List_Olist(tc_List_Olist(_1710873)), tc_List_Olist(tc_List_Olist(_1710873))), c_List_Olist_OCons(tc_List_Olist(_1710873))), c_List_Olist_ONil(tc_List_Olist(_1710873)))))), _1710879))))))], (45915 ^ _781215) ^ [_1702024, _1702026] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1702024, _1702026) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1702024), hAPP(c_Nat_OSuc, _1702026))))], (47448 ^ _781215) ^ [_1735771, _1735773, _1735775] : [-(c_List_Olistsp(_1735771, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1735771, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1735771, tc_fun(_1735771, tc_HOL_Obool), tc_HOL_Obool), c_member(_1735771)), _1735773)), hAPP(hAPP(c_COMBC(_1735771, tc_fun(_1735771, tc_HOL_Obool), tc_HOL_Obool), c_member(_1735771)), _1735775))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1735771), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1735771), tc_fun(tc_List_Olist(_1735771), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1735771))), c_List_Olists(_1735771, _1735773))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1735771), tc_fun(tc_List_Olist(_1735771), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1735771))), c_List_Olists(_1735771, _1735775))))], (35793 ^ _781215) ^ [_1454189, _1454191, _1454193] : [class_Groups_Oordered__ab__group__add__abs(_1454189), -(hAPP(c_Groups_Oabs__class_Oabs(_1454189), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1454189), _1454191), _1454193)) = hAPP(c_Groups_Oabs__class_Oabs(_1454189), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1454189), _1454193), _1454191)))], (39821 ^ _781215) ^ [_1556446, _1556448, _1556450] : [-(hAPP(c_Set_Oimage(tc_prod(_1556446, _1556448), _1556448, c_Product__Type_Osnd(_1556446, _1556448)), _1556450) = hAPP(c_Relation_ORange(_1556446, _1556448), _1556450))], (20647 ^ _781215) ^ [_1151767] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1151767)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1151767))))], (6808 ^ _781215) ^ [_893197, _893199, _893201] : [hBOOL(hAPP(hAPP(c_member(_893197), _893199), hAPP(hAPP(c_Set_Oinsert(_893197), _893201), c_Orderings_Obot__class_Obot(tc_fun(_893197, tc_HOL_Obool))))), -(_893199 = _893201)], (552 ^ _781215) ^ [_789809, _789811, _789813, _789815, _789817, _789819] : [-(c_Hoare__Mirabelle_Ohoare__valids(_789817, _789813, _789809)), c_Hoare__Mirabelle_Ohoare__valids(_789819, _789815, _789811), _789819 = _789817, _789815 = _789813, _789811 = _789809], (41279 ^ _781215) ^ [_1591809, _1591811, _1591813, _1591815, _1591817, _1591819, _1591821, _1591823, _1591825, _1591827] : [-(c_Product__Type_Omap__pair(_1591809, _1591811, _1591813, _1591815, hAPP(c_Fun_Ocomp(_1591817, _1591811, _1591809, _1591819), _1591821), hAPP(c_Fun_Ocomp(_1591823, _1591815, _1591813, _1591825), _1591827)) = hAPP(c_Fun_Ocomp(tc_prod(_1591817, _1591823), tc_prod(_1591811, _1591815), tc_prod(_1591809, _1591813), c_Product__Type_Omap__pair(_1591817, _1591811, _1591823, _1591815, _1591819, _1591825)), c_Product__Type_Omap__pair(_1591809, _1591817, _1591813, _1591823, _1591821, _1591827)))], (25658 ^ _781215) ^ [_1243007, _1243009] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1243007, _1243009))))], (7171 ^ _781215) ^ [_901160, _901162, _901164] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_901160), _901162)), -(hAPP(c_Finite__Set_Ocard(_901160), hAPP(hAPP(c_Set_Oinsert(_901160), _901164), _901162)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_901160), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901160, tc_HOL_Obool)), _901162), hAPP(hAPP(c_Set_Oinsert(_901160), _901164), c_Orderings_Obot__class_Obot(tc_fun(_901160, tc_HOL_Obool)))))))], (40071 ^ _781215) ^ [_1563396, _1563398, _1563400] : [c_Wellfounded_Owf(_1563396, _1563398), c_Wellfounded_Owf(_1563396, _1563400), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1563396, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1563396, _1563396), _1563398)), hAPP(c_Relation_ORange(_1563396, _1563396), _1563400)) = c_Orderings_Obot__class_Obot(tc_fun(_1563396, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1563396, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563396, _1563396), tc_HOL_Obool)), _1563398), _1563400)))], (45365 ^ _781215) ^ [_1691410, _1691412, _1691414] : [hBOOL(hAPP(c_List_Odistinct(_1691410), _1691412)), -(hAPP(c_List_Ofilter(_1691410, hAPP(hAPP(c_COMBC(_1691410, tc_fun(_1691410, tc_HOL_Obool), tc_HOL_Obool), c_member(_1691410)), hAPP(c_List_Oset(_1691410), c_List_Osublist(_1691410, _1691412, _1691414)))), _1691412) = c_List_Osublist(_1691410, _1691412, _1691414))], (41221 ^ _781215) ^ [_1590647, _1590649] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1590647, _1590649) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1590647, _1590649)))], (46898 ^ _781215) ^ [_1724701, _1724703, _1724705, _1724707] : [hBOOL(hAPP(c_List_Odistinct(_1724701), _1724703)), hBOOL(hAPP(c_List_Odistinct(_1724705), _1724707)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1724701, _1724705)), c_Enum_Oproduct(_1724701, _1724705, _1724703, _1724707))))], (40091 ^ _781215) ^ [_1563781, _1563783] : [c_Wellfounded_Owf(_1563781, _1563783), 40094 ^ _781215 : [(40095 ^ _781215) ^ [_1563850] : [-(hBOOL(hAPP(hAPP(c_member(_1563781), _1563850), c_Wellfounded_Oacc(_1563781, _1563783))))]]], (17021 ^ _781215) ^ [_1086496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086496), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086496))], (5554 ^ _781215) ^ [_866000, _866002] : [_866002 = _866000, -(c_Orderings_Obot__class_Obot(_866002) = c_Orderings_Obot__class_Obot(_866000))], (51718 ^ _781215) ^ [_1826327, _1826329] : [hBOOL(hAPP(hAPP(c_fconj, _1826327), _1826329)), -(hBOOL(_1826329))], (2900 ^ _781215) ^ [_824559, _824561, _824563, _824565, _824567, _824569, _824571, _824573] : [-(c_Product__Type_Oapsnd(_824573, _824569, _824565, _824561) = c_Product__Type_Oapsnd(_824571, _824567, _824563, _824559)), _824573 = _824571, _824569 = _824567, _824565 = _824563, _824561 = _824559], (32056 ^ _781215) ^ [_1372544, _1372546, _1372548] : [class_Fields_Ofield(_1372544), -(_1372546 = c_Groups_Oone__class_Oone(_1372544)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1372544), hAPP(c_Power_Opower__class_Opower(_1372544), _1372546)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1372548)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1372544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1372544), hAPP(hAPP(c_Power_Opower__class_Opower(_1372544), _1372546), _1372548)), c_Groups_Oone__class_Oone(_1372544))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1372544), _1372546), c_Groups_Oone__class_Oone(_1372544))))], (35883 ^ _781215) ^ [_1455767, _1455769, _1455771, _1455773, _1455775] : [-(hAPP(c_Product__Type_Ofst(_1455767, _1455769), hAPP(c_Product__Type_Oapsnd(_1455771, _1455769, _1455767, _1455773), _1455775)) = hAPP(c_Product__Type_Ofst(_1455767, _1455771), _1455775))], (27546 ^ _781215) ^ [_1282586, _1282588, _1282590, _1282592, _1282594, _1282596] : [hBOOL(hAPP(_1282586, _1282588)), hBOOL(hAPP(_1282590, _1282592)), 27553 ^ _781215 : [(27556 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1282590, hAPP(c_Product__Type_Osnd(_1282594, _1282596), hAPP(hAPP(c_Product__Type_OPair(_1282594, _1282596), _1282588), _1282592)))))], (27554 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1282586, hAPP(c_Product__Type_Ofst(_1282594, _1282596), hAPP(hAPP(c_Product__Type_OPair(_1282594, _1282596), _1282588), _1282592)))))]]], (51230 ^ _781215) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (46524 ^ _781215) ^ [_1716755, _1716757, _1716759, _1716761] : [hBOOL(hAPP(_1716755, _1716757)), -(c_List_OtakeWhile(_1716759, _1716755, hAPP(hAPP(c_List_Olist_OCons(_1716759), _1716757), _1716761)) = hAPP(hAPP(c_List_Olist_OCons(_1716759), _1716757), c_List_OtakeWhile(_1716759, _1716755, _1716761)))], (44816 ^ _781215) ^ [_1680107, _1680109] : [-(_1680107 = c_List_Olist_ONil(_1680109)), -(hAPP(c_List_Orotate1(_1680109), _1680107) = hAPP(hAPP(c_List_Oappend(_1680109), hAPP(c_List_Otl(_1680109), _1680107)), hAPP(hAPP(c_List_Olist_OCons(_1680109), hAPP(c_List_Ohd(_1680109), _1680107)), c_List_Olist_ONil(_1680109))))], (29782 ^ _781215) ^ [_1324176, _1324178, _1324180, _1324182] : [class_Fields_Olinordered__field(_1324176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324176), _1324178), c_Groups_Ozero__class_Ozero(_1324176))), 29789 ^ _781215 : [(29796 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324176), _1324182), _1324178)), _1324180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324176), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324176), _1324180), _1324178)), _1324182)))], (29790 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324176), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324176), _1324180), _1324178)), _1324182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324176), _1324182), _1324178)), _1324180)))]]], (39945 ^ _781215) ^ [_1561230, _1561232] : [-(c_HOL_OThe(_1561230, hAPP(c_fequal, _1561232)) = _1561232)], (33062 ^ _781215) ^ [_1394615, _1394617, _1394619, _1394621] : [class_Lattices_Osemilattice__inf(_1394615), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394615), _1394617), _1394619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394615), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1394615), _1394617), _1394621)), _1394619)))], (45596 ^ _781215) ^ [_1696320, _1696322, _1696324] : [class_Orderings_Olinorder(_1696320), c_List_Olinorder__class_Osorted(_1696320, _1696322), -(c_List_Olinorder__class_Osorted(_1696320, hAPP(hAPP(c_List_Otake(_1696320), _1696324), _1696322)))], (47509 ^ _781215) ^ [_1737199, _1737201, _1737203, _1737205] : [-(hBOOL(hAPP(c_List_Olistsp(_1737199, hAPP(hAPP(c_COMBS(_1737199, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1737199), c_fconj), _1737201)), _1737203)), _1737205))), hBOOL(hAPP(c_List_Olistsp(_1737199, _1737201), _1737205)), hBOOL(hAPP(c_List_Olistsp(_1737199, _1737203), _1737205))], (31288 ^ _781215) ^ [_1354229, _1354231, _1354233, _1354235, _1354237, _1354239] : [-(hAPP(c_Relation_OImage(_1354229, _1354231, _1354233), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1354235, tc_fun(_1354229, tc_HOL_Obool)), _1354237), _1354239)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1354235, tc_fun(_1354231, tc_HOL_Obool)), _1354237), hAPP(hAPP(c_COMBB(tc_fun(_1354229, tc_HOL_Obool), tc_fun(_1354231, tc_HOL_Obool), _1354235), c_Relation_OImage(_1354229, _1354231, _1354233)), _1354239)))], (27436 ^ _781215) ^ [_1280445, _1280447, _1280449, _1280451, _1280453] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1280445, _1280447, _1280449), _1280451), _1280453) = hAPP(hAPP(_1280451, hAPP(c_Product__Type_Ofst(_1280445, _1280447), _1280453)), hAPP(c_Product__Type_Osnd(_1280445, _1280447), _1280453)))], (37277 ^ _781215) ^ [_1487626, _1487628, _1487630, _1487632, _1487634] : [class_Complete__Lattice_Ocomplete__lattice(_1487626), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487628), _1487630)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1487626), _1487632), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1487628, _1487626), _1487630), _1487634)) = hAPP(hAPP(c_Finite__Set_Ofold(_1487628, _1487626, hAPP(hAPP(c_COMBB(_1487626, tc_fun(_1487626, _1487626), _1487628), c_Lattices_Osemilattice__inf__class_Oinf(_1487626)), _1487634)), _1487632), _1487630))], (39947 ^ _781215) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (37649 ^ _781215) ^ [_1496674, _1496676, _1496678] : [class_Complete__Lattice_Ocomplete__lattice(_1496674), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496674), _1496676)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1496674), _1496678), c_Complete__Lattice_OInf__class_OInf(_1496674, _1496676)) = hAPP(hAPP(c_Finite__Set_Ofold(_1496674, _1496674, c_Lattices_Osemilattice__inf__class_Oinf(_1496674)), _1496678), _1496676))], (7826 ^ _781215) ^ [_913303, _913305, _913307] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913303), _913305)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913303), _913307)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _913305), _913307))], (42258 ^ _781215) ^ [_1616648, _1616650, _1616652, _1616654] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616648), tc_List_Olist(_1616648))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616648), tc_List_Olist(_1616648)), _1616650), _1616652)), c_List_Olistrel(_1616648, _1616654)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616648)), _1616650) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616648)), _1616652), 42264 ^ _781215 : [(42267 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1616648, _1616648, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1616648, tc_fun(tc_prod(_1616648, _1616648), tc_HOL_Obool), tc_fun(_1616648, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616648, tc_fun(tc_fun(tc_prod(_1616648, _1616648), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1616648, _1616648), tc_HOL_Obool), tc_fun(_1616648, tc_HOL_Obool)), _1616648), c_COMBC(_1616648, tc_fun(tc_prod(_1616648, _1616648), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616648, tc_prod(_1616648, _1616648)), tc_fun(_1616648, tc_fun(tc_fun(tc_prod(_1616648, _1616648), tc_HOL_Obool), tc_HOL_Obool)), _1616648), hAPP(c_COMBB(tc_prod(_1616648, _1616648), tc_fun(tc_fun(tc_prod(_1616648, _1616648), tc_HOL_Obool), tc_HOL_Obool), _1616648), c_member(tc_prod(_1616648, _1616648)))), c_Product__Type_OPair(_1616648, _1616648)))), _1616654)), 42263 ^ [_1616648, _1616650, _1616652, _1616654]))], (42265 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616648, _1616648)), 42263 ^ [_1616648, _1616650, _1616652, _1616654]), hAPP(c_List_Oset(tc_prod(_1616648, _1616648)), hAPP(hAPP(c_List_Ozip(_1616648, _1616648), _1616650), _1616652)))))]]], (25748 ^ _781215) ^ [] : [-(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))], (11604 ^ _781215) ^ [_983839, _983841] : [class_Groups_Olinordered__ab__group__add(_983839), 11607 ^ _781215 : [(11614 ^ _781215) ^ [] : [_983841 = c_Groups_Ozero__class_Ozero(_983839), -(c_Groups_Ozero__class_Ozero(_983839) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983839), _983841), _983841))], (11608 ^ _781215) ^ [] : [c_Groups_Ozero__class_Ozero(_983839) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983839), _983841), _983841), -(_983841 = c_Groups_Ozero__class_Ozero(_983839))]]], (50298 ^ _781215) ^ [_1803665, _1803667] : [-(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)))), _1803665)) = 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)))), _1803667))), 50300 ^ _781215 : [(50303 ^ _781215) ^ [] : [50304 ^ _781215 : [(50307 ^ _781215) ^ [] : [hBOOL(hAPP(_1803667, 50299 ^ [_1803665, _1803667]))], (50305 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1803665, 50299 ^ [_1803665, _1803667])))]], 50308 ^ _781215 : [(50311 ^ _781215) ^ [] : [hBOOL(hAPP(_1803665, 50299 ^ [_1803665, _1803667]))], (50309 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1803667, 50299 ^ [_1803665, _1803667])))]]], (50301 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 50299 ^ [_1803665, _1803667])))]]], (7977 ^ _781215) ^ [_915722, _915724, _915726] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _915722), _915724)), _915726) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _915722), _915726)), _915724))], (10410 ^ _781215) ^ [_958746, _958748, _958750, _958752] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_958746), _958748)), hBOOL(hAPP(c_Finite__Set_Ofinite(_958750), _958752)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_958746, _958750)), c_Sum__Type_OPlus(_958746, _958750, _958748, _958752))))], (11904 ^ _781215) ^ [_988224, _988226] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988224), _988226) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 11907 ^ _781215 : [(11910 ^ _781215) ^ [] : [-(_988226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11908 ^ _781215) ^ [] : [-(_988224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21848 ^ _781215) ^ [_1173493, _1173495, _1173497, _1173499] : [_1173493 = c_Orderings_Obot__class_Obot(tc_fun(_1173495, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1173495, tc_fun(_1173497, tc_HOL_Obool)), _1173493), hAPP(c_COMBK(tc_fun(_1173497, tc_HOL_Obool), _1173495), _1173499)) = c_Orderings_Obot__class_Obot(tc_fun(_1173497, tc_HOL_Obool)))], (30066 ^ _781215) ^ [_1330929, _1330931, _1330933, _1330935, _1330937, _1330939] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1330935, _1330935)), hAPP(hAPP(c_Product__Type_OPair(_1330935, _1330935), hAPP(_1330939, _1330931)), hAPP(_1330939, _1330933))), _1330937)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1330929, _1330929)), hAPP(hAPP(c_Product__Type_OPair(_1330929, _1330929), _1330931), _1330933)), hAPP(hAPP(c_Relation_Oinv__image(_1330935, _1330929), _1330937), _1330939))))], (10070 ^ _781215) ^ [_952462, _952464, _952466, _952468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952462), _952464)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952466), _952468)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952462), _952466)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952464), _952468))))], (2954 ^ _781215) ^ [_825462, _825464, _825466, _825468] : [-(c_Option_Omap(_825468, _825464) = c_Option_Omap(_825466, _825462)), _825468 = _825466, _825464 = _825462], (15542 ^ _781215) ^ [_1053841, _1053843, _1053845, _1053847, _1053849] : [-(hAPP(c_Map_Omap__add(_1053841, _1053843, _1053845, _1053847), _1053849) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1053843), _1053843, hAPP(_1053845, _1053849), c_Option_Ooption_OSome(_1053843)), hAPP(_1053847, _1053849)))], (51702 ^ _781215) ^ [_1826101, _1826103] : [hBOOL(_1826101), hBOOL(_1826103), -(hBOOL(hAPP(hAPP(c_fconj, _1826101), _1826103)))], (24564 ^ _781215) ^ [_1224563, _1224565, _1224567] : [class_Rings_Olinordered__idom(_1224563), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224563), c_Groups_Ozero__class_Ozero(_1224563)), hAPP(hAPP(c_Power_Opower__class_Opower(_1224563), _1224565), 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)))), _1224567))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224563), c_Groups_Ozero__class_Ozero(_1224563)), _1224565)))], (7250 ^ _781215) ^ [_903193, _903195, _903197] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903193), _903195)), hBOOL(hAPP(hAPP(c_member(_903193), _903197), _903195)), -(hAPP(c_Finite__Set_Ocard(_903193), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903193, tc_HOL_Obool)), _903195), hAPP(hAPP(c_Set_Oinsert(_903193), _903197), c_Orderings_Obot__class_Obot(tc_fun(_903193, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_903193), _903195)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11090 ^ _781215) ^ [_973000, _973002, _973004, _973006, _973008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973000), _973002)), -(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), _973000), _973004)), _973006)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973002), _973004)), _973008)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _973006), 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), _973002), _973000)), _973004)), _973008)))], (15016 ^ _781215) ^ [_1044816, _1044818, _1044820, _1044822] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044816), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044816), _1044818), _1044820)), hAPP(c_Int_Onumber__class_Onumber__of(_1044816), _1044822)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044816), _1044818), hAPP(c_Int_Onumber__class_Onumber__of(_1044816), _1044822))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044816), _1044820), hAPP(c_Int_Onumber__class_Onumber__of(_1044816), _1044822)))), class_Int_Onumber(_1044816), class_Rings_Oring(_1044816)], (5839 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (21932 ^ _781215) ^ [_1175663, _1175665, _1175667, _1175669, _1175671, _1175673] : [class_Complete__Lattice_Ocomplete__lattice(_1175663), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175665, _1175663), _1175667), hAPP(hAPP(c_COMBB(tc_fun(_1175669, _1175663), _1175663, _1175665), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175669, _1175663), _1175671)), _1175673)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175669, _1175663), _1175671), hAPP(hAPP(c_COMBB(tc_fun(_1175665, _1175663), _1175663, _1175669), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175665, _1175663), _1175667)), hAPP(c_COMBC(_1175665, _1175669, _1175663), _1175673))))], (13964 ^ _781215) ^ [_1024566, _1024568] : [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), _1024566), _1024568))), 13967 ^ _781215 : [(13970 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1024568)))], (13968 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1024566)))]]], (25408 ^ _781215) ^ [_1238929] : [c_Nat__Transfer_Ois__nat(_1238929), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238929)))], (51310 ^ _781215) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (49505 ^ _781215) ^ [_1782712, _1782714, _1782716, _1782718, _1782720] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1782712), tc_List_Olist(_1782712))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1782712), tc_List_Olist(_1782712)), _1782714), _1782716)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1782712), c_List_Olistrel1(_1782712, _1782718)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1782712), tc_List_Olist(_1782712))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1782712), tc_List_Olist(_1782712)), hAPP(hAPP(c_List_Olist_OCons(_1782712), _1782720), _1782714)), hAPP(hAPP(c_List_Olist_OCons(_1782712), _1782720), _1782716))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1782712), c_List_Olistrel1(_1782712, _1782718)))))], (51332 ^ _781215) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (12026 ^ _781215) ^ [_989982, _989984, _989986] : [12027 ^ _781215 : [(12030 ^ _781215) ^ [] : [_989984 = _989986], (12028 ^ _781215) ^ [] : [_989982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989982), _989984) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989982), _989986))], (22114 ^ _781215) ^ [_1179767, _1179769, _1179771, _1179773, _1179775] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179767, tc_fun(_1179769, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1179767), _1179771), _1179773)), _1179775) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1179769, tc_HOL_Obool)), hAPP(_1179775, _1179771)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179767, tc_fun(_1179769, tc_HOL_Obool)), _1179773), _1179775)))], (47980 ^ _781215) ^ [_1747314, _1747316, _1747318, _1747320] : [-(c_List_Oconcat(_1747314, hAPP(hAPP(c_List_Omap(_1747316, tc_List_Olist(_1747314)), _1747318), _1747320)) = c_List_Omaps(_1747316, _1747314, _1747318, _1747320))], (5961 ^ _781215) ^ [_876138, _876140, _876142] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _876140))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_876138, _876140, _876142))))], (51574 ^ _781215) ^ [_1824715] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1824715)))], (5352 ^ _781215) ^ [_862989, _862991, _862993, _862995, _862997, _862999] : [-(c_Lazy__Sequence_Oappend(_862999, _862995, _862991) = c_Lazy__Sequence_Oappend(_862997, _862993, _862989)), _862999 = _862997, _862995 = _862993, _862991 = _862989], (3122 ^ _781215) ^ [_828194, _828196, _828198, _828200] : [-(c_Nitpick_Ocard_H(_828200, _828196) = c_Nitpick_Ocard_H(_828198, _828194)), _828200 = _828198, _828196 = _828194], (48565 ^ _781215) ^ [_1761830, _1761832, _1761834, _1761836] : [class_Lattices_Osemilattice__inf(_1761830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1761830), _1761832)), 48575 ^ _781215 : [(48578 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1761830), _1761834), 48574 ^ [_1761830, _1761832, _1761834, _1761836]))], (48576 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1761830), 48574 ^ [_1761830, _1761832, _1761834, _1761836]), _1761832)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1761830), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1761830), _1761834), _1761836)), hAPP(hAPP(c_Finite__Set_Ofold(_1761830, _1761830, c_Lattices_Osemilattice__inf__class_Oinf(_1761830)), _1761836), _1761832))))], (22288 ^ _781215) ^ [_1183402, _1183404, _1183406, _1183408] : [class_Divides_Osemiring__div(_1183402), -(c_Divides_Odiv__class_Omod(_1183402, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183402), c_Divides_Odiv__class_Omod(_1183402, _1183404, _1183406)), _1183408), _1183406) = c_Divides_Odiv__class_Omod(_1183402, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1183402), _1183404), _1183408), _1183406))], (29018 ^ _781215) ^ [_1310261, _1310263, _1310265, _1310267] : [class_Fields_Olinordered__field(_1310261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), _1310263), _1310265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), c_Groups_Ozero__class_Ozero(_1310261)), _1310267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310261), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310261), _1310263), _1310267)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310261), _1310265), _1310267))))], (32964 ^ _781215) ^ [_1392518, _1392520, _1392522, _1392524] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392518, tc_HOL_Obool)), _1392520), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392518, tc_HOL_Obool)), _1392522), _1392524)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392518, tc_HOL_Obool)), _1392522), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392518, tc_HOL_Obool)), _1392520), _1392524)))], (15799 ^ _781215) ^ [_1059153, _1059155, _1059157, _1059159, _1059161] : [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), _1059153), _1059155)), _1059157)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1059153), _1059159)), _1059161))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059161), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059153), _1059161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059153), _1059157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059159), _1059155)))], (33569 ^ _781215) ^ [_1406724, _1406726, _1406728, _1406730, _1406732] : [class_Groups_Ocomm__monoid__add(_1406724), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406726), _1406728)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406726, _1406724), _1406730), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406726, tc_HOL_Obool)), _1406728), _1406732)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406726, _1406724), hAPP(hAPP(c_COMBC(_1406726, _1406724, _1406724), hAPP(hAPP(c_COMBS(_1406726, _1406724, tc_fun(_1406724, _1406724)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1406724, tc_fun(_1406724, _1406724)), _1406726), c_If(_1406724)), hAPP(hAPP(c_COMBC(_1406726, tc_fun(_1406726, tc_HOL_Obool), tc_HOL_Obool), c_member(_1406726)), _1406732))), _1406730)), c_Groups_Ozero__class_Ozero(_1406724))), _1406728))], (18025 ^ _781215) ^ [_1103083, _1103085] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103083) = hAPP(c_Nat_OSuc, _1103085), -(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(_1103083))), 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)), _1103085))))))], (2624 ^ _781215) ^ [_820207, _820209, _820211, _820213] : [-(c_Divides_Odivmod__nat(_820213, _820209) = c_Divides_Odivmod__nat(_820211, _820207)), _820213 = _820211, _820209 = _820207], (31780 ^ _781215) ^ [_1366135, _1366137, _1366139, _1366141, _1366143] : [class_Groups_Ocomm__monoid__add(_1366135), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366137), _1366139)), 31787 ^ _781215 : [(31794 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366137), _1366141), _1366139))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1366137, _1366135), hAPP(hAPP(c_COMBC(_1366137, _1366135, _1366135), hAPP(hAPP(c_COMBS(_1366137, _1366135, tc_fun(_1366135, _1366135)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1366135, tc_fun(_1366135, _1366135)), _1366137), c_If(_1366135)), hAPP(hAPP(c_COMBC(_1366137, _1366137, tc_HOL_Obool), c_fequal), _1366141))), _1366143)), c_Groups_Ozero__class_Ozero(_1366135))), _1366139) = c_Groups_Ozero__class_Ozero(_1366135))], (31788 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1366137), _1366141), _1366139)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1366137, _1366135), hAPP(hAPP(c_COMBC(_1366137, _1366135, _1366135), hAPP(hAPP(c_COMBS(_1366137, _1366135, tc_fun(_1366135, _1366135)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1366135, tc_fun(_1366135, _1366135)), _1366137), c_If(_1366135)), hAPP(hAPP(c_COMBC(_1366137, _1366137, tc_HOL_Obool), c_fequal), _1366141))), _1366143)), c_Groups_Ozero__class_Ozero(_1366135))), _1366139) = hAPP(_1366143, _1366141))]]], (1888 ^ _781215) ^ [_807785, _807787] : [-(hBOOL(_807785)), _807787 = _807785, hBOOL(_807787)], (36853 ^ _781215) ^ [_1475673, _1475675, _1475677, _1475679, _1475681, _1475683] : [hBOOL(hAPP(hAPP(c_member(_1475673), _1475675), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1475677, tc_fun(_1475673, tc_HOL_Obool)), _1475679), _1475681))), hBOOL(hAPP(hAPP(c_member(_1475677), _1475683), _1475679)), -(hBOOL(hAPP(hAPP(c_member(_1475673), _1475675), hAPP(_1475681, _1475683))))], (51590 ^ _781215) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (11004 ^ _781215) ^ [_970874, _970876, _970878, _970880, _970882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970874), _970876)), 11007 ^ _781215 : [(11014 ^ _781215) ^ [] : [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), _970876), _970874)), _970878)), _970880)), _970882)), -(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), _970876), _970878)), _970880)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970874), _970878)), _970882))))], (11008 ^ _781215) ^ [] : [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), _970876), _970878)), _970880)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970874), _970878)), _970882))), -(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), _970876), _970874)), _970878)), _970880)), _970882)))]]], (27504 ^ _781215) ^ [_1281775, _1281777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1281775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1281777), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1281775), _1281777) = 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), _1281775), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1281777)))))], (1368 ^ _781215) ^ [_801285, _801287] : [-(class_Lattices_Odistrib__lattice(_801285)), _801287 = _801285, class_Lattices_Odistrib__lattice(_801287)], (11306 ^ _781215) ^ [_977964, _977966, _977968, _977970] : [c_Sum__Type_OPlus(_977964, _977966, _977968, _977970) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_977964, _977966), tc_HOL_Obool)), 11309 ^ _781215 : [(11312 ^ _781215) ^ [] : [-(_977970 = c_Orderings_Obot__class_Obot(tc_fun(_977966, tc_HOL_Obool)))], (11310 ^ _781215) ^ [] : [-(_977968 = c_Orderings_Obot__class_Obot(tc_fun(_977964, tc_HOL_Obool)))]]], (16103 ^ _781215) ^ [_1065827, _1065829] : [class_Lattices_Osemilattice__sup(_1065827), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065827), _1065829), _1065829) = _1065829)], (44596 ^ _781215) ^ [_1675077, _1675079, _1675081] : [hBOOL(hAPP(c_List_Odistinct(_1675077), _1675079)), -(hBOOL(hAPP(c_List_Odistinct(_1675077), hAPP(hAPP(c_List_Odrop(_1675077), _1675081), _1675079))))], (28472 ^ _781215) ^ [_1299896, _1299898] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299896), hAPP(c_Int_Onumber__class_Onumber__of(_1299896), c_Int_OMin)), _1299898) = hAPP(c_Groups_Ouminus__class_Ouminus(_1299896), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299896), c_Groups_Oone__class_Oone(_1299896)), _1299898))), class_Fields_Ofield__inverse__zero(_1299896), class_Int_Onumber__ring(_1299896)], (23799 ^ _781215) ^ [_1210161, _1210163, _1210165] : [-(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), _1210161), _1210163)), _1210165), _1210163) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1210165, _1210163))], (31449 ^ _781215) ^ [_1357878, _1357880, _1357882, _1357884] : [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), _1357878), _1357880)), 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), _1357882), _1357884)), 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), _1357878), _1357884)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1357882), _1357880))))], (50029 ^ _781215) ^ [_1796227, _1796229, _1796231] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1796227, _1796227)), _1796229), c_Transitive__Closure_Otrancl(_1796227, _1796231))), 50033 ^ _781215 : [(50036 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1796227, _1796227)), _1796229), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1796227, _1796227), tc_HOL_Obool), 50032 ^ [_1796227, _1796229, _1796231]), _1796231))))], (50034 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 50032 ^ [_1796227, _1796229, _1796231])))]]], (1818 ^ _781215) ^ [_806910, _806912] : [-(class_Groups_Ominus(_806910)), _806912 = _806910, class_Groups_Ominus(_806912)], (25524 ^ _781215) ^ [_1240691, _1240693] : [c_Nat__Transfer_Onat__set(_1240691), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1240693), _1240691)), -(c_Nat__Transfer_Ois__nat(_1240693))], (39162 ^ _781215) ^ [_1533154, _1533156, _1533158] : [-(hAPP(hAPP(c_Set_Oinsert(_1533154), _1533156), _1533158) = hAPP(c_Set_OCollect(_1533154), hAPP(hAPP(c_COMBS(_1533154, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533154), c_fdisj), hAPP(hAPP(c_COMBC(_1533154, _1533154, tc_HOL_Obool), c_fequal), _1533156))), hAPP(hAPP(c_COMBC(_1533154, tc_fun(_1533154, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533154)), _1533158))))], (46165 ^ _781215) ^ [_1707681, _1707683, _1707685] : [-(hAPP(c_List_Orev(_1707681), hAPP(hAPP(c_List_Oappend(_1707681), _1707683), _1707685)) = hAPP(hAPP(c_List_Oappend(_1707681), hAPP(c_List_Orev(_1707681), _1707685)), hAPP(c_List_Orev(_1707681), _1707683)))], (8476 ^ _781215) ^ [_924942, _924944, _924946] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_924942), _924944)), hBOOL(hAPP(_924946, c_Orderings_Obot__class_Obot(tc_fun(_924942, tc_HOL_Obool)))), 8487 ^ _781215 : [(8490 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_924942), 8485 ^ [_924942, _924944, _924946]), 8486 ^ [_924942, _924944, _924946]))], (8492 ^ _781215) ^ [] : [-(hBOOL(hAPP(_924946, 8486 ^ [_924942, _924944, _924946])))], (8494 ^ _781215) ^ [] : [hBOOL(hAPP(_924946, hAPP(hAPP(c_Set_Oinsert(_924942), 8485 ^ [_924942, _924944, _924946]), 8486 ^ [_924942, _924944, _924946])))], (8488 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_924942), 8486 ^ [_924942, _924944, _924946])))]], -(hBOOL(hAPP(_924946, _924944)))], (21817 ^ _781215) ^ [_1172691, _1172693, _1172695, _1172697, _1172699] : [-(hBOOL(hAPP(hAPP(c_member(_1172691), _1172693), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1172695, tc_fun(_1172691, tc_HOL_Obool)), _1172697), _1172699)))), 21818 ^ _781215 : [(21819 ^ _781215) ^ [_1172773] : [hBOOL(hAPP(hAPP(c_member(_1172695), _1172773), _1172697)), hBOOL(hAPP(hAPP(c_member(_1172691), _1172693), hAPP(_1172699, _1172773)))]]], (31146 ^ _781215) ^ [_1351425, _1351427, _1351429] : [class_Groups_Oordered__ab__group__add(_1351425), -(hAPP(c_Set_Oimage(_1351425, _1351425, c_Groups_Ouminus__class_Ouminus(_1351425)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1351425, _1351427, _1351429)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1351425, hAPP(c_Groups_Ouminus__class_Ouminus(_1351425), _1351429)), hAPP(c_Groups_Ouminus__class_Ouminus(_1351425), _1351427)))], (51688 ^ _781215) ^ [] : [-(hBOOL(c_fTrue))], (30233 ^ _781215) ^ [_1334254, _1334256, _1334258, _1334260, _1334262] : [class_Orderings_Oorder(_1334254), 30236 ^ _781215 : [(30249 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1334254, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1334254, _1334256, _1334258)), c_SetInterval_Oord__class_OatLeastAtMost(_1334254, _1334260, _1334262)))), 30250 ^ _781215 : [(30253 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334254), _1334260), _1334256)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334254), _1334258), _1334262))], (30251 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334254), _1334256), _1334258)))]]], (30237 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1334254, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1334254, _1334256, _1334258)), c_SetInterval_Oord__class_OatLeastAtMost(_1334254, _1334260, _1334262))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334254), _1334256), _1334258)), 30244 ^ _781215 : [(30247 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334254), _1334258), _1334262)))], (30245 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334254), _1334260), _1334256)))]]]]], (41186 ^ _781215) ^ [_1589770, _1589772, _1589774, _1589776, _1589778] : [hBOOL(hAPP(c_List_Odistinct(_1589770), hAPP(hAPP(c_List_Omap(tc_prod(_1589770, _1589772), _1589770), c_Product__Type_Ofst(_1589770, _1589772)), _1589774))), 41189 ^ _781215 : [(41196 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589770, _1589772)), hAPP(hAPP(c_Product__Type_OPair(_1589770, _1589772), _1589776), _1589778)), hAPP(c_List_Oset(tc_prod(_1589770, _1589772)), _1589774))), -(hAPP(hAPP(c_Map_Omap__of(_1589770, _1589772), _1589774), _1589776) = hAPP(c_Option_Ooption_OSome(_1589772), _1589778))], (41190 ^ _781215) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1589770, _1589772), _1589774), _1589776) = hAPP(c_Option_Ooption_OSome(_1589772), _1589778), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589770, _1589772)), hAPP(hAPP(c_Product__Type_OPair(_1589770, _1589772), _1589776), _1589778)), hAPP(c_List_Oset(tc_prod(_1589770, _1589772)), _1589774))))]]], (4176 ^ _781215) ^ [_844603, _844605, _844607, _844609] : [-(c_Random_Oselect__weight(_844609, _844605) = c_Random_Oselect__weight(_844607, _844603)), _844609 = _844607, _844605 = _844603], (35869 ^ _781215) ^ [_1455456, _1455458, _1455460, _1455462, _1455464] : [class_Rings_Olinordered__idom(_1455456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455456), hAPP(c_Groups_Oabs__class_Oabs(_1455456), _1455458)), _1455460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455456), hAPP(c_Groups_Oabs__class_Oabs(_1455456), _1455462)), _1455464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455456), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1455456), hAPP(c_Groups_Oabs__class_Oabs(_1455456), _1455458)), hAPP(c_Groups_Oabs__class_Oabs(_1455456), _1455462))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1455456), _1455460), _1455464))))], (5066 ^ _781215) ^ [_858386, _858388, _858390, _858392, _858394, _858396, _858398, _858400] : [-(c_New__DSequence_Oneg__decr__bind(_858400, _858396, _858392, _858388) = c_New__DSequence_Oneg__decr__bind(_858398, _858394, _858390, _858386)), _858400 = _858398, _858396 = _858394, _858392 = _858390, _858388 = _858386], (14256 ^ _781215) ^ [_1030429] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1030429)), c_Option_Ooption_ONone(_1030429)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41519 ^ _781215) ^ [_1597686, _1597688, _1597690, _1597692, _1597694, _1597696, _1597698, _1597700, _1597702, _1597704, _1597706] : [c_Finite__Set_Ofolding(_1597686, _1597688, _1597690, _1597692), -(hAPP(c_Fun_Ocomp(_1597694, _1597696, _1597698, _1597700), hAPP(c_Fun_Ocomp(_1597702, _1597694, _1597698, _1597704), _1597706)) = hAPP(c_Fun_Ocomp(_1597702, _1597696, _1597698, hAPP(c_Fun_Ocomp(_1597694, _1597696, _1597702, _1597700), _1597704)), _1597706))], (51624 ^ _781215) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (21147 ^ _781215) ^ [_1159685, _1159687] : [class_Int_Onumber__ring(_1159685), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1159685), c_Groups_Oone__class_Oone(_1159685)), hAPP(c_Int_Onumber__class_Onumber__of(_1159685), _1159687)) = hAPP(c_Int_Onumber__class_Onumber__of(_1159685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1159687)))], (49517 ^ _781215) ^ [_1783167, _1783169, _1783171, _1783173] : [c_Wellfounded_Oacyclic(_1783167, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1783167, _1783167)), hAPP(hAPP(c_Product__Type_OPair(_1783167, _1783167), _1783169), _1783171)), _1783173)), 49520 ^ _781215 : [(49523 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1783167, _1783167)), hAPP(hAPP(c_Product__Type_OPair(_1783167, _1783167), _1783171), _1783169)), c_Transitive__Closure_Ortrancl(_1783167, _1783173)))], (49521 ^ _781215) ^ [] : [-(c_Wellfounded_Oacyclic(_1783167, _1783173))]]], (16453 ^ _781215) ^ [_1072315, _1072317, _1072319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072315, tc_HOL_Obool)), _1072317), _1072319)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072315, tc_HOL_Obool)), _1072317), _1072319) = _1072319)], (44804 ^ _781215) ^ [_1680009, _1680011] : [-(_1680009 = c_List_Olist_ONil(_1680011)), -(hBOOL(hAPP(hAPP(c_member(_1680011), hAPP(c_List_Ohd(_1680011), _1680009)), hAPP(c_List_Oset(_1680011), _1680009))))], (23809 ^ _781215) ^ [_1210369, _1210371] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210369)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210371)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1210369), _1210371)))], (37303 ^ _781215) ^ [_1488405, _1488407, _1488409, _1488411, _1488413] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1488405, tc_fun(_1488407, tc_HOL_Obool)), _1488409), _1488411), _1488413)), 37306 ^ _781215 : [(37307 ^ _781215) ^ [_1488514] : [hBOOL(hAPP(hAPP(c_member(_1488405), _1488514), _1488409)), -(hBOOL(hAPP(hAPP(_1488411, _1488514), _1488413)))]]], (28746 ^ _781215) ^ [_1305171, _1305173, _1305175, _1305177] : [class_Fields_Olinordered__field__inverse__zero(_1305171), 28749 ^ _781215 : [(28750 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305171), _1305173), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305171), _1305175), _1305177))), 28753 ^ _781215 : [(28760 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305171), c_Groups_Ozero__class_Ozero(_1305171)), _1305177))), 28763 ^ _781215 : [(28770 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305171), _1305177), c_Groups_Ozero__class_Ozero(_1305171)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305171), _1305173), c_Groups_Ozero__class_Ozero(_1305171))))], (28764 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305171), _1305177), c_Groups_Ozero__class_Ozero(_1305171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305171), _1305175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305171), _1305173), _1305177))))]]], (28754 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305171), c_Groups_Ozero__class_Ozero(_1305171)), _1305177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305171), _1305173), _1305177)), _1305175)))]]], (28776 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305171), _1305173), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305171), _1305175), _1305177)))), 28779 ^ _781215 : [(28782 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305171), _1305173), _1305177)), _1305175))], (28780 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305171), c_Groups_Ozero__class_Ozero(_1305171)), _1305177)))]], 28783 ^ _781215 : [(28786 ^ _781215) ^ [] : [28787 ^ _781215 : [(28790 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305171), _1305175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305171), _1305173), _1305177)))], (28788 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305171), _1305177), c_Groups_Ozero__class_Ozero(_1305171))))]], 28791 ^ _781215 : [(28794 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305171), _1305173), c_Groups_Ozero__class_Ozero(_1305171)))], (28792 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305171), _1305177), c_Groups_Ozero__class_Ozero(_1305171)))]]], (28784 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305171), c_Groups_Ozero__class_Ozero(_1305171)), _1305177))]]]]], (49056 ^ _781215) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (18758 ^ _781215) ^ [_1117532, _1117534, _1117536, _1117538] : [class_Orderings_Olinorder(_1117532), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117532), _1117534), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117532), _1117536), _1117538)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117532), _1117536), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117532), _1117534), _1117538)))], (39749 ^ _781215) ^ [_1554440, _1554442, _1554444, _1554446, _1554448, _1554450, _1554452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1554440, _1554442), tc_HOL_Obool)), _1554444), _1554446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1554442, _1554448), tc_HOL_Obool)), _1554450), _1554452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1554440, _1554448), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1554440, _1554442, _1554448), _1554444), _1554450)), hAPP(hAPP(c_Relation_Orel__comp(_1554440, _1554442, _1554448), _1554446), _1554452))))], (36654 ^ _781215) ^ [_1470329, _1470331] : [class_Lattices_Oboolean__algebra(_1470329), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1470329), _1470331), hAPP(c_Groups_Ouminus__class_Ouminus(_1470329), _1470331)) = c_Orderings_Otop__class_Otop(_1470329))], (47978 ^ _781215) ^ [_1747266, _1747268, _1747270, _1747272] : [-(c_List_Omaps(_1747266, _1747268, _1747270, _1747272) = c_List_Oconcat(_1747268, hAPP(hAPP(c_List_Omap(_1747266, tc_List_Olist(_1747268)), _1747270), _1747272)))], (9325 ^ _781215) ^ [_940119, _940121, _940123] : [-(hBOOL(hAPP(hAPP(c_member(_940119), _940121), _940123))), -(hBOOL(hAPP(hAPP(c_member(_940119), _940121), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_940119, tc_HOL_Obool)), _940123))))], (11214 ^ _781215) ^ [_976025, _976027, _976029, _976031, _976033] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_976025), 11217 ^ _781215 : [(11218 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976025), _976027), _976029)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976025), _976031), _976033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976025), _976027), _976033)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976025), _976031), _976029)), -(_976027 = _976031), -(_976029 = _976033)], (11228 ^ _781215) ^ [] : [11229 ^ _781215 : [(11232 ^ _781215) ^ [] : [_976029 = _976033], (11230 ^ _781215) ^ [] : [_976027 = _976031]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976025), _976027), _976029)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976025), _976031), _976033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976025), _976027), _976033)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976025), _976031), _976029)))]]], (7394 ^ _781215) ^ [_905780, _905782, _905784] : [class_Orderings_Olinorder(_905780), -(_905782 = _905784), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905780), _905782), _905784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905780), _905784), _905782)))], (26143 ^ _781215) ^ [_1255334, _1255336] : [class_Int_Onumber__ring(_1255334), -(hAPP(c_Int_Oring__1__class_Oof__int(_1255334), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1255336)) = hAPP(c_Int_Onumber__class_Onumber__of(_1255334), _1255336))], (25354 ^ _781215) ^ [_1238186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1238186), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1238186)), c_Int_OMin)))], (15574 ^ _781215) ^ [_1054654, _1054656] : [-(c_Map_Odom(_1054654, _1054656, hAPP(c_COMBK(tc_Option_Ooption(_1054656), _1054654), c_Option_Ooption_ONone(_1054656))) = c_Orderings_Obot__class_Obot(tc_fun(_1054654, tc_HOL_Obool)))], (43017 ^ _781215) ^ [_1637384, _1637386, _1637388, _1637390, _1637392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1637384), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637386)), _1637388))), 43020 ^ _781215 : [(43027 ^ _781215) ^ [] : [-(_1637384 = _1637390), -(hAPP(hAPP(c_List_Onth(_1637386), hAPP(hAPP(c_List_Olist__update(_1637386, _1637388), _1637384), _1637392)), _1637390) = hAPP(hAPP(c_List_Onth(_1637386), _1637388), _1637390))], (43021 ^ _781215) ^ [] : [_1637384 = _1637390, -(hAPP(hAPP(c_List_Onth(_1637386), hAPP(hAPP(c_List_Olist__update(_1637386, _1637388), _1637384), _1637392)), _1637390) = _1637392)]]], (23548 ^ _781215) ^ [_1205376] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1205376)), 23552 ^ _781215 : [(23553 ^ _781215) ^ [_1205456] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1205456), _1205376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205456), 23551 ^ [_1205376])))]]], (13142 ^ _781215) ^ [_1010016] : [13143 ^ _781215 : [(13144 ^ _781215) ^ [_1010058] : [_1010016 = hAPP(c_Nat_OSuc, _1010058)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1010016)))], (45191 ^ _781215) ^ [_1687758, _1687760, _1687762, _1687764] : [hAPP(hAPP(c_List_Oappend(_1687758), _1687760), hAPP(hAPP(c_List_Olist_OCons(_1687758), _1687762), c_List_Olist_ONil(_1687758))) = _1687764, 45194 ^ _781215 : [(45199 ^ _781215) ^ [] : [-(c_List_Olast(_1687758, _1687764) = _1687762)], (45197 ^ _781215) ^ [] : [-(c_List_Obutlast(_1687758, _1687764) = _1687760)], (45195 ^ _781215) ^ [] : [_1687764 = c_List_Olist_ONil(_1687758)]]], (26936 ^ _781215) ^ [_1270770, _1270772] : [-(c_Divides_Odivmod__int(_1270770, _1270772) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1270770), _1270772)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1270770, _1270772)))], (4452 ^ _781215) ^ [_848745, _848747] : [_848747 = _848745, -(c_Lattices_Osemilattice__sup__class_Osup(_848747) = c_Lattices_Osemilattice__sup__class_Osup(_848745))], (5907 ^ _781215) ^ [_875276, _875278] : [c_Option_Ooption_ONone(_875276) = hAPP(c_Option_Ooption_OSome(_875276), _875278)], (32802 ^ _781215) ^ [_1388750, _1388752, _1388754, _1388756] : [hBOOL(hAPP(hAPP(c_member(_1388750), _1388752), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388750, tc_HOL_Obool)), _1388754), _1388756))), -(hBOOL(hAPP(hAPP(c_member(_1388750), _1388752), _1388754)))], (6136 ^ _781215) ^ [_879867, _879869, _879871, _879873, _879875] : [c_Com_Ocom_OSemi(_879867, _879869) = c_Com_Ocom_OCall(_879871, _879873, _879875)], (40211 ^ _781215) ^ [_1566515, _1566517] : [c_FunDef_Oreduction__pair(_1566515, _1566517), 40214 ^ _781215 : [(40217 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566515, _1566515), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1566515, _1566515, _1566515), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1566515, _1566515), tc_HOL_Obool), tc_fun(tc_prod(_1566515, _1566515), tc_HOL_Obool)), _1566517)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1566515, _1566515), tc_HOL_Obool), tc_fun(tc_prod(_1566515, _1566515), tc_HOL_Obool)), _1566517))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1566515, _1566515), tc_HOL_Obool), tc_fun(tc_prod(_1566515, _1566515), tc_HOL_Obool)), _1566517))))], (40215 ^ _781215) ^ [] : [-(c_Wellfounded_Owf(_1566515, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1566515, _1566515), tc_HOL_Obool), tc_fun(tc_prod(_1566515, _1566515), tc_HOL_Obool)), _1566517)))]]], (37606 ^ _781215) ^ [_1495467, _1495469, _1495471, _1495473] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1495467, tc_HOL_Obool), hAPP(c_Set_Oimage(_1495469, tc_fun(_1495467, tc_HOL_Obool), _1495471), _1495473)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1495469, tc_fun(_1495467, tc_HOL_Obool)), _1495473), _1495471))], (32588 ^ _781215) ^ [_1384743, _1384745, _1384747, _1384749] : [hBOOL(hAPP(hAPP(c_member(_1384743), _1384745), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384743, tc_HOL_Obool)), _1384747), _1384749))), 32591 ^ _781215 : [(32594 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1384743), _1384745), _1384749)))], (32592 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1384743), _1384745), _1384747)))]]], (50894 ^ _781215) ^ [_1815372, _1815374] : [-(hAPP(c_New__DSequence_Opos__empty(_1815372), _1815374) = c_Lazy__Sequence_Oempty(_1815372))], (3722 ^ _781215) ^ [_837622, _837624] : [_837624 = _837622, -(c_Option_Othe(_837624) = c_Option_Othe(_837622))], (23032 ^ _781215) ^ [_1196466, _1196468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196466), _1196468)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1196466, _1196468) = _1196466)], (39208 ^ _781215) ^ [_1534346, _1534348, _1534350] : [-(hBOOL(hAPP(_1534346, _1534348))), -(hAPP(c_Set_OCollect(_1534350), hAPP(hAPP(c_COMBS(_1534350, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534350), c_fconj), hAPP(hAPP(c_COMBC(_1534350, _1534350, tc_HOL_Obool), c_fequal), _1534348))), _1534346)) = c_Orderings_Obot__class_Obot(tc_fun(_1534350, tc_HOL_Obool)))], (37261 ^ _781215) ^ [_1487327, _1487329, _1487331, _1487333, _1487335] : [-(_1487327 = c_Orderings_Obot__class_Obot(tc_fun(_1487329, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1487329, tc_fun(_1487331, tc_HOL_Obool)), _1487327), hAPP(hAPP(c_COMBB(tc_fun(_1487331, tc_HOL_Obool), tc_fun(_1487331, tc_HOL_Obool), _1487329), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1487331, tc_HOL_Obool)), _1487333)), _1487335)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1487331, tc_HOL_Obool)), _1487333), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1487329, tc_fun(_1487331, tc_HOL_Obool)), _1487327), _1487335)))], (45000 ^ _781215) ^ [_1683920, _1683922] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1683920), _1683922) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1683920 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45006 ^ _781215 : [(45009 ^ _781215) ^ [] : [45005 ^ [_1683920, _1683922] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45007 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 45005 ^ [_1683920, _1683922]), hAPP(c_List_Oset(tc_Nat_Onat), _1683922))))]]], (15168 ^ _781215) ^ [_1047483, _1047485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047483)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1047483), _1047485)))], (26719 ^ _781215) ^ [_1266157, _1266159] : [class_Rings_Oring__1(_1266157), 26722 ^ _781215 : [(26729 ^ _781215) ^ [] : [-(_1266159 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26732 ^ _781215 : [(26739 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266159), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1266157), _1266159) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1266157), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1266157, _1266157)), tc_fun(tc_Int_Oint, _1266157)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1266157, _1266157), _1266157), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1266157, _1266157)), tc_fun(tc_Int_Oint, _1266157)), tc_Int_Oint), c_COMBB(tc_fun(_1266157, _1266157), _1266157, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1266157, tc_fun(tc_fun(_1266157, _1266157), _1266157), tc_Int_Oint), c_HOL_OLet(_1266157, _1266157)), c_Int_Oring__1__class_Oof__int(_1266157)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1266157, _1266157), tc_fun(_1266157, _1266157)), hAPP(hAPP(c_COMBB(tc_fun(_1266157, tc_fun(_1266157, _1266157)), tc_fun(tc_fun(_1266157, _1266157), tc_fun(_1266157, _1266157)), tc_Int_Oint), c_COMBS(_1266157, _1266157, _1266157)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1266157, _1266157), tc_fun(_1266157, tc_fun(_1266157, _1266157))), hAPP(hAPP(c_COMBB(tc_fun(_1266157, tc_fun(_1266157, _1266157)), tc_fun(tc_fun(_1266157, _1266157), tc_fun(_1266157, tc_fun(_1266157, _1266157))), tc_Int_Oint), c_COMBB(_1266157, tc_fun(_1266157, _1266157), _1266157)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1266157, tc_fun(_1266157, _1266157)), tc_Int_Oint), c_If(_1266157)), 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(_1266157, _1266157, _1266157), c_Groups_Oplus__class_Oplus(_1266157)), c_COMBI(_1266157))))), hAPP(hAPP(c_COMBC(_1266157, _1266157, _1266157), hAPP(hAPP(c_COMBB(_1266157, tc_fun(_1266157, _1266157), _1266157), c_Groups_Oplus__class_Oplus(_1266157)), hAPP(hAPP(c_COMBS(_1266157, _1266157, _1266157), c_Groups_Oplus__class_Oplus(_1266157)), c_COMBI(_1266157)))), c_Groups_Oone__class_Oone(_1266157))))), c_Divides_Odivmod__int(_1266159, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (26733 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266159), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1266157), _1266159) = hAPP(c_Groups_Ouminus__class_Ouminus(_1266157), hAPP(c_Int_Oring__1__class_Oof__int(_1266157), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1266159))))]]], (26723 ^ _781215) ^ [] : [_1266159 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1266157), _1266159) = c_Groups_Ozero__class_Ozero(_1266157))]]], (21668 ^ _781215) ^ [_1169928, _1169930] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1169928)), c_Int_OBit0(_1169930)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1169928), _1169930)))], (16617 ^ _781215) ^ [_1077618, _1077620, _1077622, _1077624, _1077626] : [c_Finite__Set_Ofun__left__comm(_1077618, _1077620, _1077622), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077618), _1077624)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1077618, _1077620, _1077622, _1077626, _1077624), hAPP(hAPP(c_Finite__Set_Ofold(_1077618, _1077620, _1077622), _1077626), _1077624))))], (30173 ^ _781215) ^ [_1333318, _1333320, _1333322, _1333324] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1333318, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1333320, tc_fun(tc_fun(_1333318, tc_HOL_Obool), tc_HOL_Obool)), _1333322), hAPP(hAPP(c_COMBB(tc_fun(_1333318, tc_HOL_Obool), tc_fun(tc_fun(_1333318, tc_HOL_Obool), tc_HOL_Obool), _1333320), c_Set_OPow(_1333318)), _1333324))), hAPP(c_Set_OPow(_1333318), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1333320, tc_fun(_1333318, tc_HOL_Obool)), _1333322), _1333324)))))], (47725 ^ _781215) ^ [_1742020, _1742022, _1742024, _1742026] : [_1742026 = c_List_Olist_ONil(_1742020), -(c_List_Olist__all2(_1742020, _1742022, _1742024, _1742026, c_List_Olist_ONil(_1742022)))], (3310 ^ _781215) ^ [_831114, _831116, _831118, _831120] : [-(c_List_Olexord(_831120, _831116) = c_List_Olexord(_831118, _831114)), _831120 = _831118, _831116 = _831114], (25809 ^ _781215) ^ [_1246119, _1246121, _1246123, _1246125, _1246127, _1246129] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1246119, tc_fun(_1246121, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1246119, tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_fun(_1246121, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246121, tc_fun(tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_fun(_1246121, tc_HOL_Obool)), _1246119), c_COMBC(_1246121, tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246121, tc_prod(_1246119, _1246121)), tc_fun(_1246121, tc_fun(tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_HOL_Obool)), _1246119), hAPP(c_COMBB(tc_prod(_1246119, _1246121), tc_fun(tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_HOL_Obool), _1246121), c_member(tc_prod(_1246119, _1246121)))), c_Product__Type_OPair(_1246119, _1246121)))), _1246123)), hAPP(hAPP(c_COMBC(_1246119, tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_fun(_1246121, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246121, tc_fun(tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_fun(_1246121, tc_HOL_Obool)), _1246119), c_COMBC(_1246121, tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246121, tc_prod(_1246119, _1246121)), tc_fun(_1246121, tc_fun(tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_HOL_Obool)), _1246119), hAPP(c_COMBB(tc_prod(_1246119, _1246121), tc_fun(tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool), tc_HOL_Obool), _1246121), c_member(tc_prod(_1246119, _1246121)))), c_Product__Type_OPair(_1246119, _1246121)))), _1246125)), _1246127), _1246129)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1246119, _1246121)), hAPP(hAPP(c_Product__Type_OPair(_1246119, _1246121), _1246127), _1246129)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1246119, _1246121), tc_HOL_Obool)), _1246123), _1246125))))], (35891 ^ _781215) ^ [_1455971, _1455973, _1455975] : [class_Groups_Oordered__ab__group__add__abs(_1455971), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455971), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1455971), hAPP(c_Groups_Oabs__class_Oabs(_1455971), _1455973)), hAPP(c_Groups_Oabs__class_Oabs(_1455971), _1455975))), hAPP(c_Groups_Oabs__class_Oabs(_1455971), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1455971), _1455973), _1455975)))))], (3166 ^ _781215) ^ [_828878, _828880] : [_828880 = _828878, -(c_Hilbert__Choice_OGreatest(_828880) = c_Hilbert__Choice_OGreatest(_828878))], (39052 ^ _781215) ^ [_1531018] : [class_Lattices_Osemilattice__inf(_1531018), -(c_Finite__Set_Ofun__left__comm__idem(_1531018, _1531018, c_Lattices_Osemilattice__inf__class_Oinf(_1531018)))], (14357 ^ _781215) ^ [_1032354, _1032356, _1032358] : [class_Rings_Oring__1(_1032354), hBOOL(hAPP(hAPP(c_member(_1032354), _1032356), c_Int_Oring__1__class_OInts(_1032354))), hBOOL(hAPP(hAPP(c_member(_1032354), _1032358), c_Int_Oring__1__class_OInts(_1032354))), -(hBOOL(hAPP(hAPP(c_member(_1032354), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032354), _1032356), _1032358)), c_Int_Oring__1__class_OInts(_1032354))))], (10228 ^ _781215) ^ [_955441] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955441), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _955441)], (50844 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (43259 ^ _781215) ^ [_1643530, _1643532, _1643534, _1643536] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643530), tc_List_Olist(_1643530))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643530), tc_List_Olist(_1643530)), _1643532), _1643534)), c_List_Olistrel1(_1643530, _1643536)))), 43260 ^ _781215 : [(43261 ^ _781215) ^ [_1643663, _1643665] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643530, _1643530)), hAPP(hAPP(c_Product__Type_OPair(_1643530, _1643530), hAPP(hAPP(c_List_Onth(_1643530), _1643532), _1643663)), _1643665)), _1643536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1643663), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643530)), _1643532))), _1643534 = hAPP(hAPP(c_List_Olist__update(_1643530, _1643532), _1643663), _1643665)]]], (3086 ^ _781215) ^ [_827592, _827594, _827596, _827598, _827600, _827602, _827604, _827606] : [-(c_Map_Orestrict__map(_827606, _827602, _827598, _827594) = c_Map_Orestrict__map(_827604, _827600, _827596, _827592)), _827606 = _827604, _827602 = _827600, _827598 = _827596, _827594 = _827592], (46850 ^ _781215) ^ [_1723534, _1723536, _1723538] : [hBOOL(hAPP(c_List_Odistinct(_1723534), _1723536)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1723534)), c_Enum_On__lists(_1723534, _1723538, _1723536))))], (23817 ^ _781215) ^ [_1210556, _1210558, _1210560] : [class_Rings_Oring__1(_1210556), hBOOL(hAPP(hAPP(c_member(_1210556), _1210558), c_Int_Oring__1__class_OInts(_1210556))), -(hBOOL(hAPP(hAPP(c_member(_1210556), hAPP(hAPP(c_Power_Opower__class_Opower(_1210556), _1210558), _1210560)), c_Int_Oring__1__class_OInts(_1210556))))], (41789 ^ _781215) ^ [_1604229, _1604231, _1604233, _1604235, _1604237, _1604239] : [c_Finite__Set_Ofolding__idem(_1604229, _1604231, _1604233, _1604235), hBOOL(hAPP(c_Finite__Set_Ofinite(_1604229), _1604237)), -(hAPP(_1604235, hAPP(hAPP(c_Set_Oinsert(_1604229), _1604239), _1604237)) = hAPP(c_Fun_Ocomp(_1604231, _1604231, _1604231, hAPP(_1604235, _1604237)), hAPP(_1604233, _1604239)))], (7943 ^ _781215) ^ [_915172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915172), _915172))], (30952 ^ _781215) ^ [_1347791, _1347793] : [30954 ^ _781215 : [(30957 ^ _781215) ^ [] : [hBOOL(hAPP(_1347793, 30953 ^ [_1347791, _1347793]))], (30955 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30953 ^ [_1347791, _1347793]), _1347791)))]], 30958 ^ _781215 : [(30959 ^ _781215) ^ [_1347941] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1347941), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1347791))), -(hBOOL(hAPP(_1347793, _1347941)))]]], (48636 ^ _781215) ^ [_1763379, _1763381, _1763383] : [-(c_List_Olist__ex(_1763379, _1763381, _1763383)), 48637 ^ _781215 : [(48638 ^ _781215) ^ [_1763436] : [hBOOL(hAPP(hAPP(c_member(_1763379), _1763436), hAPP(c_List_Oset(_1763379), _1763383))), hBOOL(hAPP(_1763381, _1763436))]]], (51208 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (9887 ^ _781215) ^ [_949395, _949397, _949399] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949395), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949397), _949399)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949395), _949397)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _949395), _949399)))], (1408 ^ _781215) ^ [_801785, _801787] : [-(class_Orderings_Obot(_801785)), _801787 = _801785, class_Orderings_Obot(_801787)], (42656 ^ _781215) ^ [_1628149, _1628151, _1628153, _1628155, _1628157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628149), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628151)), _1628153))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628149), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628155)), _1628157))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1628151, _1628155)), hAPP(hAPP(c_List_Ozip(_1628151, _1628155), _1628153), _1628157)), _1628149) = hAPP(hAPP(c_Product__Type_OPair(_1628151, _1628155), hAPP(hAPP(c_List_Onth(_1628151), _1628153), _1628149)), hAPP(hAPP(c_List_Onth(_1628155), _1628157), _1628149)))], (6104 ^ _781215) ^ [_879326, _879328, _879330] : [hAPP(c_Com_Ocom_OBODY, _879326) = c_Com_Ocom_OSemi(_879328, _879330)], (23336 ^ _781215) ^ [_1201603, _1201605, _1201607] : [hBOOL(hAPP(_1201603, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1201605, _1201607))), 23339 ^ _781215 : [(23364 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201607), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23367 ^ _781215 : [(23368 ^ _781215) ^ [_1202225, _1202227] : [-(hBOOL(hAPP(_1201603, _1202225))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201607), _1202225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202225), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1201605 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201607), _1202227)), _1202225)]]], (23346 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201607)), 23349 ^ _781215 : [(23350 ^ _781215) ^ [_1201933, _1201935] : [-(hBOOL(hAPP(_1201603, _1201933))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201933), _1201607)), _1201605 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201607), _1201935)), _1201933)]]], (23340 ^ _781215) ^ [] : [_1201607 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1201603, _1201605)))]]], (27160 ^ _781215) ^ [_1275144, _1275146, _1275148] : [27162 ^ _781215 : [(27165 ^ _781215) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1275148, 27161 ^ [_1275144, _1275146, _1275148]))], (27163 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1275144), 27161 ^ [_1275144, _1275146, _1275148]), _1275146)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1275144, tc_Int_Oint), _1275148), _1275146) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1275144, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1275144), c_Int_Onat), _1275148)), _1275146)))], (49467 ^ _781215) ^ [_1781828, _1781830, _1781832, _1781834] : [hBOOL(hAPP(hAPP(c_member(_1781828), _1781830), c_Wellfounded_Oacc(_1781828, _1781832))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1781828, _1781828)), hAPP(hAPP(c_Product__Type_OPair(_1781828, _1781828), _1781834), _1781830)), c_Transitive__Closure_Ortrancl(_1781828, _1781832))), -(hBOOL(hAPP(hAPP(c_member(_1781828), _1781834), c_Wellfounded_Oacc(_1781828, _1781832))))], (50330 ^ _781215) ^ [_1804386, _1804388, _1804390] : [hBOOL(hAPP(hAPP(c_member(_1804386), _1804388), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1804386, tc_HOL_Obool), _1804390))), 50334 ^ _781215 : [(50337 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1804386, tc_HOL_Obool)), 50333 ^ [_1804386, _1804388, _1804390]), _1804390)))], (50335 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804386), _1804388), 50333 ^ [_1804386, _1804388, _1804390])))]]], (15266 ^ _781215) ^ [_1048955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1048955), 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)), _1048955)), _1048955)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6267 ^ _781215) ^ [_882422, _882424, _882426] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _882422))), _882424), _882426)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _882422)), _882424), _882426)))], (20281 ^ _781215) ^ [_1145206, _1145208, _1145210, _1145212] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1145206), _1145208)), 20284 ^ _781215 : [(20285 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1145210), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1145206, tc_fun(_1145210, tc_HOL_Obool)), _1145208), _1145212))), 20288 ^ _781215 : [(20289 ^ _781215) ^ [_1145390] : [hBOOL(hAPP(hAPP(c_member(_1145206), _1145390), _1145208)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1145210), hAPP(_1145212, _1145390))))]]], (20295 ^ _781215) ^ [] : [20297 ^ _781215 : [(20300 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1145210), hAPP(_1145212, 20296 ^ [_1145206, _1145208, _1145210, _1145212])))], (20298 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1145206), 20296 ^ [_1145206, _1145208, _1145210, _1145212]), _1145208)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1145210), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1145206, tc_fun(_1145210, tc_HOL_Obool)), _1145208), _1145212))))]]], (50904 ^ _781215) ^ [_1815646, _1815648] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1815646)), _1815648) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1815646, tc_Lazy__Sequence_Olazy__sequence(_1815646)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1815646, tc_Lazy__Sequence_Olazy__sequence(_1815646), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1815646), tc_Nat_Onat), _1815646), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1815646), 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(_1815646)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1815646)))), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), hAPP(c_Lazy__Sequence_Oyield(_1815646), _1815648)))], (17513 ^ _781215) ^ [_1094631, _1094633] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094631), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094633)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094631)) = 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), _1094633), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094631)))), 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)))], (50176 ^ _781215) ^ [_1800458, _1800460, _1800462, _1800464] : [50178 ^ _781215 : [(50183 ^ _781215) ^ [] : [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(_1800462, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50177 ^ [_1800458, _1800460, _1800462, _1800464]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1800462, 50177 ^ [_1800458, _1800460, _1800462, _1800464])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (50181 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50177 ^ [_1800458, _1800460, _1800462, _1800464]), _1800460)))], (50179 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1800458), 50177 ^ [_1800458, _1800460, _1800462, _1800464])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1800458), _1800460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1800462, _1800458)), _1800464)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1800464), hAPP(_1800462, _1800460))), 50197 ^ _781215 : [(50202 ^ _781215) ^ [] : [-(hAPP(_1800462, 50196 ^ [_1800458, _1800460, _1800462, _1800464]) = _1800464)], (50200 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50196 ^ [_1800458, _1800460, _1800462, _1800464]), _1800460)))], (50198 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1800458), 50196 ^ [_1800458, _1800460, _1800462, _1800464])))]]], (10290 ^ _781215) ^ [_956491, _956493, _956495, _956497] : [c_Hoare__Mirabelle_Ohoare__derivs(_956491, _956493, _956495), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_956491), tc_HOL_Obool)), _956497), _956495)), -(c_Hoare__Mirabelle_Ohoare__derivs(_956491, _956493, _956497))], (41799 ^ _781215) ^ [_1604436, _1604438, _1604440, _1604442, _1604444, _1604446] : [c_Finite__Set_Ofolding__idem(_1604436, _1604438, _1604440, _1604442), hBOOL(hAPP(c_Finite__Set_Ofinite(_1604436), _1604444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1604436, tc_HOL_Obool)), _1604446), _1604444)), -(hAPP(c_Fun_Ocomp(_1604438, _1604438, _1604438, hAPP(_1604442, _1604444)), hAPP(_1604442, _1604446)) = hAPP(_1604442, _1604444))], (40735 ^ _781215) ^ [_1579631, _1579633, _1579635, _1579637] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1579631, _1579633)), _1579635), _1579637)), 40740 ^ _781215 : [(40743 ^ _781215) ^ [] : [hBOOL(hAPP(_1579631, _1579635))], (40741 ^ _781215) ^ [] : [-(_1579637 = _1579635)]], 40744 ^ _781215 : [(40750 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1579631, _1579633)), 40746 ^ [_1579631, _1579633, _1579635, _1579637]), _1579637)))], (40748 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1579633), _1579635), 40746 ^ [_1579631, _1579633, _1579635, _1579637])))], (40745 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1579631, _1579635)))]]], (45087 ^ _781215) ^ [_1686083, _1686085, _1686087] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1686083), tc_List_Olist(_1686083))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1686083), tc_List_Olist(_1686083)), c_List_Olist_ONil(_1686083)), _1686085)), c_List_Olexord(_1686083, _1686087))), -(_1686085 = hAPP(hAPP(c_List_Olist_OCons(_1686083), 45090 ^ [_1686083, _1686085, _1686087]), 45091 ^ [_1686083, _1686085, _1686087]))], (49644 ^ _781215) ^ [_1786836, _1786838, _1786840, _1786842] : [-(hAPP(c_Relation_Oconverse(_1786836, _1786836), hAPP(hAPP(c_Relation_Oinv__image(_1786838, _1786836), _1786840), _1786842)) = hAPP(hAPP(c_Relation_Oinv__image(_1786838, _1786836), hAPP(c_Relation_Oconverse(_1786838, _1786838), _1786840)), _1786842))], (24354 ^ _781215) ^ [_1220323, _1220325] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220323)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220323)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1220325)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220323)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220325))))], (50914 ^ _781215) ^ [_1816096, _1816098, _1816100, _1816102, _1816104, _1816106] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1816096, _1816098, _1816100, _1816102, c_Lazy__Sequence_Olazy__sequence_OInsert(_1816098, _1816104, _1816106)) = hAPP(hAPP(_1816102, _1816104), _1816106))], (6720 ^ _781215) ^ [_891259, _891261, _891263, _891265] : [hBOOL(hAPP(hAPP(c_member(_891259), _891261), _891263)), -(hBOOL(hAPP(hAPP(c_member(_891259), _891261), hAPP(hAPP(c_Set_Oinsert(_891259), _891265), _891263))))], (14756 ^ _781215) ^ [_1039548, _1039550] : [class_Int_Onumber__ring(_1039548), -(hAPP(c_Int_Onumber__class_Onumber__of(_1039548), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1039550)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1039548), hAPP(c_Int_Onumber__class_Onumber__of(_1039548), _1039550)))], (36121 ^ _781215) ^ [_1460432, _1460434, _1460436] : [class_Rings_Olinordered__idom(_1460432), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460432), c_Groups_Ozero__class_Ozero(_1460432)), hAPP(hAPP(c_Power_Opower__class_Opower(_1460432), hAPP(c_Groups_Oabs__class_Oabs(_1460432), _1460434)), _1460436))))], (2850 ^ _781215) ^ [_823798, _823800, _823802, _823804] : [-(c_Com_Ocom_OSemi(_823804, _823800) = c_Com_Ocom_OSemi(_823802, _823798)), _823804 = _823802, _823800 = _823798], (44810 ^ _781215) ^ [_1680060, _1680062] : [-(_1680060 = c_List_Olist_ONil(_1680062)), -(hAPP(c_List_Ohd(_1680062), _1680060) = hAPP(hAPP(c_List_Onth(_1680062), _1680060), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (36364 ^ _781215) ^ [_1464831, _1464833, _1464835, _1464837, _1464839] : [c_Fun_Oinj__on(_1464831, _1464833, _1464835, c_Orderings_Otop__class_Otop(tc_fun(_1464831, tc_HOL_Obool))), hAPP(_1464835, _1464837) = hAPP(_1464835, _1464839), -(_1464837 = _1464839)], (368 ^ _781215) ^ [_786907, _786909, _786911, _786913] : [-(c_Predicate_Oreflp(_786911, _786907)), c_Predicate_Oreflp(_786913, _786909), _786913 = _786911, _786909 = _786907], (25374 ^ _781215) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (4700 ^ _781215) ^ [_852445, _852447] : [_852447 = _852445, -(c_List_Orev(_852447) = c_List_Orev(_852445))], (45504 ^ _781215) ^ [_1694771, _1694773, _1694775, _1694777] : [class_Orderings_Olinorder(_1694771), 45507 ^ _781215 : [(45516 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1694771, hAPP(hAPP(c_List_Olist_OCons(_1694771), _1694773), hAPP(hAPP(c_List_Olist_OCons(_1694771), _1694775), _1694777)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1694771), _1694773), _1694775)), c_List_Olinorder__class_Osorted(_1694771, hAPP(hAPP(c_List_Olist_OCons(_1694771), _1694775), _1694777))], (45508 ^ _781215) ^ [] : [c_List_Olinorder__class_Osorted(_1694771, hAPP(hAPP(c_List_Olist_OCons(_1694771), _1694773), hAPP(hAPP(c_List_Olist_OCons(_1694771), _1694775), _1694777))), 45511 ^ _781215 : [(45514 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1694771, hAPP(hAPP(c_List_Olist_OCons(_1694771), _1694775), _1694777)))], (45512 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1694771), _1694773), _1694775)))]]]]], (39675 ^ _781215) ^ [_1552224, _1552226] : [-(c_Product__Type_Omap__pair(_1552224, _1552224, _1552226, _1552226, c_Fun_Oid(_1552224), c_Fun_Oid(_1552226)) = c_Fun_Oid(tc_prod(_1552224, _1552226)))], (34766 ^ _781215) ^ [_1432713, _1432715, _1432717] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1432713), _1432715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432713, tc_HOL_Obool)), _1432715), hAPP(c_Set_Oimage(_1432713, _1432713, _1432717), _1432715))), -(c_Fun_Oinj__on(_1432713, _1432713, _1432717, _1432715))], (21540 ^ _781215) ^ [_1167690] : [_1167690 = c_Int_OPls, -(c_Int_OBit0(_1167690) = c_Int_OPls)], (9065 ^ _781215) ^ [_935012, _935014, _935016] : [class_Lattices_Oab__semigroup__idem__mult(_935012), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935012), _935014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935012), _935014), _935016)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935012), _935014), _935016))], (4982 ^ _781215) ^ [_856940, _856942] : [_856942 = _856940, -(c_Lazy__Sequence_Oyield(_856942) = c_Lazy__Sequence_Oyield(_856940))], (3754 ^ _781215) ^ [_838090, _838092, _838094, _838096] : [-(c_List_Olist__update(_838096, _838092) = c_List_Olist__update(_838094, _838090)), _838096 = _838094, _838092 = _838090], (4468 ^ _781215) ^ [_848979, _848981, _848983, _848985] : [-(c_Transitive__Closure_Otrancl(_848985, _848981) = c_Transitive__Closure_Otrancl(_848983, _848979)), _848985 = _848983, _848981 = _848979], (51460 ^ _781215) ^ [] : [-(class_Nat_Osize(tc_Com_Ovname))], (18091 ^ _781215) ^ [_1104764, _1104766, _1104768, _1104770, _1104772] : [-(hAPP(c_Nat_Onat_Onat__rec(_1104764, _1104766, _1104768), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104770)), _1104772)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1104764), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1104770))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1104764, _1104764), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1104764, tc_fun(_1104764, _1104764)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1104764, tc_fun(_1104764, _1104764)), tc_Int_Oint), c_If(_1104764)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1104764, _1104766, _1104768), _1104772))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1104764, _1104764), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1104764, _1104764), tc_Int_Oint), _1104768), 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)), _1104772))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1104764, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1104764, _1104766, _1104768)), 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)), _1104772))))))], (35184 ^ _781215) ^ [_1441769, _1441771, _1441773, _1441775, _1441777, _1441779] : [c_Fun_Oinj__on(_1441769, _1441771, _1441773, _1441775), hBOOL(hAPP(hAPP(c_member(_1441771), _1441777), hAPP(c_Set_Oimage(_1441769, _1441771, _1441773), _1441775))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1441769, tc_HOL_Obool)), _1441775), _1441779)), -(hBOOL(hAPP(hAPP(c_member(_1441769), hAPP(c_Fun_Othe__inv__into(_1441769, _1441771, _1441775, _1441773), _1441777)), _1441779)))], (49405 ^ _781215) ^ [_1780297, _1780299] : [-(c_List_Olistrel(_1780297, c_Transitive__Closure_Ortrancl(_1780297, _1780299)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1780297), c_List_Olistrel1(_1780297, _1780299)))], (16997 ^ _781215) ^ [_1086123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1086123)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1086123))], (22665 ^ _781215) ^ [_1190335, _1190337, _1190339, _1190341] : [class_Divides_Osemiring__div(_1190335), -(_1190337 = c_Groups_Ozero__class_Ozero(_1190335)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190335), _1190339), _1190337)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190335), _1190341), _1190337)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190335), _1190339), _1190341))], (216 ^ _781215) ^ [_784451, _784453, _784455, _784457, _784459, _784461, _784463, _784465, _784467, _784469, _784471, _784473] : [-(c_Equiv__Relations_Ocongruent2(_784471, _784467, _784463, _784459, _784455, _784451)), c_Equiv__Relations_Ocongruent2(_784473, _784469, _784465, _784461, _784457, _784453), _784473 = _784471, _784469 = _784467, _784465 = _784463, _784461 = _784459, _784457 = _784455, _784453 = _784451], (33374 ^ _781215) ^ [_1402252, _1402254, _1402256, _1402258, _1402260] : [class_Orderings_Olinorder(_1402252), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402252, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1402252, _1402254, _1402256)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1402252, _1402258, _1402260)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1402252, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1402252), _1402254), _1402258), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1402252), _1402256), _1402260)))], (16153 ^ _781215) ^ [_1066753, _1066755, _1066757, _1066759] : [class_Lattices_Osemilattice__sup(_1066753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066753), _1066755), _1066757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066753), _1066759), _1066757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066753), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066753), _1066755), _1066759)), _1066757)))], (44064 ^ _781215) ^ [_1662269, _1662271, _1662273, _1662275, _1662277] : [-(hAPP(hAPP(c_List_Olist_OCons(_1662269), _1662271), _1662273) = hAPP(hAPP(c_List_Oappend(_1662269), _1662275), _1662277)), 44065 ^ _781215 : [(44072 ^ _781215) ^ [_1662452] : [hAPP(hAPP(c_List_Olist_OCons(_1662269), _1662271), _1662452) = _1662275, _1662273 = hAPP(hAPP(c_List_Oappend(_1662269), _1662452), _1662277)], (44066 ^ _781215) ^ [] : [_1662275 = c_List_Olist_ONil(_1662269), hAPP(hAPP(c_List_Olist_OCons(_1662269), _1662271), _1662273) = _1662277]]], (47490 ^ _781215) ^ [_1736783, _1736785, _1736787] : [47492 ^ _781215 : [(47495 ^ _781215) ^ [] : [hBOOL(hAPP(_1736785, 47491 ^ [_1736783, _1736785, _1736787]))], (47493 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736783), 47491 ^ [_1736783, _1736785, _1736787]), hAPP(c_List_Oset(_1736783), _1736787))))]], -(hBOOL(hAPP(c_List_Olistsp(_1736783, _1736785), _1736787)))], (18802 ^ _781215) ^ [_1118371, _1118373, _1118375] : [class_Orderings_Olinorder(_1118371), 18805 ^ _781215 : [(18812 ^ _781215) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1118371), _1118373), _1118375) = _1118375, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118371), _1118373), _1118375)))], (18806 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118371), _1118373), _1118375)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1118371), _1118373), _1118375) = _1118375)]]], (44353 ^ _781215) ^ [_1668620, _1668622, _1668624, _1668626] : [hBOOL(hAPP(hAPP(c_member(_1668620), _1668622), hAPP(c_List_Oset(_1668620), _1668624))), -(c_List_Oremove1(_1668620, _1668622, hAPP(hAPP(c_List_Oappend(_1668620), _1668624), _1668626)) = hAPP(hAPP(c_List_Oappend(_1668620), c_List_Oremove1(_1668620, _1668622, _1668624)), _1668626))], (26711 ^ _781215) ^ [_1265911] : [-(c_Divides_Oadjust(_1265911) = 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)), _1265911))))), 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)), _1265911))))), 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))))))))], (14106 ^ _781215) ^ [_1027200, _1027202, _1027204, _1027206, _1027208] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_1027200, _1027202, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1027200), _1027204), _1027206), _1027208)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17967 ^ _781215) ^ [_1102022, _1102024] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1102022))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1102024)), hAPP(c_Int_Onat, _1102022)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1102024), _1102022)), 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)))], (14836 ^ _781215) ^ [_1041213, _1041215, _1041217, _1041219, _1041221] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1041213, _1041215, _1041217)), _1041219), _1041221))), 14837 ^ _781215 : [(14844 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1041213, _1041219))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1041217), _1041219), _1041221))], (14838 ^ _781215) ^ [] : [hBOOL(hAPP(_1041213, _1041219)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1041215), _1041219), _1041221))]]], (40467 ^ _781215) ^ [_1573652, _1573654, _1573656] : [c_Wellfounded_Oacyclic(_1573652, _1573654), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573652, _1573652), tc_HOL_Obool)), _1573656), _1573654)), -(c_Wellfounded_Oacyclic(_1573652, _1573656))], (40023 ^ _781215) ^ [_1562576, _1562578, _1562580, _1562582] : [c_Wellfounded_Owf(_1562576, _1562578), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562576, _1562576)), hAPP(hAPP(c_Product__Type_OPair(_1562576, _1562576), _1562580), _1562582)), _1562578)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562576, _1562576)), hAPP(hAPP(c_Product__Type_OPair(_1562576, _1562576), _1562582), _1562580)), _1562578))], (16115 ^ _781215) ^ [_1066009, _1066011, _1066013, _1066015, _1066017] : [class_Lattices_Olattice(_1066009), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1066011, _1066009)), _1066013), _1066015), _1066017) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066009), hAPP(_1066013, _1066017)), hAPP(_1066015, _1066017)))], (31920 ^ _781215) ^ [_1369357, _1369359, _1369361, _1369363, _1369365] : [class_Groups_Ocomm__monoid__add(_1369357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369359), _1369361)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1369359, _1369357), _1369363), hAPP(hAPP(c_Set_Oinsert(_1369359), _1369365), _1369361)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369357), hAPP(_1369363, _1369365)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1369359, _1369357), _1369363), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369359, tc_HOL_Obool)), _1369361), hAPP(hAPP(c_Set_Oinsert(_1369359), _1369365), c_Orderings_Obot__class_Obot(tc_fun(_1369359, tc_HOL_Obool)))))))], (23066 ^ _781215) ^ [_1197028] : [-(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)), _1197028)))], (3320 ^ _781215) ^ [_831263, _831265, _831267, _831269, _831271, _831273] : [-(c_List_Opartition(_831273, _831269, _831265) = c_List_Opartition(_831271, _831267, _831263)), _831273 = _831271, _831269 = _831267, _831265 = _831263], (35661 ^ _781215) ^ [_1451487, _1451489, _1451491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451489), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1451491), 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), _1451491), _1451489))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1451487)))))], (30103 ^ _781215) ^ [_1331675, _1331677] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1331675, _1331677))))], (48120 ^ _781215) ^ [_1751491, _1751493, _1751495, _1751497, _1751499] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751491)), _1751493) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751495)), _1751497), 48126 ^ _781215 : [(48129 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1751499, hAPP(hAPP(c_List_Onth(_1751491), _1751493), 48125 ^ [_1751491, _1751493, _1751495, _1751497, _1751499])), hAPP(hAPP(c_List_Onth(_1751495), _1751497), 48125 ^ [_1751491, _1751493, _1751495, _1751497, _1751499])))], (48127 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48125 ^ [_1751491, _1751493, _1751495, _1751497, _1751499]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751491)), _1751493))))]], -(c_List_Olist__all2(_1751491, _1751495, _1751499, _1751493, _1751497))], (14776 ^ _781215) ^ [_1039972, _1039974, _1039976, _1039978, _1039980, _1039982] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1039972, _1039974, _1039976)), _1039978), _1039980), _1039982))), 14777 ^ _781215 : [(14784 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1039972, _1039978))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1039976), _1039978), _1039980), _1039982))], (14778 ^ _781215) ^ [] : [hBOOL(hAPP(_1039972, _1039978)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1039974), _1039978), _1039980), _1039982))]]], (3518 ^ _781215) ^ [_834450, _834452, _834454, _834456, _834458, _834460, _834462, _834464, _834466, _834468] : [-(c_Map_Omap__upds(_834468, _834464, _834460, _834456, _834452) = c_Map_Omap__upds(_834466, _834462, _834458, _834454, _834450)), _834468 = _834466, _834464 = _834462, _834460 = _834458, _834456 = _834454, _834452 = _834450], (49097 ^ _781215) ^ [_1771906, _1771908] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1771906, _1771906)), c_Transitive__Closure_Otrancl(_1771906, _1771908))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1771906, _1771906)), _1771908)))], (33264 ^ _781215) ^ [_1399924, _1399926, _1399928] : [-(hAPP(c_Relation_OImage(_1399924, _1399924, c_Relation_OId__on(_1399924, _1399926)), _1399928) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399924, tc_HOL_Obool)), _1399926), _1399928))], (9337 ^ _781215) ^ [_940300, _940302, _940304, _940306] : [class_Rings_Ocomm__semiring(_940300), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940300), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940300), _940302), _940304)), _940306) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940300), _940302), _940306)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940300), _940304), _940306)))], (51668 ^ _781215) ^ [_1825611, _1825613, _1825615, _1825617, _1825619, _1825621] : [-(hAPP(hAPP(hAPP(c_COMBB(_1825611, _1825613, _1825615), _1825617), _1825619), _1825621) = hAPP(_1825617, hAPP(_1825619, _1825621)))], (29968 ^ _781215) ^ [_1327742, _1327744, _1327746, _1327748] : [c_Wellfounded_Omax__extp(_1327742, hAPP(hAPP(c_COMBC(_1327742, tc_fun(tc_prod(_1327742, _1327742), tc_HOL_Obool), tc_fun(_1327742, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1327742, tc_fun(tc_fun(tc_prod(_1327742, _1327742), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1327742, _1327742), tc_HOL_Obool), tc_fun(_1327742, tc_HOL_Obool)), _1327742), c_COMBC(_1327742, tc_fun(tc_prod(_1327742, _1327742), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1327742, tc_prod(_1327742, _1327742)), tc_fun(_1327742, tc_fun(tc_fun(tc_prod(_1327742, _1327742), tc_HOL_Obool), tc_HOL_Obool)), _1327742), hAPP(c_COMBB(tc_prod(_1327742, _1327742), tc_fun(tc_fun(tc_prod(_1327742, _1327742), tc_HOL_Obool), tc_HOL_Obool), _1327742), c_member(tc_prod(_1327742, _1327742)))), c_Product__Type_OPair(_1327742, _1327742)))), _1327744), _1327746, _1327748), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1327742, tc_HOL_Obool), tc_fun(_1327742, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1327742, tc_HOL_Obool), tc_fun(_1327742, tc_HOL_Obool)), _1327746), _1327748)), c_Wellfounded_Omax__ext(_1327742, _1327744))))], (24057 ^ _781215) ^ [_1215044, _1215046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215046)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215044, _1215046)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1215044), hAPP(c_Int_Onat, _1215046)))], (42317 ^ _781215) ^ [_1618967, _1618969, _1618971] : [-(hAPP(c_List_Olexn(_1618967, _1618969), hAPP(c_Nat_OSuc, _1618971)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1618967), tc_List_Olist(_1618967)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1618967, tc_List_Olist(_1618967)), tc_prod(_1618967, tc_List_Olist(_1618967))), tc_prod(tc_List_Olist(_1618967), tc_List_Olist(_1618967)), c_Product__Type_Omap__pair(tc_prod(_1618967, tc_List_Olist(_1618967)), tc_List_Olist(_1618967), tc_prod(_1618967, tc_List_Olist(_1618967)), tc_List_Olist(_1618967), hAPP(c_Product__Type_Oprod_Oprod__case(_1618967, tc_List_Olist(_1618967), tc_List_Olist(_1618967)), c_List_Olist_OCons(_1618967)), hAPP(c_Product__Type_Oprod_Oprod__case(_1618967, tc_List_Olist(_1618967), tc_List_Olist(_1618967)), c_List_Olist_OCons(_1618967)))), c_Wellfounded_Olex__prod(_1618967, tc_List_Olist(_1618967), _1618969, hAPP(c_List_Olexn(_1618967, _1618969), _1618971)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1618967), tc_List_Olist(_1618967))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1618967), tc_List_Olist(_1618967), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1618967), tc_fun(tc_List_Olist(_1618967), tc_HOL_Obool), tc_fun(tc_List_Olist(_1618967), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1618967), tc_HOL_Obool), tc_fun(tc_List_Olist(_1618967), tc_HOL_Obool)), tc_List_Olist(_1618967)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1618967))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1618967)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1618967), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1618967)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1618967)))), hAPP(c_Nat_OSuc, _1618971))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1618967), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1618967)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1618967)))), hAPP(c_Nat_OSuc, _1618971)))))))], (47777 ^ _781215) ^ [_1743043, _1743045, _1743047, _1743049, _1743051, _1743053, _1743055] : [c_List_Olist__all2(_1743043, _1743045, _1743047, _1743049, _1743051), c_List_Olist__all2(_1743043, _1743045, _1743047, _1743053, _1743055), -(c_List_Olist__all2(_1743043, _1743045, _1743047, hAPP(hAPP(c_List_Oappend(_1743043), _1743049), _1743053), hAPP(hAPP(c_List_Oappend(_1743045), _1743051), _1743055)))], (49646 ^ _781215) ^ [_1786895, _1786897, _1786899, _1786901] : [-(hAPP(c_Relation_Oconverse(_1786895, _1786897), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1786895, _1786897), tc_HOL_Obool)), _1786899), _1786901)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1786897, _1786895), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1786895, _1786897), _1786899)), hAPP(c_Relation_Oconverse(_1786895, _1786897), _1786901)))], (33100 ^ _781215) ^ [_1395433, _1395435, _1395437] : [-(hAPP(c_Set_OPow(_1395433), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395433, tc_HOL_Obool)), _1395435), _1395437)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1395433, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1395433), _1395435)), hAPP(c_Set_OPow(_1395433), _1395437)))], (37877 ^ _781215) ^ [_1501191, _1501193] : [-(hAPP(c_Relation_OField(_1501191), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1501191, _1501191), tc_HOL_Obool), _1501193)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1501191, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1501191, _1501191), tc_HOL_Obool), tc_fun(_1501191, tc_HOL_Obool), c_Relation_OField(_1501191)), _1501193)))], (45129 ^ _781215) ^ [_1686912, _1686914, _1686916] : [_1686912 = c_List_Olist_ONil(_1686914), -(c_List_Olast(_1686914, hAPP(hAPP(c_List_Oappend(_1686914), _1686916), _1686912)) = c_List_Olast(_1686914, _1686916))], (31930 ^ _781215) ^ [_1369641, _1369643, _1369645, _1369647] : [hBOOL(hAPP(hAPP(c_member(_1369641), _1369643), _1369645)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1369641, tc_Nat_Onat), _1369647), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369641, tc_HOL_Obool)), _1369645), hAPP(hAPP(c_Set_Oinsert(_1369641), _1369643), c_Orderings_Obot__class_Obot(tc_fun(_1369641, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1369641, tc_Nat_Onat), _1369647), _1369645)), hAPP(_1369647, _1369643)))], (5704 ^ _781215) ^ [_871413, _871415] : [c_Hoare__Mirabelle_Ostate__not__singleton, 5710 ^ _781215 : [(5713 ^ _781215) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _871413, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, 5709 ^ [_871413, _871415]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))], (5711 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), 5709 ^ [_871413, _871415]), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))]], hBOOL(hAPP(c_Com_OWT, _871415)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _871413, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _871415)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (51340 ^ _781215) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (2326 ^ _781215) ^ [_815552, _815554, _815556, _815558, _815560, _815562, _815564, _815566] : [-(c_SetInterval_Oord_OatLeastAtMost(_815566, _815562, _815558, _815554) = c_SetInterval_Oord_OatLeastAtMost(_815564, _815560, _815556, _815552)), _815566 = _815564, _815562 = _815560, _815558 = _815556, _815554 = _815552], (51364 ^ _781215) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (40251 ^ _781215) ^ [_1567690, _1567692] : [-(hAPP(c_Relation_OField(_1567690), _1567692) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567690, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1567690, _1567690), _1567692)), hAPP(c_Relation_ORange(_1567690, _1567690), _1567692)))], (20539 ^ _781215) ^ [_1149865, _1149867] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149865)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149867), 20542 ^ _781215 : [(20545 ^ _781215) ^ [] : [-(_1149867 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20543 ^ _781215) ^ [] : [-(_1149865 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (47731 ^ _781215) ^ [_1742141, _1742143, _1742145, _1742147, _1742149] : [c_List_Olist__all2(_1742141, _1742143, _1742145, hAPP(c_List_Orev(_1742141), _1742147), hAPP(c_List_Orev(_1742143), _1742149)), -(c_List_Olist__all2(_1742141, _1742143, _1742145, _1742147, _1742149))], (42056 ^ _781215) ^ [_1610897, _1610899] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1610897), hAPP(c_List_Oset(_1610897), _1610899))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610897)), _1610899))))], (5306 ^ _781215) ^ [_862198, _862200, _862202, _862204, _862206, _862208, _862210, _862212, _862214, _862216, _862218, _862220] : [-(c_New__Random__Sequence_Opos__union(_862220, _862216, _862212, _862208, _862204, _862200) = c_New__Random__Sequence_Opos__union(_862218, _862214, _862210, _862206, _862202, _862198)), _862220 = _862218, _862216 = _862214, _862212 = _862210, _862208 = _862206, _862204 = _862202, _862200 = _862198], (48814 ^ _781215) ^ [_1766667, _1766669, _1766671] : [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, _1766667), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1766667)), _1766669)))), -(hBOOL(hAPP(hAPP(c_member(_1766667), hAPP(c_Product__Type_Ofst(_1766667, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1766667, _1766669), _1766671))), hAPP(c_List_Oset(_1766667), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1766667), _1766667), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1766667)), _1766669)))))], (39747 ^ _781215) ^ [_1554365, _1554367, _1554369, _1554371, _1554373, _1554375, _1554377] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1554365, _1554367, _1554369), hAPP(hAPP(c_Relation_Orel__comp(_1554365, _1554371, _1554367), _1554373), _1554375)), _1554377) = hAPP(hAPP(c_Relation_Orel__comp(_1554365, _1554371, _1554369), _1554373), hAPP(hAPP(c_Relation_Orel__comp(_1554371, _1554367, _1554369), _1554375), _1554377)))], (44461 ^ _781215) ^ [_1671318, _1671320, _1671322, _1671324, _1671326, _1671328, _1671330] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1671318, _1671318)), hAPP(hAPP(c_Product__Type_OPair(_1671318, _1671318), _1671320), _1671322)), _1671324)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671318), tc_List_Olist(_1671318))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671318), tc_List_Olist(_1671318)), hAPP(hAPP(c_List_Oappend(_1671318), _1671326), hAPP(hAPP(c_List_Olist_OCons(_1671318), _1671320), _1671328))), hAPP(hAPP(c_List_Oappend(_1671318), _1671326), hAPP(hAPP(c_List_Olist_OCons(_1671318), _1671322), _1671330)))), c_List_Olexord(_1671318, _1671324))))], (14914 ^ _781215) ^ [_1042660, _1042662, _1042664, _1042666, _1042668, _1042670] : [c_Com_Ocom_OCall(_1042660, _1042662, _1042664) = c_Com_Ocom_OCond(_1042666, _1042668, _1042670)], (47755 ^ _781215) ^ [_1742621, _1742623, _1742625, _1742627, _1742629, _1742631, _1742633] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742621)), _1742623) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742625)), _1742627), 47758 ^ _781215 : [(47767 ^ _781215) ^ [] : [-(c_List_Olist__all2(_1742621, _1742625, _1742629, hAPP(hAPP(c_List_Oappend(_1742621), _1742623), _1742631), hAPP(hAPP(c_List_Oappend(_1742625), _1742627), _1742633))), c_List_Olist__all2(_1742621, _1742625, _1742629, _1742623, _1742627), c_List_Olist__all2(_1742621, _1742625, _1742629, _1742631, _1742633)], (47759 ^ _781215) ^ [] : [c_List_Olist__all2(_1742621, _1742625, _1742629, hAPP(hAPP(c_List_Oappend(_1742621), _1742623), _1742631), hAPP(hAPP(c_List_Oappend(_1742625), _1742627), _1742633)), 47762 ^ _781215 : [(47765 ^ _781215) ^ [] : [-(c_List_Olist__all2(_1742621, _1742625, _1742629, _1742631, _1742633))], (47763 ^ _781215) ^ [] : [-(c_List_Olist__all2(_1742621, _1742625, _1742629, _1742623, _1742627))]]]]], (37436 ^ _781215) ^ [_1491720] : [-(c_Equiv__Relations_Oequivp(_1491720, c_fequal))], (37578 ^ _781215) ^ [_1494926, _1494928, _1494930] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494926, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1494926, tc_HOL_Obool), tc_HOL_Obool)), _1494928), _1494930)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494926, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494926, tc_HOL_Obool), _1494928)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494926, tc_HOL_Obool), _1494930)))], (25885 ^ _781215) ^ [_1250636, _1250638, _1250640, _1250642] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1250636), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250638, tc_Nat_Onat), _1250640), _1250642)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250638, _1250636), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1250636, _1250638), c_Nat_Osemiring__1__class_Oof__nat(_1250636)), _1250640)), _1250642)), class_Groups_Ocomm__monoid__mult(_1250636), class_Rings_Osemiring__1(_1250636)], (43666 ^ _781215) ^ [_1653429, _1653431, _1653433] : [c_List_Olist_ONil(_1653429) = hAPP(hAPP(c_List_Olist_OCons(_1653429), _1653431), _1653433)], (188 ^ _781215) ^ [_784057, _784059] : [-(c_Nat__Transfer_Ois__nat(_784057)), _784059 = _784057, c_Nat__Transfer_Ois__nat(_784059)], (31292 ^ _781215) ^ [_1354342, _1354344, _1354346, _1354348, _1354350, _1354352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1354342, _1354344), tc_HOL_Obool)), _1354346), _1354348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1354342, tc_HOL_Obool)), _1354350), _1354352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1354344, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1354342, _1354344, _1354346), _1354350)), hAPP(c_Relation_OImage(_1354342, _1354344, _1354348), _1354352))))], (23744 ^ _781215) ^ [_1209277, _1209279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1209277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1209279, _1209277)), _1209277)))], (21404 ^ _781215) ^ [_1165358, _1165360] : [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)), _1165358)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1165360))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1165358), _1165360)))], (7760 ^ _781215) ^ [_912004, _912006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912004), _912006)), _912004))], (33428 ^ _781215) ^ [_1403517, _1403519, _1403521, _1403523, _1403525, _1403527, _1403529, _1403531] : [c_Finite__Set_Ofolding__image__simple(_1403517, _1403519, _1403521, _1403523, _1403525, _1403527), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403519), _1403529)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403519), _1403531)), -(hAPP(hAPP(_1403521, hAPP(_1403527, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403519, tc_HOL_Obool)), _1403529), _1403531))), hAPP(_1403527, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1403519, tc_HOL_Obool)), _1403529), _1403531))) = hAPP(hAPP(_1403521, hAPP(_1403527, _1403529)), hAPP(_1403527, _1403531)))], (26414 ^ _781215) ^ [_1260458, _1260460] : [class_Rings_Olinordered__idom(_1260458), 26417 ^ _781215 : [(26424 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260458), c_Groups_Ozero__class_Ozero(_1260458)), hAPP(c_Int_Oring__1__class_Oof__int(_1260458), _1260460))))], (26418 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260458), c_Groups_Ozero__class_Ozero(_1260458)), hAPP(c_Int_Oring__1__class_Oof__int(_1260458), _1260460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260460)))]]], (1388 ^ _781215) ^ [_801535, _801537] : [-(class_Lattices_Olattice(_801535)), _801537 = _801535, class_Lattices_Olattice(_801537)], (34199 ^ _781215) ^ [_1421609, _1421611, _1421613, _1421615, _1421617] : [class_Groups_Ocomm__monoid__mult(_1421609), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421611), _1421613)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421611), _1421615)), 34213 ^ _781215 : [(34216 ^ _781215) ^ [] : [hAPP(_1421617, 34212 ^ [_1421609, _1421611, _1421613, _1421615, _1421617]) = c_Groups_Oone__class_Oone(_1421609)], (34214 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1421611), 34212 ^ [_1421609, _1421611, _1421613, _1421615, _1421617]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421611, tc_HOL_Obool)), _1421613), _1421615))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1421611, _1421609), _1421617), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421611, tc_HOL_Obool)), _1421613), _1421615)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421609), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1421611, _1421609), _1421617), _1421613)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1421611, _1421609), _1421617), _1421615)))], (26684 ^ _781215) ^ [_1265289, _1265291, _1265293, _1265295, _1265297] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1265289, _1265291, _1265293), _1265295), _1265297)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1265289, _1265291)), hAPP(hAPP(c_Product__Type_OPair(_1265289, _1265291), _1265295), _1265297)), _1265293)))], (34714 ^ _781215) ^ [_1431720, _1431722, _1431724, _1431726] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1431720), hAPP(c_Set_Oimage(_1431722, _1431720, _1431724), _1431726))), c_Fun_Oinj__on(_1431722, _1431720, _1431724, _1431726), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1431722), _1431726)))], (26057 ^ _781215) ^ [_1253839, _1253841, _1253843, _1253845, _1253847] : [class_Groups_Ocomm__monoid__mult(_1253839), hBOOL(hAPP(c_Finite__Set_Ofinite(_1253841), _1253843)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1253841, _1253839), hAPP(hAPP(c_COMBS(_1253841, _1253839, _1253839), hAPP(hAPP(c_COMBB(_1253839, tc_fun(_1253839, _1253839), _1253841), c_Groups_Otimes__class_Otimes(_1253839)), _1253845)), _1253847)), _1253843) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253839), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1253841, _1253839), _1253845), _1253843)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1253841, _1253839), _1253847), _1253843)))], (3716 ^ _781215) ^ [_837537, _837539] : [_837539 = _837537, -(c_Enum_Oenum__class_Oenum__all(_837539) = c_Enum_Oenum__class_Oenum__all(_837537))], (50440 ^ _781215) ^ [_1807016, _1807018, _1807020] : [50442 ^ _781215 : [(50445 ^ _781215) ^ [] : [hBOOL(hAPP(_1807020, 50441 ^ [_1807016, _1807018, _1807020]))], (50443 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1807016), 50441 ^ [_1807016, _1807018, _1807020]), hAPP(c_List_Oset(_1807016), _1807018))))]], -(c_List_Olist__all(_1807016, _1807020, _1807018))], (1004 ^ _781215) ^ [_796595, _796597, _796599, _796601, _796603, _796605] : [-(c_List_Olist__ex1(_796603, _796599, _796595)), c_List_Olist__ex1(_796605, _796601, _796597), _796605 = _796603, _796601 = _796599, _796597 = _796595], (44746 ^ _781215) ^ [_1678759, _1678761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678759)), _1678761)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1678759), _1678761) = _1678761)], (49371 ^ _781215) ^ [_1779508, _1779510] : [-(c_Transitive__Closure_Ortrancl(_1779508, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1779508, _1779508), tc_HOL_Obool)), _1779510), c_Relation_OId(_1779508))) = c_Transitive__Closure_Ortrancl(_1779508, _1779510))], (20503 ^ _781215) ^ [_1149264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1149264))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1149264)))], (5266 ^ _781215) ^ [_861594, _861596, _861598, _861600, _861602, _861604] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_861604, _861600, _861596) = c_Lazy__Sequence_Olazy__sequence_OInsert(_861602, _861598, _861594)), _861604 = _861602, _861600 = _861598, _861596 = _861594], (1966 ^ _781215) ^ [_809772, _809774, _809776, _809778, _809780, _809782] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_809782, _809778, _809774) = c_Hoare__Mirabelle_Otriple_Otriple__size(_809780, _809776, _809772)), _809782 = _809780, _809778 = _809776, _809774 = _809772], (45303 ^ _781215) ^ [_1689946, _1689948, _1689950] : [45305 ^ _781215 : [(45308 ^ _781215) ^ [] : [hBOOL(hAPP(_1689948, 45304 ^ [_1689946, _1689948, _1689950]))], (45306 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1689946), 45304 ^ [_1689946, _1689948, _1689950]), hAPP(c_List_Oset(_1689946), _1689950))))]], -(hAPP(c_List_Ofilter(_1689946, _1689948), _1689950) = _1689950)], (16919 ^ _781215) ^ [_1085110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085110), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085110)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33242 ^ _781215) ^ [_1399302, _1399304] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399302, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1399302, tc_HOL_Obool)), _1399304)), _1399304) = c_Orderings_Obot__class_Obot(tc_fun(_1399302, tc_HOL_Obool)))], (39685 ^ _781215) ^ [_1552427, _1552429] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1552427, _1552429, tc_prod(_1552427, _1552429)), c_Product__Type_OPair(_1552427, _1552429)) = c_Fun_Oid(tc_prod(_1552427, _1552429)))], (21944 ^ _781215) ^ [] : [-(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))))], (17719 ^ _781215) ^ [_1097864] : [hAPP(c_Int_Onat, _1097864) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097864), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18013 ^ _781215) ^ [_1102816, _1102818] : [hAPP(c_Nat_OSuc, _1102816) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102818), -(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(_1102818))), 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)), _1102816))))))], (16981 ^ _781215) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51612 ^ _781215) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (32956 ^ _781215) ^ [_1392354, _1392356] : [class_Lattices_Olattice(_1392354), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1392354), _1392356), _1392356) = _1392356)], (32676 ^ _781215) ^ [_1386324, _1386326, _1386328, _1386330] : [class_Lattices_Osemilattice__inf(_1386324), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386324), _1386326), _1386328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386324), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1386324), _1386330), _1386326)), _1386328)))], (39258 ^ _781215) ^ [_1535929, _1535931, _1535933, _1535935, _1535937, _1535939] : [-(hAPP(c_Set_Oimage(_1535929, _1535931, hAPP(hAPP(c_COMBS(_1535929, _1535931, _1535931), hAPP(hAPP(c_COMBS(_1535929, _1535931, tc_fun(_1535931, _1535931)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1535931, tc_fun(_1535931, _1535931)), _1535929), c_If(_1535931)), _1535933)), _1535935)), _1535937)), _1535939) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1535931, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1535929, _1535931, _1535935), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535929, tc_HOL_Obool)), _1535939), hAPP(c_Set_OCollect(_1535929), _1535933)))), hAPP(c_Set_Oimage(_1535929, _1535931, _1535937), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535929, tc_HOL_Obool)), _1535939), hAPP(c_Set_OCollect(_1535929), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1535929), c_fNot), _1535933))))))], (23204 ^ _781215) ^ [_1199085, _1199087, _1199089] : [class_Divides_Osemiring__div(_1199085), -(_1199087 = c_Groups_Ozero__class_Ozero(_1199085)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1199085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199085), _1199089), _1199087)), _1199087) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199085), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1199085), _1199089), _1199087)), c_Groups_Oone__class_Oone(_1199085)))], (17009 ^ _781215) ^ [_1086306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086306), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1086306)))], (39196 ^ _781215) ^ [_1534086, _1534088, _1534090] : [-(hBOOL(hAPP(_1534086, _1534088))), -(hAPP(c_Set_OCollect(_1534090), hAPP(hAPP(c_COMBS(_1534090, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534090), c_fconj), hAPP(c_fequal, _1534088))), _1534086)) = c_Orderings_Obot__class_Obot(tc_fun(_1534090, tc_HOL_Obool)))], (15248 ^ _781215) ^ [_1048681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1048681)))], (43878 ^ _781215) ^ [_1657344, _1657346, _1657348, _1657350, _1657352] : [c_List_Opartition(_1657344, _1657346, _1657348) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657344), tc_List_Olist(_1657344)), _1657350), _1657352), 43881 ^ _781215 : [(43888 ^ _781215) ^ [_1657606] : [hBOOL(hAPP(hAPP(c_member(_1657344), _1657606), hAPP(c_List_Oset(_1657344), _1657352))), hBOOL(hAPP(_1657346, _1657606))], (43882 ^ _781215) ^ [_1657497] : [hBOOL(hAPP(hAPP(c_member(_1657344), _1657497), hAPP(c_List_Oset(_1657344), _1657350))), -(hBOOL(hAPP(_1657346, _1657497)))]]], (47653 ^ _781215) ^ [_1740424, _1740426, _1740428, _1740430, _1740432, _1740434, _1740436] : [c_List_Olist__all2(_1740424, _1740426, _1740428, hAPP(hAPP(c_List_Omap(_1740430, _1740424), _1740432), _1740434), _1740436), -(c_List_Olist__all2(_1740430, _1740426, hAPP(hAPP(c_COMBB(_1740424, tc_fun(_1740426, tc_HOL_Obool), _1740430), _1740428), _1740432), _1740434, _1740436))], (4262 ^ _781215) ^ [_845904, _845906] : [_845906 = _845904, -(c_Lazy__Sequence_Ohb__not__seq(_845906) = c_Lazy__Sequence_Ohb__not__seq(_845904))], (13436 ^ _781215) ^ [_1014770, _1014772, _1014774, _1014776, _1014778, _1014780] : [-(hBOOL(hAPP(hAPP(c_member(_1014770), _1014772), _1014774))), -(hAPP(c_Set_Oimage(_1014770, tc_Option_Ooption(_1014776), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1014770, tc_Option_Ooption(_1014776)), _1014778), _1014772), hAPP(c_Option_Ooption_OSome(_1014776), _1014780))), _1014774) = hAPP(c_Set_Oimage(_1014770, tc_Option_Ooption(_1014776), _1014778), _1014774))], (45351 ^ _781215) ^ [_1691085, _1691087, _1691089, _1691091] : [hBOOL(hAPP(hAPP(c_member(_1691085), _1691087), hAPP(c_List_Oset(_1691085), _1691089))), -(hBOOL(hAPP(_1691091, _1691087))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691085)), hAPP(c_List_Ofilter(_1691085, _1691091), _1691089))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691085)), _1691089))))], (24414 ^ _781215) ^ [_1221413] : [-(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), _1221413)) = 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), _1221413))))], (7143 ^ _781215) ^ [_900549, _900551, _900553] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_900549), _900551)), 7146 ^ _781215 : [(7153 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900549), _900553), _900551))), -(hAPP(c_Finite__Set_Ocard(_900549), hAPP(hAPP(c_Set_Oinsert(_900549), _900553), _900551)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_900549), _900551)))], (7147 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_900549), _900553), _900551)), -(hAPP(c_Finite__Set_Ocard(_900549), hAPP(hAPP(c_Set_Oinsert(_900549), _900553), _900551)) = hAPP(c_Finite__Set_Ocard(_900549), _900551))]]], (36362 ^ _781215) ^ [] : [-(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))))], (37420 ^ _781215) ^ [_1491391, _1491393] : [-(c_Equiv__Relations_Oequivp(_1491391, _1491393)), 37425 ^ _781215 : [(37428 ^ _781215) ^ [] : [hAPP(_1491393, 37421 ^ [_1491391, _1491393]) = hAPP(_1491393, 37422 ^ [_1491391, _1491393])], (37426 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1491393, 37421 ^ [_1491391, _1491393]), 37422 ^ [_1491391, _1491393])))]], 37429 ^ _781215 : [(37432 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1491393, 37421 ^ [_1491391, _1491393]), 37422 ^ [_1491391, _1491393]))], (37430 ^ _781215) ^ [] : [-(hAPP(_1491393, 37421 ^ [_1491391, _1491393]) = hAPP(_1491393, 37422 ^ [_1491391, _1491393]))]]], (26807 ^ _781215) ^ [_1268337, _1268339, _1268341, _1268343] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1268337, _1268339), _1268341)), hBOOL(hAPP(hAPP(_1268339, _1268343), _1268341)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1268337, _1268339), _1268343)))], (43399 ^ _781215) ^ [_1647152, _1647154, _1647156, _1647158] : [class_Groups_Ocomm__monoid__add(_1647152), hBOOL(hAPP(c_List_Odistinct(_1647154), _1647156)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1647152), hAPP(hAPP(c_List_Omap(_1647154, _1647152), _1647158), _1647156)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1647154, _1647152), _1647158), hAPP(c_List_Oset(_1647154), _1647156)))], (24035 ^ _781215) ^ [_1214609, _1214611, _1214613, _1214615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1214611), _1214613)), -(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), _1214613), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1214615, _1214609))), _1214611)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214613), _1214609))))], (12952 ^ _781215) ^ [_1006853, _1006855] : [class_Groups_Olinordered__ab__group__add(_1006853), 12955 ^ _781215 : [(12962 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006853), _1006855), c_Groups_Ozero__class_Ozero(_1006853))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006853), _1006855), hAPP(c_Groups_Ouminus__class_Ouminus(_1006853), _1006855))))], (12956 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006853), _1006855), hAPP(c_Groups_Ouminus__class_Ouminus(_1006853), _1006855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006853), _1006855), c_Groups_Ozero__class_Ozero(_1006853))))]]], (5518 ^ _781215) ^ [_865460, _865462, _865464, _865466, _865468, _865470] : [-(c_COMBS(_865470, _865466, _865462) = c_COMBS(_865468, _865464, _865460)), _865470 = _865468, _865466 = _865464, _865462 = _865460], (39110 ^ _781215) ^ [_1532146, _1532148, _1532150] : [-(hAPP(hAPP(c_Set_Oinsert(_1532146), _1532148), hAPP(c_Set_OCollect(_1532146), _1532150)) = hAPP(c_Set_OCollect(_1532146), hAPP(hAPP(c_COMBS(_1532146, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532146), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1532146), c_fNot), hAPP(hAPP(c_COMBC(_1532146, _1532146, tc_HOL_Obool), c_fequal), _1532148)))), _1532150)))], (23382 ^ _781215) ^ [_1202480, _1202482, _1202484] : [-(hBOOL(hAPP(_1202480, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202482, _1202484)))), 23385 ^ _781215 : [(23388 ^ _781215) ^ [] : [hBOOL(hAPP(_1202480, _1202482))], (23386 ^ _781215) ^ [] : [-(_1202484 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 23391 ^ _781215 : [(23392 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202484)))], (23398 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23394 ^ [_1202480, _1202482, _1202484]), _1202484)))], (23402 ^ _781215) ^ [] : [hBOOL(hAPP(_1202480, 23394 ^ [_1202480, _1202482, _1202484]))], (23400 ^ _781215) ^ [] : [-(_1202482 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202484), 23393 ^ [_1202480, _1202482, _1202484])), 23394 ^ [_1202480, _1202482, _1202484]))], (23396 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23394 ^ [_1202480, _1202482, _1202484])))]], 23403 ^ _781215 : [(23404 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202484), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23410 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23406 ^ [_1202480, _1202482, _1202484]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23414 ^ _781215) ^ [] : [hBOOL(hAPP(_1202480, 23406 ^ [_1202480, _1202482, _1202484]))], (23412 ^ _781215) ^ [] : [-(_1202482 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202484), 23405 ^ [_1202480, _1202482, _1202484])), 23406 ^ [_1202480, _1202482, _1202484]))], (23408 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202484), 23406 ^ [_1202480, _1202482, _1202484])))]]], (20448 ^ _781215) ^ [_1148194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1148194)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1148194), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (49772 ^ _781215) ^ [_1789958, _1789960, _1789962, _1789964, _1789966, _1789968] : [c_Relation_Osingle__valued(_1789958, _1789960, hAPP(c_Relation_Oconverse(_1789960, _1789958), _1789962)), -(_1789964 = c_Orderings_Obot__class_Obot(tc_fun(_1789966, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1789960, _1789958, _1789962), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1789966, tc_fun(_1789960, tc_HOL_Obool)), _1789964), _1789968)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1789966, tc_fun(_1789958, tc_HOL_Obool)), _1789964), hAPP(hAPP(c_COMBB(tc_fun(_1789960, tc_HOL_Obool), tc_fun(_1789958, tc_HOL_Obool), _1789966), c_Relation_OImage(_1789960, _1789958, _1789962)), _1789968)))], (4782 ^ _781215) ^ [_853644, _853646, _853648, _853650] : [-(c_Product__Type_Ofst(_853650, _853646) = c_Product__Type_Ofst(_853648, _853644)), _853650 = _853648, _853646 = _853644], (46760 ^ _781215) ^ [_1721354, _1721356, _1721358] : [46762 ^ _781215 : [(46765 ^ _781215) ^ [] : [hBOOL(hAPP(_1721356, 46761 ^ [_1721354, _1721356, _1721358]))], (46763 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1721354), 46761 ^ [_1721354, _1721356, _1721358]), hAPP(c_List_Oset(_1721354), _1721358))))]], -(c_List_OdropWhile(_1721354, _1721356, _1721358) = c_List_Olist_ONil(_1721354))], (29190 ^ _781215) ^ [_1313341, _1313343, _1313345, _1313347] : [class_Fields_Ofield__inverse__zero(_1313341), -(_1313343 = c_Groups_Ozero__class_Ozero(_1313341)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313341), _1313345), _1313343)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1313341), _1313347), _1313343)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1313341), _1313345), _1313347))], (18297 ^ _781215) ^ [_1108745, _1108747, _1108749] : [class_Orderings_Olinorder(_1108745), 18300 ^ _781215 : [(18307 ^ _781215) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1108745), _1108747), _1108749) = _1108747, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108745), _1108747), _1108749)))], (18301 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108745), _1108747), _1108749)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1108745), _1108747), _1108749) = _1108747)]]], (38580 ^ _781215) ^ [_1519022, _1519024, _1519026, _1519028, _1519030, _1519032] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1519022, _1519024)), hAPP(hAPP(c_Product__Type_OPair(_1519022, _1519024), _1519026), _1519028)), hAPP(hAPP(c_Product__Type_OSigma(_1519022, _1519024), _1519030), _1519032))), 38583 ^ _781215 : [(38586 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519024), _1519028), hAPP(_1519032, _1519026))))], (38584 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519022), _1519026), _1519030)))]]], (51560 ^ _781215) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (30141 ^ _781215) ^ [_1332592, _1332594] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1332592, _1332594)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1332592), hAPP(c_Nat_OSuc, _1332594)))], (30474 ^ _781215) ^ [_1338668, _1338670, _1338672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1338668)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1338670), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1338672)), 30484 ^ _781215 : [(30490 ^ _781215) ^ [] : [-(_1338670 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30486 ^ [_1338668, _1338670, _1338672]), 30483 ^ [_1338668, _1338670, _1338672]))], (30488 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30486 ^ [_1338668, _1338670, _1338672]), _1338672)))], (30485 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30483 ^ [_1338668, _1338670, _1338672]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1338668))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1338670), _1338668) = _1338670)], (41041 ^ _781215) ^ [] : [41043 ^ _781215 : [(41046 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), 41042 ^ []))], (41044 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 41042 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))]], -(c_Com_OWT__bodies)], (36021 ^ _781215) ^ [_1458524, _1458526] : [class_Rings_Olinordered__idom(_1458524), -(hAPP(c_Groups_Oabs__class_Oabs(_1458524), _1458526) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1458524), _1458526), c_Groups_Osgn__class_Osgn(_1458524, _1458526)))], (40331 ^ _781215) ^ [_1569686, _1569688, _1569690, _1569692] : [40333 ^ _781215 : [(40336 ^ _781215) ^ [] : [c_Wellfounded_Owf(_1569688, hAPP(_1569690, 40332 ^ [_1569686, _1569688, _1569690, _1569692]))], (40334 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1569686, 40332 ^ [_1569686, _1569688, _1569690, _1569692])))]], -(c_Wellfounded_Owf(tc_prod(_1569692, _1569688), c_Recdef_Osame__fst(_1569692, _1569688, _1569686, _1569690)))], (36243 ^ _781215) ^ [_1462479, _1462481] : [-(_1462479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36246 ^ _781215 : [(36253 ^ _781215) ^ [] : [-(_1462481 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1462479, _1462481) = 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, _1462481))), 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, _1462479)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1462481))), c_Divides_Opdivmod(_1462479, _1462481)), 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), _1462481))))), c_Divides_Opdivmod(_1462479, _1462481)))))], (36247 ^ _781215) ^ [] : [_1462481 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1462479, _1462481) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1462479))]]], (16780 ^ _781215) ^ [_1082486, _1082488] : [class_Lattices_Olattice(_1082486), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1082486), _1082488), _1082488) = _1082488)], (45073 ^ _781215) ^ [_1685478, _1685480, _1685482, _1685484] : [class_Complete__Lattice_Ocomplete__lattice(_1685478), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1685480, _1685478), hAPP(c_List_Oset(_1685480), _1685482)), _1685484) = hAPP(c_List_Ofoldl(_1685478, _1685480, hAPP(c_COMBC(_1685480, _1685478, _1685478), hAPP(hAPP(c_COMBB(_1685478, tc_fun(_1685478, _1685478), _1685480), c_Lattices_Osemilattice__inf__class_Oinf(_1685478)), _1685484)), c_Orderings_Otop__class_Otop(_1685478)), _1685482))], (37255 ^ _781215) ^ [_1487158, _1487160, _1487162, _1487164, _1487166] : [_1487158 = c_Orderings_Obot__class_Obot(tc_fun(_1487160, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1487160, tc_fun(_1487162, tc_HOL_Obool)), _1487158), hAPP(hAPP(c_COMBB(tc_fun(_1487162, tc_HOL_Obool), tc_fun(_1487162, tc_HOL_Obool), _1487160), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1487162, tc_HOL_Obool)), _1487164)), _1487166)) = c_Orderings_Otop__class_Otop(tc_fun(_1487162, tc_HOL_Obool)))], (11555 ^ _781215) ^ [_982768, _982770, _982772, _982774] : [_982774 = c_Orderings_Obot__class_Obot(tc_fun(_982770, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_982768, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_982770, _982768, _982772), _982774))], (41399 ^ _781215) ^ [_1594901, _1594903, _1594905, _1594907, _1594909, _1594911, _1594913, _1594915] : [class_Groups_Ocomm__monoid__mult(_1594901), c_Fun_Oinj__on(_1594903, _1594905, _1594907, _1594909), _1594911 = hAPP(c_Set_Oimage(_1594903, _1594905, _1594907), _1594909), _1594913 = hAPP(c_Fun_Ocomp(_1594905, _1594901, _1594903, _1594915), _1594907), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1594905, _1594901), _1594915), _1594911) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1594903, _1594901), _1594913), _1594909))], (46439 ^ _781215) ^ [_1714733, _1714735] : [-(c_List_Oconcat(tc_List_Olist(_1714733), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714733), tc_List_Olist(tc_List_Olist(_1714733))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1714733)), _1714733, c_List_Olist_ONil(tc_List_Olist(_1714733)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1714733), tc_List_Olist(tc_List_Olist(_1714733))), _1714733), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714733), tc_List_Olist(tc_List_Olist(_1714733)), tc_List_Olist(tc_List_Olist(_1714733))), c_List_Olist_OCons(tc_List_Olist(_1714733))), c_List_Olist_ONil(tc_List_Olist(_1714733)))))), _1714735)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714733), tc_List_Olist(_1714733)), c_List_Otl(_1714733)), hAPP(c_List_Ofilter(tc_List_Olist(_1714733), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1714733)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714733), tc_List_Olist(_1714733), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1714733)))), _1714735)))], (41299 ^ _781215) ^ [_1592439, _1592441, _1592443, _1592445, _1592447, _1592449, _1592451] : [-(hAPP(c_Product__Type_Oapsnd(_1592439, _1592441, _1592443, _1592445), hAPP(c_Product__Type_Oapsnd(_1592447, _1592439, _1592443, _1592449), _1592451)) = hAPP(c_Product__Type_Oapsnd(_1592447, _1592441, _1592443, hAPP(c_Fun_Ocomp(_1592439, _1592441, _1592447, _1592445), _1592449)), _1592451))], (15602 ^ _781215) ^ [_1055205, _1055207, _1055209, _1055211, _1055213] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1055205, tc_Option_Ooption(_1055207)), _1055209), _1055211), hAPP(c_Option_Ooption_OSome(_1055207), _1055213)) = hAPP(c_COMBK(tc_Option_Ooption(_1055207), _1055205), c_Option_Ooption_ONone(_1055207))], (44098 ^ _781215) ^ [_1663032, _1663034] : [-(hAPP(hAPP(c_List_Oappend(_1663032), c_List_Olist_ONil(_1663032)), _1663034) = _1663034)], (30632 ^ _781215) ^ [_1341729, _1341731, _1341733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1341729)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1341731), _1341733)), 30639 ^ _781215 : [(30640 ^ _781215) ^ [_1341925] : [30642 ^ _781215 : [(30648 ^ _781215) ^ [] : [-(_1341925 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30644 ^ [_1341729, _1341731, _1341733, _1341925]), 30641 ^ [_1341729, _1341731, _1341733, _1341925]))], (30646 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30644 ^ [_1341729, _1341731, _1341733, _1341925]), _1341733)))], (30643 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30641 ^ [_1341729, _1341731, _1341733, _1341925]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1341729))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1341731), _1341925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1341731), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1341925), _1341729))))]]], (32252 ^ _781215) ^ [_1377091, _1377093, _1377095] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377091), _1377093), _1377095) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377091, tc_HOL_Obool), tc_HOL_Obool)), -(_1377093 = c_Orderings_Obot__class_Obot(tc_fun(_1377091, tc_HOL_Obool)))], (25628 ^ _781215) ^ [_1242402, _1242404, _1242406, _1242408] : [hBOOL(hAPP(hAPP(_1242406, _1242404), _1242408)), -(hBOOL(hAPP(hAPP(c_member(_1242402), _1242404), c_SetInterval_Oord_OatMost(_1242402, _1242406, _1242408))))], (3584 ^ _781215) ^ [_835523, _835525] : [_835525 = _835523, -(c_List_Oreturn__list(_835525) = c_List_Oreturn__list(_835523))], (3446 ^ _781215) ^ [_833292, _833294] : [_833294 = _833292, -(c_SetInterval_Oord__class_OatMost(_833294) = c_SetInterval_Oord__class_OatMost(_833292))], (16881 ^ _781215) ^ [_1084410, _1084412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084410), _1084412)), -(c_Nat__Transfer_Otsub(_1084412, _1084410) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1084412), _1084410))], (10558 ^ _781215) ^ [_961825, _961827, _961829] : [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, _961825)), _961827)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961825)), _961829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961827), _961829)))], (44832 ^ _781215) ^ [_1680350] : [-(hAPP(c_List_Otl(_1680350), c_List_Olist_ONil(_1680350)) = c_List_Olist_ONil(_1680350))], (49738 ^ _781215) ^ [_1789112, _1789114, _1789116, _1789118, _1789120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1789114, tc_HOL_Obool)), _1789118), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1789114, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1789112, _1789114, hAPP(c_Relation_Oconverse(_1789114, _1789112), _1789116)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1789112, tc_HOL_Obool)), _1789120))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1789112, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1789114, _1789112, _1789116), _1789118)), _1789120)))], (44192 ^ _781215) ^ [_1664689, _1664691, _1664693] : [_1664689 = c_List_Olist_ONil(_1664691), -(c_List_Obutlast(_1664691, hAPP(hAPP(c_List_Oappend(_1664691), _1664693), _1664689)) = c_List_Obutlast(_1664691, _1664693))], (46321 ^ _781215) ^ [_1711276, _1711278, _1711280] : [c_List_Oconcat(_1711276, _1711278) = c_List_Oconcat(_1711276, _1711280), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1711276))), _1711278) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1711276))), _1711280), 46331 ^ _781215 : [(46334 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1711276), tc_List_Olist(_1711276), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1711276), tc_fun(tc_List_Olist(_1711276), tc_Nat_Onat), tc_fun(tc_List_Olist(_1711276), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1711276), tc_Nat_Onat), tc_fun(tc_List_Olist(_1711276), tc_HOL_Obool)), tc_List_Olist(_1711276)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1711276))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1711276)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1711276))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1711276)))), 46330 ^ [_1711276, _1711278, _1711280]))], (46332 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711276), tc_List_Olist(_1711276))), 46330 ^ [_1711276, _1711278, _1711280]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1711276), tc_List_Olist(_1711276))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1711276), tc_List_Olist(_1711276)), _1711278), _1711280)))))]], -(_1711278 = _1711280)], (37659 ^ _781215) ^ [_1496859, _1496861] : [class_Complete__Lattice_Ocomplete__lattice(_1496859), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496859), _1496861)), -(_1496861 = c_Orderings_Obot__class_Obot(tc_fun(_1496859, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1496859, _1496861) = c_Complete__Lattice_OInf__class_OInf(_1496859, _1496861))], (25682 ^ _781215) ^ [_1243425, _1243427, _1243429, _1243431, _1243433, _1243435] : [hBOOL(hAPP(hAPP(c_member(_1243425), _1243427), c_SetInterval_Oord_OatLeastLessThan(_1243425, _1243429, _1243431, _1243433, _1243435))), 25685 ^ _781215 : [(25688 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1243431, _1243427), _1243435)))], (25686 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1243429, _1243433), _1243427)))]]], (22116 ^ _781215) ^ [_1179844, _1179846, _1179848, _1179850] : [class_Complete__Lattice_Ocomplete__lattice(_1179844), -(_1179846 = c_Orderings_Obot__class_Obot(tc_fun(_1179848, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1179848, _1179844), _1179846), hAPP(c_COMBK(_1179844, _1179848), _1179850)) = _1179850)], (29692 ^ _781215) ^ [_1322425, _1322427, _1322429, _1322431, _1322433] : [class_Fields_Ofield(_1322425), -(_1322427 = c_Groups_Ozero__class_Ozero(_1322425)), -(_1322429 = c_Groups_Ozero__class_Ozero(_1322425)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322425), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322425), _1322431), _1322427)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322425), _1322433), _1322429)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322425), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322425), _1322431), _1322429)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322425), _1322433), _1322427))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322425), _1322427), _1322429)))], (20515 ^ _781215) ^ [_1149448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1149448)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1149448), c_Int_OPls)))], (24802 ^ _781215) ^ [_1228888, _1228890, _1228892] : [class_Power_Opower(_1228888), class_Rings_Omult__zero(_1228888), class_Rings_Ono__zero__divisors(_1228888), class_Rings_Ozero__neq__one(_1228888), 24817 ^ _781215 : [(24826 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1228888), _1228890), _1228892) = c_Groups_Ozero__class_Ozero(_1228888)), _1228890 = c_Groups_Ozero__class_Ozero(_1228888), -(_1228892 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24818 ^ _781215) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1228888), _1228890), _1228892) = c_Groups_Ozero__class_Ozero(_1228888), 24821 ^ _781215 : [(24824 ^ _781215) ^ [] : [_1228892 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24822 ^ _781215) ^ [] : [-(_1228890 = c_Groups_Ozero__class_Ozero(_1228888))]]]]], (1288 ^ _781215) ^ [_800285, _800287] : [-(class_Rings_Oidom(_800285)), _800287 = _800285, class_Rings_Oidom(_800287)], (37995 ^ _781215) ^ [_1503784, _1503786, _1503788, _1503790] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1503784, tc_fun(_1503786, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1503784, tc_HOL_Obool), _1503788)), _1503790) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1503784, tc_HOL_Obool), tc_fun(_1503786, tc_HOL_Obool)), _1503788), hAPP(hAPP(c_COMBC(tc_fun(_1503784, tc_HOL_Obool), tc_fun(_1503784, tc_fun(_1503786, tc_HOL_Obool)), tc_fun(_1503786, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1503784, tc_fun(_1503786, tc_HOL_Obool))), _1503790)))], (47531 ^ _781215) ^ [_1737678, _1737680, _1737682, _1737684] : [hBOOL(hAPP(c_List_Olistsp(_1737678, _1737680), hAPP(hAPP(c_List_Olist_OCons(_1737678), _1737682), _1737684))), 47534 ^ _781215 : [(47537 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1737678, _1737680), _1737684)))], (47535 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1737680, _1737682)))]]], (10432 ^ _781215) ^ [_959149, _959151, _959153] : [class_Groups_Ogroup__add(_959149), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959149), _959151), hAPP(c_Groups_Ouminus__class_Ouminus(_959149), _959153)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959149), _959151), _959153))], (670 ^ _781215) ^ [_791572, _791574, _791576, _791578, _791580, _791582] : [-(c_Enum_Oex__n__lists(_791580, _791576, _791572)), c_Enum_Oex__n__lists(_791582, _791578, _791574), _791582 = _791580, _791578 = _791576, _791574 = _791572], (50581 ^ _781215) ^ [_1809696, _1809698] : [class_Enum_Oenum(_1809696), 50584 ^ _781215 : [(50598 ^ _781215) ^ [] : [c_List_Olist__ex1(_1809696, _1809698, c_Enum_Oenum__class_Oenum(_1809696)), 50602 ^ _781215 : [(50605 ^ _781215) ^ [_1810095] : [hBOOL(hAPP(_1809698, _1810095)), -(_1810095 = 50601 ^ [_1809696, _1809698])], (50603 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1809698, 50601 ^ [_1809696, _1809698])))]]], (50585 ^ _781215) ^ [] : [-(c_List_Olist__ex1(_1809696, _1809698, c_Enum_Oenum__class_Oenum(_1809696))), 50586 ^ _781215 : [(50587 ^ _781215) ^ [_1809811] : [hBOOL(hAPP(_1809698, _1809811)), 50591 ^ _781215 : [(50594 ^ _781215) ^ [] : [50590 ^ [_1809696, _1809698, _1809811] = _1809811], (50592 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1809698, 50590 ^ [_1809696, _1809698, _1809811])))]]]]]]], (45570 ^ _781215) ^ [_1695934, _1695936, _1695938] : [class_Orderings_Olinorder(_1695934), c_List_Olinorder__class_Osorted(_1695934, _1695936), -(c_List_Olinorder__class_Osorted(_1695934, c_List_Oremove1(_1695934, _1695938, _1695936)))], (8089 ^ _781215) ^ [_917545, _917547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917545), hAPP(c_Nat_OSuc, _917547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917545), _917547))), -(_917545 = _917547)], (31473 ^ _781215) ^ [_1358578] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1358578) = 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, _1358578)), 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))))))))], (18325 ^ _781215) ^ [_1109215, _1109217, _1109219, _1109221] : [class_Orderings_Olinorder(_1109215), 18328 ^ _781215 : [(18329 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109215), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1109215), _1109217), _1109219)), _1109221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109215), _1109217), _1109221))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109215), _1109219), _1109221)))], (18339 ^ _781215) ^ [] : [18340 ^ _781215 : [(18343 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109215), _1109219), _1109221))], (18341 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109215), _1109217), _1109221))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109215), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1109215), _1109217), _1109219)), _1109221)))]]], (18079 ^ _781215) ^ [_1104374, _1104376] : [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(_1104374))), 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)), _1104376)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104374)), hAPP(c_Nat_OSuc, _1104376))))], (46886 ^ _781215) ^ [_1724227, _1724229, _1724231] : [-(c_Enum_Osublists(_1724227, hAPP(hAPP(c_List_Olist_OCons(_1724227), _1724229), _1724231)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1724227)), tc_List_Olist(tc_List_Olist(_1724227))), c_Enum_Osublists(_1724227, _1724231)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1724227)), tc_List_Olist(tc_List_Olist(_1724227)), tc_List_Olist(tc_List_Olist(_1724227))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1724227)), tc_fun(tc_List_Olist(tc_List_Olist(_1724227)), tc_List_Olist(tc_List_Olist(_1724227))), tc_List_Olist(tc_List_Olist(_1724227))), c_List_Oappend(tc_List_Olist(_1724227))), hAPP(c_List_Omap(tc_List_Olist(_1724227), tc_List_Olist(_1724227)), hAPP(c_List_Olist_OCons(_1724227), _1724229)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1724227))))))], (18061 ^ _781215) ^ [_1103936, _1103938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1103936)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103938))), -(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(_1103938))), 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), _1103936)), c_Int_Onat))))))], (51320 ^ _781215) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (51308 ^ _781215) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (18465 ^ _781215) ^ [_1111908, _1111910, _1111912] : [class_Orderings_Olinorder(_1111908), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111908), _1111910)), hBOOL(hAPP(hAPP(c_member(_1111908), _1111912), _1111910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111908), hAPP(c_Finite__Set_Ofold1(_1111908, c_Orderings_Oord__class_Omin(_1111908)), _1111910)), _1111912)))], (9289 ^ _781215) ^ [_939358, _939360, _939362] : [class_Groups_Ogroup__add(_939358), -(hAPP(c_Groups_Ouminus__class_Ouminus(_939358), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939358), _939360), _939362)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939358), hAPP(c_Groups_Ouminus__class_Ouminus(_939358), _939362)), hAPP(c_Groups_Ouminus__class_Ouminus(_939358), _939360)))], (29362 ^ _781215) ^ [_1316270, _1316272, _1316274] : [class_Fields_Olinordered__field(_1316270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316270), c_Groups_Ozero__class_Ozero(_1316270)), _1316272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316270), _1316274), c_Groups_Ozero__class_Ozero(_1316270))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316270), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1316270), _1316272), _1316274)), c_Groups_Ozero__class_Ozero(_1316270))))], (23048 ^ _781215) ^ [_1196722, _1196724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196722), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23051 ^ _781215 : [(23054 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196722), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1196724, _1196722))))], (23052 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1196724, _1196722)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (48826 ^ _781215) ^ [_1766922, _1766924, _1766926] : [-(c_Random_Oselect__weight(_1766922, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1766922)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1766922), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1766924)), _1766926)) = c_Random_Oselect__weight(_1766922, _1766926))], (1738 ^ _781215) ^ [_805910, _805912] : [-(class_Groups_Omonoid__mult(_805910)), _805912 = _805910, class_Groups_Omonoid__mult(_805912)], (35225 ^ _781215) ^ [_1442692, _1442694, _1442696, _1442698, _1442700, _1442702] : [c_Fun_Oinj__on(_1442692, _1442694, _1442696, _1442698), hAPP(_1442696, _1442700) = _1442702, hBOOL(hAPP(hAPP(c_member(_1442692), _1442700), _1442698)), -(hAPP(c_Fun_Othe__inv__into(_1442692, _1442694, _1442698, _1442696), _1442702) = _1442700)], (5728 ^ _781215) ^ [_871835, _871837] : [-(c_Option_Oset(_871835, hAPP(c_Option_Ooption_OSome(_871835), _871837)) = hAPP(hAPP(c_Set_Oinsert(_871835), _871837), c_Orderings_Obot__class_Obot(tc_fun(_871835, tc_HOL_Obool))))], (25144 ^ _781215) ^ [_1235091] : [-(_1235091 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 25147 ^ _781215 : [(25154 ^ _781215) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1235091, 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, _1235091) = 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), _1235091), 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)))], (25148 ^ _781215) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1235091, 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, _1235091) = 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), _1235091), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (37187 ^ _781215) ^ [_1485261, _1485263, _1485265, _1485267, _1485269] : [-(_1485261 = c_Orderings_Obot__class_Obot(tc_fun(_1485263, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1485263, tc_fun(_1485265, tc_HOL_Obool)), _1485261), hAPP(hAPP(c_COMBC(_1485263, tc_fun(_1485265, tc_HOL_Obool), tc_fun(_1485265, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485265, tc_HOL_Obool), tc_fun(tc_fun(_1485265, tc_HOL_Obool), tc_fun(_1485265, tc_HOL_Obool)), _1485263), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485265, tc_HOL_Obool))), _1485267)), _1485269)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485265, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1485263, tc_fun(_1485265, tc_HOL_Obool)), _1485261), _1485267)), _1485269))], (43533 ^ _781215) ^ [_1650243, _1650245, _1650247, _1650249] : [hBOOL(hAPP(_1650243, _1650245)), 43536 ^ _781215 : [(43539 ^ _781215) ^ [_1650373] : [hBOOL(hAPP(_1650243, _1650373)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1650249, c_Hilbert__Choice_OLeastM(_1650247, tc_Nat_Onat, _1650249, _1650243))), hAPP(_1650249, _1650373))))], (43537 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1650243, c_Hilbert__Choice_OLeastM(_1650247, tc_Nat_Onat, _1650249, _1650243))))]]], (36225 ^ _781215) ^ [_1462158, _1462160] : [class_Rings_Olinordered__idom(_1462158), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1462158), hAPP(c_Groups_Oabs__class_Oabs(_1462158), _1462160)), 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(_1462158), _1462160), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (11716 ^ _781215) ^ [_985490, _985492] : [class_Rings_Omult__zero(_985490), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985490), c_Groups_Ozero__class_Ozero(_985490)), _985492) = c_Groups_Ozero__class_Ozero(_985490))], (21956 ^ _781215) ^ [] : [-(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)))))], (49962 ^ _781215) ^ [_1794350, _1794352, _1794354, _1794356] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1794350, _1794352), tc_fun(_1794350, _1794352)), _1794354), c_Fun_Ocomp(_1794352, _1794352, _1794350, _1794356)) = c_Fun_Ocomp(_1794352, _1794352, _1794350, hAPP(hAPP(c_Nat_Ocompow(_1794352, _1794352), _1794354), _1794356)))], (1448 ^ _781215) ^ [_802285, _802287] : [-(class_Smallcheck_Osmall(_802285)), _802287 = _802285, class_Smallcheck_Osmall(_802287)], (11020 ^ _781215) ^ [_971265, _971267, _971269, _971271, _971273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971265), _971267)), 11023 ^ _781215 : [(11030 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _971271), 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), _971267), _971265)), _971269)), _971273))), -(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), _971265), _971269)), _971271)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971267), _971269)), _971273))))], (11024 ^ _781215) ^ [] : [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), _971265), _971269)), _971271)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971267), _971269)), _971273))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _971271), 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), _971267), _971265)), _971269)), _971273))))]]], (10332 ^ _781215) ^ [_957292, _957294, _957296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957292, tc_HOL_Obool)), _957294), _957296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_957292, tc_HOL_Obool)), _957294), _957296))), -(_957294 = _957296)], (43575 ^ _781215) ^ [_1651437, _1651439, _1651441, _1651443] : [-(hAPP(hAPP(c_List_Omap(_1651437, _1651439), _1651441), c_List_Obutlast(_1651437, _1651443)) = c_List_Obutlast(_1651439, hAPP(hAPP(c_List_Omap(_1651437, _1651439), _1651441), _1651443)))], (42513 ^ _781215) ^ [_1624480, _1624482, _1624484, _1624486, _1624488] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1624480), tc_List_Olist(_1624480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1624480), tc_List_Olist(_1624480)), hAPP(hAPP(c_List_Olist_OCons(_1624480), _1624482), _1624484)), _1624486)), c_List_Olistrel(_1624480, _1624488))), 42518 ^ _781215 : [(42523 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1624480), tc_List_Olist(_1624480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1624480), tc_List_Olist(_1624480)), _1624484), 42517 ^ [_1624480, _1624482, _1624484, _1624486, _1624488])), c_List_Olistrel(_1624480, _1624488))))], (42521 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624480, _1624480)), hAPP(hAPP(c_Product__Type_OPair(_1624480, _1624480), _1624482), 42516 ^ [_1624480, _1624482, _1624484, _1624486, _1624488])), _1624488)))], (42519 ^ _781215) ^ [] : [-(_1624486 = hAPP(hAPP(c_List_Olist_OCons(_1624480), 42516 ^ [_1624480, _1624482, _1624484, _1624486, _1624488]), 42517 ^ [_1624480, _1624482, _1624484, _1624486, _1624488]))]]], (41531 ^ _781215) ^ [_1597994, _1597996, _1597998, _1598000, _1598002, _1598004, _1598006, _1598008] : [c_Finite__Set_Ofolding(_1597994, _1597996, _1597998, _1598000), -(hAPP(c_Fun_Ocomp(_1597996, _1597996, _1598002, hAPP(_1597998, _1598004)), hAPP(c_Fun_Ocomp(_1597996, _1597996, _1598002, hAPP(_1597998, _1598006)), _1598008)) = hAPP(c_Fun_Ocomp(_1597996, _1597996, _1598002, hAPP(_1597998, _1598006)), hAPP(c_Fun_Ocomp(_1597996, _1597996, _1598002, hAPP(_1597998, _1598004)), _1598008)))], (10532 ^ _781215) ^ [_961291, _961293, _961295, _961297] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961291, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_961291), _961293), _961295)), _961297))), hBOOL(hAPP(hAPP(c_member(_961291), _961293), _961297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961291, tc_HOL_Obool)), _961295), _961297))], (48878 ^ _781215) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (38358 ^ _781215) ^ [_1512672, _1512674, _1512676, _1512678] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512672), _1512674)), c_Fun_Oinj__on(_1512676, _1512672, _1512678, c_Orderings_Otop__class_Otop(tc_fun(_1512676, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512676), hAPP(c_Set_Ovimage(_1512676, _1512672, _1512678), _1512674))))], (41247 ^ _781215) ^ [_1591117, _1591119, _1591121] : [-(hAPP(c_Fun_Ocomp(_1591117, _1591117, _1591119, c_Fun_Oid(_1591117)), _1591121) = _1591121)], (51292 ^ _781215) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (7895 ^ _781215) ^ [_914616, _914618] : [hAPP(c_Nat_OSuc, _914616) = hAPP(c_Nat_OSuc, _914618), -(_914616 = _914618)], (30588 ^ _781215) ^ [_1340918, _1340920, _1340922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340918)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1340920), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1340922)), 30598 ^ _781215 : [(30604 ^ _781215) ^ [] : [-(_1340920 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30600 ^ [_1340918, _1340920, _1340922]), 30597 ^ [_1340918, _1340920, _1340922]))], (30602 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30600 ^ [_1340918, _1340920, _1340922]), _1340922)))], (30599 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30597 ^ [_1340918, _1340920, _1340922]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1340918))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1340920), _1340918) = _1340920)], (38846 ^ _781215) ^ [_1526520, _1526522, _1526524] : [c_Relation_Orefl__on(_1526520, _1526522, _1526524), 38849 ^ _781215 : [(38852 ^ _781215) ^ [_1526702] : [hBOOL(hAPP(hAPP(c_member(_1526520), _1526702), _1526522)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526520, _1526520)), hAPP(hAPP(c_Product__Type_OPair(_1526520, _1526520), _1526702), _1526702)), _1526524)))], (38850 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526520, _1526520), tc_HOL_Obool)), _1526524), hAPP(hAPP(c_Product__Type_OSigma(_1526520, _1526520), _1526522), hAPP(c_COMBK(tc_fun(_1526520, tc_HOL_Obool), _1526520), _1526522)))))]]], (49251 ^ _781215) ^ [_1776566, _1776568, _1776570, _1776572] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776566, _1776566)), hAPP(hAPP(c_Product__Type_OPair(_1776566, _1776566), _1776568), _1776570)), c_Transitive__Closure_Ortrancl(_1776566, _1776572))), -(_1776568 = _1776570), 49258 ^ _781215 : [(49261 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776566, _1776566)), hAPP(hAPP(c_Product__Type_OPair(_1776566, _1776566), _1776568), _1776570)), c_Transitive__Closure_Otrancl(_1776566, _1776572))))], (49259 ^ _781215) ^ [] : [_1776568 = _1776570]]], (48908 ^ _781215) ^ [_1768567, _1768569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1768567), _1768569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1768567)), hAPP(c_Code__Numeral_Oof__nat, _1768569))))], (41825 ^ _781215) ^ [_1605059, _1605061, _1605063, _1605065, _1605067] : [-(hBOOL(hAPP(hAPP(c_member(_1605059), _1605061), hAPP(c_List_Oset(_1605059), _1605063)))), -(hAPP(hAPP(c_Map_Omap__of(_1605059, _1605065), hAPP(hAPP(c_List_Ozip(_1605059, _1605065), _1605063), hAPP(hAPP(c_List_Omap(_1605059, _1605065), _1605067), _1605063))), _1605061) = c_Option_Ooption_ONone(_1605065))], (40998 ^ _781215) ^ [] : [-(c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))], (5296 ^ _781215) ^ [_862049, _862051, _862053, _862055] : [-(c_Lazy__Sequence_Ohb__single(_862055, _862051) = c_Lazy__Sequence_Ohb__single(_862053, _862049)), _862055 = _862053, _862051 = _862049], (27444 ^ _781215) ^ [_1280723, _1280725, _1280727] : [-(hAPP(c_Product__Type_Ofst(_1280723, _1280725), _1280727) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1280723, _1280725, _1280723), c_COMBK(_1280723, _1280725)), _1280727))], (3788 ^ _781215) ^ [_838609, _838611, _838613, _838615] : [-(c_List_OremoveAll(_838615, _838611) = c_List_OremoveAll(_838613, _838609)), _838615 = _838613, _838611 = _838609], (33386 ^ _781215) ^ [_1402542, _1402544, _1402546, _1402548, _1402550] : [class_Orderings_Olinorder(_1402542), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402542, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1402542, _1402544, _1402546)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1402542, _1402548, _1402550)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1402542, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1402542), _1402544), _1402548), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1402542), _1402546), _1402550)))], (17051 ^ _781215) ^ [_1086999, _1087001] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086999)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087001)))), 17054 ^ _781215 : [(17057 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1087001))], (17055 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086999), _1087001)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086999), _1087001))], (46538 ^ _781215) ^ [_1716968, _1716970, _1716972, _1716974, _1716976] : [hBOOL(hAPP(hAPP(c_member(_1716968), _1716970), hAPP(c_List_Oset(_1716968), _1716972))), -(hBOOL(hAPP(_1716974, _1716970))), -(c_List_OtakeWhile(_1716968, _1716974, hAPP(hAPP(c_List_Oappend(_1716968), _1716972), _1716976)) = c_List_OtakeWhile(_1716968, _1716974, _1716972))], (48892 ^ _781215) ^ [_1768292, _1768294] : [_1768292 = _1768294, -(hAPP(c_Code__Numeral_Oof__nat, _1768292) = hAPP(c_Code__Numeral_Oof__nat, _1768294))], (32266 ^ _781215) ^ [_1377425] : [-(c_Relation_OId__on(_1377425, c_Orderings_Obot__class_Obot(tc_fun(_1377425, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1377425, _1377425), tc_HOL_Obool)))], (5855 ^ _781215) ^ [_874354, _874356, _874358, _874360, _874362, _874364] : [c_Com_Ocom_OCall(_874354, _874356, _874358) = c_Com_Ocom_OCall(_874360, _874362, _874364), 5858 ^ _781215 : [(5863 ^ _781215) ^ [] : [-(_874358 = _874364)], (5861 ^ _781215) ^ [] : [-(_874356 = _874362)], (5859 ^ _781215) ^ [] : [-(_874354 = _874360)]]], (33158 ^ _781215) ^ [_1397234, _1397236, _1397238, _1397240] : [hBOOL(hAPP(hAPP(c_member(_1397234), _1397236), _1397238)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397234, tc_HOL_Obool)), _1397238), hAPP(hAPP(c_Set_Oinsert(_1397234), _1397236), _1397240)) = hAPP(hAPP(c_Set_Oinsert(_1397234), _1397236), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397234, tc_HOL_Obool)), _1397238), _1397240)))], (21938 ^ _781215) ^ [_1175872, _1175874, _1175876, _1175878, _1175880] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1175872, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175874, tc_fun(_1175872, tc_HOL_Obool)), _1175876), _1175878)), _1175880) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175874, tc_fun(_1175872, tc_HOL_Obool)), _1175876), hAPP(hAPP(c_COMBC(_1175874, tc_fun(_1175872, tc_HOL_Obool), tc_fun(_1175872, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1175872, tc_HOL_Obool), tc_fun(tc_fun(_1175872, tc_HOL_Obool), tc_fun(_1175872, tc_HOL_Obool)), _1175874), c_Groups_Ominus__class_Ominus(tc_fun(_1175872, tc_HOL_Obool))), _1175878)), _1175880)))], (37749 ^ _781215) ^ [_1498394, _1498396, _1498398, _1498400] : [c_Wellfounded_Omax__extp(_1498394, _1498396, _1498398, _1498400), 37752 ^ _781215 : [(37755 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1498394), _1498400)))], (37757 ^ _781215) ^ [] : [_1498400 = c_Orderings_Obot__class_Obot(tc_fun(_1498394, tc_HOL_Obool))], (37759 ^ _781215) ^ [_1498610] : [hBOOL(hAPP(hAPP(c_member(_1498394), _1498610), _1498398)), 37763 ^ _781215 : [(37766 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1498396, _1498610), 37762 ^ [_1498394, _1498396, _1498398, _1498400, _1498610])))], (37764 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1498394), 37762 ^ [_1498394, _1498396, _1498398, _1498400, _1498610]), _1498400)))]]], (37753 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1498394), _1498398)))]]], (14477 ^ _781215) ^ [_1034297, _1034299, _1034301, _1034303, _1034305] : [c_Finite__Set_Ofolding__one__idem(_1034297, _1034299, _1034301), hAPP(_1034303, hAPP(hAPP(_1034299, 14482 ^ [_1034297, _1034299, _1034301, _1034303, _1034305]), 14483 ^ [_1034297, _1034299, _1034301, _1034303, _1034305])) = hAPP(hAPP(_1034299, hAPP(_1034303, 14482 ^ [_1034297, _1034299, _1034301, _1034303, _1034305])), hAPP(_1034303, 14483 ^ [_1034297, _1034299, _1034301, _1034303, _1034305])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034297), _1034305)), -(_1034305 = c_Orderings_Obot__class_Obot(tc_fun(_1034297, tc_HOL_Obool))), -(hAPP(_1034303, hAPP(_1034301, _1034305)) = hAPP(_1034301, hAPP(c_Set_Oimage(_1034297, _1034297, _1034303), _1034305)))], (42185 ^ _781215) ^ [_1614458, _1614460, _1614462, _1614464, _1614466] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614458)), _1614460) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614462)), _1614464), 42188 ^ _781215 : [(42195 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614458), _1614466), hAPP(c_List_Oset(_1614458), _1614460)))), -(hAPP(hAPP(c_Map_Omap__of(_1614458, _1614462), hAPP(hAPP(c_List_Ozip(_1614458, _1614462), _1614460), _1614464)), _1614466) = c_Option_Ooption_ONone(_1614462))], (42189 ^ _781215) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1614458, _1614462), hAPP(hAPP(c_List_Ozip(_1614458, _1614462), _1614460), _1614464)), _1614466) = c_Option_Ooption_ONone(_1614462), hBOOL(hAPP(hAPP(c_member(_1614458), _1614466), hAPP(c_List_Oset(_1614458), _1614460)))]]], (41114 ^ _781215) ^ [_1588017, _1588019, _1588021, _1588023] : [-(hBOOL(hAPP(hAPP(c_member(_1588017), _1588023), hAPP(c_Set_Oimage(tc_prod(_1588017, _1588019), _1588017, c_Product__Type_Ofst(_1588017, _1588019)), hAPP(c_List_Oset(tc_prod(_1588017, _1588019)), _1588021))))), -(hAPP(hAPP(c_Map_Omap__of(_1588017, _1588019), _1588021), _1588023) = c_Option_Ooption_ONone(_1588019))], (39632 ^ _781215) ^ [_1551099, _1551101, _1551103, _1551105, _1551107, _1551109] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1551099), _1551101)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551103), _1551105)), 39642 ^ _781215 : [(39645 ^ _781215) ^ [] : [hAPP(c_Finite__Set_Ocard(_1551099), hAPP(c_Set_OCollect(_1551099), hAPP(hAPP(c_COMBS(_1551099, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551099), c_fconj), hAPP(hAPP(c_COMBC(_1551099, tc_fun(_1551099, tc_HOL_Obool), tc_HOL_Obool), c_member(_1551099)), _1551101))), hAPP(hAPP(c_COMBC(_1551099, _1551103, tc_HOL_Obool), _1551107), 39641 ^ [_1551099, _1551101, _1551103, _1551105, _1551107, _1551109])))) = hAPP(_1551109, 39641 ^ [_1551099, _1551101, _1551103, _1551105, _1551107, _1551109])], (39643 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1551103), 39641 ^ [_1551099, _1551101, _1551103, _1551105, _1551107, _1551109]), _1551105)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1551099, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1551103, tc_HOL_Obool), tc_Nat_Onat, _1551099), c_Finite__Set_Ocard(_1551103)), hAPP(hAPP(c_COMBB(tc_fun(_1551103, tc_HOL_Obool), tc_fun(_1551103, tc_HOL_Obool), _1551099), c_Set_OCollect(_1551103)), hAPP(hAPP(c_COMBB(tc_fun(_1551103, tc_HOL_Obool), tc_fun(_1551103, tc_HOL_Obool), _1551099), hAPP(c_COMBS(_1551103, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551103), c_fconj), hAPP(hAPP(c_COMBC(_1551103, tc_fun(_1551103, tc_HOL_Obool), tc_HOL_Obool), c_member(_1551103)), _1551105)))), _1551107)))), _1551101) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1551103, tc_Nat_Onat), _1551109), _1551105))], (3884 ^ _781215) ^ [_840113, _840115, _840117, _840119] : [-(c_List_Ozip(_840119, _840115) = c_List_Ozip(_840117, _840113)), _840119 = _840117, _840115 = _840113], (6303 ^ _781215) ^ [_883234, _883236] : [-(_883234 = c_Option_Ooption_ONone(_883236)), -(_883234 = hAPP(c_Option_Ooption_OSome(_883236), 6306 ^ [_883234, _883236]))], (35133 ^ _781215) ^ [_1440689, _1440691, _1440693, _1440695, _1440697] : [class_Groups_Ocomm__monoid__mult(_1440689), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440691), _1440693)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440691), _1440695)), 35147 ^ _781215 : [(35150 ^ _781215) ^ [] : [hAPP(_1440697, 35146 ^ [_1440689, _1440691, _1440693, _1440695, _1440697]) = c_Groups_Oone__class_Oone(_1440689)], (35148 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1440691), 35146 ^ [_1440689, _1440691, _1440693, _1440695, _1440697]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440691, tc_HOL_Obool)), _1440693), _1440695))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1440689, _1440691, c_Groups_Otimes__class_Otimes(_1440689)), _1440697), c_Groups_Oone__class_Oone(_1440689)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440691, tc_HOL_Obool)), _1440693), _1440695)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1440689), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1440689, _1440691, c_Groups_Otimes__class_Otimes(_1440689)), _1440697), c_Groups_Oone__class_Oone(_1440689)), _1440693)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1440689, _1440691, c_Groups_Otimes__class_Otimes(_1440689)), _1440697), c_Groups_Oone__class_Oone(_1440689)), _1440695)))], (36536 ^ _781215) ^ [] : [-(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)))], (1598 ^ _781215) ^ [_804160, _804162] : [-(class_Groups_Oab__semigroup__mult(_804160)), _804162 = _804160, class_Groups_Oab__semigroup__mult(_804162)], (5090 ^ _781215) ^ [_858772, _858774, _858776, _858778] : [-(c_New__DSequence_Opos__single(_858778, _858774) = c_New__DSequence_Opos__single(_858776, _858772)), _858778 = _858776, _858774 = _858772], (23002 ^ _781215) ^ [_1195946, _1195948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1195948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195946), _1195948)), _1195946)))], (46960 ^ _781215) ^ [_1725951, _1725953, _1725955, _1725957] : [class_Orderings_Olinorder(_1725951), 46963 ^ _781215 : [(46970 ^ _781215) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1725953), _1725957)), -(hBOOL(hAPP(c_List_Odistinct(_1725953), c_List_Olinorder__class_Osort__key(_1725953, _1725951, _1725955, _1725957))))], (46964 ^ _781215) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1725953), c_List_Olinorder__class_Osort__key(_1725953, _1725951, _1725955, _1725957))), -(hBOOL(hAPP(c_List_Odistinct(_1725953), _1725957)))]]], (46604 ^ _781215) ^ [_1718390, _1718392] : [class_Orderings_Olinorder(_1718390), c_List_Olinorder__class_Osorted(_1718390, _1718392), -(c_List_Olinorder__class_Osorted(_1718390, c_List_Oremdups(_1718390, _1718392)))], (35481 ^ _781215) ^ [_1448022, _1448024, _1448026] : [class_Orderings_Olinorder(_1448022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1448022), _1448024), _1448026)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448022, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1448022, _1448024, _1448026)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1448022), _1448026)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1448022), _1448024))], (15685 ^ _781215) ^ [_1057153, _1057155, _1057157, _1057159, _1057161] : [c_Finite__Set_Ofolding__one(_1057153, _1057155, _1057157), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057153), _1057159)), -(hBOOL(hAPP(hAPP(c_member(_1057153), _1057161), _1057159))), -(hAPP(_1057157, hAPP(hAPP(c_Set_Oinsert(_1057153), _1057161), _1057159)) = hAPP(hAPP(c_Finite__Set_Ofold(_1057153, _1057153, _1057155), _1057161), _1057159))], (26612 ^ _781215) ^ [_1264097, _1264099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264099)), -(c_Divides_OposDivAlg(_1264097, _1264099) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1264097), _1264099)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1264097, _1264099)))], (25622 ^ _781215) ^ [_1242293, _1242295, _1242297, _1242299] : [hBOOL(hAPP(hAPP(c_member(_1242293), _1242295), c_SetInterval_Oord_OatMost(_1242293, _1242297, _1242299))), -(hBOOL(hAPP(hAPP(_1242297, _1242295), _1242299)))], (49407 ^ _781215) ^ [_1780336, _1780338] : [-(hAPP(c_Relation_OImage(_1780336, _1780336, c_Relation_OId(_1780336)), _1780338) = _1780338)], (40518 ^ _781215) ^ [_1574634, _1574636, _1574638] : [hBOOL(hAPP(hAPP(c_member(_1574636), _1574634), c_Orderings_Obot__class_Obot(tc_fun(_1574636, tc_HOL_Obool)))), -(hBOOL(hAPP(_1574638, _1574634)))], (25330 ^ _781215) ^ [_1237794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237794), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1237794)), c_Int_OMin)))], (48154 ^ _781215) ^ [_1752326, _1752328, _1752330, _1752332, _1752334, _1752336] : [hBOOL(hAPP(hAPP(c_member(_1752326), _1752328), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1752330, _1752332, tc_fun(_1752326, tc_HOL_Obool)), _1752334), _1752336))), 48159 ^ _781215 : [(48162 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752326), _1752328), hAPP(hAPP(_1752334, 48157 ^ [_1752326, _1752328, _1752330, _1752332, _1752334, _1752336]), 48158 ^ [_1752326, _1752328, _1752330, _1752332, _1752334, _1752336]))))], (48160 ^ _781215) ^ [] : [-(_1752336 = hAPP(hAPP(c_Product__Type_OPair(_1752330, _1752332), 48157 ^ [_1752326, _1752328, _1752330, _1752332, _1752334, _1752336]), 48158 ^ [_1752326, _1752328, _1752330, _1752332, _1752334, _1752336]))]]], (13348 ^ _781215) ^ [_1013308, _1013310, _1013312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1013308)), 13351 ^ _781215 : [(13358 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013310), _1013312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013308), _1013310)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013308), _1013312))))], (13352 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013308), _1013310)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013308), _1013312))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013310), _1013312)))]]], (7670 ^ _781215) ^ [_910230, _910232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910230), _910232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _910230)), hAPP(c_Nat_OSuc, _910232))))], (47112 ^ _781215) ^ [_1728938, _1728940, _1728942] : [class_Enum_Oenum(_1728938), class_Enum_Oenum(_1728940), 47119 ^ _781215 : [(47126 ^ _781215) ^ [] : [c_Enum_Oall__n__lists(_1728938, hAPP(hAPP(c_COMBB(tc_fun(_1728940, _1728938), tc_HOL_Obool, tc_List_Olist(_1728938)), _1728942), hAPP(hAPP(c_COMBB(tc_fun(_1728940, tc_Option_Ooption(_1728938)), tc_fun(_1728940, _1728938), tc_List_Olist(_1728938)), c_Fun_Ocomp(tc_Option_Ooption(_1728938), _1728938, _1728940, c_Option_Othe(_1728938))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1728940, _1728938)), tc_fun(_1728940, tc_Option_Ooption(_1728938)), tc_List_Olist(_1728938)), c_Map_Omap__of(_1728940, _1728938)), hAPP(c_List_Ozip(_1728940, _1728938), c_Enum_Oenum__class_Oenum(_1728940))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728940)), c_Enum_Oenum__class_Oenum(_1728940))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1728940, _1728938)), _1728942)))], (47120 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1728940, _1728938)), _1728942)), -(c_Enum_Oall__n__lists(_1728938, hAPP(hAPP(c_COMBB(tc_fun(_1728940, _1728938), tc_HOL_Obool, tc_List_Olist(_1728938)), _1728942), hAPP(hAPP(c_COMBB(tc_fun(_1728940, tc_Option_Ooption(_1728938)), tc_fun(_1728940, _1728938), tc_List_Olist(_1728938)), c_Fun_Ocomp(tc_Option_Ooption(_1728938), _1728938, _1728940, c_Option_Othe(_1728938))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1728940, _1728938)), tc_fun(_1728940, tc_Option_Ooption(_1728938)), tc_List_Olist(_1728938)), c_Map_Omap__of(_1728940, _1728938)), hAPP(c_List_Ozip(_1728940, _1728938), c_Enum_Oenum__class_Oenum(_1728940))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728940)), c_Enum_Oenum__class_Oenum(_1728940))))]]], (112 ^ _781215) ^ [_783027, _783029, _783031, _783033, _783035, _783037] : [-(c_Big__Operators_Osemilattice__big(_783035, _783031, _783027)), c_Big__Operators_Osemilattice__big(_783037, _783033, _783029), _783037 = _783035, _783033 = _783031, _783029 = _783027], (10670 ^ _781215) ^ [_963876, _963878, _963880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963876), _963878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963876), _963880)), 10677 ^ _781215 : [(10684 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963878), _963880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963878), _963876)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963880), _963876))))], (10678 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963878), _963876)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963880), _963876))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963878), _963880)))]]], (42371 ^ _781215) ^ [_1620367, _1620369, _1620371, _1620373, _1620375, _1620377] : [-(c_List_Olistrelp(_1620367, _1620369, hAPP(hAPP(c_List_Olist_OCons(_1620367), _1620371), _1620373), hAPP(hAPP(c_List_Olist_OCons(_1620367), _1620375), _1620377))), hBOOL(hAPP(hAPP(_1620369, _1620371), _1620375)), c_List_Olistrelp(_1620367, _1620369, _1620373, _1620377)], (42058 ^ _781215) ^ [_1610944, _1610946] : [hBOOL(hAPP(c_List_Odistinct(_1610944), _1610946)), -(hAPP(c_Finite__Set_Ocard(_1610944), hAPP(c_List_Oset(_1610944), _1610946)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610944)), _1610946))], (22424 ^ _781215) ^ [_1186311, _1186313] : [-(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, _1186311, _1186313)), _1186313) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186311), _1186313))], (43922 ^ _781215) ^ [_1658601] : [-(c_List_Olists(_1658601, c_Orderings_Obot__class_Obot(tc_fun(_1658601, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1658601)), c_List_Olist_ONil(_1658601)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1658601), tc_HOL_Obool))))], (2502 ^ _781215) ^ [_818374, _818376, _818378, _818380] : [-(c_Divides_Odivmod__int(_818380, _818376) = c_Divides_Odivmod__int(_818378, _818374)), _818380 = _818378, _818376 = _818374], (37927 ^ _781215) ^ [_1502368] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502368, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1502368, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1502368, tc_HOL_Obool)))], (31152 ^ _781215) ^ [_1351569, _1351571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1351569), _1351571)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1351569), hAPP(c_Nat_OSuc, _1351571)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1351571), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1351569), _1351571)))], (51368 ^ _781215) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (47916 ^ _781215) ^ [_1746149, _1746151, _1746153] : [hBOOL(hAPP(c_List_Odistinct(_1746149), _1746151)), -(hBOOL(hAPP(c_List_Odistinct(_1746149), hAPP(c_List_OremoveAll(_1746149, _1746153), _1746151))))], (48023 ^ _781215) ^ [_1748491, _1748493, _1748495] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1748491, _1748491)), hAPP(hAPP(c_Product__Type_OPair(_1748491, _1748491), _1748493), _1748495)), c_List_Omeasures(_1748491, c_List_Olist_ONil(tc_fun(_1748491, tc_Nat_Onat)))))], (2108 ^ _781215) ^ [_812059, _812061] : [_812061 = _812059, -(c_Nat_Osemiring__1__class_ONats(_812061) = c_Nat_Osemiring__1__class_ONats(_812059))], (21920 ^ _781215) ^ [_1175405] : [class_Int_Onumber__ring(_1175405), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1175405), c_Groups_Oone__class_Oone(_1175405)), c_Groups_Oone__class_Oone(_1175405)) = hAPP(c_Int_Onumber__class_Onumber__of(_1175405), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (40395 ^ _781215) ^ [_1571307, _1571309, _1571311] : [c_Wellfounded_OwfP(_1571307, _1571309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1571307, tc_fun(_1571307, tc_HOL_Obool))), _1571311), _1571309)), -(c_Wellfounded_OwfP(_1571307, _1571311))], (23672 ^ _781215) ^ [_1208001, _1208003] : [class_Rings_Ocomm__semiring__1(_1208001), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1208001), _1208003), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1208003)], (48727 ^ _781215) ^ [_1765264, _1765266, _1765268, _1765270, _1765272] : [_1765264 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1765266, _1765268, _1765264, _1765270), _1765272) = hAPP(c_Product__Type_OPair(_1765266, _1765268), _1765272))], (13846 ^ _781215) ^ [_1022441, _1022443] : [13847 ^ _781215 : [(13850 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1022441), _1022443)))], (13848 ^ _781215) ^ [] : [_1022443 = c_Orderings_Obot__class_Obot(tc_fun(_1022441, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1022441), _1022443) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3032 ^ _781215) ^ [_826657, _826659, _826661, _826663, _826665, _826667, _826669, _826671, _826673, _826675, _826677, _826679] : [-(c_Product__Type_Omap__pair(_826679, _826675, _826671, _826667, _826663, _826659) = c_Product__Type_Omap__pair(_826677, _826673, _826669, _826665, _826661, _826657)), _826679 = _826677, _826675 = _826673, _826671 = _826669, _826667 = _826665, _826663 = _826661, _826659 = _826657], (30115 ^ _781215) ^ [_1331949, _1331951] : [hAPP(c_Set_OPow(_1331949), _1331951) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1331949, tc_HOL_Obool), tc_HOL_Obool))], (23224 ^ _781215) ^ [_1199442, _1199444, _1199446] : [hBOOL(hAPP(_1199442, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1199444), _1199446))), 23227 ^ _781215 : [(23252 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199446), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23255 ^ _781215 : [(23256 ^ _781215) ^ [_1200106] : [-(hBOOL(hAPP(_1199442, _1200106))), 23257 ^ _781215 : [(23258 ^ _781215) ^ [_1200180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199446), _1200180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1200180), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1199444 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1199446), _1200106)), _1200180)]]]]], (23234 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199446)), 23237 ^ _781215 : [(23238 ^ _781215) ^ [_1199776] : [-(hBOOL(hAPP(_1199442, _1199776))), 23239 ^ _781215 : [(23240 ^ _781215) ^ [_1199847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199847), _1199446)), _1199444 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1199446), _1199776)), _1199847)]]]]], (23228 ^ _781215) ^ [] : [_1199446 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1199442, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (35547 ^ _781215) ^ [_1449193, _1449195] : [class_Orderings_Olinorder(_1449193), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1449193, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1449193), _1449195)) = hAPP(c_SetInterval_Oord__class_OatMost(_1449193), _1449195))], (42627 ^ _781215) ^ [_1627430, _1627432, _1627434] : [-(hAPP(hAPP(c_List_Onth(_1627430), hAPP(hAPP(c_List_Olist_OCons(_1627430), _1627432), _1627434)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1627432)], (51194 ^ _781215) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (40839 ^ _781215) ^ [_1581550, _1581552] : [c_Com_Ocom_OWhile(_1581550, _1581552) = c_Com_Ocom_OSKIP], (44590 ^ _781215) ^ [_1674972, _1674974] : [hBOOL(hAPP(c_List_Odistinct(_1674972), _1674974)), -(hBOOL(hAPP(c_List_Odistinct(_1674972), hAPP(c_List_Orotate1(_1674972), _1674974))))], (876 ^ _781215) ^ [_794739, _794741, _794743, _794745, _794747, _794749] : [-(c_Relation_Ototal__on(_794747, _794743, _794739)), c_Relation_Ototal__on(_794749, _794745, _794741), _794749 = _794747, _794745 = _794743, _794741 = _794739], (44822 ^ _781215) ^ [_1680174, _1680176, _1680178] : [-(_1680174 = c_List_Olist_ONil(_1680176)), -(hAPP(c_List_Ohd(_1680176), hAPP(c_List_Orotate(_1680176, _1680178), _1680174)) = hAPP(hAPP(c_List_Onth(_1680176), _1680174), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1680178, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680176)), _1680174))))], (43318 ^ _781215) ^ [_1645073] : [43320 ^ _781215 : [(43323 ^ _781215) ^ [] : [43319 ^ [_1645073] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43321 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43319 ^ [_1645073]), hAPP(c_List_Oset(tc_Nat_Onat), _1645073))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1645073) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39046 ^ _781215) ^ [_1530939] : [class_Lattices_Osemilattice__sup(_1530939), -(c_Finite__Set_Ofun__left__comm__idem(_1530939, _1530939, c_Lattices_Osemilattice__sup__class_Osup(_1530939)))], (27446 ^ _781215) ^ [_1280769, _1280771, _1280773] : [-(hAPP(c_Product__Type_Osnd(_1280769, _1280771), _1280773) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1280769, _1280771, _1280771), hAPP(c_COMBK(tc_fun(_1280771, _1280771), _1280769), c_COMBI(_1280771))), _1280773))], (36265 ^ _781215) ^ [_1462964, _1462966, _1462968, _1462970, _1462972, _1462974] : [-(hAPP(c_Product__Type_Oapfst(_1462964, _1462966, _1462968, _1462970), hAPP(hAPP(c_Product__Type_OPair(_1462964, _1462968), _1462972), _1462974)) = hAPP(hAPP(c_Product__Type_OPair(_1462966, _1462968), hAPP(_1462970, _1462972)), _1462974))], (7165 ^ _781215) ^ [_901009, _901011, _901013, _901015] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _901009))), _901011), _901013), _901015)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _901009)), _901011), hAPP(c_Nat_OSuc, _901013)), _901015)))], (51022 ^ _781215) ^ [_1818595, _1818597, _1818599] : [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), _1818595), _1818597))), -(hBOOL(hAPP(hAPP(_1818599, _1818595), _1818597))), 51029 ^ _781215 : [(51032 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 51027 ^ [_1818595, _1818597, _1818599]), 51028 ^ [_1818595, _1818597, _1818599]))), -(hBOOL(hAPP(hAPP(_1818599, 51027 ^ [_1818595, _1818597, _1818599]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 51028 ^ [_1818595, _1818597, _1818599]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (51038 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1818599, 51027 ^ [_1818595, _1818597, _1818599]), 51028 ^ [_1818595, _1818597, _1818599]))], (51030 ^ _781215) ^ [] : [-(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), 51027 ^ [_1818595, _1818597, _1818599]), 51028 ^ [_1818595, _1818597, _1818599]))))]]], (20828 ^ _781215) ^ [_1154639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154639), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1154639)), c_Int_OPls)))], (22912 ^ _781215) ^ [_1194431, _1194433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194433), 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), _1194431), _1194433)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39590 ^ _781215) ^ [_1548853, _1548855, _1548857] : [class_Orderings_Olinorder(_1548853), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548853), _1548855)), -(_1548855 = c_Orderings_Obot__class_Obot(tc_fun(_1548853, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1548853), _1548857), c_Big__Operators_Olattice_OInf__fin(_1548853, c_Orderings_Oord__class_Omin(_1548853), _1548855)) = c_Big__Operators_Olattice_OInf__fin(_1548853, c_Orderings_Oord__class_Omin(_1548853), hAPP(c_Set_OCollect(_1548853), hAPP(hAPP(c_COMBB(tc_fun(_1548853, tc_HOL_Obool), tc_HOL_Obool, _1548853), c_HOL_OEx(_1548853)), hAPP(hAPP(c_COMBC(_1548853, tc_fun(_1548853, tc_HOL_Obool), tc_fun(_1548853, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548853, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1548853, tc_HOL_Obool), tc_fun(_1548853, tc_HOL_Obool)), _1548853), c_COMBS(_1548853, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548853, tc_HOL_Obool), tc_fun(_1548853, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1548853), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548853), c_fconj)), hAPP(hAPP(c_COMBC(_1548853, tc_fun(_1548853, _1548853), tc_fun(_1548853, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548853, tc_HOL_Obool), tc_fun(tc_fun(_1548853, _1548853), tc_fun(_1548853, tc_HOL_Obool)), _1548853), c_COMBB(_1548853, tc_HOL_Obool, _1548853)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1548853), _1548857))))), hAPP(hAPP(c_COMBC(_1548853, tc_fun(_1548853, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548853)), _1548855))))))], (43988 ^ _781215) ^ [_1660297, _1660299, _1660301] : [-(c_List_Olistset(_1660297, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1660297, tc_HOL_Obool)), _1660299), _1660301)) = c_List_Oset__Cons(_1660297, _1660299, c_List_Olistset(_1660297, _1660301)))], (46488 ^ _781215) ^ [_1716134, _1716136, _1716138, _1716140] : [hBOOL(hAPP(hAPP(c_member(_1716134), _1716136), hAPP(c_List_Oset(_1716134), c_List_OtakeWhile(_1716134, _1716138, _1716140)))), 46491 ^ _781215 : [(46494 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1716138, _1716136)))], (46492 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1716134), _1716136), hAPP(c_List_Oset(_1716134), _1716140))))]]], (22590 ^ _781215) ^ [_1189104, _1189106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189106, _1189104)), _1189104)))], (31890 ^ _781215) ^ [_1368710, _1368712, _1368714] : [class_Groups_Ocomm__monoid__add(_1368710), hAPP(_1368712, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1368710), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1368710), _1368712), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1368714)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1368710), _1368712), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1368714)))], (30105 ^ _781215) ^ [_1331706, _1331708, _1331710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331706, tc_HOL_Obool)), _1331708), _1331710)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1331706, tc_HOL_Obool)), _1331708), hAPP(c_Set_OPow(_1331706), _1331710))))], (40954 ^ _781215) ^ [_1584523, _1584525, _1584527] : [c_Fun_Oinj__on(_1584523, _1584525, _1584527, c_Orderings_Otop__class_Otop(tc_fun(_1584523, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1584523), tc_List_Olist(_1584525), hAPP(c_List_Omap(_1584523, _1584525), _1584527), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1584523), tc_HOL_Obool))))], (19072 ^ _781215) ^ [_1123141, _1123143, _1123145, _1123147] : [class_Orderings_Olinorder(_1123141), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1123141), _1123143), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123141), _1123145), _1123147)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123141), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1123141), _1123143), _1123145)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1123141), _1123143), _1123147)))], (12706 ^ _781215) ^ [_1002414, _1002416, _1002418, _1002420] : [class_Rings_Olinordered__ring__strict(_1002414), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002414), _1002416), c_Groups_Ozero__class_Ozero(_1002414))), 12713 ^ _781215 : [(12720 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002414), _1002420), _1002418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002414), _1002416), _1002418)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002414), _1002416), _1002420))))], (12714 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002414), _1002416), _1002418)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002414), _1002416), _1002420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002414), _1002420), _1002418)))]]], (7310 ^ _781215) ^ [_904792, _904794] : [class_Orderings_Opreorder(_904792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904792), _904794), _904794))], (8372 ^ _781215) ^ [_922470, _922472, _922474, _922476, _922478] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_922470, _922472, hAPP(hAPP(c_Set_Oinsert(_922470), _922474), _922476)), _922478)), 8377 ^ _781215 : [(8382 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_922470), 8375 ^ [_922470, _922472, _922474, _922476, _922478]), 8376 ^ [_922470, _922472, _922474, _922476, _922478]))], (8380 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922470, _922470, _922472, 8375 ^ [_922470, _922472, _922474, _922476, _922478], 8376 ^ [_922470, _922472, _922474, _922476, _922478]), _922478)))], (8378 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_922470), _922474), _922476) = hAPP(hAPP(c_Set_Oinsert(_922470), 8375 ^ [_922470, _922472, _922474, _922476, _922478]), 8376 ^ [_922470, _922472, _922474, _922476, _922478]))]]], (33691 ^ _781215) ^ [_1409365, _1409367, _1409369, _1409371, _1409373] : [class_Groups_Ocomm__monoid__mult(_1409365), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409367), _1409369)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409367), _1409371)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409367, tc_HOL_Obool)), _1409369), _1409371) = c_Orderings_Obot__class_Obot(tc_fun(_1409367, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409367, _1409365), _1409373), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409367, tc_HOL_Obool)), _1409369), _1409371)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409365), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409367, _1409365), _1409373), _1409369)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1409367, _1409365), _1409373), _1409371)))], (6187 ^ _781215) ^ [_880896, _880898] : [class_Finite__Set_Ofinite(_880896), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_880896), _880898)))], (4390 ^ _781215) ^ [_847806, _847808, _847810, _847812] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_847812, _847808) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_847810, _847806)), _847812 = _847810, _847808 = _847806], (30582 ^ _781215) ^ [_1340781, _1340783, _1340785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1340781, tc_HOL_Obool)), _1340783), _1340785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1340781, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1340781, _1340783)), c_Predicate_OPowp(_1340781, _1340785))))], (15456 ^ _781215) ^ [_1052253, _1052255, _1052257, _1052259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052253), _1052255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052257), _1052259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052253), _1052257)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052255), _1052259))))], (48646 ^ _781215) ^ [_1763593, _1763595, _1763597] : [c_List_Olist__ex(_1763593, _1763595, hAPP(c_List_Orev(_1763593), _1763597)), -(c_List_Olist__ex(_1763593, _1763595, _1763597))], (11588 ^ _781215) ^ [_983573, _983575, _983577, _983579] : [-(c_Nitpick_Ofold__graph_H(_983573, _983575, _983577, _983579, c_Orderings_Obot__class_Obot(tc_fun(_983573, tc_HOL_Obool)), _983579))], (42795 ^ _781215) ^ [_1631471, _1631473] : [-(hAPP(c_List_Oset(_1631471), _1631473) = hAPP(c_Set_OCollect(_1631471), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1631471), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1631471, 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)), _1631471), 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)), _1631471), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1631471, tc_fun(tc_Nat_Onat, _1631471), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1631471, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1631471), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1631471), c_COMBB(_1631471, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1631471), _1631473))))), 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(_1631471)), _1631473))))))], (25230 ^ _781215) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (31491 ^ _781215) ^ [_1359116] : [-(_1359116 = 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), 31488 ^ [_1359116]), 31489 ^ [_1359116])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (31656 ^ _781215) ^ [_1363515, _1363517, _1363519, _1363521, _1363523] : [class_Groups_Ocomm__monoid__add(_1363515), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363515), _1363517), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1363519), _1363521), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1363523), _1363521))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363515), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1363515, tc_Nat_Onat), _1363517), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1363521))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1363519, _1363523)))], (8031 ^ _781215) ^ [_916658, _916660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916658), _916660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _916658)), hAPP(c_Nat_OSuc, _916660))))], (35280 ^ _781215) ^ [_1443773, _1443775, _1443777, _1443779, _1443781] : [class_Groups_Ocomm__monoid__add(_1443773), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443775), _1443777)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443775, tc_HOL_Obool)), _1443779), _1443777)), 35294 ^ _781215 : [(35297 ^ _781215) ^ [] : [hAPP(_1443781, 35293 ^ [_1443773, _1443775, _1443777, _1443779, _1443781]) = c_Groups_Ozero__class_Ozero(_1443773)], (35295 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1443775), 35293 ^ [_1443773, _1443775, _1443777, _1443779, _1443781]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443775, tc_HOL_Obool)), _1443777), _1443779))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443775, _1443773), _1443781), _1443777) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443775, _1443773), _1443781), _1443779))], (36971 ^ _781215) ^ [_1479126, _1479128, _1479130, _1479132] : [-(_1479126 = c_Orderings_Obot__class_Obot(tc_fun(_1479128, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1479128, tc_fun(_1479130, tc_HOL_Obool)), _1479126), hAPP(c_COMBK(tc_fun(_1479130, tc_HOL_Obool), _1479128), _1479132)) = _1479132)], (46592 ^ _781215) ^ [_1718134, _1718136] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718134)), c_List_Oremdups(_1718134, _1718136))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718134)), _1718136))))], (21714 ^ _781215) ^ [_1170694] : [-(c_Int_Osucc(c_Int_OBit1(_1170694)) = c_Int_OBit0(c_Int_Osucc(_1170694)))], (51260 ^ _781215) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (48344 ^ _781215) ^ [_1757045, _1757047, _1757049] : [-(hBOOL(hAPP(hAPP(c_member(_1757045), _1757047), c_Wellfounded_Oacc(_1757045, _1757049)))), 48348 ^ _781215 : [(48351 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1757045), 48347 ^ [_1757045, _1757047, _1757049]), c_Wellfounded_Oacc(_1757045, _1757049)))], (48349 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757045, _1757045)), hAPP(hAPP(c_Product__Type_OPair(_1757045, _1757045), 48347 ^ [_1757045, _1757047, _1757049]), _1757047)), _1757049)))]]], (46413 ^ _781215) ^ [_1714114, _1714116] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714114), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1714114))), _1714116))), 46416 ^ _781215 : [(46423 ^ _781215) ^ [] : [-(_1714116 = c_List_Olist_ONil(tc_List_Olist(_1714114))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714114))), c_List_Otranspose(_1714114, _1714116)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714114)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714114)), _1714116), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46417 ^ _781215) ^ [] : [_1714116 = c_List_Olist_ONil(tc_List_Olist(_1714114)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714114))), c_List_Otranspose(_1714114, _1714116)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (35909 ^ _781215) ^ [_1456396, _1456398, _1456400] : [class_Groups_Oordered__ab__group__add__abs(_1456396), 35912 ^ _781215 : [(35921 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456396), hAPP(c_Groups_Oabs__class_Oabs(_1456396), _1456398)), _1456400))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456396), _1456398), _1456400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456396), hAPP(c_Groups_Ouminus__class_Ouminus(_1456396), _1456398)), _1456400))], (35913 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456396), hAPP(c_Groups_Oabs__class_Oabs(_1456396), _1456398)), _1456400)), 35916 ^ _781215 : [(35919 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456396), hAPP(c_Groups_Ouminus__class_Ouminus(_1456396), _1456398)), _1456400)))], (35917 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456396), _1456398), _1456400)))]]]]], (3972 ^ _781215) ^ [_841465, _841467, _841469, _841471, _841473, _841475] : [-(c_List_OtakeWhile(_841475, _841471, _841467) = c_List_OtakeWhile(_841473, _841469, _841465)), _841475 = _841473, _841471 = _841469, _841467 = _841465], (8992 ^ _781215) ^ [_933769, _933771, _933773] : [class_Orderings_Olinorder(_933769), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933769), _933771), _933773))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933769), _933773), _933771)))], (41170 ^ _781215) ^ [_1589384, _1589386, _1589388, _1589390, _1589392] : [hBOOL(hAPP(c_List_Odistinct(_1589384), hAPP(hAPP(c_List_Omap(tc_prod(_1589384, _1589386), _1589384), c_Product__Type_Ofst(_1589384, _1589386)), _1589388))), 41173 ^ _781215 : [(41180 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589384, _1589386)), hAPP(hAPP(c_Product__Type_OPair(_1589384, _1589386), _1589392), _1589390)), hAPP(c_List_Oset(tc_prod(_1589384, _1589386)), _1589388))), -(hAPP(c_Option_Ooption_OSome(_1589386), _1589390) = hAPP(hAPP(c_Map_Omap__of(_1589384, _1589386), _1589388), _1589392))], (41174 ^ _781215) ^ [] : [hAPP(c_Option_Ooption_OSome(_1589386), _1589390) = hAPP(hAPP(c_Map_Omap__of(_1589384, _1589386), _1589388), _1589392), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589384, _1589386)), hAPP(hAPP(c_Product__Type_OPair(_1589384, _1589386), _1589392), _1589390)), hAPP(c_List_Oset(tc_prod(_1589384, _1589386)), _1589388))))]]], (31212 ^ _781215) ^ [_1352724, _1352726, _1352728, _1352730] : [class_Orderings_Olinorder(_1352724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1352724), _1352726), _1352728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352724), _1352728), _1352730)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352724, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1352724, _1352726, _1352728)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1352724, _1352728, _1352730)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1352724, _1352726), _1352730))], (20533 ^ _781215) ^ [_1149747, _1149749] : [class_Rings_Olinordered__semidom(_1149747), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149747), c_Groups_Ozero__class_Ozero(_1149747)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1149747), _1149749))))], (47972 ^ _781215) ^ [_1747202, _1747204, _1747206] : [-(hBOOL(hAPP(hAPP(c_member(_1747202), _1747204), hAPP(c_List_Oset(_1747202), _1747206)))), -(c_List_Oinsert(_1747202, _1747204, _1747206) = hAPP(hAPP(c_List_Olist_OCons(_1747202), _1747204), _1747206))], (20422 ^ _781215) ^ [_1147689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147689)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9433 ^ _781215) ^ [_941932, _941934, _941936] : [class_Orderings_Oorder(_941932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941932), _941934), _941936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941932), _941934), _941936))), -(_941934 = _941936)], (6820 ^ _781215) ^ [_893445, _893447, _893449, _893451] : [-(hAPP(_893451, _893447) = c_Option_Ooption_ONone(_893449)), -(hBOOL(hAPP(hAPP(c_member(_893445), _893447), c_Map_Odom(_893445, _893449, _893451))))], (18409 ^ _781215) ^ [_1110778, _1110780] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1110778)), _1110780) = 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), _1110778)), _1110780))], (15859 ^ _781215) ^ [_1060234, _1060236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1060234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1060236)), -(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), _1060234), _1060236))))], (22202 ^ _781215) ^ [_1181658, _1181660] : [-(_1181658 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181660), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181658), _1181660))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181658, _1181660)))], (32866 ^ _781215) ^ [_1390492, _1390494, _1390496] : [class_Lattices_Olattice(_1390492), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1390492), _1390494), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1390492), _1390494), _1390496)) = _1390494)], (43712 ^ _781215) ^ [_1654279, _1654281, _1654283, _1654285] : [-(c_Map_Omap__upds(_1654279, _1654281, _1654283, c_List_Olist_ONil(_1654279), _1654285) = _1654283)], (33116 ^ _781215) ^ [_1396266, _1396268, _1396270, _1396272] : [class_Lattices_Olattice(_1396266), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396266), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1396266), _1396268), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1396266), _1396270), _1396272))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1396266), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1396266), _1396268), _1396270)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1396266), _1396268), _1396272)))))], (23811 ^ _781215) ^ [_1210415, _1210417, _1210419] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1210415), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1210417), _1210419)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1210415), _1210417)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1210415), _1210419)))], (33222 ^ _781215) ^ [_1398702, _1398704, _1398706, _1398708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398702, tc_HOL_Obool)), _1398708), _1398704)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398702, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398702, tc_HOL_Obool)), _1398704), _1398706)), _1398708) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398702, tc_HOL_Obool)), _1398704), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398702, tc_HOL_Obool)), _1398706), _1398708)))], (44152 ^ _781215) ^ [_1663987, _1663989, _1663991] : [-(hAPP(hAPP(c_List_Oappend(_1663987), _1663989), _1663991) = c_List_Olist_ONil(_1663987)), _1663989 = c_List_Olist_ONil(_1663987), _1663991 = c_List_Olist_ONil(_1663987)], (33332 ^ _781215) ^ [_1401283, _1401285, _1401287, _1401289, _1401291] : [class_Orderings_Olinorder(_1401283), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401283, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1401283, _1401285, _1401287)), c_SetInterval_Oord__class_OatLeastAtMost(_1401283, _1401289, _1401291)) = c_SetInterval_Oord__class_OatLeastAtMost(_1401283, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1401283), _1401285), _1401289), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1401283), _1401287), _1401291)))], (51484 ^ _781215) ^ [_1823623, _1823625] : [-(class_Enum_Oenum(tc_sum(_1823623, _1823625))), class_Enum_Oenum(_1823623), class_Enum_Oenum(_1823625)], (22697 ^ _781215) ^ [_1190791, _1190793, _1190795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190791)), 22700 ^ _781215 : [(22701 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1190793, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1190795), _1190791)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190795, _1190791))), 22704 ^ _781215 : [(22705 ^ _781215) ^ [_1190992, _1190994] : [-(hBOOL(hAPP(hAPP(_1190793, _1190994), _1190992))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190992)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190992), _1190791)), _1190795 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1190791), _1190994)), _1190992)]]], (22719 ^ _781215) ^ [] : [22722 ^ _781215 : [(22725 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 22721 ^ [_1190791, _1190793, _1190795]), _1190791)))], (22727 ^ _781215) ^ [] : [-(_1190795 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1190791), 22720 ^ [_1190791, _1190793, _1190795])), 22721 ^ [_1190791, _1190793, _1190795]))], (22729 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1190793, 22720 ^ [_1190791, _1190793, _1190795]), 22721 ^ [_1190791, _1190793, _1190795]))], (22723 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22721 ^ [_1190791, _1190793, _1190795])))]], -(hBOOL(hAPP(hAPP(_1190793, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1190795), _1190791)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190795, _1190791))))]]], (40698 ^ _781215) ^ [_1578850, _1578852, _1578854, _1578856, _1578858] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1578850, _1578852)), _1578854), _1578856), _1578858)), 40703 ^ _781215 : [(40706 ^ _781215) ^ [] : [hBOOL(hAPP(_1578850, _1578854))], (40704 ^ _781215) ^ [] : [-(_1578858 = _1578854)]], 40707 ^ _781215 : [(40713 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1578850, _1578852)), 40709 ^ [_1578850, _1578852, _1578854, _1578856, _1578858]), _1578856), _1578858)))], (40711 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1578852), _1578854), _1578856), 40709 ^ [_1578850, _1578852, _1578854, _1578856, _1578858])))], (40708 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1578850, _1578854)))]]], (49028 ^ _781215) ^ [_1770635, _1770637] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1770635), _1770637) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1770635)), hAPP(c_Code__Numeral_Onat__of, _1770637))))], (20729 ^ _781215) ^ [_1153069] : [_1153069 = 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), _1153069)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (46262 ^ _781215) ^ [_1709722, _1709724] : [46264 ^ _781215 : [(46267 ^ _781215) ^ [] : [46263 ^ [_1709722, _1709724] = c_List_Olist_ONil(_1709722)], (46265 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709722)), 46263 ^ [_1709722, _1709724]), hAPP(c_List_Oset(tc_List_Olist(_1709722)), _1709724))))]], -(c_List_Olist_ONil(_1709722) = c_List_Oconcat(_1709722, _1709724))], (43778 ^ _781215) ^ [_1655495, _1655497] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655495)), _1655497) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1655497 = c_List_Olist_ONil(_1655495))], (51410 ^ _781215) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (51372 ^ _781215) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (642 ^ _781215) ^ [_791178, _791180] : [-(c_List_Onat__list(_791178)), _791180 = _791178, c_List_Onat__list(_791180)], (25212 ^ _781215) ^ [_1236158] : [_1236158 = c_Int_OMin, -(c_Int_OBit1(_1236158) = c_Int_OMin)], (20705 ^ _781215) ^ [_1152623, _1152625] : [class_Int_Onumber__ring(_1152623), -(hAPP(c_Int_Onumber__class_Onumber__of(_1152623), c_Int_OBit1(_1152625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152623), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152623), c_Groups_Oone__class_Oone(_1152623)), hAPP(c_Int_Onumber__class_Onumber__of(_1152623), _1152625))), hAPP(c_Int_Onumber__class_Onumber__of(_1152623), _1152625)))], (15362 ^ _781215) ^ [_1050540, _1050542] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1050540)), _1050542) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050540), _1050542)))], (7189 ^ _781215) ^ [_901636, _901638, _901640, _901642] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _901636)), _901638), _901640), _901642)), 7193 ^ _781215 : [(7196 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _901636))), _901638), 7192 ^ [_901636, _901638, _901640, _901642]), _901642)))], (7194 ^ _781215) ^ [] : [-(_901640 = hAPP(c_Nat_OSuc, 7192 ^ [_901636, _901638, _901640, _901642]))]]], (38282 ^ _781215) ^ [_1510747, _1510749, _1510751, _1510753, _1510755] : [hBOOL(hAPP(hAPP(c_member(_1510747), _1510749), hAPP(c_Set_Ovimage(_1510747, _1510751, _1510753), _1510755))), -(hBOOL(hAPP(hAPP(c_member(_1510751), hAPP(_1510753, _1510749)), _1510755)))], (49221 ^ _781215) ^ [_1775753, _1775755, _1775757, _1775759, _1775761] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775753, _1775753)), hAPP(hAPP(c_Product__Type_OPair(_1775753, _1775753), _1775755), _1775757)), c_Transitive__Closure_Ortrancl(_1775753, _1775759))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775753, _1775753)), hAPP(hAPP(c_Product__Type_OPair(_1775753, _1775753), _1775757), _1775761)), c_Transitive__Closure_Otrancl(_1775753, _1775759))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775753, _1775753)), hAPP(hAPP(c_Product__Type_OPair(_1775753, _1775753), _1775755), _1775761)), c_Transitive__Closure_Otrancl(_1775753, _1775759))))], (21347 ^ _781215) ^ [_1164051, _1164053] : [_1164051 = _1164053, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1164051) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1164053))], (44778 ^ _781215) ^ [_1679674, _1679676, _1679678] : [-(hAPP(c_List_Ohd(_1679674), hAPP(hAPP(c_List_Olist_OCons(_1679674), _1679676), _1679678)) = _1679676)], (6487 ^ _781215) ^ [_886922, _886924, _886926, _886928] : [hBOOL(hAPP(hAPP(c_member(_886922), _886924), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886922, tc_HOL_Obool)), _886926), _886928))), hBOOL(hAPP(hAPP(c_member(_886922), _886924), _886928))], (25394 ^ _781215) ^ [_1238735] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1238735), c_Int_OMin) = c_Int_Opred(_1238735))], (9873 ^ _781215) ^ [_949060, _949062, _949064, _949066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949060, tc_HOL_Obool)), _949062), _949064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949060, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_949060), _949066), _949062)), hAPP(hAPP(c_Set_Oinsert(_949060), _949066), _949064))))], (36015 ^ _781215) ^ [_1458417, _1458419] : [class_Rings_Olinordered__idom(_1458417), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1458417), c_Groups_Osgn__class_Osgn(_1458417, _1458419)), hAPP(c_Groups_Oabs__class_Oabs(_1458417), _1458419)) = _1458419)], (39014 ^ _781215) ^ [_1530153, _1530155, _1530157] : [39015 ^ _781215 : [(39018 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530153), hAPP(c_Set_OCollect(_1530153), _1530157)))], (39016 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530153), hAPP(c_Set_OCollect(_1530153), _1530155)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1530153), hAPP(c_Set_OCollect(_1530153), hAPP(hAPP(c_COMBS(_1530153, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1530153), c_fconj), _1530155)), _1530157)))))], (6624 ^ _781215) ^ [_889637, _889639] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889637, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_889637, tc_HOL_Obool))), _889639) = c_Orderings_Obot__class_Obot(tc_fun(_889637, tc_HOL_Obool)))], (16367 ^ _781215) ^ [_1070510, _1070512, _1070514] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1070510, tc_HOL_Obool)), _1070512), _1070514) = c_Orderings_Obot__class_Obot(tc_fun(_1070510, tc_HOL_Obool)), 16370 ^ _781215 : [(16373 ^ _781215) ^ [] : [-(_1070514 = c_Orderings_Obot__class_Obot(tc_fun(_1070510, tc_HOL_Obool)))], (16371 ^ _781215) ^ [] : [-(_1070512 = c_Orderings_Obot__class_Obot(tc_fun(_1070510, tc_HOL_Obool)))]]], (25252 ^ _781215) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33140 ^ _781215) ^ [_1396822, _1396824, _1396826] : [class_Lattices_Oboolean__algebra(_1396822), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1396822), _1396824), _1396826) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1396822), _1396824), hAPP(c_Groups_Ouminus__class_Ouminus(_1396822), _1396826)))], (24172 ^ _781215) ^ [_1217217] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1217217), _1217217)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1217217)], (6383 ^ _781215) ^ [_885011, _885013, _885015] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_885011), _885013)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_885011), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_885011, tc_HOL_Obool)), _885013), _885015))))], (10960 ^ _781215) ^ [_969859, _969861, _969863, _969865] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969859, tc_HOL_Obool)), _969861), hAPP(hAPP(c_Set_Oinsert(_969859), _969863), _969865)))), 10963 ^ _781215 : [(10966 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969859, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969859, tc_HOL_Obool)), _969861), hAPP(hAPP(c_Set_Oinsert(_969859), _969863), c_Orderings_Obot__class_Obot(tc_fun(_969859, tc_HOL_Obool))))), _969865))], (10964 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_969859), _969863), _969861)))]], 10967 ^ _781215 : [(10970 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969859, tc_HOL_Obool)), _969861), _969865))], (10968 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_969859), _969863), _969861))]]], (2964 ^ _781215) ^ [_825611, _825613, _825615, _825617, _825619, _825621] : [-(c_Set_Ovimage(_825621, _825617, _825613) = c_Set_Ovimage(_825619, _825615, _825611)), _825621 = _825619, _825617 = _825615, _825613 = _825611], (47287 ^ _781215) ^ [_1732354, _1732356] : [class_Enum_Oenum(_1732354), 47290 ^ _781215 : [(47298 ^ _781215) ^ [] : [47299 ^ _781215 : [(47300 ^ _781215) ^ [_1732534] : [hBOOL(hAPP(_1732356, _1732534))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732354), _1732356)))], (47291 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732354), _1732356)), -(hBOOL(hAPP(_1732356, 47294 ^ [_1732354, _1732356])))]]], (46293 ^ _781215) ^ [_1710524, _1710526] : [-(_1710524 = c_List_Olist_ONil(_1710526)), -(hAPP(c_List_Ohd(_1710526), hAPP(c_List_Orev(_1710526), _1710524)) = c_List_Olast(_1710526, _1710524))], (1158 ^ _781215) ^ [_798660, _798662] : [-(class_Rings_Olinordered__ring(_798660)), _798662 = _798660, class_Rings_Olinordered__ring(_798662)], (29860 ^ _781215) ^ [_1325679, _1325681, _1325683, _1325685] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1325679), _1325681)), 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)), _1325683), _1325679)), 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)), _1325685), _1325681)), 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)), _1325683), _1325685)), _1325681)), c_FunDef_Omax__strict)))], (31541 ^ _781215) ^ [_1360757, _1360759, _1360761, _1360763, _1360765, _1360767, _1360769] : [class_Rings_Osemiring__0(_1360757), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360757), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360759, _1360757), _1360761), _1360763)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360765, _1360757), _1360767), _1360769)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360759, _1360757), hAPP(hAPP(c_COMBC(_1360759, tc_fun(_1360765, tc_HOL_Obool), _1360757), hAPP(hAPP(c_COMBB(tc_fun(_1360765, _1360757), tc_fun(tc_fun(_1360765, tc_HOL_Obool), _1360757), _1360759), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360765, _1360757)), hAPP(hAPP(c_COMBC(_1360759, tc_fun(_1360765, _1360757), tc_fun(_1360765, _1360757)), hAPP(hAPP(c_COMBB(tc_fun(_1360757, _1360757), tc_fun(tc_fun(_1360765, _1360757), tc_fun(_1360765, _1360757)), _1360759), c_COMBB(_1360757, _1360757, _1360765)), hAPP(hAPP(c_COMBB(_1360757, tc_fun(_1360757, _1360757), _1360759), c_Groups_Otimes__class_Otimes(_1360757)), _1360761))), _1360767))), _1360769)), _1360763))], (35463 ^ _781215) ^ [_1447660, _1447662] : [class_Groups_Oordered__ab__group__add(_1447660), -(hAPP(c_Set_Oimage(_1447660, _1447660, c_Groups_Ouminus__class_Ouminus(_1447660)), hAPP(c_SetInterval_Oord__class_OatLeast(_1447660), _1447662)) = hAPP(c_SetInterval_Oord__class_OatMost(_1447660), hAPP(c_Groups_Ouminus__class_Ouminus(_1447660), _1447662)))], (10934 ^ _781215) ^ [_969251, _969253, _969255, _969257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969251, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969251, tc_HOL_Obool)), _969253), hAPP(hAPP(c_Set_Oinsert(_969251), _969255), c_Orderings_Obot__class_Obot(tc_fun(_969251, tc_HOL_Obool))))), _969257)), hBOOL(hAPP(hAPP(c_member(_969251), _969255), _969253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969251, tc_HOL_Obool)), _969253), hAPP(hAPP(c_Set_Oinsert(_969251), _969255), _969257))))], (37949 ^ _781215) ^ [_1502840, _1502842] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1502840, tc_HOL_Obool), tc_HOL_Obool)), _1502842), hAPP(c_Set_OPow(_1502840), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1502840, tc_HOL_Obool), _1502842)))))], (47707 ^ _781215) ^ [_1741720, _1741722, _1741724, _1741726] : [c_List_Olist__all2(_1741720, _1741722, _1741724, c_List_Olist_ONil(_1741720), _1741726), -(_1741726 = c_List_Olist_ONil(_1741722))], (38177 ^ _781215) ^ [_1508250, _1508252, _1508254, _1508256, _1508258] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1508250, _1508252, _1508254), _1508256), _1508258) = c_HOL_OThe(_1508252, c_Finite__Set_Ofold__graph(_1508250, _1508252, _1508254, _1508256, _1508258)))], (9467 ^ _781215) ^ [_942360, _942362, _942364] : [class_Orderings_Opreorder(_942360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942360), _942362), _942364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942360), _942362), _942364)))], (5560 ^ _781215) ^ [_866085, _866087, _866089, _866091] : [-(tc_fun(_866091, _866087) = tc_fun(_866089, _866085)), _866091 = _866089, _866087 = _866085], (45373 ^ _781215) ^ [_1691645, _1691647, _1691649, _1691651] : [-(c_List_Omap__filter(_1691645, _1691647, _1691649, _1691651) = hAPP(hAPP(c_List_Omap(_1691645, _1691647), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1691647), _1691647, _1691645, c_Option_Othe(_1691647)), _1691649)), hAPP(c_List_Ofilter(_1691645, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1691645), c_fNot), hAPP(hAPP(c_COMBC(_1691645, tc_Option_Ooption(_1691647), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1691647), tc_fun(tc_Option_Ooption(_1691647), tc_HOL_Obool), _1691645), c_fequal), _1691649)), c_Option_Ooption_ONone(_1691647)))), _1691651)))], (17257 ^ _781215) ^ [_1090340, _1090342, _1090344] : [class_Lattices_Olattice(_1090340), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090340), _1090342)), -(_1090342 = c_Orderings_Obot__class_Obot(tc_fun(_1090340, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090340), _1090344)), -(_1090344 = c_Orderings_Obot__class_Obot(tc_fun(_1090340, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1090340, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1090340, tc_HOL_Obool)), _1090342), _1090344)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1090340), c_Big__Operators_Olattice__class_OSup__fin(_1090340, _1090342)), c_Big__Operators_Olattice__class_OSup__fin(_1090340, _1090344)))], (22484 ^ _781215) ^ [_1187440, _1187442] : [-(_1187440 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22487 ^ _781215 : [(22494 ^ _781215) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187442, _1187440) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1187442), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187440)) = 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), _1187442), _1187440))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22488 ^ _781215) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187442, _1187440) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1187442), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1187440)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1187442), _1187440)))]]], (26398 ^ _781215) ^ [_1260196, _1260198] : [class_Rings_Olinordered__idom(_1260196), 26401 ^ _781215 : [(26408 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1260198), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260196), hAPP(c_Int_Oring__1__class_Oof__int(_1260196), _1260198)), c_Groups_Ozero__class_Ozero(_1260196))))], (26402 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260196), hAPP(c_Int_Oring__1__class_Oof__int(_1260196), _1260198)), c_Groups_Ozero__class_Ozero(_1260196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1260198), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (43784 ^ _781215) ^ [_1655586, _1655588] : [_1655588 = c_List_Olist_ONil(_1655586), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655586)), _1655588) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33579 ^ _781215) ^ [_1407045, _1407047, _1407049, _1407051, _1407053] : [c_Equiv__Relations_Oequiv(_1407045, _1407047, _1407049), hBOOL(hAPP(hAPP(c_member(tc_fun(_1407045, tc_HOL_Obool)), _1407051), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1407045), _1407047), _1407049))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1407045, tc_HOL_Obool)), _1407053), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1407045), _1407047), _1407049))), -(_1407051 = _1407053), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407045, tc_HOL_Obool)), _1407051), _1407053) = c_Orderings_Obot__class_Obot(tc_fun(_1407045, tc_HOL_Obool)))], (45159 ^ _781215) ^ [_1687290, _1687292, _1687294] : [_1687290 = c_List_Olist_ONil(_1687292), -(c_List_Olast(_1687292, hAPP(hAPP(c_List_Olist_OCons(_1687292), _1687294), _1687290)) = _1687294)], (17505 ^ _781215) ^ [] : [-(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))))], (30207 ^ _781215) ^ [_1333872, _1333874, _1333876] : [class_Orderings_Oorder(_1333872), 30210 ^ _781215 : [(30217 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333872), _1333874), _1333876))), -(c_Orderings_Obot__class_Obot(tc_fun(_1333872, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1333872, _1333874, _1333876))], (30211 ^ _781215) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1333872, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1333872, _1333874, _1333876), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333872), _1333874), _1333876))]]], (25470 ^ _781215) ^ [_1239916] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1239916)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1239916)))], (33881 ^ _781215) ^ [_1413088, _1413090, _1413092] : [class_Orderings_Olinorder(_1413088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413088), _1413090)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413088), _1413092)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413088, tc_HOL_Obool)), _1413090), _1413092) = c_Orderings_Obot__class_Obot(tc_fun(_1413088, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1413088), c_Big__Operators_Olinorder__class_OMax(_1413088, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413088, tc_HOL_Obool)), _1413090), _1413092))), c_Big__Operators_Olinorder__class_OMax(_1413088, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1413088, tc_HOL_Obool)), _1413090), _1413092))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1413088), c_Big__Operators_Olinorder__class_OMax(_1413088, _1413090)), c_Big__Operators_Olinorder__class_OMax(_1413088, _1413092)))], (5629 ^ _781215) ^ [_869948, _869950] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _869948) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _869950), -(hBOOL(hAPP(c_Com_OWT, _869950)))], (25652 ^ _781215) ^ [_1242892, _1242894, _1242896, _1242898] : [hBOOL(hAPP(hAPP(_1242896, _1242894), _1242898)), -(hBOOL(hAPP(hAPP(c_member(_1242892), _1242894), c_SetInterval_Oord_OlessThan(_1242892, _1242896, _1242898))))], (15304 ^ _781215) ^ [_1049692] : [-(c_Int_Osucc(_1049692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049692), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31312 ^ _781215) ^ [_1354775] : [-(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)), _1354775))))], (25542 ^ _781215) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (3214 ^ _781215) ^ [_829626, _829628, _829630, _829632] : [-(c_List_Olistset(_829632, _829628) = c_List_Olistset(_829630, _829626)), _829632 = _829630, _829628 = _829626], (18788 ^ _781215) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (7133 ^ _781215) ^ [_900391, _900393, _900395] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_900391), _900393)), -(hBOOL(hAPP(hAPP(c_member(_900391), _900395), _900393))), -(hAPP(c_Finite__Set_Ocard(_900391), hAPP(hAPP(c_Set_Oinsert(_900391), _900395), _900393)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_900391), _900393)))], (7074 ^ _781215) ^ [_898981, _898983, _898985, _898987, _898989] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_898981, _898983, _898985, _898987, c_Orderings_Obot__class_Obot(tc_fun(_898981, tc_HOL_Obool))), _898989)), -(_898989 = _898987)], (17985 ^ _781215) ^ [_1102274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1102274)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1102274)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1102274)))], (43668 ^ _781215) ^ [_1653481, _1653483, _1653485] : [hAPP(hAPP(c_List_Olist_OCons(_1653481), _1653483), _1653485) = c_List_Olist_ONil(_1653481)], (20982 ^ _781215) ^ [_1157091, _1157093] : [-(hBOOL(hAPP(_1157091, hAPP(c_Int_Onat, _1157093)))), 20986 ^ _781215 : [(20989 ^ _781215) ^ [] : [hBOOL(hAPP(_1157091, 20985 ^ [_1157091, _1157093]))], (20987 ^ _781215) ^ [] : [-(_1157093 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20985 ^ [_1157091, _1157093]))]], 20990 ^ _781215 : [(20993 ^ _781215) ^ [] : [hBOOL(hAPP(_1157091, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20991 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157093), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (28290 ^ _781215) ^ [_1296360, _1296362, _1296364, _1296366] : [class_Fields_Olinordered__field__inverse__zero(_1296360), class_Int_Onumber(_1296360), 28297 ^ _781215 : [(28298 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), hAPP(c_Int_Onumber__class_Onumber__of(_1296360), _1296362)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296360), _1296364), _1296366))), 28301 ^ _781215 : [(28308 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), c_Groups_Ozero__class_Ozero(_1296360)), _1296366))), 28311 ^ _781215 : [(28318 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), _1296366), c_Groups_Ozero__class_Ozero(_1296360)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), hAPP(c_Int_Onumber__class_Onumber__of(_1296360), _1296362)), c_Groups_Ozero__class_Ozero(_1296360))))], (28312 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), _1296366), c_Groups_Ozero__class_Ozero(_1296360))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), _1296364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296360), hAPP(c_Int_Onumber__class_Onumber__of(_1296360), _1296362)), _1296366))))]]], (28302 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), c_Groups_Ozero__class_Ozero(_1296360)), _1296366)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296360), hAPP(c_Int_Onumber__class_Onumber__of(_1296360), _1296362)), _1296366)), _1296364)))]]], (28324 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), hAPP(c_Int_Onumber__class_Onumber__of(_1296360), _1296362)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296360), _1296364), _1296366)))), 28327 ^ _781215 : [(28330 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296360), hAPP(c_Int_Onumber__class_Onumber__of(_1296360), _1296362)), _1296366)), _1296364))], (28328 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), c_Groups_Ozero__class_Ozero(_1296360)), _1296366)))]], 28331 ^ _781215 : [(28334 ^ _781215) ^ [] : [28335 ^ _781215 : [(28338 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), _1296364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296360), hAPP(c_Int_Onumber__class_Onumber__of(_1296360), _1296362)), _1296366)))], (28336 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), _1296366), c_Groups_Ozero__class_Ozero(_1296360))))]], 28339 ^ _781215 : [(28342 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), hAPP(c_Int_Onumber__class_Onumber__of(_1296360), _1296362)), c_Groups_Ozero__class_Ozero(_1296360)))], (28340 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), _1296366), c_Groups_Ozero__class_Ozero(_1296360)))]]], (28332 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296360), c_Groups_Ozero__class_Ozero(_1296360)), _1296366))]]]]], (22370 ^ _781215) ^ [_1185207, _1185209, _1185211, _1185213] : [class_Divides_Oring__div(_1185207), -(c_Divides_Odiv__class_Omod(_1185207, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185207), _1185209), _1185211), _1185213) = c_Divides_Odiv__class_Omod(_1185207, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185207), c_Divides_Odiv__class_Omod(_1185207, _1185209, _1185213)), c_Divides_Odiv__class_Omod(_1185207, _1185211, _1185213)), _1185213))], (51074 ^ _781215) ^ [_1819460, _1819462] : [class_Lattices_Olattice(_1819460), -(class_Lattices_Osemilattice__inf(tc_fun(_1819462, _1819460)))], (45841 ^ _781215) ^ [_1700595, _1700597] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700595)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700597)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700595), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1700597)) = c_List_Olist_ONil(tc_Nat_Onat))], (8804 ^ _781215) ^ [_930500, _930502, _930504, _930506] : [class_Orderings_Oorder(_930500), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930500), _930502), _930504)), _930502 = _930506, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930500), _930506), _930504)))], (36356 ^ _781215) ^ [_1464700, _1464702] : [-(hBOOL(hAPP(hAPP(c_member(_1464700), _1464702), c_Orderings_Otop__class_Otop(tc_fun(_1464700, tc_HOL_Obool)))))], (31268 ^ _781215) ^ [_1353870, _1353872, _1353874] : [-(hAPP(c_Relation_OImage(_1353870, _1353872, _1353874), c_Orderings_Obot__class_Obot(tc_fun(_1353870, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1353872, tc_HOL_Obool)))], (21602 ^ _781215) ^ [_1168760, _1168762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1168760), _1168762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1168760)), c_Int_OBit1(_1168762))))], (5766 ^ _781215) ^ [_872517, _872519, _872521] : [hAPP(c_Option_Ooption_OSome(_872517), _872519) = hAPP(c_Option_Ooption_OSome(_872517), _872521), -(_872519 = _872521)], (49103 ^ _781215) ^ [_1772013, _1772015] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1772013, _1772013)), _1772015)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1772013, _1772013)), c_Transitive__Closure_Otrancl(_1772013, _1772015))))], (4000 ^ _781215) ^ [_841907, _841909, _841911, _841913] : [-(c_Wellfounded_Omax__ext(_841913, _841909) = c_Wellfounded_Omax__ext(_841911, _841907)), _841913 = _841911, _841909 = _841907], (39866 ^ _781215) ^ [_1558536, _1558538, _1558540, _1558542] : [hBOOL(hAPP(hAPP(c_member(_1558536), _1558538), hAPP(c_Relation_ORange(_1558540, _1558536), _1558542))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1558540, _1558536)), hAPP(hAPP(c_Product__Type_OPair(_1558540, _1558536), 39869 ^ [_1558536, _1558538, _1558540, _1558542]), _1558538)), _1558542)))], (14606 ^ _781215) ^ [_1036769, _1036771, _1036773, _1036775, _1036777, _1036779] : [-(c_Com_Ocom_OCond(_1036769, _1036771, _1036773) = c_Com_Ocom_OCond(_1036775, _1036777, _1036779)), _1036769 = _1036775, _1036771 = _1036777, _1036773 = _1036779], (9487 ^ _781215) ^ [_942679, _942681, _942683] : [class_Orderings_Oorder(_942679), -(_942681 = _942683), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942679), _942683), _942681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942679), _942683), _942681)))], (43557 ^ _781215) ^ [_1650880, _1650882, _1650884, _1650886] : [class_Orderings_Oord(_1650880), -(hAPP(c_Hilbert__Choice_OGreatestM(_1650882, _1650880, _1650884), _1650886) = c_Hilbert__Choice_OEps(_1650882, hAPP(hAPP(c_COMBS(_1650882, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1650882), c_fconj), _1650886)), hAPP(hAPP(c_COMBB(tc_fun(_1650882, tc_HOL_Obool), tc_HOL_Obool, _1650882), c_HOL_OAll(_1650882)), hAPP(hAPP(c_COMBB(tc_fun(_1650882, tc_HOL_Obool), tc_fun(_1650882, tc_HOL_Obool), _1650882), hAPP(c_COMBS(_1650882, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1650882), c_fimplies), _1650886))), hAPP(hAPP(c_COMBB(_1650880, tc_fun(_1650882, tc_HOL_Obool), _1650882), hAPP(c_COMBC(_1650882, _1650880, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1650880, tc_fun(_1650880, tc_HOL_Obool), _1650882), c_Orderings_Oord__class_Oless__eq(_1650880)), _1650884))), _1650884))))))], (31166 ^ _781215) ^ [_1351762, _1351764, _1351766] : [class_Orderings_Olinorder(_1351762), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351762), _1351764), _1351766)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351762, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1351762), _1351764)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1351762, _1351764, _1351766)) = hAPP(c_SetInterval_Oord__class_OatMost(_1351762), _1351766))], (36394 ^ _781215) ^ [_1465337, _1465339] : [class_Lattices_Obounded__lattice__top(_1465337), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465337), c_Orderings_Otop__class_Otop(_1465337)), _1465339) = _1465339)], (5721 ^ _781215) ^ [_871724] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _871724))), -(hAPP(c_Com_Obody, _871724) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 5724 ^ [_871724]))], (21221 ^ _781215) ^ [_1161128, _1161130] : [class_Int_Onumber__ring(_1161128), 21224 ^ _781215 : [(21231 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1161130)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1161128), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161130)) = hAPP(c_Int_Onumber__class_Onumber__of(_1161128), _1161130))], (21225 ^ _781215) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1161130))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1161128), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161130)) = c_Groups_Ozero__class_Ozero(_1161128))]]], (25002 ^ _781215) ^ [_1232416, _1232418, _1232420, _1232422] : [class_Rings_Olinordered__semidom(_1232416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232416), c_Groups_Oone__class_Oone(_1232416)), _1232418)), 25009 ^ _781215 : [(25016 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232420), _1232422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232416), hAPP(hAPP(c_Power_Opower__class_Opower(_1232416), _1232418), _1232420)), hAPP(hAPP(c_Power_Opower__class_Opower(_1232416), _1232418), _1232422))))], (25010 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232416), hAPP(hAPP(c_Power_Opower__class_Opower(_1232416), _1232418), _1232420)), hAPP(hAPP(c_Power_Opower__class_Opower(_1232416), _1232418), _1232422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232420), _1232422)))]]], (51454 ^ _781215) ^ [] : [-(class_HOL_Oequal(tc_Com_Ostate))], (43974 ^ _781215) ^ [_1659630, _1659632, _1659634, _1659636, _1659638] : [-(_1659630 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1659632, _1659634, _1659636), _1659630), _1659638) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1659634), _1659632), tc_prod(_1659634, _1659632), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659634), _1659632), c_List_Olist_ONil(_1659634)), _1659638), hAPP(c_Product__Type_Oprod_Oprod__case(_1659634, _1659632, tc_prod(tc_List_Olist(_1659634), _1659632)), hAPP(hAPP(c_COMBC(_1659634, tc_fun(_1659632, tc_prod(tc_List_Olist(_1659634), _1659632)), tc_fun(_1659632, tc_prod(tc_List_Olist(_1659634), _1659632))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1659634), _1659632), tc_prod(tc_List_Olist(_1659634), _1659632)), tc_fun(tc_fun(_1659632, tc_prod(tc_List_Olist(_1659634), _1659632)), tc_fun(_1659632, tc_prod(tc_List_Olist(_1659634), _1659632))), _1659634), c_COMBB(tc_prod(tc_List_Olist(_1659634), _1659632), tc_prod(tc_List_Olist(_1659634), _1659632), _1659632)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1659634), tc_fun(_1659632, tc_prod(tc_List_Olist(_1659634), _1659632))), tc_fun(tc_prod(tc_List_Olist(_1659634), _1659632), tc_prod(tc_List_Olist(_1659634), _1659632)), _1659634), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1659634), _1659632, tc_prod(tc_List_Olist(_1659634), _1659632))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1659634), tc_List_Olist(_1659634)), tc_fun(tc_List_Olist(_1659634), tc_fun(_1659632, tc_prod(tc_List_Olist(_1659634), _1659632))), _1659634), hAPP(c_COMBB(tc_List_Olist(_1659634), tc_fun(_1659632, tc_prod(tc_List_Olist(_1659634), _1659632)), tc_List_Olist(_1659634)), c_Product__Type_OPair(tc_List_Olist(_1659634), _1659632))), c_List_Olist_OCons(_1659634))))), hAPP(c_Lazy__Sequence_Oanamorph(_1659632, _1659634, _1659636), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1659630), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1659636, _1659638)))], (50838 ^ _781215) ^ [_1814336, _1814338] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1814336), _1814338) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1814336), _1814338)))], (9131 ^ _781215) ^ [_936157, _936159, _936161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936157), _936159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936157), _936161)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936159), _936161))))], (51470 ^ _781215) ^ [_1823443] : [-(class_Nat_Osize(tc_List_Olist(_1823443)))], (36528 ^ _781215) ^ [_1467715, _1467717, _1467719, _1467721, _1467723] : [_1467715 = hAPP(_1467717, _1467719), -(hBOOL(hAPP(hAPP(c_member(_1467721), _1467715), hAPP(c_Set_Oimage(_1467723, _1467721, _1467717), c_Orderings_Otop__class_Otop(tc_fun(_1467723, tc_HOL_Obool))))))], (43870 ^ _781215) ^ [_1657063, _1657065] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657063), tc_List_Olist(_1657063))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657063), tc_List_Olist(_1657063)), c_List_Olist_ONil(_1657063)), c_List_Olist_ONil(_1657063))), c_List_Olistrel(_1657063, _1657065))))], (25602 ^ _781215) ^ [_1241967, _1241969, _1241971] : [class_Groups_Oordered__ab__group__add(_1241967), -(hAPP(c_Set_Oimage(_1241967, _1241967, c_Groups_Ouminus__class_Ouminus(_1241967)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1241967, _1241969, _1241971)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1241967, hAPP(c_Groups_Ouminus__class_Ouminus(_1241967), _1241971), hAPP(c_Groups_Ouminus__class_Ouminus(_1241967), _1241969)))], (6916 ^ _781215) ^ [_895626, _895628, _895630] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895626), _895628)), hBOOL(hAPP(hAPP(c_member(_895626), _895630), _895628)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_895626), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895626, tc_HOL_Obool)), _895628), hAPP(hAPP(c_Set_Oinsert(_895626), _895630), c_Orderings_Obot__class_Obot(tc_fun(_895626, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_895626), _895628))], (3774 ^ _781215) ^ [_838388, _838390, _838392, _838394, _838396, _838398] : [-(c_List_Oremove1(_838398, _838394, _838390) = c_List_Oremove1(_838396, _838392, _838388)), _838398 = _838396, _838394 = _838392, _838390 = _838388], (8007 ^ _781215) ^ [_916283, _916285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916283), hAPP(c_Nat_OSuc, _916285))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916283), _916285))), -(_916283 = _916285)], (17435 ^ _781215) ^ [_1093368] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093368), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093368)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1093368)))], (49553 ^ _781215) ^ [_1784238, _1784240] : [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), _1784238), _1784240)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1784238), _1784240)))], (10034 ^ _781215) ^ [_951741, _951743] : [10035 ^ _781215 : [(10036 ^ _781215) ^ [_951791] : [_951743 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951741), _951791)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951741), _951743)))], (40928 ^ _781215) ^ [_1583614, _1583616, _1583618] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1583614)), hAPP(c_Set_Oimage(_1583616, tc_Option_Ooption(_1583614), hAPP(c_Map_Omap__of(_1583616, _1583614), _1583618)), c_Orderings_Otop__class_Otop(tc_fun(_1583616, tc_HOL_Obool))))))], (49449 ^ _781215) ^ [] : [-(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))))], (43670 ^ _781215) ^ [_1653518, _1653520, _1653522, _1653524] : [class_Orderings_Olinorder(_1653518), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1653520, _1653518, _1653522), _1653524), c_List_Olist_ONil(_1653520)) = hAPP(hAPP(c_List_Olist_OCons(_1653520), _1653524), c_List_Olist_ONil(_1653520)))], (38486 ^ _781215) ^ [_1516063, _1516065, _1516067] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1516063, _1516065), c_Orderings_Obot__class_Obot(tc_fun(_1516063, tc_HOL_Obool))), _1516067) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516063, _1516065), tc_HOL_Obool)))], (39302 ^ _781215) ^ [_1537742, _1537744, _1537746, _1537748, _1537750, _1537752] : [c_Finite__Set_Ofun__left__comm__idem(_1537742, _1537744, _1537746), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537742), _1537748)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1537742, _1537744, _1537746), _1537750), hAPP(hAPP(c_Set_Oinsert(_1537742), _1537752), _1537748)) = hAPP(hAPP(_1537746, _1537752), hAPP(hAPP(c_Finite__Set_Ofold(_1537742, _1537744, _1537746), _1537750), _1537748)))], (23750 ^ _781215) ^ [_1209376, _1209378] : [class_Rings_Ocomm__semiring__1(_1209376), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1209376), _1209378), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1209376))], (43065 ^ _781215) ^ [_1638604, _1638606, _1638608, _1638610, _1638612, _1638614] : [-(hBOOL(hAPP(hAPP(c_member(_1638604), _1638606), hAPP(c_List_Oset(_1638604), _1638608)))), -(hAPP(c_Map_Omap__upds(_1638604, _1638610, _1638612, _1638608, _1638614), _1638606) = hAPP(_1638612, _1638606))], (26214 ^ _781215) ^ [_1256668, _1256670, _1256672] : [class_Orderings_Oorder(_1256668), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256668), _1256670), _1256672)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1256668, _1256672, _1256670) = c_Orderings_Obot__class_Obot(tc_fun(_1256668, tc_HOL_Obool)))], (11886 ^ _781215) ^ [_988006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988006), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15350 ^ _781215) ^ [_1050326, _1050328, _1050330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050326), _1050328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050328), _1050330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050326), _1050330)))], (41265 ^ _781215) ^ [_1591494, _1591496, _1591498, _1591500, _1591502, _1591504] : [c_Fun_Oinj__on(_1591494, _1591496, hAPP(c_Fun_Ocomp(_1591498, _1591496, _1591494, _1591500), _1591502), _1591504), -(c_Fun_Oinj__on(_1591494, _1591498, _1591502, _1591504))], (38882 ^ _781215) ^ [_1527368, _1527370] : [-(c_Relation_Orefl__on(_1527368, _1527370, c_Relation_OId__on(_1527368, _1527370)))], (49058 ^ _781215) ^ [_1771112, _1771114] : [c_Wellfounded_Owf(_1771112, _1771114), -(c_Wellfounded_Owf(_1771112, c_Transitive__Closure_Otrancl(_1771112, _1771114)))], (1378 ^ _781215) ^ [_801410, _801412] : [-(class_Lattices_Oboolean__algebra(_801410)), _801412 = _801410, class_Lattices_Oboolean__algebra(_801412)], (2768 ^ _781215) ^ [_822515, _822517, _822519, _822521, _822523, _822525] : [-(c_Wellfounded_Omlex__prod(_822525, _822521, _822517) = c_Wellfounded_Omlex__prod(_822523, _822519, _822515)), _822525 = _822523, _822521 = _822519, _822517 = _822515], (10618 ^ _781215) ^ [_962924, _962926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962924)), _962926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962924), _962926)))], (20197 ^ _781215) ^ [_1143782, _1143784] : [class_Int_Onumber__ring(_1143782), 20200 ^ _781215 : [(20207 ^ _781215) ^ [] : [c_Int_Oiszero(_1143782, hAPP(c_Int_Onumber__class_Onumber__of(_1143782), 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), _1143784)))), -(c_Groups_Oone__class_Oone(_1143782) = hAPP(c_Int_Onumber__class_Onumber__of(_1143782), _1143784))], (20201 ^ _781215) ^ [] : [c_Groups_Oone__class_Oone(_1143782) = hAPP(c_Int_Onumber__class_Onumber__of(_1143782), _1143784), -(c_Int_Oiszero(_1143782, hAPP(c_Int_Onumber__class_Onumber__of(_1143782), 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), _1143784)))))]]], (13162 ^ _781215) ^ [_1010315, _1010317] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1010315), _1010317) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 13163 ^ _781215 : [(13170 ^ _781215) ^ [] : [_1010315 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1010317 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13164 ^ _781215) ^ [] : [_1010315 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1010317 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (47635 ^ _781215) ^ [_1740026, _1740028, _1740030, _1740032, _1740034, _1740036, _1740038] : [c_List_Olist__all2(_1740026, _1740028, _1740030, hAPP(hAPP(c_List_Olist_OCons(_1740026), _1740032), _1740034), hAPP(hAPP(c_List_Olist_OCons(_1740028), _1740036), _1740038)), 47638 ^ _781215 : [(47641 ^ _781215) ^ [] : [-(c_List_Olist__all2(_1740026, _1740028, _1740030, _1740034, _1740038))], (47639 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1740030, _1740032), _1740036)))]]], (21520 ^ _781215) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (15538 ^ _781215) ^ [_1053757, _1053759, _1053761] : [-(c_Map_Omap__add(_1053757, _1053759, _1053761, hAPP(c_COMBK(tc_Option_Ooption(_1053759), _1053757), c_Option_Ooption_ONone(_1053759))) = _1053761)], (31058 ^ _781215) ^ [_1349624, _1349626, _1349628, _1349630] : [class_Orderings_Olinorder(_1349624), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349624), _1349626), _1349628)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349624, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349624, _1349626), _1349630)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349624, _1349626), _1349628)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1349624, _1349628), _1349630))], (45793 ^ _781215) ^ [_1699585, _1699587, _1699589] : [class_Orderings_Olinorder(_1699585), 45796 ^ _781215 : [(45815 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1699585, hAPP(hAPP(c_List_Oappend(_1699585), _1699587), _1699589))), c_List_Olinorder__class_Osorted(_1699585, _1699587), c_List_Olinorder__class_Osorted(_1699585, _1699589), 45825 ^ _781215 : [(45831 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699585), 45824 ^ [_1699585, _1699587, _1699589]), 45827 ^ [_1699585, _1699587, _1699589]))], (45829 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699585), 45827 ^ [_1699585, _1699587, _1699589]), hAPP(c_List_Oset(_1699585), _1699589))))], (45826 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699585), 45824 ^ [_1699585, _1699587, _1699589]), hAPP(c_List_Oset(_1699585), _1699587))))]]], (45797 ^ _781215) ^ [] : [c_List_Olinorder__class_Osorted(_1699585, hAPP(hAPP(c_List_Oappend(_1699585), _1699587), _1699589)), 45800 ^ _781215 : [(45805 ^ _781215) ^ [_1699821] : [hBOOL(hAPP(hAPP(c_member(_1699585), _1699821), hAPP(c_List_Oset(_1699585), _1699587))), 45808 ^ _781215 : [(45809 ^ _781215) ^ [_1699931] : [hBOOL(hAPP(hAPP(c_member(_1699585), _1699931), hAPP(c_List_Oset(_1699585), _1699589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1699585), _1699821), _1699931)))]]], (45803 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1699585, _1699589))], (45801 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1699585, _1699587))]]]]], (39428 ^ _781215) ^ [_1542168, _1542170] : [-(c_Fun_Oinj__on(tc_fun(_1542168, _1542170), tc_fun(tc_prod(_1542168, _1542170), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1542168, _1542170), tc_HOL_Obool), tc_fun(tc_prod(_1542168, _1542170), tc_HOL_Obool), tc_fun(_1542168, _1542170)), c_Set_OCollect(tc_prod(_1542168, _1542170))), hAPP(hAPP(c_COMBB(tc_fun(_1542168, tc_fun(_1542170, tc_HOL_Obool)), tc_fun(tc_prod(_1542168, _1542170), tc_HOL_Obool), tc_fun(_1542168, _1542170)), c_Product__Type_Oprod_Oprod__case(_1542168, _1542170, tc_HOL_Obool)), hAPP(c_COMBB(_1542170, tc_fun(_1542170, tc_HOL_Obool), _1542168), hAPP(c_COMBC(_1542170, _1542170, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1542168, _1542170), tc_HOL_Obool))))], (37912 ^ _781215) ^ [_1501974, _1501976, _1501978] : [37914 ^ _781215 : [(37917 ^ _781215) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501974, tc_HOL_Obool)), 37913 ^ [_1501974, _1501976, _1501978]), _1501978) = c_Orderings_Obot__class_Obot(tc_fun(_1501974, tc_HOL_Obool))], (37915 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1501974, tc_HOL_Obool)), 37913 ^ [_1501974, _1501976, _1501978]), _1501976)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501974, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1501974, tc_HOL_Obool), _1501976)), _1501978) = c_Orderings_Obot__class_Obot(tc_fun(_1501974, tc_HOL_Obool)))], (12896 ^ _781215) ^ [_1005929] : [class_Rings_Olinordered__semidom(_1005929), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1005929), c_Groups_Ozero__class_Ozero(_1005929)), c_Groups_Oone__class_Oone(_1005929))))], (40585 ^ _781215) ^ [_1576659, _1576661] : [c_Nitpick_Owf_H(_1576659, _1576661), 40588 ^ _781215 : [(40591 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576659, _1576659)), _1576661))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (40589 ^ _781215) ^ [] : [-(c_Wellfounded_Oacyclic(_1576659, _1576661))]]], (41879 ^ _781215) ^ [_1606007, _1606009] : [-(hAPP(hAPP(c_List_Ozip(_1606007, _1606007), _1606009), _1606009) = hAPP(hAPP(c_List_Omap(_1606007, tc_prod(_1606007, _1606007)), hAPP(hAPP(c_COMBS(_1606007, _1606007, tc_prod(_1606007, _1606007)), c_Product__Type_OPair(_1606007, _1606007)), c_COMBI(_1606007))), _1606009))], (30329 ^ _781215) ^ [_1336039, _1336041, _1336043, _1336045, _1336047] : [class_Orderings_Oorder(_1336039), 30332 ^ _781215 : [(30353 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1336039, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1336039, _1336041, _1336043)), c_SetInterval_Oord__class_OatLeastAtMost(_1336039, _1336045, _1336047)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336039), _1336045), _1336047)), 30356 ^ _781215 : [(30359 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336039), _1336045), _1336041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336039), _1336043), _1336047)), 30366 ^ _781215 : [(30369 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336039), _1336043), _1336047))], (30367 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336039), _1336045), _1336041))]]], (30357 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336039), _1336041), _1336043)))]]], (30333 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1336039, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1336039, _1336041, _1336043)), c_SetInterval_Oord__class_OatLeastAtMost(_1336039, _1336045, _1336047))), 30336 ^ _781215 : [(30337 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336039), _1336041), _1336043)), 30340 ^ _781215 : [(30345 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336039), _1336045), _1336041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336039), _1336043), _1336047)))], (30343 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336039), _1336043), _1336047)))], (30341 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336039), _1336045), _1336041)))]]], (30351 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336039), _1336045), _1336047)))]]]]], (25254 ^ _781215) ^ [_1236707, _1236709] : [c_Nat__Transfer_Ois__nat(_1236707), c_Nat__Transfer_Ois__nat(_1236709), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236707), _1236709)))], (7710 ^ _781215) ^ [_911025, _911027] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _911025)), hAPP(c_Nat_OSuc, _911027)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _911025), _911027))], (7730 ^ _781215) ^ [_911437, _911439, _911441] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911437), _911439) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911437), _911441), -(_911439 = _911441)], (51318 ^ _781215) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (44049 ^ _781215) ^ [_1661976, _1661978, _1661980, _1661982, _1661984] : [hAPP(hAPP(c_List_Olist_OCons(_1661976), _1661978), _1661980) = hAPP(hAPP(c_List_Oappend(_1661976), _1661982), _1661984), 44054 ^ _781215 : [(44057 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1661976), _1661978), _1661980) = _1661984)], (44055 ^ _781215) ^ [] : [-(_1661982 = c_List_Olist_ONil(_1661976))]], 44059 ^ _781215 : [(44062 ^ _781215) ^ [] : [-(_1661980 = hAPP(hAPP(c_List_Oappend(_1661976), 44058 ^ [_1661976, _1661978, _1661980, _1661982, _1661984]), _1661984))], (44060 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1661976), _1661978), 44058 ^ [_1661976, _1661978, _1661980, _1661982, _1661984]) = _1661982)]]], (27534 ^ _781215) ^ [_1282332, _1282334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1282332), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1282334), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1282332, _1282334) = 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), _1282332), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1282334)))))], (22460 ^ _781215) ^ [_1186941, _1186943, _1186945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186941)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1186943, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186945), _1186941)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186945), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1186943), _1186945), _1186941))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1186943, _1186945)))], (4720 ^ _781215) ^ [_852751, _852753, _852755, _852757] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_852757, _852753) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_852755, _852751)), _852757 = _852755, _852753 = _852751], (30413 ^ _781215) ^ [_1337492, _1337494, _1337496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337492)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1337494), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1337496)), 30420 ^ _781215 : [(30421 ^ _781215) ^ [_1337700] : [30423 ^ _781215 : [(30429 ^ _781215) ^ [] : [-(_1337700 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30425 ^ [_1337492, _1337494, _1337496, _1337700]), 30422 ^ [_1337492, _1337494, _1337496, _1337700]))], (30427 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30425 ^ [_1337492, _1337494, _1337496, _1337700]), _1337496)))], (30424 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30422 ^ [_1337492, _1337494, _1337496, _1337700]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1337492))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337494), _1337700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337494), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1337700), _1337492))))]]], (44740 ^ _781215) ^ [_1678550, _1678552, _1678554, _1678556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1678550), _1678552)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678554)), _1678556))), -(hAPP(hAPP(c_List_Otake(_1678554), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1678550), _1678552)), _1678556) = hAPP(hAPP(c_List_Oappend(_1678554), hAPP(hAPP(c_List_Otake(_1678554), _1678550), _1678556)), hAPP(hAPP(c_List_Otake(_1678554), _1678552), hAPP(hAPP(c_List_Odrop(_1678554), _1678550), _1678556))))], (31190 ^ _781215) ^ [_1352226, _1352228, _1352230] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1352226, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1352228)), _1352230) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352226, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1352226, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1352228)), _1352230)), hAPP(_1352230, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2604 ^ _781215) ^ [_819909, _819911, _819913, _819915] : [-(c_Nitpick_Onorm__frac(_819915, _819911) = c_Nitpick_Onorm__frac(_819913, _819909)), _819915 = _819913, _819911 = _819909], (15294 ^ _781215) ^ [_1049495] : [-(c_Int_Osucc(c_Int_Opred(_1049495)) = _1049495)], (41457 ^ _781215) ^ [_1596125, _1596127, _1596129, _1596131, _1596133, _1596135, _1596137] : [c_Fun_Oinj__on(_1596125, _1596127, _1596129, hAPP(c_Set_Oimage(_1596131, _1596125, _1596133), _1596135)), c_Fun_Oinj__on(_1596131, _1596125, _1596133, _1596135), hBOOL(hAPP(hAPP(c_member(_1596127), _1596137), hAPP(c_Set_Oimage(_1596125, _1596127, _1596129), hAPP(c_Set_Oimage(_1596131, _1596125, _1596133), _1596135)))), -(hAPP(c_Fun_Othe__inv__into(_1596131, _1596127, _1596135, hAPP(c_Fun_Ocomp(_1596125, _1596127, _1596131, _1596129), _1596133)), _1596137) = hAPP(hAPP(c_Fun_Ocomp(_1596125, _1596131, _1596127, c_Fun_Othe__inv__into(_1596131, _1596125, _1596135, _1596133)), c_Fun_Othe__inv__into(_1596125, _1596127, hAPP(c_Set_Oimage(_1596131, _1596125, _1596133), _1596135), _1596129)), _1596137))], (13320 ^ _781215) ^ [_1012832, _1012834, _1012836] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012832), _1012834)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012832), _1012836)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1012832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1012834), _1012836))], (18649 ^ _781215) ^ [_1115250, _1115252, _1115254] : [class_Orderings_Olinorder(_1115250), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115250), _1115252)), hBOOL(hAPP(hAPP(c_member(_1115250), _1115254), _1115252)), 18660 ^ _781215 : [(18667 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1115250, tc_HOL_Obool)), _1115252), hAPP(hAPP(c_Set_Oinsert(_1115250), _1115254), c_Orderings_Obot__class_Obot(tc_fun(_1115250, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1115250, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1115250, _1115252) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1115250), _1115254), c_Big__Operators_Olinorder__class_OMin(_1115250, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1115250, tc_HOL_Obool)), _1115252), hAPP(hAPP(c_Set_Oinsert(_1115250), _1115254), c_Orderings_Obot__class_Obot(tc_fun(_1115250, tc_HOL_Obool)))))))], (18661 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1115250, tc_HOL_Obool)), _1115252), hAPP(hAPP(c_Set_Oinsert(_1115250), _1115254), c_Orderings_Obot__class_Obot(tc_fun(_1115250, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1115250, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1115250, _1115252) = _1115254)]]], (44323 ^ _781215) ^ [_1667749, _1667751, _1667753, _1667755] : [-(hAPP(hAPP(c_List_Oappend(_1667749), hAPP(hAPP(c_List_Oappend(_1667749), _1667751), _1667753)), _1667755) = hAPP(hAPP(c_List_Oappend(_1667749), _1667751), hAPP(hAPP(c_List_Oappend(_1667749), _1667753), _1667755)))], (26946 ^ _781215) ^ [_1271104, _1271106] : [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), _1271104), _1271106))), 26949 ^ _781215 : [(26958 ^ _781215) ^ [] : [-(c_Divides_OposDivAlg(_1271104, _1271106) = hAPP(c_Divides_Oadjust(_1271106), c_Divides_OposDivAlg(_1271104, 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)))), _1271106)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1271104), _1271106))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1271106), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26950 ^ _781215) ^ [] : [26951 ^ _781215 : [(26954 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1271106), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (26952 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1271104), _1271106))]], -(c_Divides_OposDivAlg(_1271104, _1271106) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1271104))]]], (43628 ^ _781215) ^ [_1652607, _1652609, _1652611, _1652613] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652607) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1652609), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652607)), hAPP(hAPP(c_List_Olist_OCons(_1652609), _1652611), _1652613)) = c_List_Olist_ONil(_1652609))], (51326 ^ _781215) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (17627 ^ _781215) ^ [_1096418, _1096420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096418)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096420)), 17634 ^ _781215 : [(17641 ^ _781215) ^ [] : [_1096418 = _1096420, -(hAPP(c_Int_Onat, _1096418) = hAPP(c_Int_Onat, _1096420))], (17635 ^ _781215) ^ [] : [hAPP(c_Int_Onat, _1096418) = hAPP(c_Int_Onat, _1096420), -(_1096418 = _1096420)]]], (43527 ^ _781215) ^ [_1649898, _1649900, _1649902, _1649904] : [class_Orderings_Oord(_1649898), -(c_Hilbert__Choice_OLeastM(_1649900, _1649898, _1649902, _1649904) = c_Hilbert__Choice_OEps(_1649900, hAPP(hAPP(c_COMBS(_1649900, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1649900), c_fconj), _1649904)), hAPP(hAPP(c_COMBB(tc_fun(_1649900, tc_HOL_Obool), tc_HOL_Obool, _1649900), c_HOL_OAll(_1649900)), hAPP(hAPP(c_COMBB(tc_fun(_1649900, tc_HOL_Obool), tc_fun(_1649900, tc_HOL_Obool), _1649900), hAPP(c_COMBS(_1649900, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1649900), c_fimplies), _1649904))), hAPP(hAPP(c_COMBC(_1649900, tc_fun(_1649900, _1649898), tc_fun(_1649900, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649898, tc_HOL_Obool), tc_fun(tc_fun(_1649900, _1649898), tc_fun(_1649900, tc_HOL_Obool)), _1649900), c_COMBB(_1649898, tc_HOL_Obool, _1649900)), hAPP(hAPP(c_COMBB(_1649898, tc_fun(_1649898, tc_HOL_Obool), _1649900), c_Orderings_Oord__class_Oless__eq(_1649898)), _1649902))), _1649902))))))], (24952 ^ _781215) ^ [_1231543, _1231545, _1231547] : [class_Rings_Olinordered__semidom(_1231543), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231543), c_Groups_Oone__class_Oone(_1231543)), _1231545)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231543), c_Groups_Oone__class_Oone(_1231543)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231543), _1231545), hAPP(hAPP(c_Power_Opower__class_Opower(_1231543), _1231545), _1231547)))))], (1698 ^ _781215) ^ [_805410, _805412] : [-(class_Nat_Osemiring__char__0(_805410)), _805412 = _805410, class_Nat_Osemiring__char__0(_805412)], (6682 ^ _781215) ^ [_890616, _890618, _890620, _890622] : [hBOOL(hAPP(hAPP(c_member(_890616), _890618), hAPP(hAPP(c_Set_Oinsert(_890616), _890620), _890622))), -(_890618 = _890620), -(hBOOL(hAPP(hAPP(c_member(_890616), _890618), _890622)))], (45847 ^ _781215) ^ [_1700674, _1700676, _1700678, _1700680] : [c_List_Oupt(_1700674, _1700676) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1700678), _1700680), 45850 ^ _781215 : [(45855 ^ _781215) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1700674), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1700676) = _1700680)], (45853 ^ _781215) ^ [] : [-(_1700674 = _1700678)], (45851 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1700674), _1700676)))]]], (13408 ^ _781215) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3678 ^ _781215) ^ [_836930, _836932, _836934, _836936, _836938, _836940, _836942, _836944] : [-(c_List_Olinorder__class_Osort__key(_836944, _836940, _836936, _836932) = c_List_Olinorder__class_Osort__key(_836942, _836938, _836934, _836930)), _836944 = _836942, _836940 = _836938, _836936 = _836934, _836932 = _836930], (25022 ^ _781215) ^ [_1232791, _1232793, _1232795, _1232797] : [class_Rings_Olinordered__semidom(_1232791), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232791), c_Groups_Oone__class_Oone(_1232791)), _1232793)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232791), hAPP(hAPP(c_Power_Opower__class_Opower(_1232791), _1232793), _1232795)), hAPP(hAPP(c_Power_Opower__class_Opower(_1232791), _1232793), _1232797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232795), _1232797)))], (15364 ^ _781215) ^ [_1050579, _1050581] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050579), _1050581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050581), _1050579)))], (39176 ^ _781215) ^ [_1533613, _1533615, _1533617, _1533619] : [-(hBOOL(hAPP(hAPP(c_member(_1533613), _1533615), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533613, tc_HOL_Obool)), _1533617), hAPP(c_Set_OCollect(_1533613), _1533619))))), hBOOL(hAPP(hAPP(c_member(_1533613), _1533615), _1533617)), hBOOL(hAPP(_1533619, _1533615))], (8928 ^ _781215) ^ [_932570, _932572, _932574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932570, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_932570, tc_HOL_Obool)), _932572)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_932570, tc_HOL_Obool)), _932574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932570, tc_HOL_Obool)), _932574), _932572)))], (38514 ^ _781215) ^ [_1516804, _1516806, _1516808] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1516804, _1516806), _1516808), hAPP(c_COMBK(tc_fun(_1516806, tc_HOL_Obool), _1516804), c_Orderings_Obot__class_Obot(tc_fun(_1516806, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516804, _1516806), tc_HOL_Obool)))], (36073 ^ _781215) ^ [_1459528, _1459530, _1459532, _1459534, _1459536] : [class_Groups_Oordered__ab__group__add__abs(_1459528), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459528), hAPP(c_Groups_Oabs__class_Oabs(_1459528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1459528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1459528), _1459530), _1459532)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1459528), _1459534), _1459536)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1459528), hAPP(c_Groups_Oabs__class_Oabs(_1459528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1459528), _1459530), _1459534))), hAPP(c_Groups_Oabs__class_Oabs(_1459528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1459528), _1459532), _1459536))))))], (94 ^ _781215) ^ [_782758, _782760, _782762, _782764, _782766, _782768] : [-(c_Finite__Set_Ofolding__one__idem(_782766, _782762, _782758)), c_Finite__Set_Ofolding__one__idem(_782768, _782764, _782760), _782768 = _782766, _782764 = _782762, _782760 = _782758], (9769 ^ _781215) ^ [_947206, _947208, _947210, _947212] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_947206), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947206), _947208), _947210)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947206), _947208), _947212))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947206), _947210), _947212)))], (4960 ^ _781215) ^ [_856551, _856553, _856555, _856557, _856559, _856561, _856563, _856565, _856567, _856569] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_856569, _856565, _856561, _856557, _856553) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_856567, _856563, _856559, _856555, _856551)), _856569 = _856567, _856565 = _856563, _856561 = _856559, _856557 = _856555, _856553 = _856551], (2286 ^ _781215) ^ [_814862, _814864, _814866, _814868, _814870, _814872, _814874, _814876, _814878, _814880] : [-(c_SetInterval_Oord_OatLeastLessThan(_814880, _814876, _814872, _814868, _814864) = c_SetInterval_Oord_OatLeastLessThan(_814878, _814874, _814870, _814866, _814862)), _814880 = _814878, _814876 = _814874, _814872 = _814870, _814868 = _814866, _814864 = _814862], (34804 ^ _781215) ^ [_1433474, _1433476, _1433478, _1433480] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1433474), _1433476)), 34807 ^ _781215 : [(34814 ^ _781215) ^ [] : [hAPP(c_Finite__Set_Ocard(_1433478), hAPP(c_Set_Oimage(_1433474, _1433478, _1433480), _1433476)) = hAPP(c_Finite__Set_Ocard(_1433474), _1433476), -(c_Fun_Oinj__on(_1433474, _1433478, _1433480, _1433476))], (34808 ^ _781215) ^ [] : [c_Fun_Oinj__on(_1433474, _1433478, _1433480, _1433476), -(hAPP(c_Finite__Set_Ocard(_1433478), hAPP(c_Set_Oimage(_1433474, _1433478, _1433480), _1433476)) = hAPP(c_Finite__Set_Ocard(_1433474), _1433476))]]], (21534 ^ _781215) ^ [_1167615] : [c_Int_OBit0(_1167615) = c_Int_OPls, -(_1167615 = c_Int_OPls)], (44582 ^ _781215) ^ [_1674825, _1674827] : [-(hAPP(hAPP(c_List_Odrop(_1674825), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1674827) = _1674827)], (49585 ^ _781215) ^ [_1784914, _1784916, _1784918, _1784920, _1784922] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1784914, _1784914)), hAPP(hAPP(c_Product__Type_OPair(_1784914, _1784914), hAPP(_1784916, hAPP(c_Nat_OSuc, 49586 ^ [_1784914, _1784916, _1784918, _1784920, _1784922]))), hAPP(_1784916, 49586 ^ [_1784914, _1784916, _1784918, _1784920, _1784922]))), c_Transitive__Closure_Ortrancl(_1784914, _1784918))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1784914, _1784914)), hAPP(hAPP(c_Product__Type_OPair(_1784914, _1784914), hAPP(_1784916, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1784920), _1784922))), hAPP(_1784916, _1784920))), c_Transitive__Closure_Ortrancl(_1784914, _1784918))))], (35741 ^ _781215) ^ [_1453356] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1453356)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1453356))], (6439 ^ _781215) ^ [_886104, _886106, _886108, _886110] : [_886104 = _886106, 6442 ^ _781215 : [(6449 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886108), _886110), _886106)), -(hBOOL(hAPP(hAPP(c_member(_886108), _886110), _886104)))], (6443 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886108), _886110), _886104)), -(hBOOL(hAPP(hAPP(c_member(_886108), _886110), _886106)))]]], (38598 ^ _781215) ^ [_1519456, _1519458, _1519460, _1519462] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1519456, _1519458)), hAPP(hAPP(c_Product__Type_OSigma(_1519456, _1519458), hAPP(hAPP(c_Set_Oinsert(_1519456), _1519460), c_Orderings_Obot__class_Obot(tc_fun(_1519456, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1519458, tc_HOL_Obool), _1519456), _1519462))) = hAPP(c_Finite__Set_Ocard(_1519458), _1519462))], (35154 ^ _781215) ^ [_1441232, _1441234] : [-(c_Fun_Oinj__on(_1441232, tc_Option_Ooption(_1441232), c_Option_Ooption_OSome(_1441232), _1441234))], (50740 ^ _781215) ^ [_1812745, _1812747] : [-(c_FunDef_Ois__measure(_1812745, _1812747))], (1838 ^ _781215) ^ [_807160, _807162] : [-(class_Groups_Ozero(_807160)), _807162 = _807160, class_Groups_Ozero(_807162)], (2806 ^ _781215) ^ [_823122, _823124, _823126, _823128, _823130, _823132] : [-(c_FunDef_Oin__rel(_823132, _823128, _823124) = c_FunDef_Oin__rel(_823130, _823126, _823122)), _823132 = _823130, _823128 = _823126, _823124 = _823122], (44530 ^ _781215) ^ [_1673476, _1673478] : [-(hAPP(c_List_Orotate1(_1673476), _1673478) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1673476), _1673476, c_List_Olist_ONil(_1673476), hAPP(hAPP(c_COMBB(tc_List_Olist(_1673476), tc_fun(tc_List_Olist(_1673476), tc_List_Olist(_1673476)), _1673476), hAPP(c_COMBC(tc_List_Olist(_1673476), tc_List_Olist(_1673476), tc_List_Olist(_1673476)), c_List_Oappend(_1673476))), hAPP(hAPP(c_COMBC(_1673476, tc_List_Olist(_1673476), tc_List_Olist(_1673476)), c_List_Olist_OCons(_1673476)), c_List_Olist_ONil(_1673476)))), _1673478))], (17551 ^ _781215) ^ [_1095222, _1095224] : [class_Lattices_Olattice(_1095222), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095222), _1095224)), -(_1095224 = c_Orderings_Obot__class_Obot(tc_fun(_1095222, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1095222), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1095222), 17564 ^ [_1095222, _1095224]), 17565 ^ [_1095222, _1095224])), hAPP(hAPP(c_Set_Oinsert(_1095222), 17564 ^ [_1095222, _1095224]), hAPP(hAPP(c_Set_Oinsert(_1095222), 17565 ^ [_1095222, _1095224]), c_Orderings_Obot__class_Obot(tc_fun(_1095222, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1095222), c_Big__Operators_Olattice__class_OSup__fin(_1095222, _1095224)), _1095224)))], (25620 ^ _781215) ^ [_1242237] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1242237)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1242237)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44762 ^ _781215) ^ [_1679273, _1679275, _1679277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679273), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679275)), _1679277))), -(hAPP(hAPP(c_List_Oappend(_1679275), hAPP(hAPP(c_List_Otake(_1679275), _1679273), _1679277)), hAPP(hAPP(c_List_Olist_OCons(_1679275), hAPP(c_List_Ohd(_1679275), hAPP(hAPP(c_List_Odrop(_1679275), _1679273), _1679277))), c_List_Olist_ONil(_1679275))) = hAPP(hAPP(c_List_Otake(_1679275), hAPP(c_Nat_OSuc, _1679273)), _1679277))], (16842 ^ _781215) ^ [_1083666, _1083668, _1083670, _1083672] : [c_Big__Operators_Osemilattice__big(_1083666, _1083668, _1083670), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083666), _1083672)), -(hAPP(_1083670, _1083672) = hAPP(c_Finite__Set_Ofold1(_1083666, _1083668), _1083672))], (42856 ^ _781215) ^ [_1633248, _1633250, _1633252, _1633254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633248), tc_List_Olist(_1633248))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633248), tc_List_Olist(_1633248)), _1633250), _1633252)), c_List_Olexord(_1633248, _1633254))), 42861 ^ _781215 : [(42864 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1633248), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633248)), _1633250)), _1633252) = _1633250)], (42862 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633248)), _1633250)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633248)), _1633252))))]], 42866 ^ _781215 : [(42871 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633248, _1633248)), hAPP(hAPP(c_Product__Type_OPair(_1633248, _1633248), hAPP(hAPP(c_List_Onth(_1633248), _1633250), 42865 ^ [_1633248, _1633250, _1633252, _1633254])), hAPP(hAPP(c_List_Onth(_1633248), _1633252), 42865 ^ [_1633248, _1633250, _1633252, _1633254]))), _1633254)))], (42869 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1633248), 42865 ^ [_1633248, _1633250, _1633252, _1633254]), _1633250) = hAPP(hAPP(c_List_Otake(_1633248), 42865 ^ [_1633248, _1633250, _1633252, _1633254]), _1633252))], (42867 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42865 ^ [_1633248, _1633250, _1633252, _1633254]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633248)), _1633250)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633248)), _1633252)))))]]], (38033 ^ _781215) ^ [_1504655] : [-(c_Nitpick_Ozero__frac(_1504655) = c_Nitpick_OAbs__Frac(_1504655, 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))))], (6100 ^ _781215) ^ [_879235, _879237] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_879235, _879237)], (17867 ^ _781215) ^ [_1100274, _1100276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100274)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100276)), 17874 ^ _781215 : [(17881 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100274), _1100276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1100274)), hAPP(c_Int_Onat, _1100276))))], (17875 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1100274)), hAPP(c_Int_Onat, _1100276))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100274), _1100276)))]]], (27010 ^ _781215) ^ [_1272034, _1272036, _1272038] : [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), _1272034), _1272036))), -(hBOOL(hAPP(hAPP(_1272038, _1272034), _1272036))), 27017 ^ _781215 : [(27020 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1272038, 27015 ^ [_1272034, _1272036, _1272038]), 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)))), 27016 ^ [_1272034, _1272036, _1272038])))), -(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), 27015 ^ [_1272034, _1272036, _1272038]), 27016 ^ [_1272034, _1272036, _1272038])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 27016 ^ [_1272034, _1272036, _1272038]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27030 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1272038, 27015 ^ [_1272034, _1272036, _1272038]), 27016 ^ [_1272034, _1272036, _1272038]))], (27018 ^ _781215) ^ [] : [-(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), 27015 ^ [_1272034, _1272036, _1272038]), 27016 ^ [_1272034, _1272036, _1272038]))))]]], (44439 ^ _781215) ^ [_1670757, _1670759, _1670761, _1670763, _1670765] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670757), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670759)), _1670761)))), -(hAPP(hAPP(c_List_Olist__update(_1670759, hAPP(hAPP(c_List_Oappend(_1670759), _1670761), _1670763)), _1670757), _1670765) = hAPP(hAPP(c_List_Oappend(_1670759), _1670761), hAPP(hAPP(c_List_Olist__update(_1670759, _1670763), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1670757), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670759)), _1670761))), _1670765)))], (30111 ^ _781215) ^ [_1331835] : [-(hAPP(c_Set_OPow(_1331835), c_Orderings_Obot__class_Obot(tc_fun(_1331835, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1331835, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1331835, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1331835, tc_HOL_Obool), tc_HOL_Obool))))], (1956 ^ _781215) ^ [_809623, _809625, _809627, _809629] : [-(c_Option_Oset(_809629, _809625) = c_Option_Oset(_809627, _809623)), _809629 = _809627, _809625 = _809623], (14034 ^ _781215) ^ [_1025841, _1025843, _1025845, _1025847] : [-(c_Hoare__Mirabelle_Otriple__valid(_1025841, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1025841), _1025843), hAPP(c_Com_Ocom_OBODY, _1025845)), _1025847)))], (39430 ^ _781215) ^ [_1542288] : [-(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)))), _1542288))))], (42271 ^ _781215) ^ [_1617386, _1617388, _1617390] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617386)), c_List_Osublist(_1617386, _1617388, _1617390)) = 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(_1617386)), _1617388)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1617390)))))], (34886 ^ _781215) ^ [_1435063, _1435065, _1435067, _1435069, _1435071] : [class_Groups_Ocomm__monoid__mult(_1435063), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435065), _1435067)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435063, _1435065, c_Groups_Otimes__class_Otimes(_1435063)), hAPP(hAPP(c_COMBS(_1435065, _1435063, _1435063), hAPP(hAPP(c_COMBB(_1435063, tc_fun(_1435063, _1435063), _1435065), c_Groups_Otimes__class_Otimes(_1435063)), _1435069)), _1435071)), c_Groups_Oone__class_Oone(_1435063)), _1435067) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435063), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435063, _1435065, c_Groups_Otimes__class_Otimes(_1435063)), _1435069), c_Groups_Oone__class_Oone(_1435063)), _1435067)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435063, _1435065, c_Groups_Otimes__class_Otimes(_1435063)), _1435071), c_Groups_Oone__class_Oone(_1435063)), _1435067)))], (40942 ^ _781215) ^ [_1584247, _1584249, _1584251] : [c_Fun_Oinj__on(_1584247, _1584249, _1584251, c_Orderings_Otop__class_Otop(tc_fun(_1584247, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1584247), tc_List_Olist(_1584249), hAPP(c_List_Omap(_1584247, _1584249), _1584251), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1584247), tc_HOL_Obool))))], (29836 ^ _781215) ^ [_1325207, _1325209, _1325211, _1325213] : [class_Fields_Olinordered__field(_1325207), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1325207), c_Groups_Ozero__class_Ozero(_1325207)), _1325209)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325207), _1325211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325207), _1325213), _1325209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325207), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325207), _1325211), _1325209)), _1325213)))], (37608 ^ _781215) ^ [_1495524, _1495526, _1495528, _1495530] : [hBOOL(hAPP(hAPP(c_member(_1495524), _1495526), c_Wellfounded_Oacc(_1495524, _1495528))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1495524, _1495524)), hAPP(hAPP(c_Product__Type_OPair(_1495524, _1495524), _1495530), _1495526)), _1495528)), -(hBOOL(hAPP(hAPP(c_member(_1495524), _1495530), c_Wellfounded_Oacc(_1495524, _1495528))))], (14321 ^ _781215) ^ [_1031731] : [class_Rings_Oring__1(_1031731), -(hBOOL(hAPP(hAPP(c_member(_1031731), c_Groups_Ozero__class_Ozero(_1031731)), c_Int_Oring__1__class_OInts(_1031731))))], (14750 ^ _781215) ^ [_1039437, _1039439] : [class_Int_Onumber__ring(_1039437), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1039437), hAPP(c_Int_Onumber__class_Onumber__of(_1039437), _1039439)) = hAPP(c_Int_Onumber__class_Onumber__of(_1039437), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1039439)))], (19556 ^ _781215) ^ [_1132171, _1132173, _1132175] : [class_Orderings_Olinorder(_1132171), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132171), _1132173)), hBOOL(hAPP(hAPP(c_member(_1132171), _1132175), _1132173)), 19567 ^ _781215 : [(19574 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1132171, tc_HOL_Obool)), _1132173), hAPP(hAPP(c_Set_Oinsert(_1132171), _1132175), c_Orderings_Obot__class_Obot(tc_fun(_1132171, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1132171, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1132171, _1132173) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1132171), _1132175), c_Big__Operators_Olinorder__class_OMax(_1132171, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1132171, tc_HOL_Obool)), _1132173), hAPP(hAPP(c_Set_Oinsert(_1132171), _1132175), c_Orderings_Obot__class_Obot(tc_fun(_1132171, tc_HOL_Obool)))))))], (19568 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1132171, tc_HOL_Obool)), _1132173), hAPP(hAPP(c_Set_Oinsert(_1132171), _1132175), c_Orderings_Obot__class_Obot(tc_fun(_1132171, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1132171, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1132171, _1132173) = _1132175)]]], (4256 ^ _781215) ^ [_845819, _845821] : [_845821 = _845819, -(c_Code__Numeral_OSuc__code__numeral(_845821) = c_Code__Numeral_OSuc__code__numeral(_845819))], (40349 ^ _781215) ^ [_1570279, _1570281] : [c_Wellfounded_OwfP(_1570279, _1570281), -(c_Wellfounded_Owf(_1570279, hAPP(c_Set_OCollect(tc_prod(_1570279, _1570279)), hAPP(c_Product__Type_Oprod_Oprod__case(_1570279, _1570279, tc_HOL_Obool), _1570281))))], (42311 ^ _781215) ^ [_1618584, _1618586, _1618588, _1618590] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618584), tc_List_Olist(_1618584))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618584), tc_List_Olist(_1618584)), _1618588), _1618590)), c_List_Olistrel(_1618584, _1618586))), -(c_List_Olistrelp(_1618584, hAPP(hAPP(c_COMBC(_1618584, tc_fun(tc_prod(_1618584, _1618584), tc_HOL_Obool), tc_fun(_1618584, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1618584, tc_fun(tc_fun(tc_prod(_1618584, _1618584), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1618584, _1618584), tc_HOL_Obool), tc_fun(_1618584, tc_HOL_Obool)), _1618584), c_COMBC(_1618584, tc_fun(tc_prod(_1618584, _1618584), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1618584, tc_prod(_1618584, _1618584)), tc_fun(_1618584, tc_fun(tc_fun(tc_prod(_1618584, _1618584), tc_HOL_Obool), tc_HOL_Obool)), _1618584), hAPP(c_COMBB(tc_prod(_1618584, _1618584), tc_fun(tc_fun(tc_prod(_1618584, _1618584), tc_HOL_Obool), tc_HOL_Obool), _1618584), c_member(tc_prod(_1618584, _1618584)))), c_Product__Type_OPair(_1618584, _1618584)))), _1618586), _1618588, _1618590))], (30395 ^ _781215) ^ [_1337173, _1337175] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337173), _1337175))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1337175, _1337173) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1337175), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1337175), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1337173)))], (51386 ^ _781215) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (31068 ^ _781215) ^ [_1349831, _1349833] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1349831)), _1349833) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1349831, _1349833))], (30191 ^ _781215) ^ [_1333653, _1333655, _1333657] : [class_Orderings_Oorder(_1333653), 30194 ^ _781215 : [(30201 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333653), _1333655), _1333657))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1333653, _1333655, _1333657) = c_Orderings_Obot__class_Obot(tc_fun(_1333653, tc_HOL_Obool)))], (30195 ^ _781215) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1333653, _1333655, _1333657) = c_Orderings_Obot__class_Obot(tc_fun(_1333653, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333653), _1333655), _1333657))]]], (44894 ^ _781215) ^ [_1681631] : [-(c_List_Orotate(_1681631, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1681631)))], (25284 ^ _781215) ^ [_1237108, _1237110] : [c_Nat__Transfer_Ois__nat(_1237108), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1237108), _1237110)))], (49199 ^ _781215) ^ [_1775234, _1775236] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775234, _1775234)), hAPP(hAPP(c_Product__Type_OPair(_1775234, _1775234), _1775236), _1775236)), c_Relation_OId(_1775234))))], (35156 ^ _781215) ^ [_1441263] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1441263))], (21299 ^ _781215) ^ [_1162776, _1162778, _1162780, _1162782, _1162784, _1162786] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162776, tc_fun(_1162778, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162780, tc_fun(_1162776, tc_HOL_Obool)), _1162782), _1162784)), _1162786) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162780, tc_fun(_1162778, tc_HOL_Obool)), _1162782), hAPP(hAPP(c_COMBC(_1162780, tc_fun(_1162776, tc_fun(_1162778, tc_HOL_Obool)), tc_fun(_1162778, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1162776, tc_HOL_Obool), tc_fun(tc_fun(_1162776, tc_fun(_1162778, tc_HOL_Obool)), tc_fun(_1162778, tc_HOL_Obool)), _1162780), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1162776, tc_fun(_1162778, tc_HOL_Obool))), _1162784)), _1162786)))], (40136 ^ _781215) ^ [_1564845, _1564847, _1564849, _1564851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564845, _1564847), tc_HOL_Obool)), _1564849), _1564851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564845, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1564845, _1564847), _1564849)), hAPP(c_Relation_ODomain(_1564845, _1564847), _1564851))))], (48970 ^ _781215) ^ [] : [-(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))], (2420 ^ _781215) ^ [_816997, _816999, _817001, _817003, _817005, _817007, _817009, _817011, _817013, _817015] : [-(c_Product__Type_Oprod_Oprod__size(_817015, _817011, _817007, _817003, _816999) = c_Product__Type_Oprod_Oprod__size(_817013, _817009, _817005, _817001, _816997)), _817015 = _817013, _817011 = _817009, _817007 = _817005, _817003 = _817001, _816999 = _816997], (42959 ^ _781215) ^ [_1635967, _1635969, _1635971, _1635973] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635967)), hAPP(hAPP(c_List_Olist__update(_1635967, _1635969), _1635971), _1635973)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635967)), _1635969))], (40854 ^ _781215) ^ [_1581876, _1581878, _1581880] : [c_Hoare__Mirabelle_Ohoare__valids(_1581876, _1581878, _1581880), 40857 ^ _781215 : [(40858 ^ _781215) ^ [_1581985] : [40860 ^ _781215 : [(40863 ^ _781215) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1581876, _1581985, 40859 ^ [_1581876, _1581878, _1581880, _1581985])], (40861 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1581876)), 40859 ^ [_1581876, _1581878, _1581880, _1581985]), _1581878)))]], 40864 ^ _781215 : [(40865 ^ _781215) ^ [_1582157] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1581876)), _1582157), _1581880)), -(c_Hoare__Mirabelle_Otriple__valid(_1581876, _1581985, _1582157))]]]]], (27902 ^ _781215) ^ [_1289902, _1289904, _1289906, _1289908] : [class_Rings_Odivision__ring(_1289902), -(_1289904 = c_Groups_Ozero__class_Ozero(_1289902)), 27909 ^ _781215 : [(27916 ^ _781215) ^ [] : [_1289906 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289902), _1289908), _1289904), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289902), _1289906), _1289904) = _1289908)], (27910 ^ _781215) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289902), _1289906), _1289904) = _1289908, -(_1289906 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289902), _1289908), _1289904))]]], (35610 ^ _781215) ^ [_1450506, _1450508, _1450510, _1450512, _1450514] : [class_Groups_Ocomm__monoid__add(_1450506), class_Groups_Ocomm__monoid__mult(_1450506), _1450508 = _1450510, c_Nat__Transfer_Onat__set(_1450510), 35628 ^ _781215 : [(35631 ^ _781215) ^ [] : [hAPP(_1450512, 35627 ^ [_1450506, _1450508, _1450510, _1450512, _1450514]) = hAPP(_1450514, 35627 ^ [_1450506, _1450508, _1450510, _1450512, _1450514])], (35629 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35627 ^ [_1450506, _1450508, _1450510, _1450512, _1450514])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1450506), _1450512), _1450508) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1450506), _1450514), _1450510))], (27426 ^ _781215) ^ [_1280260, _1280262, _1280264, _1280266] : [hAPP(c_Product__Type_Ofst(_1280260, _1280262), _1280264) = hAPP(c_Product__Type_Ofst(_1280260, _1280262), _1280266), hAPP(c_Product__Type_Osnd(_1280260, _1280262), _1280264) = hAPP(c_Product__Type_Osnd(_1280260, _1280262), _1280266), -(_1280264 = _1280266)], (22212 ^ _781215) ^ [_1181947, _1181949] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181947, _1181949) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181947), _1181949)), _1181949)))], (46387 ^ _781215) ^ [_1713267, _1713269, _1713271] : [class_Orderings_Olinorder(_1713267), c_List_Olinorder__class_Osorted(_1713267, hAPP(c_List_Orev(_1713267), _1713269)), 46394 ^ _781215 : [(46401 ^ _781215) ^ [] : [-(_1713269 = c_List_Olist_ONil(_1713267)), -(c_List_Ofoldr(_1713267, _1713267, c_Orderings_Oord__class_Omax(_1713267), _1713269, _1713271) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1713267), hAPP(hAPP(c_List_Onth(_1713267), _1713269), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1713271))], (46395 ^ _781215) ^ [] : [_1713269 = c_List_Olist_ONil(_1713267), -(c_List_Ofoldr(_1713267, _1713267, c_Orderings_Oord__class_Omax(_1713267), _1713269, _1713271) = _1713271)]]], (39232 ^ _781215) ^ [_1534840, _1534842, _1534844] : [-(hAPP(hAPP(c_Set_Oinsert(_1534840), _1534842), _1534844) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1534840, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1534840), hAPP(hAPP(c_COMBC(_1534840, _1534840, tc_HOL_Obool), c_fequal), _1534842))), _1534844))], (23955 ^ _781215) ^ [_1213025, _1213027, _1213029] : [-(hBOOL(hAPP(_1213025, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1213027), _1213029)))), 23958 ^ _781215 : [(23961 ^ _781215) ^ [] : [hBOOL(hAPP(_1213025, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23959 ^ _781215) ^ [] : [-(_1213029 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 23962 ^ _781215 : [(23967 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 23965 ^ [_1213025, _1213027, _1213029]), _1213029)))], (23969 ^ _781215) ^ [] : [-(_1213027 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1213029), 23964 ^ [_1213025, _1213027, _1213029])), 23965 ^ [_1213025, _1213027, _1213029]))], (23971 ^ _781215) ^ [] : [hBOOL(hAPP(_1213025, 23964 ^ [_1213025, _1213027, _1213029]))], (23963 ^ _781215) ^ [] : [_1213029 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (29004 ^ _781215) ^ [_1309992, _1309994, _1309996, _1309998] : [class_Fields_Olinordered__field(_1309992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309992), _1309994), _1309996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309992), _1309998), c_Groups_Ozero__class_Ozero(_1309992))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309992), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309992), _1309996), _1309998)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309992), _1309994), _1309998))))], (9021 ^ _781215) ^ [_934274, _934276] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934274, tc_HOL_Obool)), _934276), _934276)))], (6752 ^ _781215) ^ [_891975, _891977, _891979, _891981, _891983] : [c_Finite__Set_Ofolding__one(_891975, _891977, _891979), hBOOL(hAPP(c_Finite__Set_Ofinite(_891975), _891981)), -(hBOOL(hAPP(hAPP(c_member(_891975), _891983), _891981))), -(_891981 = c_Orderings_Obot__class_Obot(tc_fun(_891975, tc_HOL_Obool))), -(hAPP(_891979, hAPP(hAPP(c_Set_Oinsert(_891975), _891983), _891981)) = hAPP(hAPP(_891977, _891983), hAPP(_891979, _891981)))], (19090 ^ _781215) ^ [_1123618, _1123620] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123618)), _1123620) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1123618), 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), _1123618)), _1123620))], (51686 ^ _781215) ^ [] : [hBOOL(c_fFalse)], (46807 ^ _781215) ^ [_1722352, _1722354, _1722356] : [-(c_List_OdropWhile(_1722352, _1722354, _1722356) = hAPP(hAPP(c_List_Odrop(_1722352), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722352)), c_List_OtakeWhile(_1722352, _1722354, _1722356))), _1722356))], (32213 ^ _781215) ^ [_1376271, _1376273, _1376275, _1376277, _1376279] : [class_Groups_Oordered__ab__group__add(_1376271), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376273), _1376275)), 32223 ^ _781215 : [(32226 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376271), c_Groups_Ozero__class_Ozero(_1376271)), hAPP(_1376277, 32222 ^ [_1376271, _1376273, _1376275, _1376277, _1376279])))], (32224 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376273), 32222 ^ [_1376271, _1376273, _1376275, _1376277, _1376279]), _1376275)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1376273, _1376271), _1376277), _1376275) = c_Groups_Ozero__class_Ozero(_1376271), hBOOL(hAPP(hAPP(c_member(_1376273), _1376279), _1376275)), -(hAPP(_1376277, _1376279) = c_Groups_Ozero__class_Ozero(_1376271))], (22344 ^ _781215) ^ [_1184654, _1184656, _1184658, _1184660, _1184662, _1184664] : [class_Divides_Osemiring__div(_1184654), c_Divides_Odiv__class_Omod(_1184654, _1184656, _1184658) = c_Divides_Odiv__class_Omod(_1184654, _1184660, _1184658), c_Divides_Odiv__class_Omod(_1184654, _1184662, _1184658) = c_Divides_Odiv__class_Omod(_1184654, _1184664, _1184658), -(c_Divides_Odiv__class_Omod(_1184654, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184654), _1184656), _1184662), _1184658) = c_Divides_Odiv__class_Omod(_1184654, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184654), _1184660), _1184664), _1184658))], (36448 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (27448 ^ _781215) ^ [_1280823, _1280825] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1280823), _1280825) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1280823, _1280825)))], (43079 ^ _781215) ^ [_1638809, _1638811, _1638813] : [c_Relation_Orefl__on(_1638809, _1638811, _1638813), -(c_Relation_Orefl__on(tc_List_Olist(_1638809), c_List_Olists(_1638809, _1638811), c_List_Olistrel(_1638809, _1638813)))], (19990 ^ _781215) ^ [_1139828, _1139830] : [class_Groups_Olinordered__ab__group__add(_1139828), hBOOL(hAPP(c_Finite__Set_Ofinite(_1139828), _1139830)), -(_1139830 = c_Orderings_Obot__class_Obot(tc_fun(_1139828, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1139828), c_Big__Operators_Olinorder__class_OMin(_1139828, _1139830)) = c_Big__Operators_Olinorder__class_OMax(_1139828, hAPP(c_Set_Oimage(_1139828, _1139828, c_Groups_Ouminus__class_Ouminus(_1139828)), _1139830)))], (33266 ^ _781215) ^ [_1399972, _1399974] : [c_Nat__Transfer_Onat__set(_1399972), c_Nat__Transfer_Onat__set(_1399974), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1399972), _1399974) = 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), _1399972)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1399974))))], (5154 ^ _781215) ^ [_859824, _859826, _859828, _859830, _859832, _859834, _859836, _859838] : [-(c_New__Random__Sequence_Oneg__bind(_859838, _859834, _859830, _859826) = c_New__Random__Sequence_Oneg__bind(_859836, _859832, _859828, _859824)), _859838 = _859836, _859834 = _859832, _859830 = _859828, _859826 = _859824], (50706 ^ _781215) ^ [_1812270] : [class_HOL_Oequal(_1812270), -(c_fequal = c_HOL_Oequal__class_Oequal(_1812270))], (13396 ^ _781215) ^ [_1014160, _1014162] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014160), _1014162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014160), _1014162)))], (17499 ^ _781215) ^ [_1094441] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094441)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094441)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1094441)))], (46127 ^ _781215) ^ [_1706943, _1706945, _1706947] : [_1706947 = hAPP(hAPP(c_List_Olist_OCons(_1706943), _1706945), c_List_Olist_ONil(_1706943)), -(hAPP(hAPP(c_List_Olist_OCons(_1706943), _1706945), c_List_Olist_ONil(_1706943)) = hAPP(c_List_Orev(_1706943), _1706947))], (14884 ^ _781215) ^ [_1042153, _1042155, _1042157, _1042159] : [c_Com_Ocom_OCond(_1042153, _1042155, _1042157) = hAPP(c_Com_Ocom_OBODY, _1042159)], (49750 ^ _781215) ^ [_1789448, _1789450, _1789452] : [hAPP(hAPP(c_Relation_Orel__comp(_1789448, _1789448, _1789448), hAPP(c_Relation_Oconverse(_1789448, _1789448), _1789450)), _1789450) = _1789450, hAPP(c_Relation_ODomain(_1789448, _1789448), _1789450) = _1789452, -(c_Equiv__Relations_Oequiv(_1789448, _1789452, _1789450))], (37556 ^ _781215) ^ [_1494479] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1494479, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1494479, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1494479, tc_HOL_Obool)))], (36526 ^ _781215) ^ [] : [-(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)))], (15548 ^ _781215) ^ [_1053991, _1053993, _1053995, _1053997, _1053999] : [-(c_Map_Omap__comp(_1053991, _1053993, _1053995, hAPP(c_COMBK(tc_Option_Ooption(_1053993), _1053991), c_Option_Ooption_ONone(_1053993)), _1053997, _1053999) = c_Option_Ooption_ONone(_1053993))], (43472 ^ _781215) ^ [_1648888, _1648890] : [-(c_Hilbert__Choice_OEps(_1648888, hAPP(hAPP(c_COMBC(_1648888, _1648888, tc_HOL_Obool), c_fequal), _1648890)) = _1648890)], (39444 ^ _781215) ^ [_1542519] : [-(c_Wellfounded_Ofinite__psubset(_1542519) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1542519, tc_HOL_Obool), tc_fun(_1542519, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1542519, tc_HOL_Obool), tc_fun(_1542519, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1542519, tc_HOL_Obool), tc_fun(tc_fun(_1542519, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1542519, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542519, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1542519, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1542519, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1542519, tc_HOL_Obool)), c_COMBS(tc_fun(_1542519, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542519, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1542519, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1542519, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1542519, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1542519, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1542519)))))], (15727 ^ _781215) ^ [_1057833, _1057835, _1057837] : [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), _1057833), _1057835)), _1057837))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057837), _1057833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057835)))], (14732 ^ _781215) ^ [_1038992, _1038994, _1038996, _1038998] : [class_Int_Onumber__ring(_1038992), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038992), hAPP(c_Int_Onumber__class_Onumber__of(_1038992), _1038994)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038992), hAPP(c_Int_Onumber__class_Onumber__of(_1038992), _1038996)), _1038998)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038992), hAPP(c_Int_Onumber__class_Onumber__of(_1038992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1038994), _1038996))), _1038998))], (1708 ^ _781215) ^ [_805535, _805537] : [-(class_Rings_Ozero__neq__one(_805535)), _805537 = _805535, class_Rings_Ozero__neq__one(_805537)], (27197 ^ _781215) ^ [_1275782, _1275784, _1275786] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1275782, _1275782), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1275784), _1275786))), -(_1275782 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1275786 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14852 ^ _781215) ^ [_1041530, _1041532, _1041534, _1041536, _1041538] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1041530, _1041532, _1041534)), _1041536), _1041538)), 14857 ^ _781215 : [(14860 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1041532), _1041536), _1041538)))], (14858 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1041530, _1041536)))]], 14861 ^ _781215 : [(14864 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1041534), _1041536), _1041538)))], (14862 ^ _781215) ^ [] : [hBOOL(hAPP(_1041530, _1041536))]]], (30700 ^ _781215) ^ [_1343059, _1343061, _1343063] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1343059)), 30703 ^ _781215 : [(30704 ^ _781215) ^ [_1343193] : [30706 ^ _781215 : [(30712 ^ _781215) ^ [] : [-(_1343193 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30708 ^ [_1343059, _1343061, _1343063, _1343193]), 30705 ^ [_1343059, _1343061, _1343063, _1343193]))], (30710 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30708 ^ [_1343059, _1343061, _1343063, _1343193]), _1343061)))], (30707 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30705 ^ [_1343059, _1343061, _1343063, _1343193]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1343059))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1343063), _1343193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1343063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1343193), _1343059))))]]], (45580 ^ _781215) ^ [_1696073, _1696075, _1696077] : [class_Orderings_Olinorder(_1696073), 45583 ^ _781215 : [(45590 ^ _781215) ^ [] : [c_List_Olinorder__class_Osorted(_1696073, _1696077), -(c_List_Olinorder__class_Osorted(_1696073, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696073, _1696073, c_COMBI(_1696073)), _1696075), _1696077)))], (45584 ^ _781215) ^ [] : [c_List_Olinorder__class_Osorted(_1696073, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696073, _1696073, c_COMBI(_1696073)), _1696075), _1696077)), -(c_List_Olinorder__class_Osorted(_1696073, _1696077))]]], (15096 ^ _781215) ^ [_1046245, _1046247, _1046249] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_1046245, _1046247, _1046249)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1046249)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44421 ^ _781215) ^ [_1670332, _1670334, _1670336, _1670338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670332), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670334)), _1670336))), -(hAPP(hAPP(c_List_Onth(_1670334), hAPP(hAPP(c_List_Oappend(_1670334), _1670336), _1670338)), _1670332) = hAPP(hAPP(c_List_Onth(_1670334), _1670336), _1670332))], (30770 ^ _781215) ^ [_1344505, _1344507] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1344505, _1344505)), _1344507)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1344505), hAPP(c_Relation_OField(_1344505), _1344507))))], (50671 ^ _781215) ^ [] : [-(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))))], (49421 ^ _781215) ^ [_1780639, _1780641, _1780643] : [_1780641 = _1780643, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780639, _1780639)), hAPP(hAPP(c_Product__Type_OPair(_1780639, _1780639), _1780641), _1780643)), c_Relation_OId(_1780639))))], (49327 ^ _781215) ^ [_1778447, _1778449, _1778451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778447, _1778447), tc_HOL_Obool)), _1778449), _1778451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778447, _1778447), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1778447, _1778449)), c_Transitive__Closure_Ortrancl(_1778447, _1778451))))], (39608 ^ _781215) ^ [_1549525] : [-(c_Int_Oint__ge__less__than2(_1549525) = 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), _1549525)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (38554 ^ _781215) ^ [_1518271, _1518273, _1518275, _1518277, _1518279] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518271, _1518273), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518271, tc_HOL_Obool)), _1518275), _1518277)), _1518279) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1518271, _1518273), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518271, _1518273), _1518275), _1518279)), hAPP(hAPP(c_Product__Type_OSigma(_1518271, _1518273), _1518277), _1518279)))], (5662 ^ _781215) ^ [_870607, _870609, _870611, _870613, _870615] : [hAPP(hAPP(c_Set_Oinsert(_870607), _870609), hAPP(hAPP(c_Set_Oinsert(_870607), _870611), c_Orderings_Obot__class_Obot(tc_fun(_870607, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_870607), _870613), hAPP(hAPP(c_Set_Oinsert(_870607), _870615), c_Orderings_Obot__class_Obot(tc_fun(_870607, tc_HOL_Obool)))), 5667 ^ _781215 : [(5670 ^ _781215) ^ [] : [-(_870611 = _870615)], (5668 ^ _781215) ^ [] : [-(_870609 = _870613)]], 5671 ^ _781215 : [(5674 ^ _781215) ^ [] : [-(_870611 = _870613)], (5672 ^ _781215) ^ [] : [-(_870609 = _870615)]]], (5744 ^ _781215) ^ [_872128, _872130, _872132, _872134] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_872128), _872130), _872132), _872134)), -(_872130 = _872134), -(hBOOL(hAPP(_872132, _872134)))], (48721 ^ _781215) ^ [_1765022, _1765024, _1765026, _1765028] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1765022, _1765024, _1765026, tc_prod(_1765024, _1765026)), _1765028), c_Product__Type_OPair(_1765024, _1765026)) = _1765028)], (24400 ^ _781215) ^ [_1221150, _1221152, _1221154] : [class_Rings_Olinordered__semidom(_1221150), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221150), hAPP(hAPP(c_Power_Opower__class_Opower(_1221150), _1221152), 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(_1221150), _1221154), 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(_1221150), c_Groups_Ozero__class_Ozero(_1221150)), _1221154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221150), _1221152), _1221154)))], (24590 ^ _781215) ^ [_1225084, _1225086, _1225088, _1225090] : [class_Rings_Olinordered__semidom(_1225084), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225084), _1225086), _1225088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225084), c_Groups_Ozero__class_Ozero(_1225084)), _1225086)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225084), hAPP(hAPP(c_Power_Opower__class_Opower(_1225084), _1225086), _1225090)), hAPP(hAPP(c_Power_Opower__class_Opower(_1225084), _1225088), _1225090))))], (41845 ^ _781215) ^ [_1605413, _1605415, _1605417, _1605419] : [hBOOL(hAPP(c_List_Odistinct(_1605413), _1605415)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1605417, _1605413)), hAPP(hAPP(c_List_Ozip(_1605417, _1605413), _1605419), _1605415))))], (31403 ^ _781215) ^ [_1356671] : [-(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)), _1356671)) = hAPP(c_Int_Onat, _1356671))], (3058 ^ _781215) ^ [_827142, _827144, _827146, _827148, _827150, _827152, _827154, _827156] : [-(c_Wellfounded_Olex__prod(_827156, _827152, _827148, _827144) = c_Wellfounded_Olex__prod(_827154, _827150, _827146, _827142)), _827156 = _827154, _827152 = _827150, _827148 = _827146, _827144 = _827142], (39482 ^ _781215) ^ [_1544068, _1544070, _1544072] : [class_Lattices_Odistrib__lattice(_1544068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544068), _1544070)), -(_1544070 = c_Orderings_Obot__class_Obot(tc_fun(_1544068, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1544068), _1544072), c_Big__Operators_Olattice__class_OInf__fin(_1544068, _1544070)) = c_Big__Operators_Olattice__class_OInf__fin(_1544068, hAPP(c_Set_OCollect(_1544068), hAPP(hAPP(c_COMBB(tc_fun(_1544068, tc_HOL_Obool), tc_HOL_Obool, _1544068), c_HOL_OEx(_1544068)), hAPP(hAPP(c_COMBC(_1544068, tc_fun(_1544068, tc_HOL_Obool), tc_fun(_1544068, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544068, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1544068, tc_HOL_Obool), tc_fun(_1544068, tc_HOL_Obool)), _1544068), c_COMBS(_1544068, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544068, tc_HOL_Obool), tc_fun(_1544068, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1544068), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1544068), c_fconj)), hAPP(hAPP(c_COMBC(_1544068, tc_fun(_1544068, _1544068), tc_fun(_1544068, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544068, tc_HOL_Obool), tc_fun(tc_fun(_1544068, _1544068), tc_fun(_1544068, tc_HOL_Obool)), _1544068), c_COMBB(_1544068, tc_HOL_Obool, _1544068)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1544068), _1544072))))), hAPP(hAPP(c_COMBC(_1544068, tc_fun(_1544068, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544068)), _1544070))))))], (30119 ^ _781215) ^ [_1332067, _1332069, _1332071] : [-(hAPP(c_Set_OPow(_1332067), hAPP(hAPP(c_Set_Oinsert(_1332067), _1332069), _1332071)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1332067, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1332067), _1332071)), hAPP(c_Set_Oimage(tc_fun(_1332067, tc_HOL_Obool), tc_fun(_1332067, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1332067), _1332069)), hAPP(c_Set_OPow(_1332067), _1332071))))], (17709 ^ _781215) ^ [_1097717] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097717) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1097717)))], (7692 ^ _781215) ^ [_910670, _910672, _910674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910670), _910672)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910670), _910674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _910674), _910672)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _910674), _910670))))], (15360 ^ _781215) ^ [_1050489, _1050491, _1050493] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050489), _1050491)), _1050493) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050491), _1050493)))], (39143 ^ _781215) ^ [_1532792, _1532794] : [c_Orderings_Obot__class_Obot(tc_fun(_1532792, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1532792), _1532794), 39146 ^ _781215 : [(39147 ^ _781215) ^ [_1532877] : [hBOOL(hAPP(_1532794, _1532877))]]], (38336 ^ _781215) ^ [_1512162, _1512164, _1512166, _1512168] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512162), hAPP(c_Set_Ovimage(_1512162, _1512164, _1512166), _1512168))), hAPP(c_Set_Oimage(_1512162, _1512164, _1512166), c_Orderings_Otop__class_Otop(tc_fun(_1512162, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1512164, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512164), _1512168)))], (51170 ^ _781215) ^ [] : [-(class_HOL_Oequal(tc_Com_Ocom))], (40960 ^ _781215) ^ [_1584656, _1584658, _1584660, _1584662, _1584664] : [c_Fun_Oinj__on(_1584656, _1584658, _1584660, c_Orderings_Otop__class_Otop(tc_fun(_1584656, tc_HOL_Obool))), 40963 ^ _781215 : [(40970 ^ _781215) ^ [] : [_1584662 = _1584664, -(hAPP(hAPP(c_List_Omap(_1584656, _1584658), _1584660), _1584662) = hAPP(hAPP(c_List_Omap(_1584656, _1584658), _1584660), _1584664))], (40964 ^ _781215) ^ [] : [hAPP(hAPP(c_List_Omap(_1584656, _1584658), _1584660), _1584662) = hAPP(hAPP(c_List_Omap(_1584656, _1584658), _1584660), _1584664), -(_1584662 = _1584664)]]], (26356 ^ _781215) ^ [_1259412, _1259414, _1259416, _1259418, _1259420] : [class_Groups_Ocomm__monoid__mult(_1259412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1259414), _1259416)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1259414, _1259412), _1259418), hAPP(hAPP(c_Set_Oinsert(_1259414), _1259420), _1259416)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1259412), hAPP(_1259418, _1259420)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1259414, _1259412), _1259418), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1259414, tc_HOL_Obool)), _1259416), hAPP(hAPP(c_Set_Oinsert(_1259414), _1259420), c_Orderings_Obot__class_Obot(tc_fun(_1259414, tc_HOL_Obool)))))))], (30822 ^ _781215) ^ [_1345594, _1345596, _1345598] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1345594), _1345596))), 30825 ^ _781215 : [(30832 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1345598), _1345596))), -(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)), _1345594)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1345598), _1345596)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (30826 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1345598), _1345596)), -(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)), _1345594)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1345598), _1345596)) = 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))))]]], (26562 ^ _781215) ^ [_1263059, _1263061, _1263063, _1263065, _1263067, _1263069] : [26563 ^ _781215 : [(26566 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1263065, _1263061), _1263063))], (26564 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(_1263059, _1263061), _1263063))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263067, tc_fun(_1263069, tc_HOL_Obool))), _1263065), _1263059), _1263061), _1263063)))], (24684 ^ _781215) ^ [_1226807, _1226809] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1226807), _1226809) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1226809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1226807 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45744 ^ _781215) ^ [_1698732, _1698734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1698732), _1698734)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1698732, _1698734)) = _1698732)], (42128 ^ _781215) ^ [_1612400, _1612402, _1612404, _1612406, _1612408] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612400)), _1612402) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612404)), _1612406), 42131 ^ _781215 : [(42140 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1612400, _1612404), _1612402), _1612406) = _1612408), hAPP(hAPP(c_List_Omap(tc_prod(_1612400, _1612404), _1612400), c_Product__Type_Ofst(_1612400, _1612404)), _1612408) = _1612402, hAPP(hAPP(c_List_Omap(tc_prod(_1612400, _1612404), _1612404), c_Product__Type_Osnd(_1612400, _1612404)), _1612408) = _1612406], (42132 ^ _781215) ^ [] : [hAPP(hAPP(c_List_Ozip(_1612400, _1612404), _1612402), _1612406) = _1612408, 42135 ^ _781215 : [(42138 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1612400, _1612404), _1612404), c_Product__Type_Osnd(_1612400, _1612404)), _1612408) = _1612406)], (42136 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1612400, _1612404), _1612400), c_Product__Type_Ofst(_1612400, _1612404)), _1612408) = _1612402)]]]]], (40715 ^ _781215) ^ [_1579189, _1579191, _1579193, _1579195, _1579197] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1579189, _1579191)), _1579193), _1579195), _1579197))), 40716 ^ _781215 : [(40723 ^ _781215) ^ [] : [hBOOL(hAPP(_1579189, _1579193)), 40726 ^ _781215 : [(40727 ^ _781215) ^ [_1579426] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1579191), _1579193), _1579195), _1579426)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1579189, _1579191)), _1579426), _1579195), _1579197))]]], (40717 ^ _781215) ^ [] : [_1579197 = _1579193, -(hBOOL(hAPP(_1579189, _1579193)))]]], (37163 ^ _781215) ^ [_1484633, _1484635, _1484637, _1484639, _1484641] : [-(_1484633 = c_Orderings_Obot__class_Obot(tc_fun(_1484635, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484637, tc_HOL_Obool)), _1484639), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484635, tc_fun(_1484637, tc_HOL_Obool)), _1484633), _1484641)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484635, tc_fun(_1484637, tc_HOL_Obool)), _1484633), hAPP(hAPP(c_COMBB(tc_fun(_1484637, tc_HOL_Obool), tc_fun(_1484637, tc_HOL_Obool), _1484635), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484637, tc_HOL_Obool)), _1484639)), _1484641)))], (43684 ^ _781215) ^ [_1653794, _1653796, _1653798, _1653800] : [-(c_List_Ofoldr(_1653794, _1653796, _1653798, c_List_Olist_ONil(_1653794), _1653800) = _1653800)], (43095 ^ _781215) ^ [_1639192, _1639194, _1639196, _1639198] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1639192)), hAPP(hAPP(c_List_Olist_OCons(_1639192), _1639194), _1639196)), c_List_Olists(_1639192, _1639198)))), hBOOL(hAPP(hAPP(c_member(_1639192), _1639194), _1639198)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1639192)), _1639196), c_List_Olists(_1639192, _1639198)))], (38731 ^ _781215) ^ [_1523189, _1523191, _1523193, _1523195, _1523197, _1523199] : [class_Groups_Ocomm__monoid__mult(_1523189), hBOOL(hAPP(c_Finite__Set_Ofinite(_1523191), _1523193)), 38741 ^ _781215 : [(38744 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523195), hAPP(_1523197, 38740 ^ [_1523189, _1523191, _1523193, _1523195, _1523197, _1523199])))], (38742 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1523191), 38740 ^ [_1523189, _1523191, _1523193, _1523195, _1523197, _1523199]), _1523193)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1523191, _1523189), hAPP(hAPP(c_COMBS(_1523191, tc_fun(_1523195, tc_HOL_Obool), _1523189), hAPP(hAPP(c_COMBB(tc_fun(_1523195, _1523189), tc_fun(tc_fun(_1523195, tc_HOL_Obool), _1523189), _1523191), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1523195, _1523189)), _1523199)), _1523197)), _1523193) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1523191, _1523195), _1523189), hAPP(c_Product__Type_Oprod_Oprod__case(_1523191, _1523195, _1523189), _1523199)), hAPP(hAPP(c_Product__Type_OSigma(_1523191, _1523195), _1523193), _1523197)))], (8249 ^ _781215) ^ [_920341, _920343, _920345, _920347] : [class_Groups_Ocancel__ab__semigroup__add(_920341), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920341), _920343), _920345) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920341), _920343), _920347), -(_920345 = _920347)], (35711 ^ _781215) ^ [_1452697, _1452699, _1452701] : [class_Rings_Olinordered__idom(_1452697), -(hAPP(c_Groups_Oabs__class_Oabs(_1452697), hAPP(hAPP(c_Power_Opower__class_Opower(_1452697), _1452699), _1452701)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1452697), hAPP(c_Groups_Oabs__class_Oabs(_1452697), _1452699)), _1452701))], (32872 ^ _781215) ^ [_1390601, _1390603] : [class_Lattices_Obounded__lattice__bot(_1390601), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1390601), c_Orderings_Obot__class_Obot(_1390601)), _1390603) = c_Orderings_Obot__class_Obot(_1390601))], (38748 ^ _781215) ^ [_1523666, _1523668, _1523670, _1523672, _1523674, _1523676] : [class_Groups_Ocomm__monoid__add(_1523666), hBOOL(hAPP(c_Finite__Set_Ofinite(_1523668), _1523670)), 38758 ^ _781215 : [(38761 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523672), hAPP(_1523674, 38757 ^ [_1523666, _1523668, _1523670, _1523672, _1523674, _1523676])))], (38759 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1523668), 38757 ^ [_1523666, _1523668, _1523670, _1523672, _1523674, _1523676]), _1523670)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1523668, _1523666), hAPP(hAPP(c_COMBS(_1523668, tc_fun(_1523672, tc_HOL_Obool), _1523666), hAPP(hAPP(c_COMBB(tc_fun(_1523672, _1523666), tc_fun(tc_fun(_1523672, tc_HOL_Obool), _1523666), _1523668), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1523672, _1523666)), _1523676)), _1523674)), _1523670) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1523668, _1523672), _1523666), hAPP(c_Product__Type_Oprod_Oprod__case(_1523668, _1523672, _1523666), _1523676)), hAPP(hAPP(c_Product__Type_OSigma(_1523668, _1523672), _1523670), _1523674)))], (39987 ^ _781215) ^ [_1561946, _1561948, _1561950] : [c_Wellfounded_Owf(_1561946, _1561948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561946, _1561946), tc_HOL_Obool)), _1561950), _1561948)), -(c_Wellfounded_Owf(_1561946, _1561950))], (25456 ^ _781215) ^ [_1239717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1239717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1239717)))], (30552 ^ _781215) ^ [_1340180, _1340182, _1340184] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1340180, tc_HOL_Obool)), _1340184), hAPP(c_Set_OPow(_1340180), _1340182))), -(hBOOL(hAPP(c_Predicate_OPowp(_1340180, hAPP(hAPP(c_COMBC(_1340180, tc_fun(_1340180, tc_HOL_Obool), tc_HOL_Obool), c_member(_1340180)), _1340182)), _1340184)))], (49317 ^ _781215) ^ [_1778174, _1778176, _1778178, _1778180, _1778182] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1778174, _1778174)), hAPP(hAPP(c_Product__Type_OPair(_1778174, _1778174), _1778176), _1778178)), c_Transitive__Closure_Ortrancl(_1778174, _1778180))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778174, _1778174)), hAPP(hAPP(c_Product__Type_OPair(_1778174, _1778174), _1778178), _1778182)), c_Transitive__Closure_Ortrancl(_1778174, _1778180))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778174, _1778174)), hAPP(hAPP(c_Product__Type_OPair(_1778174, _1778174), _1778176), _1778182)), c_Transitive__Closure_Ortrancl(_1778174, _1778180))))], (44341 ^ _781215) ^ [_1668203, _1668205, _1668207, _1668209] : [-(hAPP(hAPP(c_List_Onth(_1668203), hAPP(hAPP(c_List_Oappend(_1668203), _1668205), _1668207)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668203)), _1668205)), _1668209)) = hAPP(hAPP(c_List_Onth(_1668203), _1668207), _1668209))], (43087 ^ _781215) ^ [_1639011, _1639013, _1639015, _1639017] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1639011)), hAPP(hAPP(c_List_Olist_OCons(_1639011), _1639013), _1639015)), c_List_Olists(_1639011, _1639017))), 43090 ^ _781215 : [(43093 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1639011)), _1639015), c_List_Olists(_1639011, _1639017))))], (43091 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1639011), _1639013), _1639017)))]]], (7634 ^ _781215) ^ [_909417, _909419, _909421, _909423, _909425, _909427] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909417, _909419), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909417, _909419), _909421), _909423), _909425)), _909423), _909427) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909417, _909419), _909421), _909423), _909427))], (14062 ^ _781215) ^ [_1026429, _1026431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1026429), _1026431))), 14065 ^ _781215 : [(14068 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1026429), _1026431)))], (14066 ^ _781215) ^ [] : [_1026431 = c_Orderings_Obot__class_Obot(tc_fun(_1026429, tc_HOL_Obool))]]], (43950 ^ _781215) ^ [_1659160, _1659162] : [-(c_List_Oset__Cons(_1659160, _1659162, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1659160)), c_List_Olist_ONil(_1659160)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1659160), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1659160, tc_List_Olist(_1659160), hAPP(hAPP(c_COMBC(_1659160, tc_List_Olist(_1659160), tc_List_Olist(_1659160)), c_List_Olist_OCons(_1659160)), c_List_Olist_ONil(_1659160))), _1659162))], (26881 ^ _781215) ^ [_1269673, _1269675, _1269677] : [hBOOL(hAPP(_1269673, 26882 ^ [_1269673, _1269675, _1269677])), 26885 ^ _781215 : [(26886 ^ _781215) ^ [_1269784, _1269786] : [-(hBOOL(hAPP(_1269673, hAPP(hAPP(c_Product__Type_OPair(_1269675, _1269677), _1269786), _1269784))))]]], (10542 ^ _781215) ^ [_961499, _961501, _961503, _961505] : [-(hBOOL(hAPP(hAPP(c_member(_961499), _961501), _961503))), 10545 ^ _781215 : [(10552 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961499, tc_HOL_Obool)), _961503), _961505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961499, tc_HOL_Obool)), _961503), hAPP(hAPP(c_Set_Oinsert(_961499), _961501), _961505))))], (10546 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961499, tc_HOL_Obool)), _961503), hAPP(hAPP(c_Set_Oinsert(_961499), _961501), _961505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961499, tc_HOL_Obool)), _961503), _961505)))]]], (18153 ^ _781215) ^ [_1106253, _1106255] : [class_Orderings_Olinorder(_1106253), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1106253), _1106255), _1106255) = _1106255)], (14391 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17519 ^ _781215) ^ [_1094704, _1094706] : [class_Int_Onumber__ring(_1094704), 17522 ^ _781215 : [(17529 ^ _781215) ^ [] : [c_Int_Oiszero(_1094704, hAPP(c_Int_Onumber__class_Onumber__of(_1094704), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094706)))), -(c_Groups_Ozero__class_Ozero(_1094704) = hAPP(c_Int_Onumber__class_Onumber__of(_1094704), _1094706))], (17523 ^ _781215) ^ [] : [c_Groups_Ozero__class_Ozero(_1094704) = hAPP(c_Int_Onumber__class_Onumber__of(_1094704), _1094706), -(c_Int_Oiszero(_1094704, hAPP(c_Int_Onumber__class_Onumber__of(_1094704), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094706)))))]]], (35469 ^ _781215) ^ [_1447783] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1447783)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1447783)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1447783), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (47737 ^ _781215) ^ [_1742252, _1742254, _1742256, _1742258, _1742260] : [c_List_Olist__all2(_1742252, _1742254, _1742256, _1742258, _1742260), -(c_List_Olist__all2(_1742252, _1742254, _1742256, hAPP(c_List_Orev(_1742252), _1742258), hAPP(c_List_Orev(_1742254), _1742260)))], (25859 ^ _781215) ^ [_1250192, _1250194, _1250196] : [class_Int_Oring__char__0(_1250192), 25862 ^ _781215 : [(25869 ^ _781215) ^ [] : [_1250194 = _1250196, -(hAPP(c_Int_Oring__1__class_Oof__int(_1250192), _1250194) = hAPP(c_Int_Oring__1__class_Oof__int(_1250192), _1250196))], (25863 ^ _781215) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1250192), _1250194) = hAPP(c_Int_Oring__1__class_Oof__int(_1250192), _1250196), -(_1250194 = _1250196)]]], (42044 ^ _781215) ^ [_1610651, _1610653, _1610655] : [class_Orderings_Olinorder(_1610651), -(c_List_Oremove1(_1610651, _1610653, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1610651, _1610651, c_COMBI(_1610651)), _1610653), _1610655)) = _1610655)], (24170 ^ _781215) ^ [_1217173] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1217173))), 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), _1217173), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (39092 ^ _781215) ^ [_1531722, _1531724, _1531726] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1531722), hAPP(c_Set_OCollect(_1531722), hAPP(hAPP(c_COMBS(_1531722, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1531722), c_fdisj), _1531724)), _1531726)))), 39095 ^ _781215 : [(39098 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1531722), hAPP(c_Set_OCollect(_1531722), _1531726))))], (39096 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1531722), hAPP(c_Set_OCollect(_1531722), _1531724))))]]], (8646 ^ _781215) ^ [_927919, _927921, _927923] : [class_Groups_Oordered__ab__group__add(_927919), 8649 ^ _781215 : [(8656 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927919), _927923), hAPP(c_Groups_Ouminus__class_Ouminus(_927919), _927921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927919), _927921), hAPP(c_Groups_Ouminus__class_Ouminus(_927919), _927923))))], (8650 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927919), _927921), hAPP(c_Groups_Ouminus__class_Ouminus(_927919), _927923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927919), _927923), hAPP(c_Groups_Ouminus__class_Ouminus(_927919), _927921))))]]], (51650 ^ _781215) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (1668 ^ _781215) ^ [_805035, _805037] : [-(class_Groups_Osemigroup__add(_805035)), _805037 = _805035, class_Groups_Osemigroup__add(_805037)], (27265 ^ _781215) ^ [_1276617, _1276619] : [-(_1276617 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1276619, _1276617), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1276619), _1276617)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1276619, _1276617)))))], (4568 ^ _781215) ^ [_850485, _850487] : [_850487 = _850485, -(c_Divides_Odiv__class_Odiv(_850487) = c_Divides_Odiv__class_Odiv(_850485))], (49974 ^ _781215) ^ [_1794637, _1794639, _1794641] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1794637, _1794637, _1794637), _1794639), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794637, _1794637), tc_HOL_Obool), _1794641), _1794639)) = hAPP(hAPP(c_Relation_Orel__comp(_1794637, _1794637, _1794637), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1794637, _1794637), tc_HOL_Obool), _1794641), _1794639)), _1794639))], (37061 ^ _781215) ^ [_1482174, _1482176, _1482178, _1482180, _1482182, _1482184] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482174, tc_fun(_1482176, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482178, tc_fun(_1482174, tc_HOL_Obool)), _1482180), _1482182)), _1482184) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482178, tc_fun(_1482176, tc_HOL_Obool)), _1482180), hAPP(hAPP(c_COMBC(_1482178, tc_fun(_1482174, tc_fun(_1482176, tc_HOL_Obool)), tc_fun(_1482176, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1482174, tc_HOL_Obool), tc_fun(tc_fun(_1482174, tc_fun(_1482176, tc_HOL_Obool)), tc_fun(_1482176, tc_HOL_Obool)), _1482178), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482174, tc_fun(_1482176, tc_HOL_Obool))), _1482182)), _1482184)))], (37604 ^ _781215) ^ [_1495410, _1495412, _1495414, _1495416] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1495410, tc_fun(_1495412, tc_HOL_Obool)), _1495414), _1495416) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1495412, tc_HOL_Obool), hAPP(c_Set_Oimage(_1495410, tc_fun(_1495412, tc_HOL_Obool), _1495416), _1495414)))], (6088 ^ _781215) ^ [_879032, _879034, _879036, _879038] : [-(c_Com_Ocom_OSemi(_879032, _879034) = c_Com_Ocom_OSemi(_879036, _879038)), _879032 = _879036, _879034 = _879038], (18441 ^ _781215) ^ [_1111418, _1111420, _1111422, _1111424] : [class_Orderings_Olinorder(_1111418), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111418), _1111420)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1111418, _1111418, c_Orderings_Oord__class_Omin(_1111418)), _1111422), hAPP(hAPP(c_Set_Oinsert(_1111418), _1111424), _1111420)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1111418), _1111424), hAPP(hAPP(c_Finite__Set_Ofold(_1111418, _1111418, c_Orderings_Oord__class_Omin(_1111418)), _1111422), _1111420)))], (39158 ^ _781215) ^ [_1532996, _1532998, _1533000] : [-(hAPP(c_Set_OCollect(_1532996), hAPP(hAPP(c_COMBS(_1532996, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532996), c_fdisj), _1532998)), _1533000)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1532996, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1532996), _1532998)), hAPP(c_Set_OCollect(_1532996), _1533000)))], (13228 ^ _781215) ^ [_1011261, _1011263] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1011261), _1011263))), -(hAPP(c_Finite__Set_Ocard(_1011261), _1011263) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21626 ^ _781215) ^ [_1169197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1169197), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1169197)), c_Int_OPls)))], (16277 ^ _781215) ^ [_1068888, _1068890, _1068892] : [class_Lattices_Olattice(_1068888), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068888), _1068890), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068888), _1068890), _1068892))))], (9829 ^ _781215) ^ [_948244, _948246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_948244, tc_HOL_Obool)), _948246), c_Orderings_Obot__class_Obot(tc_fun(_948244, tc_HOL_Obool)))), -(_948246 = c_Orderings_Obot__class_Obot(tc_fun(_948244, tc_HOL_Obool)))], (45448 ^ _781215) ^ [_1693831] : [class_Orderings_Olinorder(_1693831), -(c_List_Olinorder__class_Osorted(_1693831, c_List_Olist_ONil(_1693831)))], (14244 ^ _781215) ^ [_1030239] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _1030239)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40298 ^ _781215) ^ [_1569142, _1569144, _1569146, _1569148] : [hBOOL(hAPP(c_Predicate_ODomainP(_1569142, _1569144, _1569146), _1569148)), -(hBOOL(hAPP(hAPP(_1569146, _1569148), 40301 ^ [_1569142, _1569144, _1569146, _1569148])))], (10696 ^ _781215) ^ [_964366, _964368, _964370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964366), _964368)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964368), _964366)), _964370) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964368), _964370)), _964366))], (31202 ^ _781215) ^ [_1352511, _1352513, _1352515] : [class_Orderings_Olinorder(_1352511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352511), _1352513), _1352515)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352511, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1352511), _1352513), c_Orderings_Obot__class_Obot(tc_fun(_1352511, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1352511, _1352513, _1352515)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1352511, _1352513), _1352515))], (45332 ^ _781215) ^ [_1690658, _1690660, _1690662] : [45334 ^ _781215 : [(45337 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1690660, 45333 ^ [_1690658, _1690660, _1690662])))], (45335 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1690658), 45333 ^ [_1690658, _1690660, _1690662]), hAPP(c_List_Oset(_1690658), _1690662))))]], -(hAPP(c_List_Ofilter(_1690658, _1690660), _1690662) = c_List_Olist_ONil(_1690658))], (36588 ^ _781215) ^ [_1468834, _1468836] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468834, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468834, tc_HOL_Obool)), _1468836)), _1468836) = c_Orderings_Otop__class_Otop(tc_fun(_1468834, tc_HOL_Obool)))], (37345 ^ _781215) ^ [_1489451, _1489453, _1489455, _1489457, _1489459, _1489461, _1489463, _1489465] : [c_Fun_Oinj__on(_1489451, _1489453, _1489455, _1489457), 37351 ^ _781215 : [(37354 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489451, tc_HOL_Obool)), hAPP(_1489463, 37350 ^ [_1489451, _1489453, _1489455, _1489457, _1489459, _1489461, _1489463, _1489465])), _1489457))], (37352 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1489459), 37350 ^ [_1489451, _1489453, _1489455, _1489457, _1489459, _1489461, _1489463, _1489465]), _1489461)))]], hBOOL(hAPP(hAPP(c_member(_1489459), _1489465), _1489461)), -(hAPP(c_Set_Oimage(_1489451, _1489453, _1489455), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1489459, tc_fun(_1489451, tc_HOL_Obool)), _1489461), _1489463)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1489459, tc_fun(_1489453, tc_HOL_Obool)), _1489461), hAPP(hAPP(c_COMBB(tc_fun(_1489451, tc_HOL_Obool), tc_fun(_1489453, tc_HOL_Obool), _1489459), c_Set_Oimage(_1489451, _1489453, _1489455)), _1489463)))], (29088 ^ _781215) ^ [_1311550, _1311552, _1311554] : [class_Fields_Olinordered__field__inverse__zero(_1311550), 29091 ^ _781215 : [(29106 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311550), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311550), _1311552), _1311554)), c_Groups_Ozero__class_Ozero(_1311550)))), 29107 ^ _781215 : [(29114 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311550), _1311552), c_Groups_Ozero__class_Ozero(_1311550))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311550), c_Groups_Ozero__class_Ozero(_1311550)), _1311554))], (29108 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311550), c_Groups_Ozero__class_Ozero(_1311550)), _1311552)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311550), _1311554), c_Groups_Ozero__class_Ozero(_1311550)))]]], (29092 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311550), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1311550), _1311552), _1311554)), c_Groups_Ozero__class_Ozero(_1311550))), 29097 ^ _781215 : [(29100 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311550), _1311554), c_Groups_Ozero__class_Ozero(_1311550))))], (29098 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311550), c_Groups_Ozero__class_Ozero(_1311550)), _1311552)))]], 29101 ^ _781215 : [(29104 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311550), c_Groups_Ozero__class_Ozero(_1311550)), _1311554)))], (29102 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311550), _1311552), c_Groups_Ozero__class_Ozero(_1311550))))]]]]], (16061 ^ _781215) ^ [_1064982, _1064984, _1064986, _1064988] : [class_Lattices_Osemilattice__sup(_1064982), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064982), _1064984), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064982), _1064986), _1064988)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064982), _1064986), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064982), _1064984), _1064988)))], (9143 ^ _781215) ^ [_936363, _936365] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936363), _936365))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936365), _936363)))], (43696 ^ _781215) ^ [_1654000, _1654002, _1654004] : [-(hAPP(hAPP(c_List_Ozip(_1654000, _1654002), c_List_Olist_ONil(_1654000)), _1654004) = c_List_Olist_ONil(tc_prod(_1654000, _1654002)))], (5823 ^ _781215) ^ [_873850] : [-(hAPP(c_Com_Obody, _873850) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _873850))))], (4588 ^ _781215) ^ [_850791, _850793] : [_850793 = _850791, -(c_Groups_Otimes__class_Otimes(_850793) = c_Groups_Otimes__class_Otimes(_850791))], (30816 ^ _781215) ^ [_1345442, _1345444, _1345446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1345442), _1345444)), -(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)), _1345442)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1345446), _1345444)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1345446), _1345442)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1345444), _1345442)))], (9965 ^ _781215) ^ [_950694, _950696] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _950694), _950696))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950694), _950696)), -(_950694 = _950696)], (41291 ^ _781215) ^ [_1592268, _1592270, _1592272, _1592274, _1592276, _1592278] : [-(hAPP(hAPP(c_Fun_Ocomp(_1592268, _1592270, _1592272, hAPP(c_COMBK(_1592270, _1592268), _1592274)), _1592276), _1592278) = _1592274)], (39168 ^ _781215) ^ [_1533446, _1533448, _1533450, _1533452] : [hBOOL(hAPP(hAPP(c_member(_1533446), _1533448), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533446, tc_HOL_Obool)), _1533450), hAPP(c_Set_OCollect(_1533446), _1533452)))), 39171 ^ _781215 : [(39174 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1533452, _1533448)))], (39172 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1533446), _1533448), _1533450)))]]], (20749 ^ _781215) ^ [_1153369, _1153371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1153369), _1153371)), -(_1153371 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153369), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 20752 ^ [_1153369, _1153371]))))], (50281 ^ _781215) ^ [_1803189, _1803191] : [-(c_Wellfounded_Owf(_1803189, _1803191)), 50284 ^ _781215 : [(50287 ^ _781215) ^ [_1803409] : [hBOOL(hAPP(hAPP(c_member(_1803189), _1803409), 50282 ^ [_1803189, _1803191])), 50291 ^ _781215 : [(50294 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803189), 50290 ^ [_1803189, _1803191, _1803409]), 50282 ^ [_1803189, _1803191])))], (50292 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1803189, _1803189)), hAPP(hAPP(c_Product__Type_OPair(_1803189, _1803189), 50290 ^ [_1803189, _1803191, _1803409]), _1803409)), _1803191)))]]], (50285 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803189), 50283 ^ [_1803189, _1803191]), 50282 ^ [_1803189, _1803191])))]]], (44162 ^ _781215) ^ [_1664168, _1664170, _1664172] : [hAPP(hAPP(c_List_Oappend(_1664168), _1664170), _1664172) = _1664170, -(_1664172 = c_List_Olist_ONil(_1664168))], (1994 ^ _781215) ^ [_810214, _810216] : [_810216 = _810214, -(c_Nat_Onat_Onat__size(_810216) = c_Nat_Onat_Onat__size(_810214))], (24888 ^ _781215) ^ [_1230319, _1230321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1230319)), -(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), _1230319), _1230321))))], (11194 ^ _781215) ^ [_975559, _975561, _975563, _975565] : [class_Rings_Ocomm__semiring__1(_975559), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975559), _975561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975559), _975563), _975565)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975559), _975561), _975563)), _975565))], (33152 ^ _781215) ^ [_1397080, _1397082, _1397084] : [class_Lattices_Oboolean__algebra(_1397080), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1397080), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1397080), _1397082), _1397084)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1397080), hAPP(c_Groups_Ouminus__class_Ouminus(_1397080), _1397082)), hAPP(c_Groups_Ouminus__class_Ouminus(_1397080), _1397084)))], (3142 ^ _781215) ^ [_828492, _828494] : [_828494 = _828492, -(c_HOL_OAll(_828494) = c_HOL_OAll(_828492))], (16589 ^ _781215) ^ [_1077100, _1077102, _1077104] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1077100), _1077102)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1077100, tc_HOL_Obool)), _1077102), _1077104) = hAPP(hAPP(c_Finite__Set_Ofold(_1077100, tc_fun(_1077100, tc_HOL_Obool), c_Set_Oinsert(_1077100)), _1077104), _1077102))], (45117 ^ _781215) ^ [_1686739, _1686741, _1686743] : [_1686739 = c_List_Olist_ONil(_1686741), -(c_List_Olast(_1686741, hAPP(hAPP(c_List_Oappend(_1686741), _1686743), _1686739)) = c_List_Olast(_1686741, _1686743))], (13654 ^ _781215) ^ [_1018844, _1018846, _1018848, _1018850, _1018852] : [class_Rings_Olinordered__semiring__strict(_1018844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018844), _1018846), _1018848)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018844), _1018850), _1018852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018844), c_Groups_Ozero__class_Ozero(_1018844)), _1018846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018844), c_Groups_Ozero__class_Ozero(_1018844)), _1018850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018844), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018844), _1018846), _1018850)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018844), _1018848), _1018852))))], (32860 ^ _781215) ^ [_1390383, _1390385, _1390387] : [class_Lattices_Olattice(_1390383), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1390383), _1390385), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1390383), _1390385), _1390387)) = _1390385)], (48133 ^ _781215) ^ [_1751849, _1751851, _1751853] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1751849), c_Map_Odom(_1751849, _1751851, _1751853))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1751849), c_Orderings_Otop__class_Otop(tc_fun(_1751849, tc_HOL_Obool))))), -(hAPP(_1751853, 48140 ^ [_1751849, _1751851, _1751853]) = c_Option_Ooption_ONone(_1751851))], (36732 ^ _781215) ^ [_1471871, _1471873, _1471875, _1471877, _1471879] : [c_Fun_Oinj__on(_1471871, _1471873, _1471875, c_Orderings_Otop__class_Otop(tc_fun(_1471871, tc_HOL_Obool))), 36735 ^ _781215 : [(36742 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471871, tc_HOL_Obool)), _1471877), _1471879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471873, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471871, _1471873, _1471875), _1471877)), hAPP(c_Set_Oimage(_1471871, _1471873, _1471875), _1471879))))], (36736 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471873, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471871, _1471873, _1471875), _1471877)), hAPP(c_Set_Oimage(_1471871, _1471873, _1471875), _1471879))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471871, tc_HOL_Obool)), _1471877), _1471879)))]]], (18369 ^ _781215) ^ [_1109944, _1109946, _1109948, _1109950] : [class_Orderings_Olinorder(_1109944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109944), _1109946), _1109948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109944), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1109944), _1109950), _1109946)), _1109948)))], (47719 ^ _781215) ^ [_1741929, _1741931, _1741933, _1741935] : [c_List_Olist__all2(_1741929, _1741931, _1741933, _1741935, c_List_Olist_ONil(_1741931)), -(_1741935 = c_List_Olist_ONil(_1741929))], (9023 ^ _781215) ^ [_934309, _934311, _934313] : [class_Lattices_Oboolean__algebra(_934309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934309), _934311), _934313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934309), hAPP(c_Groups_Ouminus__class_Ouminus(_934309), _934313)), hAPP(c_Groups_Ouminus__class_Ouminus(_934309), _934311))))], (8608 ^ _781215) ^ [_927266, _927268, _927270] : [class_Groups_Oordered__ab__group__add(_927266), 8611 ^ _781215 : [(8618 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927266), hAPP(c_Groups_Ouminus__class_Ouminus(_927266), _927270)), _927268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927266), hAPP(c_Groups_Ouminus__class_Ouminus(_927266), _927268)), _927270)))], (8612 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927266), hAPP(c_Groups_Ouminus__class_Ouminus(_927266), _927268)), _927270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927266), hAPP(c_Groups_Ouminus__class_Ouminus(_927266), _927270)), _927268)))]]], (3558 ^ _781215) ^ [_835140, _835142, _835144, _835146] : [-(c_List_Olast(_835146, _835142) = c_List_Olast(_835144, _835140)), _835146 = _835144, _835142 = _835140], (39848 ^ _781215) ^ [_1557436, _1557438, _1557440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557436, _1557436), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1557436, _1557436, _1557436), _1557438), _1557440)), _1557438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1557436, tc_HOL_Obool), tc_fun(_1557436, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1557436, tc_HOL_Obool), tc_fun(_1557436, tc_HOL_Obool), tc_fun(_1557436, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1557436, _1557438)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1557436, tc_HOL_Obool), tc_fun(_1557436, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1557436, _1557440)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1557436, tc_HOL_Obool), tc_fun(_1557436, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1557436, tc_HOL_Obool), tc_fun(_1557436, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1557436, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1557436, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1557436, tc_HOL_Obool), tc_fun(_1557436, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1557436, _1557438))))], (16943 ^ _781215) ^ [_1085401] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1085401) = c_Int_OPls)], (27864 ^ _781215) ^ [_1289217, _1289219, _1289221, _1289223] : [class_Rings_Odivision__ring(_1289217), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1289217), _1289219), _1289221)), _1289223) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1289217), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289217), _1289219), _1289223)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289217), _1289221), _1289223)))], (49935 ^ _781215) ^ [_1793763, _1793765, _1793767] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1793763, _1793763)), _1793765), c_Transitive__Closure_Ortrancl(_1793763, _1793767))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1793763, _1793763)), _1793765), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1793763, _1793763), 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(_1793763, _1793763), tc_HOL_Obool), tc_fun(tc_prod(_1793763, _1793763), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1793763, _1793763), tc_HOL_Obool)), _1793767)))))], (39064 ^ _781215) ^ [_1531176, _1531178, _1531180] : [hBOOL(hAPP(hAPP(c_member(_1531176), _1531178), hAPP(c_Set_OCollect(_1531176), _1531180))), -(hBOOL(hAPP(_1531180, _1531178)))], (10158 ^ _781215) ^ [_954269, _954271, _954273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954269), _954271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954269), _954273)), 10165 ^ _781215 : [(10172 ^ _781215) ^ [] : [_954271 = _954273, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954271), _954269) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954273), _954269))], (10166 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954271), _954269) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954273), _954269), -(_954271 = _954273)]]], (1198 ^ _781215) ^ [_799160, _799162] : [-(class_Rings_Ocomm__ring__1(_799160)), _799162 = _799160, class_Rings_Ocomm__ring__1(_799162)], (42285 ^ _781215) ^ [_1617772, _1617774, _1617776] : [hBOOL(hAPP(c_List_Odistinct(_1617772), _1617774)), -(hBOOL(hAPP(c_List_Odistinct(_1617772), c_List_Osublist(_1617772, _1617774, _1617776))))], (28798 ^ _781215) ^ [_1306124, _1306126, _1306128, _1306130] : [class_Fields_Olinordered__field__inverse__zero(_1306124), 28801 ^ _781215 : [(28802 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306124), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306124), _1306126), _1306128)), _1306130)), 28805 ^ _781215 : [(28812 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306124), c_Groups_Ozero__class_Ozero(_1306124)), _1306128))), 28815 ^ _781215 : [(28822 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306124), _1306128), c_Groups_Ozero__class_Ozero(_1306124)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306124), c_Groups_Ozero__class_Ozero(_1306124)), _1306130)))], (28816 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306124), _1306128), c_Groups_Ozero__class_Ozero(_1306124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306124), _1306130), _1306128)), _1306126)))]]], (28806 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306124), c_Groups_Ozero__class_Ozero(_1306124)), _1306128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306124), _1306126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306124), _1306130), _1306128))))]]], (28828 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306124), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306124), _1306126), _1306128)), _1306130))), 28831 ^ _781215 : [(28834 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306124), _1306126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306124), _1306130), _1306128)))], (28832 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306124), c_Groups_Ozero__class_Ozero(_1306124)), _1306128)))]], 28835 ^ _781215 : [(28838 ^ _781215) ^ [] : [28839 ^ _781215 : [(28842 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306124), _1306130), _1306128)), _1306126))], (28840 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306124), _1306128), c_Groups_Ozero__class_Ozero(_1306124))))]], 28843 ^ _781215 : [(28846 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306124), c_Groups_Ozero__class_Ozero(_1306124)), _1306130))], (28844 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306124), _1306128), c_Groups_Ozero__class_Ozero(_1306124)))]]], (28836 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306124), c_Groups_Ozero__class_Ozero(_1306124)), _1306128))]]]]], (44892 ^ _781215) ^ [_1681545, _1681547, _1681549] : [-(hAPP(c_List_Otl(_1681545), hAPP(hAPP(c_List_Oappend(_1681545), _1681547), _1681549)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1681545), _1681545, hAPP(c_List_Otl(_1681545), _1681549), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1681545), tc_List_Olist(_1681545)), _1681545), hAPP(hAPP(c_COMBC(tc_List_Olist(_1681545), tc_List_Olist(_1681545), tc_List_Olist(_1681545)), c_List_Oappend(_1681545)), _1681549))), _1681547))], (48842 ^ _781215) ^ [_1767387, _1767389, _1767391, _1767393] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1767387), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1767389), _1767391)))), -(hAPP(c_Random_Opick(_1767389, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1767389)), _1767391), _1767393)), _1767387) = hAPP(c_Random_Opick(_1767389, _1767393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1767387), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1767389), _1767391))))], (10612 ^ _781215) ^ [_962806, _962808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962806), _962808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962806), hAPP(c_Nat_OSuc, _962808))))], (37135 ^ _781215) ^ [_1484070, _1484072, _1484074, _1484076] : [class_Complete__Lattice_Ocomplete__lattice(_1484070), -(_1484072 = c_Orderings_Obot__class_Obot(tc_fun(_1484074, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484074, _1484070), _1484072), hAPP(c_COMBK(_1484070, _1484074), _1484076)) = _1484076)], (36261 ^ _781215) ^ [_1462840, _1462842] : [-(c_Nitpick_Oint__lcm(_1462840, _1462842) = 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), _1462840)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1462842)))))], (42064 ^ _781215) ^ [_1611063, _1611065] : [hAPP(c_Finite__Set_Ocard(_1611063), hAPP(c_List_Oset(_1611063), _1611065)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611063)), _1611065), -(hBOOL(hAPP(c_List_Odistinct(_1611063), _1611065)))], (17595 ^ _781215) ^ [_1096016, _1096018] : [class_Rings_Osemiring__1(_1096016), 17598 ^ _781215 : [(17605 ^ _781215) ^ [] : [_1096018 = c_Groups_Ozero__class_Ozero(_1096016), -(c_Int_Oiszero(_1096016, _1096018))], (17599 ^ _781215) ^ [] : [c_Int_Oiszero(_1096016, _1096018), -(_1096018 = c_Groups_Ozero__class_Ozero(_1096016))]]], (35931 ^ _781215) ^ [_1456774, _1456776, _1456778] : [class_Groups_Oordered__ab__group__add__abs(_1456774), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456774), _1456776), _1456778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456774), hAPP(c_Groups_Ouminus__class_Ouminus(_1456774), _1456776)), _1456778)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456774), hAPP(c_Groups_Oabs__class_Oabs(_1456774), _1456776)), _1456778)))], (37472 ^ _781215) ^ [_1492844, _1492846, _1492848, _1492850] : [hBOOL(hAPP(hAPP(c_member(_1492844), _1492846), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1492844, tc_HOL_Obool), _1492848))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1492844, tc_HOL_Obool)), _1492850), _1492848)), -(hBOOL(hAPP(hAPP(c_member(_1492844), _1492846), _1492850)))], (29480 ^ _781215) ^ [_1318529, _1318531, _1318533, _1318535] : [class_Fields_Olinordered__field(_1318529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318529), c_Groups_Ozero__class_Ozero(_1318529)), _1318531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318529), _1318533), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318529), _1318535), _1318531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318529), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318529), _1318533), _1318531)), _1318535)))], (42100 ^ _781215) ^ [_1611877, _1611879, _1611881, _1611883, _1611885] : [class_Orderings_Olinorder(_1611877), 42103 ^ _781215 : [(42112 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1611879), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1611879, _1611877, _1611881), _1611883), _1611885)))), -(hBOOL(hAPP(hAPP(c_member(_1611879), _1611883), hAPP(c_List_Oset(_1611879), _1611885)))), hBOOL(hAPP(c_List_Odistinct(_1611879), _1611885))], (42104 ^ _781215) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1611879), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1611879, _1611877, _1611881), _1611883), _1611885))), 42107 ^ _781215 : [(42110 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1611879), _1611885)))], (42108 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1611879), _1611883), hAPP(c_List_Oset(_1611879), _1611885)))]]]]], (39022 ^ _781215) ^ [_1530364] : [-(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)), _1530364)))))], (32170 ^ _781215) ^ [_1375226, _1375228, _1375230] : [class_Groups_Ocomm__monoid__add(_1375226), class_Groups_Ocomm__monoid__mult(_1375226), c_Nat__Transfer_Onat__set(_1375228), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1375226), _1375230), _1375228) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1375226), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1375226, tc_Nat_Onat), _1375230), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1375228)))], (50900 ^ _781215) ^ [_1815468, _1815470, _1815472, _1815474, _1815476] : [-(hAPP(c_New__DSequence_Opos__bind(_1815468, _1815470, _1815472, _1815474), _1815476) = hAPP(c_Lazy__Sequence_Obind(_1815468, _1815470, hAPP(_1815472, _1815476)), hAPP(hAPP(c_COMBC(_1815468, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1815470)), _1815474), _1815476)))], (38276 ^ _781215) ^ [_1510546, _1510548, _1510550, _1510552] : [-(hAPP(c_Set_Ovimage(_1510546, _1510548, _1510550), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1510548, tc_HOL_Obool)), _1510552)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1510546, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1510546, _1510548, _1510550), _1510552)))], (31650 ^ _781215) ^ [_1363352, _1363354, _1363356, _1363358] : [class_Groups_Ocomm__monoid__add(_1363352), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363352), _1363354), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1363356), hAPP(c_Nat_OSuc, _1363358))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363352), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1363352, tc_Nat_Onat), _1363354), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1363356, _1363358)))], (20322 ^ _781215) ^ [_1146020, _1146022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146020), _1146022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1146020)), c_Int_OBit1(_1146022))))], (39090 ^ _781215) ^ [_1531665] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1531665, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1531665), hAPP(c_COMBK(tc_HOL_Obool, _1531665), c_fTrue)))], (16011 ^ _781215) ^ [_1063777, _1063779, _1063781, _1063783] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063777, tc_HOL_Obool)), _1063779), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063777, tc_HOL_Obool)), _1063781), _1063783)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063777, tc_HOL_Obool)), _1063781), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063777, tc_HOL_Obool)), _1063779), _1063783)))], (24972 ^ _781215) ^ [_1231953, _1231955] : [class_Power_Opower(_1231953), class_Rings_Osemiring__0(_1231953), 24979 ^ _781215 : [(24986 ^ _781215) ^ [] : [-(_1231955 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1231953), c_Groups_Ozero__class_Ozero(_1231953)), _1231955) = c_Groups_Ozero__class_Ozero(_1231953))], (24980 ^ _781215) ^ [] : [_1231955 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1231953), c_Groups_Ozero__class_Ozero(_1231953)), _1231955) = c_Groups_Oone__class_Oone(_1231953))]]], (4792 ^ _781215) ^ [_853793, _853795] : [_853795 = _853793, -(c_Nat_Osemiring__1__class_Oof__nat(_853795) = c_Nat_Osemiring__1__class_Oof__nat(_853793))], (43816 ^ _781215) ^ [_1656145] : [-(hAPP(c_List_Oset(_1656145), c_List_Olist_ONil(_1656145)) = c_Orderings_Obot__class_Obot(tc_fun(_1656145, tc_HOL_Obool)))], (24127 ^ _781215) ^ [_1216318, _1216320, _1216322] : [hBOOL(hAPP(_1216318, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1216320), _1216322))), 24132 ^ _781215 : [(24135 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1216318, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24133 ^ _781215) ^ [] : [-(_1216322 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 24137 ^ _781215 : [(24142 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1216318, 24136 ^ [_1216318, _1216320, _1216322])))], (24140 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1216320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216322), hAPP(c_Nat_OSuc, 24136 ^ [_1216318, _1216320, _1216322])))))], (24138 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216322), 24136 ^ [_1216318, _1216320, _1216322])), _1216320)))]]], (49684 ^ _781215) ^ [_1787768, _1787770, _1787772] : [-(hAPP(c_Relation_ORange(_1787768, _1787770), _1787772) = hAPP(c_Relation_ODomain(_1787770, _1787768), hAPP(c_Relation_Oconverse(_1787768, _1787770), _1787772)))], (51664 ^ _781215) ^ [_1825543, _1825545] : [-(hAPP(c_COMBI(_1825543), _1825545) = _1825545)], (5865 ^ _781215) ^ [_874501, _874503, _874505, _874507, _874509, _874511] : [-(c_Com_Ocom_OCall(_874501, _874503, _874505) = c_Com_Ocom_OCall(_874507, _874509, _874511)), _874501 = _874507, _874503 = _874509, _874505 = _874511], (51438 ^ _781215) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (3904 ^ _781215) ^ [_840411, _840413, _840415, _840417, _840419, _840421] : [-(c_Predicate_ODomainP(_840421, _840417, _840413) = c_Predicate_ODomainP(_840419, _840415, _840411)), _840421 = _840419, _840417 = _840415, _840413 = _840411], (20486 ^ _781215) ^ [_1148898, _1148900] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148898)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148900)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1148898), _1148900)))], (36067 ^ _781215) ^ [_1459375, _1459377, _1459379] : [class_Groups_Oordered__ab__group__add__abs(_1459375), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459375), hAPP(c_Groups_Oabs__class_Oabs(_1459375), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1459375), _1459377), _1459379))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1459375), hAPP(c_Groups_Oabs__class_Oabs(_1459375), _1459377)), hAPP(c_Groups_Oabs__class_Oabs(_1459375), _1459379)))))], (40982 ^ _781215) ^ [_1585080, _1585082, _1585084, _1585086, _1585088] : [hAPP(hAPP(c_List_Omap(_1585080, _1585082), _1585084), _1585086) = hAPP(hAPP(c_List_Omap(_1585080, _1585082), _1585084), _1585088), c_Fun_Oinj__on(_1585080, _1585082, _1585084, c_Orderings_Otop__class_Otop(tc_fun(_1585080, tc_HOL_Obool))), -(_1585086 = _1585088)], (7718 ^ _781215) ^ [_911177, _911179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _911177)), _911179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911177), _911179)))], (8504 ^ _781215) ^ [_925518, _925520, _925522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925518, tc_HOL_Obool)), _925520), _925522)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925518, tc_HOL_Obool)), _925522), _925520)), -(_925520 = _925522)], (4 ^ _781215) ^ [_781265, _781267] : [_781267 = _781265, -(_781265 = _781267)], (44852 ^ _781215) ^ [_1680747, _1680749, _1680751, _1680753] : [-(hAPP(hAPP(c_List_Omap(_1680747, _1680749), _1680751), hAPP(c_List_Otl(_1680747), _1680753)) = hAPP(c_List_Otl(_1680749), hAPP(hAPP(c_List_Omap(_1680747, _1680749), _1680751), _1680753)))], (8730 ^ _781215) ^ [_929274, _929276, _929278, _929280, _929282] : [class_Orderings_Oord(_929274), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929276, _929274)), _929278), _929280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929274), hAPP(_929278, _929282)), hAPP(_929280, _929282))))], (25520 ^ _781215) ^ [_1240599, _1240601, _1240603, _1240605, _1240607] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1240599, _1240601, _1240603), _1240605), hAPP(c_Nat_OSuc, _1240607)) = hAPP(hAPP(_1240603, _1240605), hAPP(hAPP(c_Power_Opower_Opower(_1240599, _1240601, _1240603), _1240605), _1240607)))], (49129 ^ _781215) ^ [_1772654, _1772656, _1772658, _1772660, _1772662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1772654, _1772654)), hAPP(hAPP(c_Product__Type_OPair(_1772654, _1772654), _1772656), _1772658)), c_Transitive__Closure_Otrancl(_1772654, _1772660))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772654, _1772654)), hAPP(hAPP(c_Product__Type_OPair(_1772654, _1772654), _1772658), _1772662)), _1772660)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1772654, _1772654)), hAPP(hAPP(c_Product__Type_OPair(_1772654, _1772654), _1772656), _1772662)), c_Transitive__Closure_Otrancl(_1772654, _1772660))))], (8542 ^ _781215) ^ [_926151, _926153, _926155] : [class_Rings_Oidom(_926151), 8545 ^ _781215 : [(8546 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926151), _926153), _926153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926151), _926155), _926155), -(_926153 = _926155), -(_926153 = hAPP(c_Groups_Ouminus__class_Ouminus(_926151), _926155))], (8556 ^ _781215) ^ [] : [8557 ^ _781215 : [(8560 ^ _781215) ^ [] : [_926153 = hAPP(c_Groups_Ouminus__class_Ouminus(_926151), _926155)], (8558 ^ _781215) ^ [] : [_926153 = _926155]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926151), _926153), _926153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926151), _926155), _926155))]]], (45722 ^ _781215) ^ [_1698357, _1698359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1698357), _1698359)), -(c_List_Oupt(_1698357, hAPP(c_Nat_OSuc, _1698359)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1698357, _1698359)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1698359), c_List_Olist_ONil(tc_Nat_Onat))))], (28118 ^ _781215) ^ [_1293423, _1293425, _1293427, _1293429] : [class_Fields_Ofield__inverse__zero(_1293423), class_Int_Onumber(_1293423), 28125 ^ _781215 : [(28126 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1293423), _1293425) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293423), _1293427), _1293429), 28129 ^ _781215 : [(28136 ^ _781215) ^ [] : [_1293429 = c_Groups_Ozero__class_Ozero(_1293423), -(hAPP(c_Int_Onumber__class_Onumber__of(_1293423), _1293425) = c_Groups_Ozero__class_Ozero(_1293423))], (28130 ^ _781215) ^ [] : [-(_1293429 = c_Groups_Ozero__class_Ozero(_1293423)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293423), hAPP(c_Int_Onumber__class_Onumber__of(_1293423), _1293425)), _1293429) = _1293427)]]], (28142 ^ _781215) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1293423), _1293425) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293423), _1293427), _1293429)), 28145 ^ _781215 : [(28148 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293423), hAPP(c_Int_Onumber__class_Onumber__of(_1293423), _1293425)), _1293429) = _1293427], (28146 ^ _781215) ^ [] : [_1293429 = c_Groups_Ozero__class_Ozero(_1293423)]], 28149 ^ _781215 : [(28152 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1293423), _1293425) = c_Groups_Ozero__class_Ozero(_1293423)], (28150 ^ _781215) ^ [] : [-(_1293429 = c_Groups_Ozero__class_Ozero(_1293423))]]]]], (44132 ^ _781215) ^ [_1663644, _1663646, _1663648] : [_1663644 = hAPP(hAPP(c_List_Oappend(_1663646), _1663648), _1663644), -(_1663648 = c_List_Olist_ONil(_1663646))], (46179 ^ _781215) ^ [_1707958, _1707960, _1707962] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1707958), tc_List_Olist(_1707958), c_List_Oappend(_1707958), _1707960), _1707962) = hAPP(hAPP(c_List_Oappend(_1707958), _1707960), c_List_Oconcat(_1707958, _1707962)))], (15665 ^ _781215) ^ [_1056765, _1056767, _1056769, _1056771, _1056773] : [c_Finite__Set_Ofolding__one__idem(_1056765, _1056767, _1056769), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056765), _1056771)), -(hAPP(_1056769, hAPP(hAPP(c_Set_Oinsert(_1056765), _1056773), _1056771)) = hAPP(hAPP(c_Finite__Set_Ofold(_1056765, _1056765, _1056767), _1056773), _1056771))], (9477 ^ _781215) ^ [_942519, _942521, _942523] : [class_Orderings_Olinorder(_942519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942519), _942521), _942523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942519), _942523), _942521))], (45682 ^ _781215) ^ [_1697690, _1697692] : [c_List_Oupt(_1697690, _1697692) = c_List_Olist_ONil(tc_Nat_Onat), -(_1697692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1697692), _1697690)))], (16657 ^ _781215) ^ [_1078327, _1078329, _1078331, _1078333, _1078335] : [c_Hoare__Mirabelle_Ohoare__derivs(_1078327, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1078327), tc_HOL_Obool)), _1078329), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1078327), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078327)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078327))), hAPP(hAPP(c_COMBB(tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078327))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1078327)), _1078331)), c_Com_Ocom_OBODY)), _1078333)), _1078335)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1078327), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078327)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078327))), hAPP(hAPP(c_COMBB(tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078327))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1078327)), _1078331)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1078333)), _1078335)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1078327, _1078329, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1078327), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078327)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078327))), hAPP(hAPP(c_COMBB(tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1078327, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1078327))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1078327)), _1078331)), c_Com_Ocom_OBODY)), _1078333)), _1078335)))], (19020 ^ _781215) ^ [_1122115, _1122117, _1122119, _1122121] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1122115), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122115), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122115), _1122117), _1122119)), _1122121) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122115), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122115), _1122117), _1122121)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122115), _1122119), _1122121)))], (24762 ^ _781215) ^ [_1228162, _1228164] : [class_Groups_Omonoid__mult(_1228162), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1228162), _1228164), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1228164)], (41271 ^ _781215) ^ [_1591603, _1591605, _1591607, _1591609] : [c_Finite__Set_Ofun__left__comm__idem(_1591603, _1591605, _1591607), -(hAPP(c_Fun_Ocomp(_1591605, _1591605, _1591605, hAPP(_1591607, _1591609)), hAPP(_1591607, _1591609)) = hAPP(_1591607, _1591609))], (51266 ^ _781215) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (38666 ^ _781215) ^ [_1520960, _1520962, _1520964, _1520966, _1520968, _1520970] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1520960, _1520962), hAPP(hAPP(c_Set_Oinsert(_1520960), _1520964), _1520966)), hAPP(c_COMBK(tc_fun(_1520962, tc_HOL_Obool), _1520960), hAPP(hAPP(c_Set_Oinsert(_1520962), _1520968), _1520970))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1520960, _1520962)), hAPP(hAPP(c_Product__Type_OPair(_1520960, _1520962), _1520964), _1520968)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520960, _1520962), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1520960, _1520962), _1520966), hAPP(c_COMBK(tc_fun(_1520962, tc_HOL_Obool), _1520960), hAPP(hAPP(c_Set_Oinsert(_1520962), _1520968), _1520970)))), hAPP(hAPP(c_Product__Type_OSigma(_1520960, _1520962), hAPP(hAPP(c_Set_Oinsert(_1520960), _1520964), _1520966)), hAPP(c_COMBK(tc_fun(_1520962, tc_HOL_Obool), _1520960), _1520970)))))], (11620 ^ _781215) ^ [_984080, _984082] : [class_Groups_Omonoid__add(_984080), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984080), _984082), c_Groups_Ozero__class_Ozero(_984080)) = _984082)], (48370 ^ _781215) ^ [_1757613, _1757615, _1757617, _1757619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757613), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757615)), _1757617))), 48376 ^ _781215 : [(48379 ^ _781215) ^ [] : [hBOOL(hAPP(_1757619, 48375 ^ [_1757613, _1757615, _1757617, _1757619]))], (48377 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757615), 48375 ^ [_1757613, _1757615, _1757617, _1757619]), hAPP(c_List_Oset(_1757615), _1757617))))]], -(hBOOL(hAPP(_1757619, hAPP(hAPP(c_List_Onth(_1757615), _1757617), _1757613))))], (51176 ^ _781215) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (14164 ^ _781215) ^ [_1028466, _1028468, _1028470] : [-(hAPP(c_Finite__Set_Ocard(_1028466), _1028468) = hAPP(c_Nat_OSuc, _1028470)), 14165 ^ _781215 : [(14166 ^ _781215) ^ [_1028566, _1028568] : [_1028468 = hAPP(hAPP(c_Set_Oinsert(_1028466), _1028568), _1028566), -(hBOOL(hAPP(hAPP(c_member(_1028466), _1028568), _1028566))), hAPP(c_Finite__Set_Ocard(_1028466), _1028566) = _1028470, 14177 ^ _781215 : [(14180 ^ _781215) ^ [] : [_1028566 = c_Orderings_Obot__class_Obot(tc_fun(_1028466, tc_HOL_Obool))], (14178 ^ _781215) ^ [] : [-(_1028470 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (7708 ^ _781215) ^ [_910968, _910970, _910972] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _910968)), _910970)), hAPP(c_Nat_OSuc, _910972)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _910968), _910970)), _910972))], (20334 ^ _781215) ^ [_1146243, _1146245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1146243), _1146245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1146243)), c_Int_OBit1(_1146245))))], (39454 ^ _781215) ^ [_1543096, _1543098, _1543100] : [class_Groups_Olinordered__ab__semigroup__add(_1543096), hBOOL(hAPP(c_Finite__Set_Ofinite(_1543096), _1543098)), -(_1543098 = c_Orderings_Obot__class_Obot(tc_fun(_1543096, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1543096), _1543100), c_Big__Operators_Olinorder__class_OMax(_1543096, _1543098)) = c_Big__Operators_Olinorder__class_OMax(_1543096, hAPP(c_Set_OCollect(_1543096), hAPP(hAPP(c_COMBB(tc_fun(_1543096, tc_HOL_Obool), tc_HOL_Obool, _1543096), c_HOL_OEx(_1543096)), hAPP(hAPP(c_COMBC(_1543096, tc_fun(_1543096, tc_HOL_Obool), tc_fun(_1543096, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543096, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1543096, tc_HOL_Obool), tc_fun(_1543096, tc_HOL_Obool)), _1543096), c_COMBS(_1543096, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543096, tc_HOL_Obool), tc_fun(_1543096, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1543096), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543096), c_fconj)), hAPP(hAPP(c_COMBC(_1543096, tc_fun(_1543096, _1543096), tc_fun(_1543096, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543096, tc_HOL_Obool), tc_fun(tc_fun(_1543096, _1543096), tc_fun(_1543096, tc_HOL_Obool)), _1543096), c_COMBB(_1543096, tc_HOL_Obool, _1543096)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1543096), _1543100))))), hAPP(hAPP(c_COMBC(_1543096, tc_fun(_1543096, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543096)), _1543098))))))], (51504 ^ _781215) ^ [_1823878] : [class_Enum_Oenum(_1823878), -(class_Enum_Oenum(tc_Option_Ooption(_1823878)))], (32786 ^ _781215) ^ [_1388374, _1388376, _1388378, _1388380, _1388382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388374, tc_HOL_Obool)), _1388376), _1388378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388374, tc_HOL_Obool)), _1388380), _1388382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388374, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388374, tc_HOL_Obool)), _1388376), _1388380)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388374, tc_HOL_Obool)), _1388378), _1388382))))], (49385 ^ _781215) ^ [_1779860, _1779862] : [-(hAPP(c_Relation_ODomain(_1779860, _1779860), c_Transitive__Closure_Ortrancl(_1779860, _1779862)) = c_Orderings_Otop__class_Otop(tc_fun(_1779860, tc_HOL_Obool)))], (51178 ^ _781215) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (20868 ^ _781215) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (8017 ^ _781215) ^ [_916395, _916397] : [8018 ^ _781215 : [(8021 ^ _781215) ^ [] : [_916395 = _916397], (8019 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916395), _916397))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916395), hAPP(c_Nat_OSuc, _916397))))], (23662 ^ _781215) ^ [_1207758, _1207760, _1207762] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1207758, _1207760)), _1207762) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1207758), _1207762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1207760), _1207762)))], (2672 ^ _781215) ^ [_820947, _820949] : [_820949 = _820947, -(c_Equiv__Relations_Oquotient(_820949) = c_Equiv__Relations_Oquotient(_820947))], (33248 ^ _781215) ^ [_1399484, _1399486, _1399488] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1399484, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399484, tc_HOL_Obool)), _1399486), _1399488)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399484, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1399484, tc_HOL_Obool)), _1399486)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1399484, tc_HOL_Obool)), _1399488)))], (20454 ^ _781215) ^ [_1148289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1148289), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1148289)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23504 ^ _781215) ^ [_1204699, _1204701] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1204699)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1204701))) = 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), _1204699), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1204701))))], (47304 ^ _781215) ^ [_1732597, _1732599, _1732601, _1732603] : [class_Orderings_Oorder(_1732597), class_Enum_Oenum(_1732599), 47311 ^ _781215 : [(47318 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1732599), hAPP(hAPP(c_COMBS(_1732599, _1732597, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1732597, tc_fun(_1732597, tc_HOL_Obool), _1732599), c_Orderings_Oord__class_Oless__eq(_1732597)), _1732601)), _1732603))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1732599, _1732597)), _1732601), _1732603)))], (47312 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1732599, _1732597)), _1732601), _1732603)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1732599), hAPP(hAPP(c_COMBS(_1732599, _1732597, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1732597, tc_fun(_1732597, tc_HOL_Obool), _1732599), c_Orderings_Oord__class_Oless__eq(_1732597)), _1732601)), _1732603))))]]], (39262 ^ _781215) ^ [_1536166, _1536168, _1536170, _1536172, _1536174] : [-(c_Map_Odom(_1536166, _1536168, hAPP(hAPP(c_COMBS(_1536166, tc_Option_Ooption(_1536168), tc_Option_Ooption(_1536168)), hAPP(hAPP(c_COMBS(_1536166, tc_Option_Ooption(_1536168), tc_fun(tc_Option_Ooption(_1536168), tc_Option_Ooption(_1536168))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1536168), tc_fun(tc_Option_Ooption(_1536168), tc_Option_Ooption(_1536168))), _1536166), c_If(tc_Option_Ooption(_1536168))), _1536170)), _1536172)), _1536174)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536166, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1536166, tc_HOL_Obool)), c_Map_Odom(_1536166, _1536168, _1536172)), hAPP(c_Set_OCollect(_1536166), _1536170))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1536166, tc_HOL_Obool)), c_Map_Odom(_1536166, _1536168, _1536174)), hAPP(c_Set_OCollect(_1536166), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536166), c_fNot), _1536170)))))], (25432 ^ _781215) ^ [_1239303] : [class_Int_Onumber__ring(_1239303), -(hAPP(c_Int_Onumber__class_Onumber__of(_1239303), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1239303), c_Groups_Oone__class_Oone(_1239303)))], (44238 ^ _781215) ^ [_1665830, _1665832, _1665834, _1665836] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665830)), hAPP(hAPP(c_List_Oappend(_1665830), _1665832), _1665834)), c_List_Olists(_1665830, _1665836))), 44241 ^ _781215 : [(44244 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665830)), _1665834), c_List_Olists(_1665830, _1665836))))], (44242 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665830)), _1665832), c_List_Olists(_1665830, _1665836))))]]], (15604 ^ _781215) ^ [_1055283, _1055285, _1055287, _1055289] : [c_Com_Ocom_OLocal(_1055283, _1055285, _1055287) = hAPP(c_Com_Ocom_OBODY, _1055289)], (15554 ^ _781215) ^ [_1054146, _1054148, _1054150] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054146), _1054148)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054146, tc_HOL_Obool)), _1054150), _1054148) = hAPP(hAPP(c_Finite__Set_Ofold(_1054146, tc_fun(_1054146, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1054146, tc_HOL_Obool), tc_fun(tc_fun(_1054146, tc_HOL_Obool), tc_fun(_1054146, tc_HOL_Obool)), _1054146), hAPP(c_COMBC(tc_fun(_1054146, tc_HOL_Obool), tc_fun(_1054146, tc_HOL_Obool), tc_fun(_1054146, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1054146, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1054146, tc_fun(_1054146, tc_HOL_Obool), tc_fun(_1054146, tc_HOL_Obool)), c_Set_Oinsert(_1054146)), c_Orderings_Obot__class_Obot(tc_fun(_1054146, tc_HOL_Obool))))), _1054150), _1054148))], (13390 ^ _781215) ^ [_1014046, _1014048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014046), _1014048)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014046), _1014048) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50946 ^ _781215) ^ [_1816735, _1816737, _1816739, _1816741, _1816743] : [-(_1816735 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1816737, _1816739, _1816741, _1816743), _1816735) = c_Lazy__Sequence_Ohb__bind(_1816737, _1816739, hAPP(_1816741, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1816735), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1816737, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1816739))), _1816743), _1816735)))], (50526 ^ _781215) ^ [_1808598, _1808600] : [-(c_List_Olist__all(_1808598, _1808600, c_List_Olist_ONil(_1808598)))], (31304 ^ _781215) ^ [_1354658] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1354658) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1354658))], (29954 ^ _781215) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (40772 ^ _781215) ^ [_1580337, _1580339, _1580341] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1580337, _1580339)), _1580341), _1580341)), hBOOL(hAPP(_1580337, _1580341)), 40780 ^ _781215 : [(40783 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1580337, _1580339)), 40779 ^ [_1580337, _1580339, _1580341]), _1580341)))], (40781 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1580339), _1580341), 40779 ^ [_1580337, _1580339, _1580341])))]]], (46718 ^ _781215) ^ [_1720621, _1720623, _1720625] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720621)), c_List_OdropWhile(_1720621, _1720623, _1720625))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720621)), _1720625))))], (6726 ^ _781215) ^ [_891384, _891386, _891388] : [hBOOL(hAPP(hAPP(c_member(_891384), _891386), _891388)), -(hAPP(hAPP(c_Set_Oinsert(_891384), _891386), _891388) = _891388)], (36502 ^ _781215) ^ [_1467292, _1467294, _1467296, _1467298, _1467300] : [-(hAPP(c_Set_Oimage(_1467292, _1467294, hAPP(hAPP(c_COMBB(_1467296, _1467294, _1467292), _1467298), _1467300)), c_Orderings_Otop__class_Otop(tc_fun(_1467292, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1467296, _1467294, _1467298), hAPP(c_Set_Oimage(_1467292, _1467296, _1467300), c_Orderings_Otop__class_Otop(tc_fun(_1467292, tc_HOL_Obool)))))], (41691 ^ _781215) ^ [_1601752, _1601754, _1601756, _1601758, _1601760, _1601762, _1601764] : [c_Hoare__Mirabelle_Ohoare__derivs(_1601752, _1601754, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1601752)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1601752), c_Hoare__Mirabelle_Opeek__and(_1601752, _1601756, _1601758)), _1601760), _1601762)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1601752), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1601752, _1601754, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1601752)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1601752), c_Hoare__Mirabelle_Opeek__and(_1601752, _1601756, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1601758))), _1601764), _1601762)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1601752), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1601752, _1601754, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1601752)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1601752), _1601756), c_Com_Ocom_OCond(_1601758, _1601760, _1601764)), _1601762)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1601752), tc_HOL_Obool)))))], (6375 ^ _781215) ^ [_884832, _884834, _884836, _884838] : [hBOOL(hAPP(hAPP(c_member(_884832), _884834), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_884832, tc_HOL_Obool)), _884836), _884838))), 6378 ^ _781215 : [(6381 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_884832), _884834), _884838))], (6379 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_884832), _884834), _884836)))]]], (15288 ^ _781215) ^ [_1049368] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1049368), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1049368)], (39967 ^ _781215) ^ [_1561562, _1561564] : [-(c_Wellfounded_Owf(_1561562, hAPP(c_Wellfounded_Omeasure(_1561562), _1561564)))], (15600 ^ _781215) ^ [_1055140, _1055142, _1055144, _1055146] : [-(hAPP(c_Map_Orestrict__map(_1055140, _1055142, _1055144, c_Orderings_Obot__class_Obot(tc_fun(_1055140, tc_HOL_Obool))), _1055146) = c_Option_Ooption_ONone(_1055142))], (7933 ^ _781215) ^ [_915110, _915112] : [-(_915110 = _915112), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915110), _915112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915112), _915110)))], (16073 ^ _781215) ^ [_1065250, _1065252, _1065254] : [class_Lattices_Olattice(_1065250), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065250), _1065252), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065250), _1065252), _1065254)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065250), _1065252), _1065254))], (4676 ^ _781215) ^ [_852105, _852107] : [_852107 = _852105, -(c_Nitpick_Onum(_852107) = c_Nitpick_Onum(_852105))], (34712 ^ _781215) ^ [_1431667, _1431669, _1431671, _1431673] : [-(hAPP(c_Finite__Set_Ofold__image(_1431667, _1431669, _1431671), _1431673) = c_Finite__Set_Ofold(_1431669, _1431667, hAPP(hAPP(c_COMBB(_1431667, tc_fun(_1431667, _1431667), _1431669), _1431671), _1431673)))], (7458 ^ _781215) ^ [_906673, _906675, _906677] : [class_Orderings_Opreorder(_906673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906673), _906675), _906677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906673), _906677), _906675))], (33176 ^ _781215) ^ [_1397658, _1397660, _1397662, _1397664] : [-(hBOOL(hAPP(hAPP(c_member(_1397658), _1397660), _1397662))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397658, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1397658), _1397660), _1397664)), _1397662) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397658, tc_HOL_Obool)), _1397664), _1397662))], (20876 ^ _781215) ^ [_1155446] : [-(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, _1155446))))))], (45261 ^ _781215) ^ [_1689241, _1689243, _1689245, _1689247] : [-(hBOOL(hAPP(_1689241, _1689243))), -(hAPP(c_List_Ofilter(_1689245, _1689241), hAPP(hAPP(c_List_Olist_OCons(_1689245), _1689243), _1689247)) = hAPP(c_List_Ofilter(_1689245, _1689241), _1689247))], (38496 ^ _781215) ^ [_1516449, _1516451, _1516453, _1516455] : [hAPP(hAPP(c_Product__Type_OSigma(_1516449, _1516451), _1516453), hAPP(c_COMBK(tc_fun(_1516451, tc_HOL_Obool), _1516449), _1516455)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516449, _1516451), tc_HOL_Obool)), -(_1516453 = c_Orderings_Obot__class_Obot(tc_fun(_1516449, tc_HOL_Obool))), -(_1516455 = c_Orderings_Obot__class_Obot(tc_fun(_1516451, tc_HOL_Obool)))], (34618 ^ _781215) ^ [_1429789, _1429791, _1429793, _1429795, _1429797, _1429799] : [c_Fun_Oinj__on(_1429789, _1429791, _1429793, _1429795), hBOOL(hAPP(hAPP(c_member(_1429789), _1429797), _1429795)), hBOOL(hAPP(hAPP(c_member(_1429789), _1429799), _1429795)), 34629 ^ _781215 : [(34636 ^ _781215) ^ [] : [_1429797 = _1429799, -(hAPP(_1429793, _1429797) = hAPP(_1429793, _1429799))], (34630 ^ _781215) ^ [] : [hAPP(_1429793, _1429797) = hAPP(_1429793, _1429799), -(_1429797 = _1429799)]]], (23610 ^ _781215) ^ [_1206617] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1206617)))), -(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), _1206617)) = 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), _1206617))))], (34910 ^ _781215) ^ [_1435656, _1435658, _1435660, _1435662] : [class_Groups_Ocomm__monoid__add(_1435656), hBOOL(hAPP(c_Finite__Set_Ofinite(_1435658), _1435660)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1435658, _1435656), _1435662), _1435660) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1435656, _1435658, c_Groups_Oplus__class_Oplus(_1435656)), _1435662), c_Groups_Ozero__class_Ozero(_1435656)), _1435660))], (26240 ^ _781215) ^ [_1257050, _1257052, _1257054] : [class_Orderings_Oorder(_1257050), 26243 ^ _781215 : [(26250 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257050), _1257052), _1257054))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1257050, _1257052, _1257054) = c_Orderings_Obot__class_Obot(tc_fun(_1257050, tc_HOL_Obool)))], (26244 ^ _781215) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1257050, _1257052, _1257054) = c_Orderings_Obot__class_Obot(tc_fun(_1257050, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257050), _1257052), _1257054))]]], (20834 ^ _781215) ^ [_1154755, _1154757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1154755)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1154757)))), 20837 ^ _781215 : [(20840 ^ _781215) ^ [] : [-(_1154757 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20838 ^ _781215) ^ [] : [-(_1154755 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23718 ^ _781215) ^ [_1208821, _1208823, _1208825] : [class_Rings_Ocomm__semiring__1(_1208821), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208821), _1208823), hAPP(hAPP(c_Power_Opower__class_Opower(_1208821), _1208823), _1208825)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1208821), _1208823), hAPP(c_Nat_OSuc, _1208825)))], (43421 ^ _781215) ^ [_1647637, _1647639, _1647641, _1647643] : [class_Rings_Osemiring__1(_1647637), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1647637), hAPP(hAPP(c_List_Omap(_1647639, _1647637), hAPP(c_COMBK(_1647637, _1647639), _1647641)), _1647643)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1647637), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1647637), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647639)), _1647643))), _1647641))], (44636 ^ _781215) ^ [_1675966, _1675968, _1675970, _1675972] : [-(hAPP(hAPP(c_List_Odrop(_1675966), _1675968), hAPP(hAPP(c_List_Oappend(_1675966), _1675970), _1675972)) = hAPP(hAPP(c_List_Oappend(_1675966), hAPP(hAPP(c_List_Odrop(_1675966), _1675968), _1675970)), hAPP(hAPP(c_List_Odrop(_1675966), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1675968), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675966)), _1675970))), _1675972)))], (13402 ^ _781215) ^ [_1014255, _1014257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014255), _1014257)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014255), _1014257) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21694 ^ _781215) ^ [_1170401, _1170403] : [class_Int_Onumber__ring(_1170401), class_Int_Oring__char__0(_1170401), 21701 ^ _781215 : [(21708 ^ _781215) ^ [] : [c_Int_Oiszero(_1170401, hAPP(c_Int_Onumber__class_Onumber__of(_1170401), _1170403)), -(c_Int_Oiszero(_1170401, hAPP(c_Int_Onumber__class_Onumber__of(_1170401), c_Int_OBit0(_1170403))))], (21702 ^ _781215) ^ [] : [c_Int_Oiszero(_1170401, hAPP(c_Int_Onumber__class_Onumber__of(_1170401), c_Int_OBit0(_1170403))), -(c_Int_Oiszero(_1170401, hAPP(c_Int_Onumber__class_Onumber__of(_1170401), _1170403)))]]], (1036 ^ _781215) ^ [_797057, _797059, _797061, _797063, _797065, _797067, _797069, _797071] : [-(c_Nat__Transfer_Otransfer__morphism(_797069, _797065, _797061, _797057)), c_Nat__Transfer_Otransfer__morphism(_797071, _797067, _797063, _797059), _797071 = _797069, _797067 = _797065, _797063 = _797061, _797059 = _797057], (31078 ^ _781215) ^ [_1350033, _1350035, _1350037] : [class_Orderings_Oord(_1350033), 31081 ^ _781215 : [(31088 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350033), _1350035), _1350037)), -(hBOOL(hAPP(hAPP(c_member(_1350033), _1350035), hAPP(c_SetInterval_Oord__class_OatMost(_1350033), _1350037))))], (31082 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1350033), _1350035), hAPP(c_SetInterval_Oord__class_OatMost(_1350033), _1350037))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350033), _1350035), _1350037)))]]], (38082 ^ _781215) ^ [_1505620, _1505622, _1505624] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1505620, tc_HOL_Obool)), _1505622), _1505624))), 38088 ^ _781215 : [(38092 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1505620, tc_HOL_Obool)), 38090 ^ [_1505620, _1505622, _1505624]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1505620, tc_HOL_Obool)), _1505622), _1505624))))], (38094 ^ _781215) ^ [] : [38087 ^ [_1505620, _1505622, _1505624] = 38090 ^ [_1505620, _1505622, _1505624]], (38096 ^ _781215) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1505620, tc_HOL_Obool)), 38087 ^ [_1505620, _1505622, _1505624]), 38090 ^ [_1505620, _1505622, _1505624]) = c_Orderings_Obot__class_Obot(tc_fun(_1505620, tc_HOL_Obool))], (38089 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1505620, tc_HOL_Obool)), 38087 ^ [_1505620, _1505622, _1505624]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1505620, tc_HOL_Obool)), _1505622), _1505624))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1505620, tc_HOL_Obool)), _1505622), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1505620, tc_HOL_Obool), _1505624)) = c_Orderings_Obot__class_Obot(tc_fun(_1505620, tc_HOL_Obool)))], (44854 ^ _781215) ^ [_1680804, _1680806, _1680808, _1680810] : [-(hAPP(c_List_Orotate(_1680804, _1680806), hAPP(c_List_Orotate(_1680804, _1680808), _1680810)) = hAPP(c_List_Orotate(_1680804, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1680806), _1680808)), _1680810))], (35761 ^ _781215) ^ [_1453689, _1453691] : [class_Groups_Oordered__ab__group__add__abs(_1453689), 35764 ^ _781215 : [(35771 ^ _781215) ^ [] : [_1453691 = c_Groups_Ozero__class_Ozero(_1453689), -(hAPP(c_Groups_Oabs__class_Oabs(_1453689), _1453691) = c_Groups_Ozero__class_Ozero(_1453689))], (35765 ^ _781215) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1453689), _1453691) = c_Groups_Ozero__class_Ozero(_1453689), -(_1453691 = c_Groups_Ozero__class_Ozero(_1453689))]]], (30117 ^ _781215) ^ [_1331987, _1331989, _1331991] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1331987, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1331987, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1331987), _1331989)), hAPP(c_Set_OPow(_1331987), _1331991))), hAPP(c_Set_OPow(_1331987), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1331987, tc_HOL_Obool)), _1331989), _1331991)))))], (44268 ^ _781215) ^ [_1666537, _1666539, _1666541, _1666543] : [hAPP(hAPP(c_List_Oappend(_1666537), _1666539), _1666541) = hAPP(hAPP(c_List_Oappend(_1666537), _1666543), _1666541), -(_1666539 = _1666543)], (50960 ^ _781215) ^ [_1817079, _1817081, _1817083, _1817085, _1817087, _1817089, _1817091] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1817079, _1817081, _1817083, _1817085), _1817087), _1817089), _1817091) = c_New__DSequence_Oneg__bind(_1817079, _1817081, hAPP(hAPP(hAPP(_1817083, _1817087), _1817089), _1817091), hAPP(hAPP(c_COMBC(_1817079, 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(_1817081)))), hAPP(hAPP(c_COMBC(_1817079, 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(_1817081))))), hAPP(hAPP(c_COMBC(_1817079, 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(_1817081)))))), _1817085), _1817087)), _1817089)), _1817091)))], (16959 ^ _781215) ^ [_1085609] : [class_Int_Onumber__ring(_1085609), -(c_Groups_Ozero__class_Ozero(_1085609) = hAPP(c_Int_Onumber__class_Onumber__of(_1085609), c_Int_OPls))], (31140 ^ _781215) ^ [_1351290, _1351292, _1351294] : [class_Groups_Oordered__ab__group__add(_1351290), -(hAPP(c_Set_Oimage(_1351290, _1351290, c_Groups_Ouminus__class_Ouminus(_1351290)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1351290, _1351292), _1351294)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1351290, hAPP(c_Groups_Ouminus__class_Ouminus(_1351290), _1351294), hAPP(c_Groups_Ouminus__class_Ouminus(_1351290), _1351292)))], (27558 ^ _781215) ^ [_1282833, _1282835, _1282837, _1282839, _1282841] : [hBOOL(hAPP(hAPP(_1282833, _1282835), _1282837)), -(hBOOL(hAPP(hAPP(_1282833, hAPP(c_Product__Type_Osnd(_1282839, _1282841), hAPP(hAPP(c_Product__Type_OPair(_1282839, _1282841), _1282837), _1282835))), hAPP(c_Product__Type_Ofst(_1282839, _1282841), hAPP(hAPP(c_Product__Type_OPair(_1282839, _1282841), _1282837), _1282835)))))], (10178 ^ _781215) ^ [_954592, _954594, _954596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954592), _954594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954592), _954596)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954594), _954592)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954596), _954592)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954594), _954596))], (48828 ^ _781215) ^ [_1766975, _1766977] : [-(c_Random_Oselect__weight(_1766975, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1766975), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1766975, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1766975, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1766975)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1766977)) = c_Random_Oselect__weight(_1766975, _1766977))], (26270 ^ _781215) ^ [_1257534, _1257536, _1257538, _1257540, _1257542] : [class_Groups_Ocomm__monoid__mult(_1257534), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257536), _1257538)), 26277 ^ _781215 : [(26284 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1257536), _1257540), _1257538))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1257536, _1257534), hAPP(hAPP(c_COMBC(_1257536, _1257534, _1257534), hAPP(hAPP(c_COMBS(_1257536, _1257534, tc_fun(_1257534, _1257534)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1257534, tc_fun(_1257534, _1257534)), _1257536), c_If(_1257534)), hAPP(hAPP(c_COMBC(_1257536, _1257536, tc_HOL_Obool), c_fequal), _1257540))), _1257542)), c_Groups_Oone__class_Oone(_1257534))), _1257538) = c_Groups_Oone__class_Oone(_1257534))], (26278 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1257536), _1257540), _1257538)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1257536, _1257534), hAPP(hAPP(c_COMBC(_1257536, _1257534, _1257534), hAPP(hAPP(c_COMBS(_1257536, _1257534, tc_fun(_1257534, _1257534)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1257534, tc_fun(_1257534, _1257534)), _1257536), c_If(_1257534)), hAPP(hAPP(c_COMBC(_1257536, _1257536, tc_HOL_Obool), c_fequal), _1257540))), _1257542)), c_Groups_Oone__class_Oone(_1257534))), _1257538) = hAPP(_1257542, _1257540))]]], (35639 ^ _781215) ^ [_1451049, _1451051] : [_1451049 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1451049, _1451051) = 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)))], (11860 ^ _781215) ^ [_987639] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _987639)], (49064 ^ _781215) ^ [_1771210, _1771212] : [c_Wellfounded_Oacyclic(_1771210, _1771212), 49067 ^ _781215 : [(49068 ^ _781215) ^ [_1771295] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1771210, _1771210)), hAPP(hAPP(c_Product__Type_OPair(_1771210, _1771210), _1771295), _1771295)), c_Transitive__Closure_Otrancl(_1771210, _1771212)))]]], (25903 ^ _781215) ^ [_1250992, _1250994, _1250996, _1250998, _1251000] : [class_Groups_Ocomm__monoid__mult(_1250992), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250994, _1250992), hAPP(hAPP(c_COMBS(_1250994, _1250992, _1250992), hAPP(hAPP(c_COMBB(_1250992, tc_fun(_1250992, _1250992), _1250994), c_Groups_Otimes__class_Otimes(_1250992)), _1250996)), _1250998)), _1251000) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250992), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250994, _1250992), _1250996), _1251000)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250994, _1250992), _1250998), _1251000)))], (15242 ^ _781215) ^ [_1048602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1048602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048602)))], (27758 ^ _781215) ^ [_1286830, _1286832, _1286834] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1286830, tc_HOL_Obool), tc_fun(_1286830, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1286830, tc_HOL_Obool), tc_fun(_1286830, tc_HOL_Obool)), _1286832), _1286834)), c_Wellfounded_Ofinite__psubset(_1286830))), 27761 ^ _781215 : [(27764 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1286830), _1286834)))], (27762 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1286830, tc_HOL_Obool)), _1286832), _1286834)))]]], (45363 ^ _781215) ^ [_1691323, _1691325, _1691327] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1691323, tc_HOL_Obool)), hAPP(c_List_Oset(_1691323), _1691325)), hAPP(hAPP(c_Set_Oinsert(_1691323), _1691327), c_Orderings_Obot__class_Obot(tc_fun(_1691323, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1691323), hAPP(c_List_Ofilter(_1691323, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1691323), c_fNot), hAPP(hAPP(c_COMBC(_1691323, _1691323, tc_HOL_Obool), c_fequal), _1691327))), _1691325)))], (23889 ^ _781215) ^ [_1211794, _1211796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1211796, _1211794)), _1211794)))], (16293 ^ _781215) ^ [_1069174, _1069176, _1069178, _1069180] : [class_Lattices_Osemilattice__sup(_1069174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069174), _1069176), _1069178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069174), _1069176), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069174), _1069178), _1069180))))], (41289 ^ _781215) ^ [_1592200, _1592202, _1592204, _1592206, _1592208, _1592210] : [-(hAPP(hAPP(c_Option_Omap(_1592200, _1592202), _1592204), hAPP(hAPP(c_Option_Omap(_1592206, _1592200), _1592208), _1592210)) = hAPP(hAPP(c_Option_Omap(_1592206, _1592202), hAPP(c_Fun_Ocomp(_1592200, _1592202, _1592206, _1592204), _1592208)), _1592210))], (17905 ^ _781215) ^ [_1100890, _1100892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100892)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1100890), _1100892)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1100890)), hAPP(c_Int_Onat, _1100892)))], (44946 ^ _781215) ^ [_1682740, _1682742, _1682744] : [class_Groups_Omonoid__add(_1682740), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1682740), _1682742), hAPP(c_List_Ofoldl(_1682740, _1682740, c_Groups_Oplus__class_Oplus(_1682740), c_Groups_Ozero__class_Ozero(_1682740)), _1682744)) = hAPP(c_List_Ofoldl(_1682740, _1682740, c_Groups_Oplus__class_Oplus(_1682740), _1682742), _1682744))], (50966 ^ _781215) ^ [_1817388, _1817390] : [class_Lazy__Sequence_Osmall__lazy(_1817388), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1817388), _1817390) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1817388), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1817388)), c_List_Olist_ONil(_1817388)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1817388))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1817390)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1817388, tc_List_Olist(_1817388)), tc_List_Olist(_1817388), c_Lazy__Sequence_Oproduct(_1817388, tc_List_Olist(_1817388), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1817388, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1817390), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1817388), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1817390), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1817388, tc_List_Olist(_1817388), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1817388))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1817388), tc_List_Olist(_1817388)), tc_fun(tc_List_Olist(_1817388), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1817388))), _1817388), hAPP(c_COMBB(tc_List_Olist(_1817388), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1817388)), tc_List_Olist(_1817388)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1817388)))), c_List_Olist_OCons(_1817388))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1817388)))))], (41212 ^ _781215) ^ [_1590417, _1590419] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1590417, _1590419) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1590417), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1590419), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (27329 ^ _781215) ^ [_1277941, _1277943, _1277945, _1277947, _1277949] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1277941, _1277943), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1277945), _1277947))), -(_1277943 = 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), _1277949), _1277941), _1277943), 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), _1277949), _1277945)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1277949), _1277947)), _1277943))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1277949), _1277947), _1277943)))))], (44938 ^ _781215) ^ [_1682562, _1682564, _1682566, _1682568, _1682570, _1682572] : [-(hAPP(c_List_Ofoldl(_1682562, _1682564, _1682566, _1682568), hAPP(hAPP(c_List_Olist_OCons(_1682564), _1682570), _1682572)) = hAPP(c_List_Ofoldl(_1682562, _1682564, _1682566, hAPP(hAPP(_1682566, _1682568), _1682570)), _1682572))], (51648 ^ _781215) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (22142 ^ _781215) ^ [_1180301, _1180303] : [-(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), _1180301)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1180303)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1180301))) = 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), _1180303)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1180301)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (10106 ^ _781215) ^ [_953137, _953139, _953141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _953137), _953139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _953137), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953141), _953139))))], (40801 ^ _781215) ^ [_1580940, _1580942] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_1580940, _1580942))), -(hBOOL(hAPP(c_Com_OWT, _1580942)))], (43273 ^ _781215) ^ [_1643963, _1643965, _1643967, _1643969] : [43276 ^ _781215 : [(43281 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643963, _1643963)), hAPP(hAPP(c_Product__Type_OPair(_1643963, _1643963), 43275 ^ [_1643963, _1643965, _1643967, _1643969]), 43274 ^ [_1643963, _1643965, _1643967, _1643969])), _1643965))], (43279 ^ _781215) ^ [] : [43274 ^ [_1643963, _1643965, _1643967, _1643969] = 43275 ^ [_1643963, _1643965, _1643967, _1643969]], (43277 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643963, _1643963)), hAPP(hAPP(c_Product__Type_OPair(_1643963, _1643963), 43274 ^ [_1643963, _1643965, _1643967, _1643969]), 43275 ^ [_1643963, _1643965, _1643967, _1643969])), _1643965))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643963), tc_List_Olist(_1643963))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643963), tc_List_Olist(_1643963)), _1643967), _1643969)), c_List_Olexord(_1643963, _1643965)))), -(_1643967 = _1643969), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643963), tc_List_Olist(_1643963))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643963), tc_List_Olist(_1643963)), _1643969), _1643967)), c_List_Olexord(_1643963, _1643965))))], (51592 ^ _781215) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (31176 ^ _781215) ^ [_1351957, _1351959, _1351961, _1351963] : [class_Orderings_Olinorder(_1351957), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351957), _1351959), _1351961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351957), _1351961), _1351963)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351957, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1351957, _1351959, _1351961)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1351957, _1351961), _1351963)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1351957, _1351959, _1351963))], (8982 ^ _781215) ^ [_933594, _933596, _933598] : [-(_933594 = _933596), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933598, tc_HOL_Obool)), _933594), _933596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933598, tc_HOL_Obool)), _933596), _933594))], (41315 ^ _781215) ^ [_1592909, _1592911, _1592913, _1592915, _1592917, _1592919, _1592921, _1592923, _1592925] : [hAPP(c_Fun_Ocomp(_1592909, _1592911, _1592913, _1592915), _1592917) = hAPP(c_Fun_Ocomp(_1592919, _1592911, _1592913, _1592921), _1592923), -(hAPP(_1592915, hAPP(_1592917, _1592925)) = hAPP(_1592921, hAPP(_1592923, _1592925)))], (15188 ^ _781215) ^ [_1047827] : [-(_1047827 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15191 ^ _781215 : [(15198 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1047827))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1047827) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15192 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1047827)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1047827) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (14395 ^ _781215) ^ [_1032976, _1032978] : [class_Int_Oring__char__0(_1032976), hBOOL(hAPP(hAPP(c_member(_1032976), _1032978), c_Int_Oring__1__class_OInts(_1032976))), 14402 ^ _781215 : [(14409 ^ _781215) ^ [] : [_1032978 = c_Groups_Ozero__class_Ozero(_1032976), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032976), _1032978), _1032978) = c_Groups_Ozero__class_Ozero(_1032976))], (14403 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032976), _1032978), _1032978) = c_Groups_Ozero__class_Ozero(_1032976), -(_1032978 = c_Groups_Ozero__class_Ozero(_1032976))]]], (41617 ^ _781215) ^ [_1600021, _1600023, _1600025, _1600027, _1600029, _1600031, _1600033] : [c_Finite__Set_Ofolding__image(_1600021, _1600023, _1600025, _1600027, _1600029), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600023), _1600031)), -(hAPP(hAPP(_1600029, _1600033), _1600031) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1600021, _1600023, _1600025), _1600033), _1600027), _1600031))], (38516 ^ _781215) ^ [_1516862, _1516864, _1516866] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1516862, _1516864), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1516862, _1516864), _1516866), hAPP(c_COMBK(tc_fun(_1516864, tc_HOL_Obool), _1516862), c_Orderings_Otop__class_Otop(tc_fun(_1516864, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1516862, _1516864), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1516862, tc_HOL_Obool)), _1516866)), hAPP(c_COMBK(tc_fun(_1516864, tc_HOL_Obool), _1516862), c_Orderings_Otop__class_Otop(tc_fun(_1516864, tc_HOL_Obool)))))], (27183 ^ _781215) ^ [_1275578, _1275580, _1275582, _1275584, _1275586, _1275588] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1275578, _1275580), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1275582), _1275584))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1275578, _1275580), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1275586), _1275588))), -(_1275580 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1275582 = _1275586)], (3894 ^ _781215) ^ [_840262, _840264, _840266, _840268] : [-(c_Map_Omap__of(_840268, _840264) = c_Map_Omap__of(_840266, _840262)), _840268 = _840266, _840264 = _840262], (30965 ^ _781215) ^ [_1348042, _1348044] : [30967 ^ _781215 : [(30970 ^ _781215) ^ [] : [hBOOL(hAPP(_1348044, 30966 ^ [_1348042, _1348044]))], (30968 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30966 ^ [_1348042, _1348044]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1348042))))]], 30971 ^ _781215 : [(30972 ^ _781215) ^ [_1348195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1348195), _1348042)), -(hBOOL(hAPP(_1348044, _1348195)))]]], (25516 ^ _781215) ^ [_1240527] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1240527)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1240527)))], (1558 ^ _781215) ^ [_803660, _803662] : [-(class_Rings_Oordered__comm__semiring(_803660)), _803662 = _803660, class_Rings_Oordered__comm__semiring(_803662)], (18746 ^ _781215) ^ [_1117264, _1117266, _1117268] : [class_Orderings_Olinorder(_1117264), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117264), _1117266), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117264), _1117266), _1117268)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117264), _1117266), _1117268))], (47462 ^ _781215) ^ [_1736233, _1736235, _1736237, _1736239] : [hBOOL(hAPP(c_List_Olistsp(_1736233, _1736235), hAPP(hAPP(c_List_Oappend(_1736233), _1736237), _1736239))), 47465 ^ _781215 : [(47468 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1736233, _1736235), _1736239)))], (47466 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1736233, _1736235), _1736237)))]]], (48627 ^ _781215) ^ [_1763225, _1763227, _1763229] : [c_List_Olist__ex(_1763225, _1763227, _1763229), 48631 ^ _781215 : [(48634 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1763227, 48630 ^ [_1763225, _1763227, _1763229])))], (48632 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763225), 48630 ^ [_1763225, _1763227, _1763229]), hAPP(c_List_Oset(_1763225), _1763229))))]]], (42467 ^ _781215) ^ [_1622579, _1622581, _1622583, _1622585, _1622587, _1622589] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622579), tc_List_Olist(_1622579))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622579), tc_List_Olist(_1622579)), hAPP(hAPP(c_List_Olist_OCons(_1622579), _1622581), _1622583)), hAPP(hAPP(c_List_Olist_OCons(_1622579), _1622585), _1622587))), c_List_Olex(_1622579, _1622589))), 42472 ^ _781215 : [(42475 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622579)), _1622583) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622579)), _1622587))], (42473 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622579, _1622579)), hAPP(hAPP(c_Product__Type_OPair(_1622579, _1622579), _1622581), _1622585)), _1622589)))]], 42476 ^ _781215 : [(42479 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622579), tc_List_Olist(_1622579))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622579), tc_List_Olist(_1622579)), _1622583), _1622587)), c_List_Olex(_1622579, _1622589))))], (42477 ^ _781215) ^ [] : [-(_1622581 = _1622585)]]], (21015 ^ _781215) ^ [] : [-(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))))))], (37975 ^ _781215) ^ [_1503373, _1503375] : [class_Complete__Lattice_Ocomplete__lattice(_1503373), -(c_Complete__Lattice_OSup__class_OSup(_1503373, hAPP(hAPP(c_Set_Oinsert(_1503373), _1503375), c_Orderings_Obot__class_Obot(tc_fun(_1503373, tc_HOL_Obool)))) = _1503375)], (25608 ^ _781215) ^ [_1242107, _1242109] : [_1242107 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1242107, _1242109) = _1242109)], (13484 ^ _781215) ^ [_1015621, _1015623, _1015625, _1015627] : [class_Groups_Oordered__comm__monoid__add(_1015621), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015621), c_Groups_Ozero__class_Ozero(_1015621)), _1015623)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015621), _1015625), _1015627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015621), _1015625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015621), _1015623), _1015627))))], (28890 ^ _781215) ^ [_1307839, _1307841, _1307843, _1307845, _1307847] : [class_Fields_Ofield__inverse__zero(_1307839), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307839), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307839), _1307841), _1307843)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307839), _1307845), _1307847)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307839), _1307841), _1307845)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307839), _1307843), _1307847)))], (1168 ^ _781215) ^ [_798785, _798787] : [-(class_Rings_Olinordered__idom(_798785)), _798787 = _798785, class_Rings_Olinordered__idom(_798787)], (17191 ^ _781215) ^ [_1089248] : [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), _1089248))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1089248)))], (25468 ^ _781215) ^ [_1239889] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1239889, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43577 ^ _781215) ^ [_1651490, _1651492, _1651494] : [hBOOL(hAPP(hAPP(c_member(_1651490), _1651492), hAPP(c_List_Oset(_1651490), c_List_Obutlast(_1651490, _1651494)))), -(hBOOL(hAPP(hAPP(c_member(_1651490), _1651492), hAPP(c_List_Oset(_1651490), _1651494))))], (33216 ^ _781215) ^ [_1398517, _1398519, _1398521, _1398523] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398517, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398517, tc_HOL_Obool)), _1398519), _1398521)), _1398523) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398517, tc_HOL_Obool)), _1398519), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398517, tc_HOL_Obool)), _1398521), _1398523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398517, tc_HOL_Obool)), _1398523), _1398519)))], (33404 ^ _781215) ^ [_1402987, _1402989, _1402991, _1402993] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402987, tc_HOL_Obool)), c_Map_Odom(_1402987, _1402989, _1402991)), c_Map_Odom(_1402987, _1402989, _1402993)) = c_Orderings_Obot__class_Obot(tc_fun(_1402987, tc_HOL_Obool)), -(c_Map_Omap__add(_1402987, _1402989, _1402991, _1402993) = c_Map_Omap__add(_1402987, _1402989, _1402993, _1402991))], (22416 ^ _781215) ^ [_1186107, _1186109, _1186111] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186107), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1186109, _1186111)), _1186111) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186107), _1186109), _1186111))], (11998 ^ _781215) ^ [_989597, _989599, _989601] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989597), _989599) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989601), _989599), -(_989597 = _989601), -(_989599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11946 ^ _781215) ^ [_988827] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988827), _988827) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4314 ^ _781215) ^ [_846670, _846672] : [_846672 = _846670, -(c_Relation_OField(_846672) = c_Relation_OField(_846670))], (5730 ^ _781215) ^ [_871896, _871898] : [hAPP(c_Com_Ocom_OBODY, _871896) = hAPP(c_Com_Ocom_OBODY, _871898), -(_871896 = _871898)], (37955 ^ _781215) ^ [_1503001, _1503003, _1503005, _1503007] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1503001, tc_HOL_Obool), hAPP(c_Set_Oimage(_1503003, tc_fun(_1503001, tc_HOL_Obool), _1503005), _1503007)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1503003, tc_fun(_1503001, tc_HOL_Obool)), _1503007), _1503005))], (51426 ^ _781215) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (40611 ^ _781215) ^ [_1577048, _1577050, _1577052, _1577054] : [-(hBOOL(hAPP(_1577048, _1577050))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1577048, _1577052)), _1577050), _1577054), _1577050)))], (17405 ^ _781215) ^ [_1092911, _1092913, _1092915] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092911), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092911)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092913)), _1092915)) = 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), _1092911), _1092913))), _1092915))], (48676 ^ _781215) ^ [_1764074, _1764076, _1764078, _1764080] : [c_List_Olist__ex(_1764074, _1764076, hAPP(hAPP(c_List_Olist_OCons(_1764074), _1764078), _1764080)), -(hBOOL(hAPP(_1764076, _1764078))), -(c_List_Olist__ex(_1764074, _1764076, _1764080))], (32696 ^ _781215) ^ [_1386664, _1386666, _1386668] : [class_Lattices_Osemilattice__inf(_1386664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386664), _1386666), _1386668)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1386664), _1386668), _1386666) = _1386666)], (43164 ^ _781215) ^ [_1640866, _1640868, _1640870] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1640866, _1640866)), hAPP(hAPP(c_Product__Type_OPair(_1640866, _1640866), 43165 ^ [_1640866, _1640868, _1640870]), 43165 ^ [_1640866, _1640868, _1640870])), _1640868))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640866), tc_List_Olist(_1640866))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640866), tc_List_Olist(_1640866)), _1640870), _1640870)), c_List_Olexord(_1640866, _1640868)))], (41281 ^ _781215) ^ [_1591904, _1591906, _1591908, _1591910, _1591912, _1591914, _1591916, _1591918, _1591920, _1591922] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1591904, _1591906), tc_prod(_1591908, _1591910), tc_prod(_1591912, _1591914), c_Product__Type_Omap__pair(_1591904, _1591908, _1591906, _1591910, _1591916, _1591918)), c_Product__Type_Omap__pair(_1591912, _1591904, _1591914, _1591906, _1591920, _1591922)) = c_Product__Type_Omap__pair(_1591912, _1591908, _1591914, _1591910, hAPP(c_Fun_Ocomp(_1591904, _1591908, _1591912, _1591916), _1591920), hAPP(c_Fun_Ocomp(_1591906, _1591910, _1591914, _1591918), _1591922)))], (16774 ^ _781215) ^ [_1082385, _1082387, _1082389] : [_1082387 = _1082389, -(hBOOL(hAPP(hAPP(c_member(_1082385), _1082387), hAPP(c_fequal, _1082389))))], (50788 ^ _781215) ^ [_1813495] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1813495))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1813495)))], (25420 ^ _781215) ^ [_1239081, _1239083] : [class_Int_Onumber__ring(_1239081), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1239081), hAPP(c_Int_Onumber__class_Onumber__of(_1239081), c_Int_OMin)), _1239083) = hAPP(c_Groups_Ouminus__class_Ouminus(_1239081), _1239083))], (31487 ^ _781215) ^ [_1359029, _1359031, _1359033] : [-(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), _1359029)), 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))), _1359031))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1359033))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1359033)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1359029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1359029), 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), _1359033), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1359031)))))], (24524 ^ _781215) ^ [_1223663, _1223665, _1223667] : [class_Int_Onumber__ring(_1223663), 24527 ^ _781215 : [(24534 ^ _781215) ^ [] : [-(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), _1223665)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1223663), _1223667), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1223665))) = c_Groups_Oone__class_Oone(_1223663))], (24528 ^ _781215) ^ [] : [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), _1223665))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1223663), _1223667), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1223665))) = hAPP(hAPP(c_HOL_OLet(_1223663, _1223663), hAPP(hAPP(c_Power_Opower__class_Opower(_1223663), _1223667), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223665))), hAPP(hAPP(c_COMBS(_1223663, _1223663, _1223663), hAPP(hAPP(c_COMBB(_1223663, tc_fun(_1223663, _1223663), _1223663), c_Groups_Otimes__class_Otimes(_1223663)), hAPP(c_Groups_Otimes__class_Otimes(_1223663), _1223667))), c_COMBI(_1223663))))]]], (10660 ^ _781215) ^ [_963689, _963691, _963693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963689), _963691)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963693), _963689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963689), _963693)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963691), _963693))))], (13902 ^ _781215) ^ [_1023379, _1023381, _1023383] : [hBOOL(hAPP(_1023379, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1023381), _1023383))), 13905 ^ _781215 : [(13912 ^ _781215) ^ [_1023570] : [_1023381 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1023383), _1023570), -(hBOOL(hAPP(_1023379, _1023570)))], (13906 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1023381), _1023383)), -(hBOOL(hAPP(_1023379, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (49712 ^ _781215) ^ [_1788361, _1788363, _1788365, _1788367] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1788361, _1788361)), hAPP(hAPP(c_Product__Type_OPair(_1788361, _1788361), _1788363), _1788365)), hAPP(c_Relation_Oconverse(_1788361, _1788361), c_Transitive__Closure_Otrancl(_1788361, _1788367)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788361, _1788361)), hAPP(hAPP(c_Product__Type_OPair(_1788361, _1788361), _1788363), _1788365)), c_Transitive__Closure_Otrancl(_1788361, hAPP(c_Relation_Oconverse(_1788361, _1788361), _1788367)))))], (17203 ^ _781215) ^ [_1089433, _1089435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089433), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089433)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089435)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089435))], (42831 ^ _781215) ^ [_1632375, _1632377, _1632379, _1632381] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632375), tc_List_Olist(_1632375))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632375), tc_List_Olist(_1632375)), _1632377), _1632379)), c_List_Olistrel(_1632375, _1632381))), 42834 ^ _781215 : [(42837 ^ _781215) ^ [_1632604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632604), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632375)), _1632377))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632375, _1632375)), hAPP(hAPP(c_Product__Type_OPair(_1632375, _1632375), hAPP(hAPP(c_List_Onth(_1632375), _1632377), _1632604)), hAPP(hAPP(c_List_Onth(_1632375), _1632379), _1632604))), _1632381)))], (42835 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632375)), _1632377) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632375)), _1632379))]]], (40547 ^ _781215) ^ [_1575812, _1575814] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1575812, _1575812)), _1575814)), 40550 ^ _781215 : [(40557 ^ _781215) ^ [] : [c_Wellfounded_Oacyclic(_1575812, _1575814), -(c_Wellfounded_Owf(_1575812, _1575814))], (40551 ^ _781215) ^ [] : [c_Wellfounded_Owf(_1575812, _1575814), -(c_Wellfounded_Oacyclic(_1575812, _1575814))]]], (47501 ^ _781215) ^ [_1737026, _1737028, _1737030, _1737032] : [hBOOL(hAPP(c_List_Olistsp(_1737026, hAPP(hAPP(c_COMBS(_1737026, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1737026), c_fconj), _1737028)), _1737030)), _1737032)), 47504 ^ _781215 : [(47507 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1737026, _1737030), _1737032)))], (47505 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1737026, _1737028), _1737032)))]]], (36626 ^ _781215) ^ [_1469851] : [class_Nat_Osemiring__char__0(_1469851), -(c_Fun_Oinj__on(tc_Nat_Onat, _1469851, c_Nat_Osemiring__1__class_Oof__nat(_1469851), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (41471 ^ _781215) ^ [_1596488, _1596490, _1596492, _1596494, _1596496, _1596498, _1596500] : [class_Groups_Oab__semigroup__mult(_1596488), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596490), _1596492)), c_Fun_Oinj__on(_1596490, _1596494, _1596496, _1596492), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1596488, _1596494, c_Groups_Otimes__class_Otimes(_1596488)), _1596498), _1596500), hAPP(c_Set_Oimage(_1596490, _1596494, _1596496), _1596492)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1596488, _1596490, c_Groups_Otimes__class_Otimes(_1596488)), hAPP(c_Fun_Ocomp(_1596494, _1596488, _1596490, _1596498), _1596496)), _1596500), _1596492))], (19160 ^ _781215) ^ [_1125115, _1125117, _1125119, _1125121] : [class_Orderings_Olinorder(_1125115), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125115), _1125117)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1125115, _1125115, c_Orderings_Oord__class_Omax(_1125115)), _1125119), hAPP(hAPP(c_Set_Oinsert(_1125115), _1125121), _1125117)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1125115), _1125121), hAPP(hAPP(c_Finite__Set_Ofold(_1125115, _1125115, c_Orderings_Oord__class_Omax(_1125115)), _1125119), _1125117)))], (29888 ^ _781215) ^ [_1326241, _1326243, _1326245, _1326247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1326241), _1326243)), -(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), _1326241), _1326245)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1326243), _1326247))), c_FunDef_Opair__leq)))], (1118 ^ _781215) ^ [_798160, _798162] : [-(class_Rings_Oring__no__zero__divisors(_798160)), _798162 = _798160, class_Rings_Oring__no__zero__divisors(_798162)], (50264 ^ _781215) ^ [_1802670, _1802672] : [c_Wellfounded_Owf(_1802670, _1802672), 50267 ^ _781215 : [(50268 ^ _781215) ^ [_1802802] : [50269 ^ _781215 : [(50270 ^ _781215) ^ [_1802907] : [hBOOL(hAPP(hAPP(c_member(_1802670), _1802907), _1802802))]], 50272 ^ _781215 : [(50275 ^ _781215) ^ [_1803029] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802670, _1802670)), hAPP(hAPP(c_Product__Type_OPair(_1802670, _1802670), _1803029), 50271 ^ [_1802670, _1802672, _1802802])), _1802672)), hBOOL(hAPP(hAPP(c_member(_1802670), _1803029), _1802802))], (50273 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802670), 50271 ^ [_1802670, _1802672, _1802802]), _1802802)))]]]]], (49373 ^ _781215) ^ [_1779555, _1779557, _1779559] : [-(c_Transitive__Closure_Ortrancl(_1779555, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1779555, _1779555), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1779555, _1779557)), c_Transitive__Closure_Ortrancl(_1779555, _1779559))) = c_Transitive__Closure_Ortrancl(_1779555, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1779555, _1779555), tc_HOL_Obool)), _1779557), _1779559)))], (11096 ^ _781215) ^ [_973201, _973203, _973205, _973207, _973209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973201), _973203)), 11099 ^ _781215 : [(11106 ^ _781215) ^ [] : [_973207 = 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), _973203), _973201)), _973205)), _973209), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973201), _973205)), _973207) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973203), _973205)), _973209))], (11100 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973201), _973205)), _973207) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _973203), _973205)), _973209), -(_973207 = 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), _973203), _973201)), _973205)), _973209))]]], (32628 ^ _781215) ^ [_1385509, _1385511, _1385513] : [class_Lattices_Osemilattice__inf(_1385509), 32631 ^ _781215 : [(32638 ^ _781215) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1385509), _1385511), _1385513) = _1385511, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385509), _1385511), _1385513)))], (32632 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385509), _1385511), _1385513)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1385509), _1385511), _1385513) = _1385511)]]], (49006 ^ _781215) ^ [_1770235, _1770237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1770235)), hAPP(c_Code__Numeral_Onat__of, _1770237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1770235), _1770237)))], (45466 ^ _781215) ^ [_1694118, _1694120, _1694122, _1694124, _1694126] : [class_Orderings_Olinorder(_1694118), -(c_List_Olinorder__class_Osorted(_1694118, hAPP(hAPP(c_List_Omap(_1694120, _1694118), _1694122), hAPP(c_List_Ofilter(_1694120, hAPP(hAPP(c_COMBC(_1694120, _1694118, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1694118, tc_fun(_1694118, tc_HOL_Obool), _1694120), c_fequal), _1694122)), hAPP(_1694124, _1694126))), _1694126))))], (15162 ^ _781215) ^ [_1047357, _1047359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1047357), _1047359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047357)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047359))))], (45347 ^ _781215) ^ [_1690928, _1690930, _1690932] : [-(hAPP(c_List_Oset(_1690928), hAPP(c_List_Ofilter(_1690928, _1690930), _1690932)) = hAPP(c_Set_OCollect(_1690928), hAPP(hAPP(c_COMBS(_1690928, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1690928), c_fconj), hAPP(hAPP(c_COMBC(_1690928, tc_fun(_1690928, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690928)), hAPP(c_List_Oset(_1690928), _1690932)))), _1690930)))], (7572 ^ _781215) ^ [_908495, _908497, _908499] : [class_Orderings_Olinorder(_908495), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908495), _908497), _908499))), -(_908497 = _908499), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908495), _908499), _908497)))], (13442 ^ _781215) ^ [_1014858, _1014860, _1014862] : [class_Groups_Oordered__comm__monoid__add(_1014858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014858), _1014860), c_Groups_Ozero__class_Ozero(_1014858))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1014858), _1014862), c_Groups_Ozero__class_Ozero(_1014858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1014858), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014858), _1014860), _1014862)), c_Groups_Ozero__class_Ozero(_1014858))))], (49551 ^ _781215) ^ [_1784182, _1784184] : [-(c_Relation_Oirrefl(_1784182, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1784182, _1784182), tc_HOL_Obool)), _1784184), c_Relation_OId(_1784182))))], (23793 ^ _781215) ^ [_1210104, _1210106] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1210104), _1210106))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1210104, _1210106) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1210104), _1210106), _1210106))], (38765 ^ _781215) ^ [_1524143, _1524145, _1524147, _1524149] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1524143), _1524145)), 38771 ^ _781215 : [(38774 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1524147), hAPP(_1524149, 38770 ^ [_1524143, _1524145, _1524147, _1524149])))], (38772 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524143), 38770 ^ [_1524143, _1524145, _1524147, _1524149]), _1524145)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1524143, _1524147)), hAPP(hAPP(c_Product__Type_OSigma(_1524143, _1524147), _1524145), _1524149)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524143, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1524147, tc_HOL_Obool), tc_Nat_Onat, _1524143), c_Finite__Set_Ocard(_1524147)), _1524149)), _1524145))], (38558 ^ _781215) ^ [_1518413, _1518415] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518413, _1518415), c_Orderings_Otop__class_Otop(tc_fun(_1518413, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1518415, tc_HOL_Obool), _1518413), c_Orderings_Otop__class_Otop(tc_fun(_1518415, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1518413, _1518415), tc_HOL_Obool)))], (26083 ^ _781215) ^ [_1254332, _1254334] : [class_Int_Oring__char__0(_1254332), 26086 ^ _781215 : [(26093 ^ _781215) ^ [] : [_1254334 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1254332) = hAPP(c_Int_Oring__1__class_Oof__int(_1254332), _1254334))], (26087 ^ _781215) ^ [] : [c_Groups_Ozero__class_Ozero(_1254332) = hAPP(c_Int_Oring__1__class_Oof__int(_1254332), _1254334), -(_1254334 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (38346 ^ _781215) ^ [_1512363, _1512365, _1512367, _1512369, _1512371] : [hAPP(c_Set_Oimage(_1512363, _1512365, _1512367), c_Orderings_Otop__class_Otop(tc_fun(_1512363, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1512365, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1512363, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1512363, _1512365, _1512367), _1512369)), _1512371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1512365, tc_HOL_Obool)), _1512369), hAPP(c_Set_Oimage(_1512363, _1512365, _1512367), _1512371))))], (22500 ^ _781215) ^ [_1187713, _1187715] : [-(_1187713 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22503 ^ _781215 : [(22510 ^ _781215) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187715, _1187713) = 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), _1187715)), _1187713) = 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), _1187715), _1187713))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22504 ^ _781215) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187715, _1187713) = 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), _1187715)), _1187713) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1187715), _1187713)))]]], (1358 ^ _781215) ^ [_801160, _801162] : [-(class_Lattices_Osemilattice__inf(_801160)), _801162 = _801160, class_Lattices_Osemilattice__inf(_801162)], (51222 ^ _781215) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (37793 ^ _781215) ^ [_1499307, _1499309] : [class_Complete__Lattice_Ocomplete__lattice(_1499307), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499307), _1499309)), -(c_Complete__Lattice_OSup__class_OSup(_1499307, _1499309) = hAPP(hAPP(c_Finite__Set_Ofold(_1499307, _1499307, c_Lattices_Osemilattice__sup__class_Osup(_1499307)), c_Orderings_Obot__class_Obot(_1499307)), _1499309))], (6521 ^ _781215) ^ [_887627, _887629, _887631, _887633] : [-(hBOOL(hAPP(hAPP(c_member(_887627), _887629), _887631))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887627, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_887627), _887629), _887633)), _887631) = hAPP(hAPP(c_Set_Oinsert(_887627), _887629), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887627, tc_HOL_Obool)), _887633), _887631)))], (43920 ^ _781215) ^ [_1658182, _1658184, _1658186, _1658188] : [-(c_List_Opartition(_1658182, _1658184, hAPP(hAPP(c_List_Olist_OCons(_1658182), _1658186), _1658188)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1658182), tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1658182), tc_fun(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182))), tc_fun(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1658182), tc_fun(tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)))), tc_fun(tc_fun(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182))), tc_fun(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)))), tc_List_Olist(_1658182)), c_COMBS(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182))), tc_fun(tc_List_Olist(_1658182), tc_fun(tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)))), tc_List_Olist(_1658182)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)), tc_fun(tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182))), tc_List_Olist(_1658182)), hAPP(c_If(tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182))), hAPP(_1658184, _1658186)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1658182), tc_fun(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182))), tc_List_Olist(_1658182)), c_Product__Type_OPair(tc_List_Olist(_1658182), tc_List_Olist(_1658182))), hAPP(c_List_Olist_OCons(_1658182), _1658186))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1658182), tc_fun(tc_List_Olist(_1658182), tc_List_Olist(_1658182)), tc_fun(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182))), tc_fun(tc_fun(tc_List_Olist(_1658182), tc_List_Olist(_1658182)), tc_fun(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)))), tc_List_Olist(_1658182)), c_COMBB(tc_List_Olist(_1658182), tc_prod(tc_List_Olist(_1658182), tc_List_Olist(_1658182)), tc_List_Olist(_1658182))), c_Product__Type_OPair(tc_List_Olist(_1658182), tc_List_Olist(_1658182)))), hAPP(c_List_Olist_OCons(_1658182), _1658186)))), c_List_Opartition(_1658182, _1658184, _1658188)))], (46548 ^ _781215) ^ [_1717126, _1717128, _1717130, _1717132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1717126), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717128)), c_List_OtakeWhile(_1717128, _1717130, _1717132)))), -(hAPP(hAPP(c_List_Onth(_1717128), c_List_OtakeWhile(_1717128, _1717130, _1717132)), _1717126) = hAPP(hAPP(c_List_Onth(_1717128), _1717132), _1717126))], (39854 ^ _781215) ^ [_1557828, _1557830, _1557832, _1557834] : [hBOOL(hAPP(c_Predicate_ORangeP(_1557828, _1557830, hAPP(hAPP(c_COMBC(_1557828, tc_fun(tc_prod(_1557828, _1557830), tc_HOL_Obool), tc_fun(_1557830, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1557830, tc_fun(tc_fun(tc_prod(_1557828, _1557830), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1557828, _1557830), tc_HOL_Obool), tc_fun(_1557830, tc_HOL_Obool)), _1557828), c_COMBC(_1557830, tc_fun(tc_prod(_1557828, _1557830), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1557830, tc_prod(_1557828, _1557830)), tc_fun(_1557830, tc_fun(tc_fun(tc_prod(_1557828, _1557830), tc_HOL_Obool), tc_HOL_Obool)), _1557828), hAPP(c_COMBB(tc_prod(_1557828, _1557830), tc_fun(tc_fun(tc_prod(_1557828, _1557830), tc_HOL_Obool), tc_HOL_Obool), _1557830), c_member(tc_prod(_1557828, _1557830)))), c_Product__Type_OPair(_1557828, _1557830)))), _1557832)), _1557834)), -(hBOOL(hAPP(hAPP(c_member(_1557830), _1557834), hAPP(c_Relation_ORange(_1557828, _1557830), _1557832))))], (19084 ^ _781215) ^ [_1123459, _1123461, _1123463, _1123465] : [class_Orderings_Olinorder(_1123459), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1123459), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123459), _1123461), _1123463)), _1123465) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123459), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1123459), _1123461), _1123465)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1123459), _1123463), _1123465)))], (36267 ^ _781215) ^ [_1463053, _1463055, _1463057, _1463059, _1463061, _1463063] : [hAPP(c_Product__Type_Oapfst(_1463053, _1463055, _1463057, _1463059), _1463061) = hAPP(c_Product__Type_Oapfst(_1463053, _1463055, _1463057, _1463063), _1463061), -(hAPP(_1463059, hAPP(c_Product__Type_Ofst(_1463053, _1463057), _1463061)) = hAPP(_1463063, hAPP(c_Product__Type_Ofst(_1463053, _1463057), _1463061)))], (16397 ^ _781215) ^ [_1071097, _1071099, _1071101] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1071097), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071097, tc_HOL_Obool)), _1071099), _1071101)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071097), _1071099)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071097), _1071101))], (5762 ^ _781215) ^ [_872387, _872389, _872391, _872393] : [-(hAPP(hAPP(c_Set_Oinsert(_872387), _872389), hAPP(hAPP(c_Set_Oinsert(_872387), _872391), _872393)) = hAPP(hAPP(c_Set_Oinsert(_872387), _872391), hAPP(hAPP(c_Set_Oinsert(_872387), _872389), _872393)))], (44658 ^ _781215) ^ [_1676554, _1676556, _1676558, _1676560] : [_1676554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1676556), _1676554), hAPP(hAPP(c_List_Olist_OCons(_1676556), _1676558), _1676560)) = hAPP(hAPP(c_List_Olist_OCons(_1676556), _1676558), _1676560))], (16719 ^ _781215) ^ [_1080429, _1080431, _1080433, _1080435] : [16720 ^ _781215 : [(16723 ^ _781215) ^ [] : [hBOOL(hAPP(_1080433, _1080431))], (16721 ^ _781215) ^ [] : [hBOOL(hAPP(_1080429, _1080431))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1080435, tc_HOL_Obool)), _1080433), _1080429), _1080431)))], (29910 ^ _781215) ^ [_1326529, _1326531, _1326533, _1326535] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1326529), _1326531)), 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)), _1326529), _1326533)), 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)), _1326531), _1326535)), 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)), _1326531), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1326533), _1326535))), c_FunDef_Omin__weak)))], (46632 ^ _781215) ^ [_1718820, _1718822] : [_1718822 = c_List_Olist_ONil(_1718820), -(c_List_Olist_ONil(_1718820) = c_List_Oremdups(_1718820, _1718822))], (49044 ^ _781215) ^ [_1770878, _1770880] : [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), _1770878), _1770880)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770878), _1770880)))], (2740 ^ _781215) ^ [_822111, _822113] : [_822113 = _822111, -(c_Wellfounded_Omeasure(_822113) = c_Wellfounded_Omeasure(_822111))], (19338 ^ _781215) ^ [_1128152, _1128154, _1128156] : [class_Orderings_Olinorder(_1128152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128152), _1128154)), -(c_Big__Operators_Olattice_OInf__fin(_1128152, c_Orderings_Oord__class_Omin(_1128152), hAPP(hAPP(c_Set_Oinsert(_1128152), _1128156), _1128154)) = hAPP(hAPP(c_Finite__Set_Ofold(_1128152, _1128152, c_Orderings_Oord__class_Omin(_1128152)), _1128156), _1128154))], (18621 ^ _781215) ^ [_1114742, _1114744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114742)), _1114744)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114742), _1114744)))], (17305 ^ _781215) ^ [_1091089, _1091091] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091089) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091091)), 17308 ^ _781215 : [(17311 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091091)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (17309 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091089))))]], 17312 ^ _781215 : [(17315 ^ _781215) ^ [] : [17316 ^ _781215 : [(17319 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091089) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (17317 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091091))))]], 17320 ^ _781215 : [(17323 ^ _781215) ^ [] : [_1091089 = _1091091], (17321 ^ _781215) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091091)))]]], (17313 ^ _781215) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091089)))]]], (7234 ^ _781215) ^ [_902829, _902831, _902833] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902829), _902831)), 7237 ^ _781215 : [(7244 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902829), _902833), _902831))), -(hAPP(c_Finite__Set_Ocard(_902829), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902829, tc_HOL_Obool)), _902831), hAPP(hAPP(c_Set_Oinsert(_902829), _902833), c_Orderings_Obot__class_Obot(tc_fun(_902829, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_902829), _902831))], (7238 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_902829), _902833), _902831)), -(hAPP(c_Finite__Set_Ocard(_902829), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902829, tc_HOL_Obool)), _902831), hAPP(hAPP(c_Set_Oinsert(_902829), _902833), c_Orderings_Obot__class_Obot(tc_fun(_902829, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_902829), _902831)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (21900 ^ _781215) ^ [_1174800, _1174802, _1174804, _1174806, _1174808, _1174810] : [-(hAPP(c_Set_Oimage(_1174800, _1174802, _1174804), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174806, tc_fun(_1174800, tc_HOL_Obool)), _1174808), _1174810)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1174806, tc_fun(_1174802, tc_HOL_Obool)), _1174808), hAPP(hAPP(c_COMBB(tc_fun(_1174800, tc_HOL_Obool), tc_fun(_1174802, tc_HOL_Obool), _1174806), c_Set_Oimage(_1174800, _1174802, _1174804)), _1174810)))], (45472 ^ _781215) ^ [_1694281, _1694283, _1694285, _1694287, _1694289] : [class_Orderings_Olinorder(_1694281), c_List_Olinorder__class_Osorted(_1694281, hAPP(hAPP(c_List_Omap(_1694283, _1694281), _1694285), _1694287)), -(c_List_Olinorder__class_Osorted(_1694281, hAPP(hAPP(c_List_Omap(_1694283, _1694281), _1694285), hAPP(c_List_Ofilter(_1694283, _1694289), _1694287))))], (32327 ^ _781215) ^ [_1378877, _1378879, _1378881, _1378883, _1378885] : [c_Equiv__Relations_Oequiv(_1378877, _1378879, _1378881), hBOOL(hAPP(hAPP(c_member(_1378877), _1378883), _1378879)), hBOOL(hAPP(hAPP(c_member(_1378877), _1378885), _1378879)), 32338 ^ _781215 : [(32345 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1378877, _1378877)), hAPP(hAPP(c_Product__Type_OPair(_1378877, _1378877), _1378883), _1378885)), _1378881)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378877), hAPP(hAPP(c_Set_Oinsert(_1378877), _1378883), c_Orderings_Obot__class_Obot(tc_fun(_1378877, tc_HOL_Obool)))), _1378881) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378877), hAPP(hAPP(c_Set_Oinsert(_1378877), _1378885), c_Orderings_Obot__class_Obot(tc_fun(_1378877, tc_HOL_Obool)))), _1378881))], (32339 ^ _781215) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378877), hAPP(hAPP(c_Set_Oinsert(_1378877), _1378883), c_Orderings_Obot__class_Obot(tc_fun(_1378877, tc_HOL_Obool)))), _1378881) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378877), hAPP(hAPP(c_Set_Oinsert(_1378877), _1378885), c_Orderings_Obot__class_Obot(tc_fun(_1378877, tc_HOL_Obool)))), _1378881), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1378877, _1378877)), hAPP(hAPP(c_Product__Type_OPair(_1378877, _1378877), _1378883), _1378885)), _1378881)))]]], (32304 ^ _781215) ^ [_1378296, _1378298, _1378300, _1378302, _1378304] : [c_Equiv__Relations_Oequiv(_1378296, _1378298, _1378300), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1378296, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1378296, _1378296, _1378300), hAPP(hAPP(c_Set_Oinsert(_1378296), _1378302), c_Orderings_Obot__class_Obot(tc_fun(_1378296, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1378296, _1378296, _1378300), hAPP(hAPP(c_Set_Oinsert(_1378296), _1378304), c_Orderings_Obot__class_Obot(tc_fun(_1378296, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1378296), _1378302), _1378298)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1378296, _1378296)), hAPP(hAPP(c_Product__Type_OPair(_1378296, _1378296), _1378304), _1378302)), _1378300)))], (32361 ^ _781215) ^ [_1379712, _1379714, _1379716, _1379718] : [c_Equiv__Relations_Oequiv(_1379712, _1379714, _1379716), hBOOL(hAPP(hAPP(c_member(_1379712), _1379718), _1379714)), -(hBOOL(hAPP(hAPP(c_member(_1379712), _1379718), hAPP(c_Relation_OImage(_1379712, _1379712, _1379716), hAPP(hAPP(c_Set_Oinsert(_1379712), _1379718), c_Orderings_Obot__class_Obot(tc_fun(_1379712, tc_HOL_Obool)))))))], (3300 ^ _781215) ^ [_830965, _830967, _830969, _830971] : [-(c_Fun_Ofun__upd(_830971, _830967) = c_Fun_Ofun__upd(_830969, _830965)), _830971 = _830969, _830967 = _830965], (46862 ^ _781215) ^ [_1723778, _1723780, _1723782] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1723778))), c_Enum_On__lists(_1723778, _1723780, _1723782)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723778)), _1723782)), _1723780))], (23730 ^ _781215) ^ [_1209083] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1209083, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32828 ^ _781215) ^ [_1389411, _1389413, _1389415, _1389417] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389411, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389411, tc_HOL_Obool)), _1389413), _1389415)), _1389417) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389411, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389411, tc_HOL_Obool)), _1389413), _1389417)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389411, tc_HOL_Obool)), _1389415), _1389417)))], (14094 ^ _781215) ^ [_1027006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1027006)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027006), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1027006)], (44848 ^ _781215) ^ [_1680643, _1680645, _1680647] : [-(hAPP(c_List_Oset(_1680643), hAPP(c_List_Orotate(_1680643, _1680645), _1680647)) = hAPP(c_List_Oset(_1680643), _1680647))], (5418 ^ _781215) ^ [_863976, _863978] : [_863978 = _863976, -(c_Orderings_Oord__class_Oless(_863978) = c_Orderings_Oord__class_Oless(_863976))], (4494 ^ _781215) ^ [_849362, _849364, _849366, _849368, _849370, _849372] : [-(c_Divides_Odiv__class_Omod(_849372, _849368, _849364) = c_Divides_Odiv__class_Omod(_849370, _849366, _849362)), _849372 = _849370, _849368 = _849366, _849364 = _849362], (2358 ^ _781215) ^ [_816074, _816076] : [_816076 = _816074, -(c_Smallcheck_Osmall__class_Osmall(_816076) = c_Smallcheck_Osmall__class_Osmall(_816074))], (19794 ^ _781215) ^ [_1136397, _1136399, _1136401] : [class_Orderings_Olinorder(_1136397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1136397, tc_HOL_Obool)), _1136399), _1136401)), -(_1136399 = c_Orderings_Obot__class_Obot(tc_fun(_1136397, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136397), _1136401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136397), c_Big__Operators_Olinorder__class_OMax(_1136397, _1136399)), c_Big__Operators_Olinorder__class_OMax(_1136397, _1136401))))], (46079 ^ _781215) ^ [_1705638, _1705640] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1705638)), c_List_Otranspose__rel(_1705638)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1705638)), c_List_Olist_ONil(_1705638)), _1705640))), -(c_List_Otranspose(_1705638, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1705638)), c_List_Olist_ONil(_1705638)), _1705640)) = c_List_Otranspose(_1705638, _1705640))], (20304 ^ _781215) ^ [_1145696, _1145698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1145696)), c_Int_OBit1(_1145698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145696), _1145698)))], (12678 ^ _781215) ^ [_1001904, _1001906, _1001908] : [class_Rings_Olinordered__semiring__strict(_1001904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001904), c_Groups_Ozero__class_Ozero(_1001904)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001904), _1001906), _1001908))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001904), c_Groups_Ozero__class_Ozero(_1001904)), _1001906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001904), c_Groups_Ozero__class_Ozero(_1001904)), _1001908)))], (32808 ^ _781215) ^ [_1388902, _1388904, _1388906, _1388908] : [hBOOL(hAPP(hAPP(c_member(_1388902), _1388904), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388902, tc_HOL_Obool)), _1388906), _1388908))), 32811 ^ _781215 : [(32814 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388902), _1388904), _1388908)))], (32812 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388902), _1388904), _1388906)))]]], (6626 ^ _781215) ^ [_889683, _889685] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889683, tc_HOL_Obool)), _889685), c_Orderings_Obot__class_Obot(tc_fun(_889683, tc_HOL_Obool))) = _889685)], (45760 ^ _781215) ^ [_1698978, _1698980, _1698982] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1698978), c_List_Oupt(_1698980, _1698982)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1698980), _1698978), _1698982))], (40423 ^ _781215) ^ [_1572190, _1572192] : [c_Wellfounded_OwfP(_1572190, _1572192), -(c_Wellfounded_Oacyclic(_1572190, hAPP(c_Set_OCollect(tc_prod(_1572190, _1572190)), hAPP(c_Product__Type_Oprod_Oprod__case(_1572190, _1572190, tc_HOL_Obool), _1572192))))], (36792 ^ _781215) ^ [_1473481, _1473483, _1473485, _1473487, _1473489, _1473491] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473481, tc_fun(_1473483, tc_fun(_1473485, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1473481, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1473483, _1473485), tc_HOL_Obool), tc_fun(_1473483, tc_fun(_1473485, tc_HOL_Obool)), _1473481), hAPP(c_COMBC(_1473483, tc_fun(tc_prod(_1473483, _1473485), tc_HOL_Obool), tc_fun(_1473485, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473485, tc_fun(tc_fun(tc_prod(_1473483, _1473485), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1473483, _1473485), tc_HOL_Obool), tc_fun(_1473485, tc_HOL_Obool)), _1473483), c_COMBC(_1473485, tc_fun(tc_prod(_1473483, _1473485), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473485, tc_prod(_1473483, _1473485)), tc_fun(_1473485, tc_fun(tc_fun(tc_prod(_1473483, _1473485), tc_HOL_Obool), tc_HOL_Obool)), _1473483), hAPP(c_COMBB(tc_prod(_1473483, _1473485), tc_fun(tc_fun(tc_prod(_1473483, _1473485), tc_HOL_Obool), tc_HOL_Obool), _1473485), c_member(tc_prod(_1473483, _1473485)))), c_Product__Type_OPair(_1473483, _1473485))))), _1473487)), _1473489), _1473491)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1473483, _1473485)), hAPP(hAPP(c_Product__Type_OPair(_1473483, _1473485), _1473489), _1473491)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473481, tc_fun(tc_prod(_1473483, _1473485), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1473481, tc_HOL_Obool))), _1473487))))], (10100 ^ _781215) ^ [_953026, _953028, _953030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _953026), _953028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _953026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953028), _953030))))], (24278 ^ _781215) ^ [_1219116, _1219118] : [class_Rings_Olinordered__idom(_1219116), 24281 ^ _781215 : [(24288 ^ _781215) ^ [] : [-(_1219118 = c_Groups_Ozero__class_Ozero(_1219116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219116), c_Groups_Ozero__class_Ozero(_1219116)), hAPP(hAPP(c_Power_Opower__class_Opower(_1219116), _1219118), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (24282 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219116), c_Groups_Ozero__class_Ozero(_1219116)), hAPP(hAPP(c_Power_Opower__class_Opower(_1219116), _1219118), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1219118 = c_Groups_Ozero__class_Ozero(_1219116)]]], (27370 ^ _781215) ^ [_1279058, _1279060, _1279062, _1279064] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1279058, _1279058)), hAPP(hAPP(c_Product__Type_OPair(_1279058, _1279058), _1279060), _1279062)), hAPP(c_Wellfounded_Omeasure(_1279058), _1279064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1279064, _1279060)), hAPP(_1279064, _1279062))))], (13860 ^ _781215) ^ [_1022684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1022684)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1022684), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1022684)], (37999 ^ _781215) ^ [_1503948, _1503950, _1503952, _1503954, _1503956] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1503948, tc_fun(_1503950, tc_HOL_Obool)), _1503952), hAPP(hAPP(c_COMBS(_1503948, tc_fun(_1503950, tc_HOL_Obool), tc_fun(_1503950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503950, tc_HOL_Obool), tc_fun(tc_fun(_1503950, tc_HOL_Obool), tc_fun(_1503950, tc_HOL_Obool)), _1503948), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1503950, tc_HOL_Obool))), _1503954)), _1503956)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1503950, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1503950, tc_HOL_Obool), hAPP(c_Set_Oimage(_1503948, tc_fun(_1503950, tc_HOL_Obool), _1503954), _1503952))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1503950, tc_HOL_Obool), hAPP(c_Set_Oimage(_1503948, tc_fun(_1503950, tc_HOL_Obool), _1503956), _1503952))))], (9885 ^ _781215) ^ [_949350, _949352, _949354] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949350, tc_HOL_Obool)), _949352), hAPP(hAPP(c_Set_Oinsert(_949350), _949354), _949352))))], (40926 ^ _781215) ^ [_1583573, _1583575, _1583577] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1583573), c_Map_Odom(_1583573, _1583575, hAPP(c_Map_Omap__of(_1583573, _1583575), _1583577)))))], (51206 ^ _781215) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (51622 ^ _781215) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (15254 ^ _781215) ^ [_1048766] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1048766)), _1048766) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37969 ^ _781215) ^ [_1503280] : [class_Complete__Lattice_Ocomplete__lattice(_1503280), -(c_Complete__Lattice_OSup__class_OSup(_1503280, c_Orderings_Obot__class_Obot(tc_fun(_1503280, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1503280))], (14246 ^ _781215) ^ [_1030267, _1030269, _1030271] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(_1030267, _1030269, _1030271)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26312 ^ _781215) ^ [_1258620, _1258622, _1258624, _1258626] : [class_Groups_Ocomm__monoid__mult(_1258620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1258622), _1258624)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1258622, _1258620), hAPP(c_COMBK(_1258620, _1258622), _1258626)), _1258624) = hAPP(hAPP(c_Power_Opower__class_Opower(_1258620), _1258626), hAPP(c_Finite__Set_Ocard(_1258622), _1258624)))], (10140 ^ _781215) ^ [_953912, _953914, _953916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _953912), _953914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _953916), _953914)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _953916), _953912))))], (25084 ^ _781215) ^ [_1234034, _1234036, _1234038, _1234040] : [class_Rings_Olinordered__semidom(_1234034), hAPP(hAPP(c_Power_Opower__class_Opower(_1234034), _1234036), _1234038) = hAPP(hAPP(c_Power_Opower__class_Opower(_1234034), _1234040), _1234038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234034), c_Groups_Ozero__class_Ozero(_1234034)), _1234036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234034), c_Groups_Ozero__class_Ozero(_1234034)), _1234040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1234038)), -(_1234036 = _1234040)], (17951 ^ _781215) ^ [_1101735, _1101737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101735)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101737)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1101735)), hAPP(c_Int_Onat, _1101737)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1101735, _1101737)))], (51362 ^ _781215) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (22675 ^ _781215) ^ [_1190497, _1190499, _1190501, _1190503] : [class_Divides_Osemiring__div(_1190497), -(_1190499 = c_Groups_Ozero__class_Ozero(_1190497)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190497), _1190499), _1190501)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190497), _1190499), _1190503)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1190497), _1190501), _1190503))], (24067 ^ _781215) ^ [_1215215, _1215217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215215)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215217)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1215215), hAPP(c_Int_Onat, _1215217)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1215215, _1215217)))], (32413 ^ _781215) ^ [_1380824, _1380826, _1380828, _1380830, _1380832, _1380834, _1380836] : [c_Equiv__Relations_Oequiv(_1380824, _1380826, _1380828), hBOOL(hAPP(hAPP(c_member(tc_fun(_1380824, tc_HOL_Obool)), _1380830), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1380824), _1380826), _1380828))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1380824, tc_HOL_Obool)), _1380832), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1380824), _1380826), _1380828))), hBOOL(hAPP(hAPP(c_member(_1380824), _1380834), _1380830)), hBOOL(hAPP(hAPP(c_member(_1380824), _1380836), _1380832)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1380824, _1380824)), hAPP(hAPP(c_Product__Type_OPair(_1380824, _1380824), _1380834), _1380836)), _1380828)), -(_1380830 = _1380832)], (44445 ^ _781215) ^ [_1670860, _1670862, _1670864, _1670866] : [-(c_List_Osublist(_1670860, hAPP(hAPP(c_List_Oappend(_1670860), _1670862), _1670864), _1670866) = hAPP(hAPP(c_List_Oappend(_1670860), c_List_Osublist(_1670860, _1670862, _1670866)), c_List_Osublist(_1670860, _1670864, 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(_1670860)), _1670862)))), _1670866)))))], (37580 ^ _781215) ^ [_1494996, _1494998] : [class_Complete__Lattice_Ocomplete__lattice(_1494996), -(c_Complete__Lattice_OInf__class_OInf(_1494996, hAPP(hAPP(c_Set_Oinsert(_1494996), _1494998), c_Orderings_Obot__class_Obot(tc_fun(_1494996, tc_HOL_Obool)))) = _1494998)], (32920 ^ _781215) ^ [_1391604, _1391606, _1391608, _1391610] : [hBOOL(hAPP(hAPP(c_member(_1391604), _1391610), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1391604, tc_HOL_Obool)), _1391606), _1391608))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1391604, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1391604, tc_fun(_1391604, tc_HOL_Obool), tc_HOL_Obool), c_member(_1391604)), _1391606)), hAPP(hAPP(c_COMBC(_1391604, tc_fun(_1391604, tc_HOL_Obool), tc_HOL_Obool), c_member(_1391604)), _1391608)), _1391610)))], (36873 ^ _781215) ^ [_1476087, _1476089, _1476091, _1476093, _1476095, _1476097] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1476087, tc_fun(_1476089, tc_HOL_Obool)), _1476091), _1476093), _1476095)), -(hBOOL(hAPP(hAPP(_1476093, _1476097), _1476095))), hBOOL(hAPP(hAPP(c_member(_1476087), _1476097), _1476091))], (45891 ^ _781215) ^ [_1701488, _1701490] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1701488), hAPP(c_List_Onth(_1701488), _1701490)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701488)), _1701490))) = _1701490)], (30016 ^ _781215) ^ [_1329782, _1329784, _1329786, _1329788, _1329790] : [class_Groups_Ocomm__monoid__mult(_1329782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329784), _1329786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329784, tc_HOL_Obool)), _1329788), _1329786)), 30030 ^ _781215 : [(30033 ^ _781215) ^ [] : [hAPP(_1329790, 30029 ^ [_1329782, _1329784, _1329786, _1329788, _1329790]) = c_Groups_Oone__class_Oone(_1329782)], (30031 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329784), 30029 ^ [_1329782, _1329784, _1329786, _1329788, _1329790]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329784, tc_HOL_Obool)), _1329786), _1329788))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329784, _1329782), _1329790), _1329788) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329784, _1329782), _1329790), _1329786))], (2386 ^ _781215) ^ [_816478, _816480, _816482, _816484, _816486, _816488] : [-(c_Smallcheck_Osmall_H(_816488, _816484, _816480) = c_Smallcheck_Osmall_H(_816486, _816482, _816478)), _816488 = _816486, _816484 = _816482, _816480 = _816478], (10230 ^ _781215) ^ [_955485, _955487] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955485), _955487) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 10233 ^ _781215 : [(10236 ^ _781215) ^ [] : [-(_955487 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10234 ^ _781215) ^ [] : [-(_955485 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (13338 ^ _781215) ^ [_1013153, _1013155] : [-(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), _1013153), _1013155)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1013153)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1013155))], (9891 ^ _781215) ^ [_949518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _949518)), _949518))], (21678 ^ _781215) ^ [_1170145] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1170145)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1170145))))], (47671 ^ _781215) ^ [_1740935, _1740937, _1740939, _1740941, _1740943, _1740945, _1740947] : [c_List_Olist__all2(_1740935, _1740943, hAPP(hAPP(c_COMBC(_1740935, tc_fun(_1740943, _1740937), tc_fun(_1740943, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1740937, tc_HOL_Obool), tc_fun(tc_fun(_1740943, _1740937), tc_fun(_1740943, tc_HOL_Obool)), _1740935), c_COMBB(_1740937, tc_HOL_Obool, _1740943)), _1740939)), _1740945), _1740941, _1740947), -(c_List_Olist__all2(_1740935, _1740937, _1740939, _1740941, hAPP(hAPP(c_List_Omap(_1740943, _1740937), _1740945), _1740947)))], (19706 ^ _781215) ^ [_1134923, _1134925] : [class_Orderings_Olinorder(_1134923), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134923), _1134925)), -(c_Big__Operators_Olattice_OSup__fin(_1134923, c_Orderings_Oord__class_Omax(_1134923), _1134925) = hAPP(c_Finite__Set_Ofold1(_1134923, c_Orderings_Oord__class_Omax(_1134923)), _1134925))], (14341 ^ _781215) ^ [_1032081, _1032083, _1032085] : [class_Rings_Oring__1(_1032081), hBOOL(hAPP(hAPP(c_member(_1032081), _1032083), c_Int_Oring__1__class_OInts(_1032081))), hBOOL(hAPP(hAPP(c_member(_1032081), _1032085), c_Int_Oring__1__class_OInts(_1032081))), -(hBOOL(hAPP(hAPP(c_member(_1032081), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032081), _1032083), _1032085)), c_Int_Oring__1__class_OInts(_1032081))))], (13192 ^ _781215) ^ [_1010740, _1010742] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1010740), _1010742)), 13193 ^ _781215 : [(13200 ^ _781215) ^ [] : [_1010740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1010742 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13194 ^ _781215) ^ [] : [_1010740 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1010742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (49535 ^ _781215) ^ [_1783588, _1783590, _1783592, _1783594] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1783588), tc_List_Olist(_1783588))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1783588), tc_List_Olist(_1783588)), _1783590), _1783592)), c_List_Olistrel1(_1783588, _1783594))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1783588), tc_List_Olist(_1783588))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1783588), tc_List_Olist(_1783588)), _1783590), _1783592)), c_List_Olistrel(_1783588, c_Transitive__Closure_Ortrancl(_1783588, _1783594)))))], (32186 ^ _781215) ^ [_1375595, _1375597, _1375599] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1375595), _1375597), _1375599) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1375595, tc_fun(tc_fun(_1375595, tc_HOL_Obool), tc_HOL_Obool)), _1375597), hAPP(hAPP(c_COMBC(_1375595, tc_fun(tc_fun(_1375595, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1375595, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1375595, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1375595, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1375595, tc_HOL_Obool), tc_HOL_Obool)), _1375595), c_Set_Oinsert(tc_fun(_1375595, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1375595, tc_HOL_Obool), tc_fun(_1375595, tc_HOL_Obool), _1375595), c_Relation_OImage(_1375595, _1375595, _1375599)), hAPP(hAPP(c_COMBC(_1375595, tc_fun(_1375595, tc_HOL_Obool), tc_fun(_1375595, tc_HOL_Obool)), c_Set_Oinsert(_1375595)), c_Orderings_Obot__class_Obot(tc_fun(_1375595, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1375595, tc_HOL_Obool), tc_HOL_Obool)))))], (7764 ^ _781215) ^ [_912106, _912108, _912110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912106), _912108)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _912106), _912110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912108), _912110)))], (14186 ^ _781215) ^ [_1028963, _1028965, _1028967, _1028969, _1028971, _1028973, _1028975] : [c_Nitpick_Ofold__graph_H(_1028963, _1028965, _1028967, _1028969, _1028971, hAPP(hAPP(_1028967, _1028973), _1028975)), 14191 ^ _781215 : [(14194 ^ _781215) ^ [] : [-(hAPP(hAPP(_1028967, _1028973), _1028975) = _1028969)], (14192 ^ _781215) ^ [] : [-(_1028971 = c_Orderings_Obot__class_Obot(tc_fun(_1028963, tc_HOL_Obool)))]], 14197 ^ _781215 : [(14202 ^ _781215) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1028963, _1028965, _1028967, _1028969, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1028963, tc_HOL_Obool)), _1028971), hAPP(hAPP(c_Set_Oinsert(_1028963), 14195 ^ [_1028963, _1028965, _1028967, _1028969, _1028971, _1028973, _1028975]), c_Orderings_Obot__class_Obot(tc_fun(_1028963, tc_HOL_Obool)))), 14196 ^ [_1028963, _1028965, _1028967, _1028969, _1028971, _1028973, _1028975]))], (14200 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1028963), 14195 ^ [_1028963, _1028965, _1028967, _1028969, _1028971, _1028973, _1028975]), _1028971)))], (14198 ^ _781215) ^ [] : [-(hAPP(hAPP(_1028967, _1028973), _1028975) = hAPP(hAPP(_1028967, 14195 ^ [_1028963, _1028965, _1028967, _1028969, _1028971, _1028973, _1028975]), 14196 ^ [_1028963, _1028965, _1028967, _1028969, _1028971, _1028973, _1028975]))]]], (34350 ^ _781215) ^ [_1424813, _1424815] : [class_Lattices_Olattice(_1424813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424813), _1424815)), -(c_Big__Operators_Olattice__class_OInf__fin(_1424813, _1424815) = hAPP(c_Finite__Set_Ofold1(_1424813, c_Lattices_Osemilattice__inf__class_Oinf(_1424813)), _1424815))], (42050 ^ _781215) ^ [_1610760, _1610762, _1610764, _1610766, _1610768] : [class_Orderings_Olinorder(_1610760), -(hAPP(c_List_Oset(_1610762), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1610762, _1610760, _1610764), _1610766), _1610768)) = hAPP(hAPP(c_Set_Oinsert(_1610762), _1610766), hAPP(c_List_Oset(_1610762), _1610768)))], (25911 ^ _781215) ^ [_1251222] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1251222)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1251222))], (33050 ^ _781215) ^ [_1394433, _1394435] : [class_Lattices_Osemilattice__inf(_1394433), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1394433), _1394435), _1394435) = _1394435)], (40645 ^ _781215) ^ [_1577644, _1577646, _1577648] : [-(hBOOL(hAPP(_1577644, _1577646))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_1577644, _1577648)), _1577646), _1577646)))], (41066 ^ _781215) ^ [_1586811, _1586813, _1586815, _1586817, _1586819] : [hAPP(hAPP(c_List_Omap(_1586811, _1586813), _1586815), _1586817) = hAPP(hAPP(c_List_Omap(_1586811, _1586813), _1586815), _1586819), c_Fun_Oinj__on(_1586811, _1586813, _1586815, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1586811, tc_HOL_Obool)), hAPP(c_List_Oset(_1586811), _1586817)), hAPP(c_List_Oset(_1586811), _1586819))), -(_1586817 = _1586819)], (30608 ^ _781215) ^ [_1341257, _1341259, _1341261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1341257)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1341259), _1341261)), 30615 ^ _781215 : [(30616 ^ _781215) ^ [_1341453] : [30618 ^ _781215 : [(30624 ^ _781215) ^ [] : [-(_1341453 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30620 ^ [_1341257, _1341259, _1341261, _1341453]), 30617 ^ [_1341257, _1341259, _1341261, _1341453]))], (30622 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30620 ^ [_1341257, _1341259, _1341261, _1341453]), _1341261)))], (30619 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30617 ^ [_1341257, _1341259, _1341261, _1341453]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1341257))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1341453), _1341259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1341453), _1341257)), _1341259)))]]], (44325 ^ _781215) ^ [_1667810, _1667812, _1667814, _1667816] : [-(hAPP(c_Map_Omap__of(_1667810, _1667812), hAPP(hAPP(c_List_Oappend(tc_prod(_1667810, _1667812)), _1667814), _1667816)) = c_Map_Omap__add(_1667810, _1667812, hAPP(c_Map_Omap__of(_1667810, _1667812), _1667816), hAPP(c_Map_Omap__of(_1667810, _1667812), _1667814)))], (11248 ^ _781215) ^ [_976755, _976757, _976759, _976761, _976763] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_976755), 11251 ^ _781215 : [(11252 ^ _781215) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976755), _976757), _976761)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976755), _976759), _976763)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976755), _976757), _976763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976755), _976759), _976761)), -(_976757 = _976759), -(_976761 = _976763)], (11262 ^ _781215) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976755), _976757), _976761)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976755), _976759), _976763)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976755), _976757), _976763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976755), _976759), _976761))), 11265 ^ _781215 : [(11268 ^ _781215) ^ [] : [_976761 = _976763], (11266 ^ _781215) ^ [] : [_976757 = _976759]]]]], (13892 ^ _781215) ^ [_1023202, _1023204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1023202)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1023204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1023202), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023204), _1023202))))], (12366 ^ _781215) ^ [_996308, _996310, _996312] : [class_Rings_Oordered__cancel__semiring(_996308), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996308), c_Groups_Ozero__class_Ozero(_996308)), _996310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996308), _996312), c_Groups_Ozero__class_Ozero(_996308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996308), _996310), _996312)), c_Groups_Ozero__class_Ozero(_996308))))], (44343 ^ _781215) ^ [_1668269, _1668271, _1668273, _1668275] : [-(hAPP(hAPP(c_List_Otake(_1668269), _1668271), hAPP(hAPP(c_List_Oappend(_1668269), _1668273), _1668275)) = hAPP(hAPP(c_List_Oappend(_1668269), hAPP(hAPP(c_List_Otake(_1668269), _1668271), _1668273)), hAPP(hAPP(c_List_Otake(_1668269), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1668271), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668269)), _1668273))), _1668275)))], (38179 ^ _781215) ^ [_1508300, _1508302] : [-(c_Divides_Odivmod__nat(_1508300, _1508302) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1508300, _1508302)))], (42923 ^ _781215) ^ [_1635032, _1635034, _1635036, _1635038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635032)), _1635034)), _1635036)), -(hAPP(hAPP(c_List_Olist__update(_1635032, _1635034), _1635036), _1635038) = _1635034)], (22958 ^ _781215) ^ [_1195172, _1195174, _1195176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195172), 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)), _1195174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195174), _1195176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195172), _1195174)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195172), _1195176))))], (20547 ^ _781215) ^ [_1149982, _1149984] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149982)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149984)), _1149982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1149984 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13148 ^ _781215) ^ [_1010131, _1010133] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1010131), _1010133) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 13153 ^ _781215 : [(13156 ^ _781215) ^ [] : [-(_1010133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13154 ^ _781215) ^ [] : [-(_1010131 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 13157 ^ _781215 : [(13160 ^ _781215) ^ [] : [-(_1010133 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13158 ^ _781215) ^ [] : [-(_1010131 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (49760 ^ _781215) ^ [_1789627, _1789629] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1789627, _1789627)), _1789629)), c_Wellfounded_Oacyclic(_1789627, _1789629), -(c_Wellfounded_Owf(_1789627, hAPP(c_Relation_Oconverse(_1789627, _1789627), _1789629)))], (8498 ^ _781215) ^ [_925429, _925431] : [class_Orderings_Opreorder(_925429), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925429), _925431), _925431)))], (40219 ^ _781215) ^ [_1566804, _1566806] : [-(c_FunDef_Oreduction__pair(_1566804, _1566806)), c_Wellfounded_Owf(_1566804, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1566804, _1566804), tc_HOL_Obool), tc_fun(tc_prod(_1566804, _1566804), tc_HOL_Obool)), _1566806)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566804, _1566804), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1566804, _1566804, _1566804), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1566804, _1566804), tc_HOL_Obool), tc_fun(tc_prod(_1566804, _1566804), tc_HOL_Obool)), _1566806)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1566804, _1566804), tc_HOL_Obool), tc_fun(tc_prod(_1566804, _1566804), tc_HOL_Obool)), _1566806))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1566804, _1566804), tc_HOL_Obool), tc_fun(tc_prod(_1566804, _1566804), tc_HOL_Obool)), _1566806)))], (24642 ^ _781215) ^ [_1226029, _1226031, _1226033, _1226035] : [class_Rings_Olinordered__semidom(_1226029), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226029), c_Groups_Oone__class_Oone(_1226029)), _1226031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226029), hAPP(hAPP(c_Power_Opower__class_Opower(_1226029), _1226031), _1226033)), hAPP(hAPP(c_Power_Opower__class_Opower(_1226029), _1226031), _1226035))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1226033), _1226035)))], (23895 ^ _781215) ^ [_1211893, _1211895, _1211897] : [-(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), _1211893), _1211895)), _1211897)), _1211895) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1211897), _1211895))], (17707 ^ _781215) ^ [_1097685] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1097685)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097685))], (17033 ^ _781215) ^ [_1086688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086688), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086688) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43611 ^ _781215) ^ [_1652175, _1652177, _1652179, _1652181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1652175), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652177)), _1652179))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1652175), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652177)), _1652181))), 43621 ^ _781215 : [(43624 ^ _781215) ^ [] : [hAPP(hAPP(c_List_Onth(_1652177), _1652179), 43620 ^ [_1652175, _1652177, _1652179, _1652181]) = hAPP(hAPP(c_List_Onth(_1652177), _1652181), 43620 ^ [_1652175, _1652177, _1652179, _1652181])], (43622 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43620 ^ [_1652175, _1652177, _1652179, _1652181]), _1652175)))]], -(hAPP(hAPP(c_List_Otake(_1652177), _1652175), _1652179) = hAPP(hAPP(c_List_Otake(_1652177), _1652175), _1652181))], (31826 ^ _781215) ^ [_1367328, _1367330, _1367332] : [class_Groups_Ocomm__monoid__add(_1367328), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1367328), _1367330), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1367332))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1367328), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1367328), _1367330), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1367332))), hAPP(_1367330, _1367332)))], (5991 ^ _781215) ^ [_876702, _876704, _876706] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_876702), hAPP(hAPP(c_Set_Oinsert(_876702), _876704), _876706))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_876702), _876706)))], (36085 ^ _781215) ^ [_1459862, _1459864] : [class_Groups_Oordered__ab__group__add__abs(_1459862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459862), _1459864), c_Groups_Ozero__class_Ozero(_1459862))), -(hAPP(c_Groups_Oabs__class_Oabs(_1459862), _1459864) = hAPP(c_Groups_Ouminus__class_Ouminus(_1459862), _1459864))], (51278 ^ _781215) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (13032 ^ _781215) ^ [_1008205, _1008207] : [class_Groups_Oordered__ab__group__add(_1008205), 13035 ^ _781215 : [(13042 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008205), _1008207), c_Groups_Ozero__class_Ozero(_1008205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008205), c_Groups_Ozero__class_Ozero(_1008205)), hAPP(c_Groups_Ouminus__class_Ouminus(_1008205), _1008207))))], (13036 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008205), c_Groups_Ozero__class_Ozero(_1008205)), hAPP(c_Groups_Ouminus__class_Ouminus(_1008205), _1008207))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008205), _1008207), c_Groups_Ozero__class_Ozero(_1008205))))]]], (42022 ^ _781215) ^ [_1610153, _1610155, _1610157] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610153)), _1610155) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610153)), _1610157)), _1610155 = _1610157], (44602 ^ _781215) ^ [_1675188, _1675190, _1675192, _1675194, _1675196] : [hAPP(hAPP(c_List_Odrop(_1675188), _1675190), _1675192) = hAPP(hAPP(c_List_Olist_OCons(_1675188), _1675194), _1675196), -(hAPP(hAPP(c_List_Onth(_1675188), _1675192), _1675190) = _1675194)], (29032 ^ _781215) ^ [_1310530, _1310532, _1310534] : [class_Fields_Olinordered__field(_1310530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310530), _1310532), c_Groups_Ozero__class_Ozero(_1310530))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310530), _1310534), c_Groups_Ozero__class_Ozero(_1310530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310530), c_Groups_Ozero__class_Ozero(_1310530)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310530), _1310532), _1310534))))], (7871 ^ _781215) ^ [_914226, _914228] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914226), _914228))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _914226), _914228)) = _914226)], (29716 ^ _781215) ^ [_1322850, _1322852, _1322854, _1322856] : [class_Fields_Ofield(_1322850), -(_1322852 = c_Groups_Ozero__class_Ozero(_1322850)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322850), _1322854), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322850), _1322856), _1322852)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322850), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1322850), _1322852), _1322854)), _1322856)), _1322852))], (5398 ^ _781215) ^ [_863678, _863680, _863682, _863684] : [-(c_Wellfounded_Oaccp(_863684, _863680) = c_Wellfounded_Oaccp(_863682, _863678)), _863684 = _863682, _863680 = _863678], (50050 ^ _781215) ^ [_1796746] : [-(c_Nat_Ofunpow(_1796746) = c_Nat_Ocompow(_1796746, _1796746))], (9745 ^ _781215) ^ [_946740, _946742, _946744, _946746, _946748] : [class_Groups_Oordered__ab__semigroup__add(_946740), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946740), _946742), _946744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946740), _946746), _946748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946740), _946742), _946746)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946740), _946744), _946748))))], (34494 ^ _781215) ^ [_1427267, _1427269, _1427271] : [class_Lattices_Olattice(_1427267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427267), _1427269)), -(_1427269 = c_Orderings_Obot__class_Obot(tc_fun(_1427267, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427267), _1427271)), -(_1427271 = c_Orderings_Obot__class_Obot(tc_fun(_1427267, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427267, tc_HOL_Obool)), _1427269), _1427271) = c_Orderings_Obot__class_Obot(tc_fun(_1427267, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1427267, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427267, tc_HOL_Obool)), _1427269), _1427271)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1427267), c_Big__Operators_Olattice__class_OInf__fin(_1427267, _1427269)), c_Big__Operators_Olattice__class_OInf__fin(_1427267, _1427271)))], (22396 ^ _781215) ^ [_1185754, _1185756, _1185758, _1185760] : [class_Divides_Oring__div(_1185754), c_Divides_Odiv__class_Omod(_1185754, _1185756, _1185758) = c_Divides_Odiv__class_Omod(_1185754, _1185760, _1185758), -(c_Divides_Odiv__class_Omod(_1185754, hAPP(c_Groups_Ouminus__class_Ouminus(_1185754), _1185756), _1185758) = c_Divides_Odiv__class_Omod(_1185754, hAPP(c_Groups_Ouminus__class_Ouminus(_1185754), _1185760), _1185758))], (4132 ^ _781215) ^ [_843935, _843937, _843939, _843941] : [-(c_Random_Olog(_843941, _843937) = c_Random_Olog(_843939, _843935)), _843941 = _843939, _843937 = _843935], (19464 ^ _781215) ^ [_1130356, _1130358, _1130360] : [class_Orderings_Olinorder(_1130356), hBOOL(hAPP(c_Finite__Set_Ofinite(_1130356), _1130358)), -(hBOOL(hAPP(hAPP(c_member(_1130356), _1130360), _1130358))), -(_1130358 = c_Orderings_Obot__class_Obot(tc_fun(_1130356, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1130356, hAPP(hAPP(c_Set_Oinsert(_1130356), _1130360), _1130358)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1130356), _1130360), c_Big__Operators_Olinorder__class_OMin(_1130356, _1130358)))], (41082 ^ _781215) ^ [_1587116, _1587118, _1587120, _1587122] : [c_Fun_Oinj__on(_1587116, _1587118, _1587120, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1587116, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1587116), tc_fun(_1587116, tc_HOL_Obool), c_List_Oset(_1587116)), _1587122))), -(c_Fun_Oinj__on(tc_List_Olist(_1587116), tc_List_Olist(_1587118), hAPP(c_List_Omap(_1587116, _1587118), _1587120), _1587122))], (39270 ^ _781215) ^ [_1536436, _1536438, _1536440, _1536442, _1536444] : [class_Groups_Ocomm__monoid__add(_1536436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536438), _1536440)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536438, _1536436), _1536442), hAPP(c_Set_OCollect(_1536438), hAPP(hAPP(c_COMBS(_1536438, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536438), c_fconj), hAPP(hAPP(c_COMBC(_1536438, tc_fun(_1536438, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536438)), _1536440))), hAPP(hAPP(c_COMBC(_1536438, tc_fun(_1536438, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536438)), _1536444)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536438, _1536436), hAPP(hAPP(c_COMBC(_1536438, _1536436, _1536436), hAPP(hAPP(c_COMBS(_1536438, _1536436, tc_fun(_1536436, _1536436)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1536436, tc_fun(_1536436, _1536436)), _1536438), c_If(_1536436)), hAPP(hAPP(c_COMBC(_1536438, tc_fun(_1536438, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536438)), _1536444))), _1536442)), c_Groups_Ozero__class_Ozero(_1536436))), _1536440))], (15626 ^ _781215) ^ [_1055698, _1055700, _1055702, _1055704, _1055706, _1055708] : [c_Com_Ocom_OLocal(_1055698, _1055700, _1055702) = c_Com_Ocom_OCond(_1055704, _1055706, _1055708)], (27219 ^ _781215) ^ [_1276046, _1276048] : [-(_1276046 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1276048, _1276046), c_Divides_Odivmod__int(_1276048, _1276046))))], (7274 ^ _781215) ^ [_903783, _903785, _903787] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903783), _903785)), hBOOL(hAPP(hAPP(c_member(_903783), _903787), _903785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_903783), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903783, tc_HOL_Obool)), _903785), hAPP(hAPP(c_Set_Oinsert(_903783), _903787), c_Orderings_Obot__class_Obot(tc_fun(_903783, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_903783), _903785))))], (20569 ^ _781215) ^ [_1150366, _1150368] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150366)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150368)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150366), _1150368)))], (35777 ^ _781215) ^ [_1453921, _1453923, _1453925] : [class_Groups_Oordered__ab__group__add__abs(_1453921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453921), hAPP(c_Groups_Oabs__class_Oabs(_1453921), _1453923)), _1453925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453921), _1453923), _1453925)))], (43868 ^ _781215) ^ [_1657004, _1657006, _1657008] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657004), tc_List_Olist(_1657004))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657004), tc_List_Olist(_1657004)), c_List_Olist_ONil(_1657004)), _1657006)), c_List_Olistrel1(_1657004, _1657008)))], (18067 ^ _781215) ^ [_1104081, _1104083] : [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(_1104083))), 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), _1104081)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104081)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104083))))], (25050 ^ _781215) ^ [_1233321, _1233323, _1233325, _1233327] : [class_Rings_Olinordered__semidom(_1233321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1233323), _1233325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233321), c_Groups_Oone__class_Oone(_1233321)), _1233327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233321), hAPP(hAPP(c_Power_Opower__class_Opower(_1233321), _1233327), _1233323)), hAPP(hAPP(c_Power_Opower__class_Opower(_1233321), _1233327), _1233325))))], (20259 ^ _781215) ^ [_1144878, _1144880] : [_1144878 = _1144880, -(c_Int_OBit1(_1144878) = c_Int_OBit1(_1144880))], (25909 ^ _781215) ^ [_1251193] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251193) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1251193))], (18097 ^ _781215) ^ [_1105065, _1105067] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105065)), hAPP(c_Nat_OSuc, _1105067)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1105065))), 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)), _1105067)))))], (27376 ^ _781215) ^ [_1279205, _1279207, _1279209, _1279211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1279211, _1279207)), hAPP(_1279211, _1279209))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1279205, _1279205)), hAPP(hAPP(c_Product__Type_OPair(_1279205, _1279205), _1279207), _1279209)), hAPP(c_Wellfounded_Omeasure(_1279205), _1279211))))], (40948 ^ _781215) ^ [_1584396, _1584398, _1584400] : [c_Fun_Oinj__on(tc_List_Olist(_1584396), tc_List_Olist(_1584398), hAPP(c_List_Omap(_1584396, _1584398), _1584400), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1584396), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1584396, _1584398, _1584400, c_Orderings_Otop__class_Otop(tc_fun(_1584396, tc_HOL_Obool))))], (45454 ^ _781215) ^ [_1693908, _1693910] : [class_Orderings_Olinorder(_1693908), -(c_List_Olinorder__class_Osorted(_1693908, hAPP(hAPP(c_List_Olist_OCons(_1693908), _1693910), c_List_Olist_ONil(_1693908))))], (39745 ^ _781215) ^ [_1554331, _1554333] : [-(hAPP(c_Relation_ORange(_1554331, _1554331), c_Relation_OId__on(_1554331, _1554333)) = _1554333)], (40361 ^ _781215) ^ [_1570490, _1570492, _1570494, _1570496] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1570490), _1570492))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570494), hAPP(c_Set_Oimage(_1570490, _1570494, _1570496), _1570492))), 40369 ^ _781215 : [(40372 ^ _781215) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1570490), hAPP(c_Set_OCollect(_1570490), hAPP(hAPP(c_COMBS(_1570490, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570490), c_fconj), hAPP(hAPP(c_COMBC(_1570490, tc_fun(_1570490, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570490)), _1570492))), hAPP(hAPP(c_COMBC(_1570490, _1570494, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1570494, tc_fun(_1570494, tc_HOL_Obool), _1570490), c_fequal), _1570496)), hAPP(_1570496, 40368 ^ [_1570490, _1570492, _1570494, _1570496]))))))], (40370 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1570490), 40368 ^ [_1570490, _1570492, _1570494, _1570496]), _1570492)))]]], (36111 ^ _781215) ^ [_1460267, _1460269] : [class_Groups_Oordered__ab__group__add__abs(_1460267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460267), _1460269), c_Groups_Ozero__class_Ozero(_1460267))), -(hAPP(c_Groups_Oabs__class_Oabs(_1460267), _1460269) = hAPP(c_Groups_Ouminus__class_Ouminus(_1460267), _1460269))], (17225 ^ _781215) ^ [_1089818, _1089820, _1089822] : [class_Lattices_Olattice(_1089818), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089818), _1089820)), -(_1089820 = c_Orderings_Obot__class_Obot(tc_fun(_1089818, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1089818, hAPP(hAPP(c_Set_Oinsert(_1089818), _1089822), _1089820)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1089818), _1089822), c_Big__Operators_Olattice__class_OSup__fin(_1089818, _1089820)))], (9709 ^ _781215) ^ [_946043, _946045, _946047, _946049] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_946043), 9712 ^ _781215 : [(9719 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946043), _946047), _946049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946043), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946043), _946045), _946047)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946043), _946045), _946049))))], (9713 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946043), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946043), _946045), _946047)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946043), _946045), _946049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946043), _946047), _946049)))]]], (2722 ^ _781215) ^ [_821810, _821812, _821814, _821816, _821818, _821820, _821822, _821824] : [-(c_Nitpick_Oprod(_821824, _821820, _821816, _821812) = c_Nitpick_Oprod(_821822, _821818, _821814, _821810)), _821824 = _821822, _821820 = _821818, _821816 = _821814, _821812 = _821810], (10152 ^ _781215) ^ [_954158, _954160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954158), _954160)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954160), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _954160), _954158)) = _954158)], (11112 ^ _781215) ^ [_973562, _973564] : [class_Rings_Ocomm__ring__1(_973562), -(hAPP(c_Groups_Ouminus__class_Ouminus(_973562), _973564) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973562), hAPP(c_Groups_Ouminus__class_Ouminus(_973562), c_Groups_Oone__class_Oone(_973562))), _973564))], (24502 ^ _781215) ^ [_1223266] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223266, 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, _1223266, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25534 ^ _781215) ^ [] : [-(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))], (25815 ^ _781215) ^ [_1246776, _1246778, _1246780, _1246782, _1246784, _1246786] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1246776, _1246778)), hAPP(hAPP(c_Product__Type_OPair(_1246776, _1246778), _1246784), _1246786)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool)), _1246780), _1246782))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1246776, tc_fun(_1246778, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1246776, tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_fun(_1246778, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246778, tc_fun(tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_fun(_1246778, tc_HOL_Obool)), _1246776), c_COMBC(_1246778, tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246778, tc_prod(_1246776, _1246778)), tc_fun(_1246778, tc_fun(tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_HOL_Obool)), _1246776), hAPP(c_COMBB(tc_prod(_1246776, _1246778), tc_fun(tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_HOL_Obool), _1246778), c_member(tc_prod(_1246776, _1246778)))), c_Product__Type_OPair(_1246776, _1246778)))), _1246780)), hAPP(hAPP(c_COMBC(_1246776, tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_fun(_1246778, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246778, tc_fun(tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_fun(_1246778, tc_HOL_Obool)), _1246776), c_COMBC(_1246778, tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1246778, tc_prod(_1246776, _1246778)), tc_fun(_1246778, tc_fun(tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_HOL_Obool)), _1246776), hAPP(c_COMBB(tc_prod(_1246776, _1246778), tc_fun(tc_fun(tc_prod(_1246776, _1246778), tc_HOL_Obool), tc_HOL_Obool), _1246778), c_member(tc_prod(_1246776, _1246778)))), c_Product__Type_OPair(_1246776, _1246778)))), _1246782)), _1246784), _1246786)))], (51354 ^ _781215) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (39873 ^ _781215) ^ [_1558731, _1558733, _1558735, _1558737, _1558739, _1558741, _1558743] : [c_Predicate_Opred__comp(_1558731, _1558733, _1558735, hAPP(hAPP(c_COMBC(_1558731, tc_fun(tc_prod(_1558731, _1558733), tc_HOL_Obool), tc_fun(_1558733, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558733, tc_fun(tc_fun(tc_prod(_1558731, _1558733), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1558731, _1558733), tc_HOL_Obool), tc_fun(_1558733, tc_HOL_Obool)), _1558731), c_COMBC(_1558733, tc_fun(tc_prod(_1558731, _1558733), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558733, tc_prod(_1558731, _1558733)), tc_fun(_1558733, tc_fun(tc_fun(tc_prod(_1558731, _1558733), tc_HOL_Obool), tc_HOL_Obool)), _1558731), hAPP(c_COMBB(tc_prod(_1558731, _1558733), tc_fun(tc_fun(tc_prod(_1558731, _1558733), tc_HOL_Obool), tc_HOL_Obool), _1558733), c_member(tc_prod(_1558731, _1558733)))), c_Product__Type_OPair(_1558731, _1558733)))), _1558737), hAPP(hAPP(c_COMBC(_1558733, tc_fun(tc_prod(_1558733, _1558735), tc_HOL_Obool), tc_fun(_1558735, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558735, tc_fun(tc_fun(tc_prod(_1558733, _1558735), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1558733, _1558735), tc_HOL_Obool), tc_fun(_1558735, tc_HOL_Obool)), _1558733), c_COMBC(_1558735, tc_fun(tc_prod(_1558733, _1558735), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558735, tc_prod(_1558733, _1558735)), tc_fun(_1558735, tc_fun(tc_fun(tc_prod(_1558733, _1558735), tc_HOL_Obool), tc_HOL_Obool)), _1558733), hAPP(c_COMBB(tc_prod(_1558733, _1558735), tc_fun(tc_fun(tc_prod(_1558733, _1558735), tc_HOL_Obool), tc_HOL_Obool), _1558735), c_member(tc_prod(_1558733, _1558735)))), c_Product__Type_OPair(_1558733, _1558735)))), _1558739), _1558741, _1558743), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1558731, _1558735)), hAPP(hAPP(c_Product__Type_OPair(_1558731, _1558735), _1558741), _1558743)), hAPP(hAPP(c_Relation_Orel__comp(_1558731, _1558733, _1558735), _1558737), _1558739))))], (39375 ^ _781215) ^ [_1540441, _1540443] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1540441), _1540443)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1540441, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1540441, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1540441, tc_HOL_Obool), tc_fun(_1540441, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1540441, tc_HOL_Obool))), _1540443)))))], (37462 ^ _781215) ^ [_1492636, _1492638] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1492636), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1492636, tc_HOL_Obool), _1492638)))), 37463 ^ _781215 : [(37464 ^ _781215) ^ [_1492700] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1492636, tc_HOL_Obool)), _1492700), _1492638)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492636), _1492700))]]], (48992 ^ _781215) ^ [_1769993, _1769995] : [_1769993 = _1769995, -(hAPP(c_Code__Numeral_Onat__of, _1769993) = hAPP(c_Code__Numeral_Onat__of, _1769995))], (22428 ^ _781215) ^ [_1186396, _1186398] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1186396, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186398)) = 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), _1186396), _1186398)))], (17101 ^ _781215) ^ [_1087841, _1087843] : [class_Lattices_Olattice(_1087841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087841), _1087843)), -(c_Big__Operators_Olattice__class_OSup__fin(_1087841, _1087843) = hAPP(c_Finite__Set_Ofold1(_1087841, c_Lattices_Osemilattice__sup__class_Osup(_1087841)), _1087843))], (1578 ^ _781215) ^ [_803910, _803912] : [-(class_Rings_Olinordered__semiring(_803910)), _803912 = _803910, class_Rings_Olinordered__semiring(_803912)], (4412 ^ _781215) ^ [_848125, _848127, _848129, _848131] : [-(c_List_Orotate(_848131, _848127) = c_List_Orotate(_848129, _848125)), _848131 = _848129, _848127 = _848125], (37117 ^ _781215) ^ [_1483545, _1483547, _1483549, _1483551, _1483553, _1483555] : [hBOOL(hAPP(hAPP(c_member(_1483545), _1483547), _1483549)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483545, tc_fun(_1483551, tc_HOL_Obool)), _1483549), hAPP(hAPP(c_COMBB(tc_fun(_1483551, tc_HOL_Obool), tc_fun(_1483551, tc_HOL_Obool), _1483545), hAPP(c_Set_Oinsert(_1483551), _1483553)), _1483555)) = hAPP(hAPP(c_Set_Oinsert(_1483551), _1483553), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483545, tc_fun(_1483551, tc_HOL_Obool)), _1483549), _1483555)))], (29736 ^ _781215) ^ [_1323243, _1323245, _1323247] : [class_Fields_Olinordered__field(_1323243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323243), _1323245), _1323247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323243), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323243), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323243), _1323245), _1323247)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323243), c_Groups_Oone__class_Oone(_1323243)), c_Groups_Oone__class_Oone(_1323243)))), _1323247)))], (48766 ^ _781215) ^ [_1766087, _1766089] : [48767 ^ _781215 : [(48770 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1766089), _1766087))], (48768 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1766087), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1766087, _1766089) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (4514 ^ _781215) ^ [_849668, _849670, _849672, _849674] : [-(c_Complete__Lattice_OSup__class_OSup(_849674, _849670) = c_Complete__Lattice_OSup__class_OSup(_849672, _849668)), _849674 = _849672, _849670 = _849668], (40273 ^ _781215) ^ [_1568407, _1568409, _1568411, _1568413] : [hBOOL(hAPP(hAPP(c_member(_1568407), _1568413), hAPP(c_Relation_ODomain(_1568407, _1568409), _1568411))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1568407, _1568409, hAPP(hAPP(c_COMBC(_1568407, tc_fun(tc_prod(_1568407, _1568409), tc_HOL_Obool), tc_fun(_1568409, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568409, tc_fun(tc_fun(tc_prod(_1568407, _1568409), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1568407, _1568409), tc_HOL_Obool), tc_fun(_1568409, tc_HOL_Obool)), _1568407), c_COMBC(_1568409, tc_fun(tc_prod(_1568407, _1568409), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568409, tc_prod(_1568407, _1568409)), tc_fun(_1568409, tc_fun(tc_fun(tc_prod(_1568407, _1568409), tc_HOL_Obool), tc_HOL_Obool)), _1568407), hAPP(c_COMBB(tc_prod(_1568407, _1568409), tc_fun(tc_fun(tc_prod(_1568407, _1568409), tc_HOL_Obool), tc_HOL_Obool), _1568409), c_member(tc_prod(_1568407, _1568409)))), c_Product__Type_OPair(_1568407, _1568409)))), _1568411)), _1568413)))], (25672 ^ _781215) ^ [_1243230] : [c_Code__Numeral_OSuc__code__numeral(_1243230) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (42381 ^ _781215) ^ [_1620564, _1620566, _1620568, _1620570, _1620572, _1620574] : [hBOOL(hAPP(hAPP(_1620564, _1620566), _1620568)), c_List_Olistrelp(_1620570, _1620564, _1620572, _1620574), -(c_List_Olistrelp(_1620570, _1620564, hAPP(hAPP(c_List_Olist_OCons(_1620570), _1620566), _1620572), hAPP(hAPP(c_List_Olist_OCons(_1620570), _1620568), _1620574)))], (47958 ^ _781215) ^ [_1746855, _1746857, _1746859, _1746861, _1746863] : [c_Fun_Oinj__on(_1746855, _1746857, _1746859, c_Orderings_Otop__class_Otop(tc_fun(_1746855, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1746855, _1746857), _1746859), hAPP(c_List_OremoveAll(_1746855, _1746861), _1746863)) = hAPP(c_List_OremoveAll(_1746857, hAPP(_1746859, _1746861)), hAPP(hAPP(c_List_Omap(_1746855, _1746857), _1746859), _1746863)))], (12902 ^ _781215) ^ [_1006024] : [class_Rings_Olinordered__semidom(_1006024), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006024), c_Groups_Oone__class_Oone(_1006024)), c_Groups_Ozero__class_Ozero(_1006024)))], (39100 ^ _781215) ^ [_1531917, _1531919, _1531921] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1531917), hAPP(c_Set_OCollect(_1531917), hAPP(hAPP(c_COMBS(_1531917, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1531917), c_fdisj), _1531919)), _1531921))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531917), hAPP(c_Set_OCollect(_1531917), _1531919))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531917), hAPP(c_Set_OCollect(_1531917), _1531921)))], (25807 ^ _781215) ^ [_1246061, _1246063] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1246061, _1246063))))], (6588 ^ _781215) ^ [_888881, _888883, _888885] : [-(hBOOL(hAPP(hAPP(c_member(_888881), _888883), _888885))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888881, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_888881), _888883), _888885)), hAPP(hAPP(c_Set_Oinsert(_888881), _888883), c_Orderings_Obot__class_Obot(tc_fun(_888881, tc_HOL_Obool)))) = _888885)], (30533 ^ _781215) ^ [_1339761, _1339763] : [30535 ^ _781215 : [(30538 ^ _781215) ^ [] : [hBOOL(hAPP(_1339763, 30534 ^ [_1339761, _1339763]))], (30536 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30534 ^ [_1339761, _1339763]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1339761))))]], 30539 ^ _781215 : [(30540 ^ _781215) ^ [_1339916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1339916), _1339761)), -(hBOOL(hAPP(_1339763, _1339916)))]]], (42696 ^ _781215) ^ [_1629187, _1629189, _1629191, _1629193, _1629195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1629187), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629189)), _1629191))), -(hAPP(hAPP(c_List_Onth(_1629193), hAPP(hAPP(c_List_Omap(_1629189, _1629193), _1629195), _1629191)), _1629187) = hAPP(_1629195, hAPP(hAPP(c_List_Onth(_1629189), _1629191), _1629187)))], (49177 ^ _781215) ^ [_1773944, _1773946, _1773948, _1773950] : [-(c_Transitive__Closure_Otrancl(_1773944, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1773944, _1773944)), hAPP(hAPP(c_Product__Type_OPair(_1773944, _1773944), _1773946), _1773948)), _1773950)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1773944, _1773944), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1773944, _1773950)), hAPP(c_Set_OCollect(tc_prod(_1773944, _1773944)), hAPP(c_Product__Type_Oprod_Oprod__case(_1773944, _1773944, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1773944, tc_fun(_1773944, tc_HOL_Obool), tc_fun(_1773944, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1773944, tc_HOL_Obool), tc_fun(_1773944, tc_HOL_Obool)), _1773944), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1773944)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1773944), c_fconj), hAPP(hAPP(c_COMBC(_1773944, tc_fun(tc_prod(_1773944, _1773944), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1773944, _1773944), tc_fun(tc_fun(tc_prod(_1773944, _1773944), tc_HOL_Obool), tc_HOL_Obool), _1773944), c_member(tc_prod(_1773944, _1773944))), hAPP(hAPP(c_COMBC(_1773944, _1773944, tc_prod(_1773944, _1773944)), c_Product__Type_OPair(_1773944, _1773944)), _1773946))), c_Transitive__Closure_Ortrancl(_1773944, _1773950))))), hAPP(hAPP(c_COMBC(_1773944, tc_fun(tc_prod(_1773944, _1773944), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1773944, _1773944), tc_fun(tc_fun(tc_prod(_1773944, _1773944), tc_HOL_Obool), tc_HOL_Obool), _1773944), c_member(tc_prod(_1773944, _1773944))), hAPP(c_Product__Type_OPair(_1773944, _1773944), _1773948))), c_Transitive__Closure_Ortrancl(_1773944, _1773950)))))))], (51414 ^ _781215) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (18840 ^ _781215) ^ [_1119007, _1119009, _1119011, _1119013] : [class_Orderings_Olinorder(_1119007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119007), _1119009), _1119011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119007), _1119009), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1119007), _1119011), _1119013))))], (20442 ^ _781215) ^ [_1148071, _1148073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1148071), _1148073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148071)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148073))))], (25678 ^ _781215) ^ [_1243320, _1243322] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1243320, _1243322)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243322), hAPP(c_Nat_OSuc, _1243320)))], (51172 ^ _781215) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (34582 ^ _781215) ^ [_1429194, _1429196, _1429198] : [-(c_Fun_Oinj__on(_1429194, _1429196, _1429198, c_Orderings_Obot__class_Obot(tc_fun(_1429194, tc_HOL_Obool))))], (29340 ^ _781215) ^ [_1315847, _1315849, _1315851, _1315853, _1315855] : [class_Fields_Olinordered__field(_1315847), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315847), c_Groups_Ozero__class_Ozero(_1315847)), _1315849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315847), _1315849), _1315851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315847), c_Groups_Ozero__class_Ozero(_1315847)), _1315853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315847), _1315853), _1315855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315847), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315847), _1315849), _1315855)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315847), _1315851), _1315853))))], (16977 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23807 ^ _781215) ^ [_1210323, _1210325] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1210323), _1210325)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210323)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210325)))], (26067 ^ _781215) ^ [_1254106, _1254108] : [class_Int_Oring__char__0(_1254106), 26070 ^ _781215 : [(26077 ^ _781215) ^ [] : [_1254108 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1254106), _1254108) = c_Groups_Ozero__class_Ozero(_1254106))], (26071 ^ _781215) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1254106), _1254108) = c_Groups_Ozero__class_Ozero(_1254106), -(_1254108 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (22010 ^ _781215) ^ [_1177469, _1177471, _1177473, _1177475, _1177477] : [-(_1177469 = c_Orderings_Obot__class_Obot(tc_fun(_1177471, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1177473), _1177475), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1177471, tc_fun(_1177473, tc_HOL_Obool)), _1177469), _1177477)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1177471, tc_fun(_1177473, tc_HOL_Obool)), _1177469), hAPP(hAPP(c_COMBB(tc_fun(_1177473, tc_HOL_Obool), tc_fun(_1177473, tc_HOL_Obool), _1177471), hAPP(c_Set_Oinsert(_1177473), _1177475)), _1177477)))], (1758 ^ _781215) ^ [_806160, _806162] : [-(class_Rings_Osemiring__1(_806160)), _806162 = _806160, class_Rings_Osemiring__1(_806162)], (23518 ^ _781215) ^ [_1204982, _1204984] : [-(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), _1204982)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1204984))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1204982))) = 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), _1204984)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1204982)))], (4994 ^ _781215) ^ [_857110, _857112, _857114, _857116, _857118, _857120, _857122, _857124] : [-(c_New__Random__Sequence_Opos__map(_857124, _857120, _857116, _857112) = c_New__Random__Sequence_Opos__map(_857122, _857118, _857114, _857110)), _857124 = _857122, _857120 = _857118, _857116 = _857114, _857112 = _857110], (18728 ^ _781215) ^ [_1116921, _1116923, _1116925] : [class_Orderings_Olinorder(_1116921), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1116921), _1116923), _1116925) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1116921), _1116925), _1116923))], (51138 ^ _781215) ^ [_1820300, _1820302] : [class_Groups_Ouminus(_1820300), -(class_Groups_Ouminus(tc_fun(_1820302, _1820300)))], (15630 ^ _781215) ^ [_1055804, _1055806] : [-(c_Map_Oran(_1055804, _1055806, hAPP(c_COMBK(tc_Option_Ooption(_1055806), _1055804), c_Option_Ooption_ONone(_1055806))) = c_Orderings_Obot__class_Obot(tc_fun(_1055806, tc_HOL_Obool)))], (4670 ^ _781215) ^ [_852020, _852022] : [_852022 = _852020, -(c_Nitpick_Odenom(_852022) = c_Nitpick_Odenom(_852020))], (39901 ^ _781215) ^ [_1560301, _1560303, _1560305, _1560307, _1560309, _1560311, _1560313] : [c_Predicate_Opred__comp(_1560301, _1560303, _1560305, _1560307, _1560309, _1560311, _1560313), 39905 ^ _781215 : [(39908 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1560309, 39904 ^ [_1560301, _1560303, _1560305, _1560307, _1560309, _1560311, _1560313]), _1560313)))], (39906 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(_1560307, _1560311), 39904 ^ [_1560301, _1560303, _1560305, _1560307, _1560309, _1560311, _1560313])))]]], (51652 ^ _781215) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (18395 ^ _781215) ^ [_1110461, _1110463, _1110465, _1110467] : [class_Groups_Oordered__ab__group__add(_1110461), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1110461), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1110461), _1110463), _1110465)), _1110467) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1110461), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1110461), _1110463), _1110467)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1110461), _1110465), _1110467)))], (49070 ^ _781215) ^ [_1771338, _1771340] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1771338, _1771338)), hAPP(hAPP(c_Product__Type_OPair(_1771338, _1771338), 49071 ^ [_1771338, _1771340]), 49071 ^ [_1771338, _1771340])), c_Transitive__Closure_Otrancl(_1771338, _1771340)))), -(c_Wellfounded_Oacyclic(_1771338, _1771340))], (38171 ^ _781215) ^ [_1507966, _1507968, _1507970] : [-(c_HOL_OThe(tc_prod(_1507966, _1507968), _1507970) = c_HOL_OThe(tc_prod(_1507966, _1507968), hAPP(c_Product__Type_Oprod_Oprod__case(_1507966, _1507968, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1507968, tc_prod(_1507966, _1507968)), tc_fun(_1507968, tc_HOL_Obool), _1507966), hAPP(c_COMBB(tc_prod(_1507966, _1507968), tc_HOL_Obool, _1507968), _1507970)), c_Product__Type_OPair(_1507966, _1507968)))))], (39166 ^ _781215) ^ [_1533332, _1533334, _1533336] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533332, tc_HOL_Obool)), _1533334), _1533336) = hAPP(c_Set_OCollect(_1533332), hAPP(hAPP(c_COMBS(_1533332, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533332), c_fconj), hAPP(hAPP(c_COMBC(_1533332, tc_fun(_1533332, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533332)), _1533334))), hAPP(hAPP(c_COMBC(_1533332, tc_fun(_1533332, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533332)), _1533336))))], (17535 ^ _781215) ^ [_1094963, _1094965] : [class_Int_Onumber__ring(_1094963), 17538 ^ _781215 : [(17545 ^ _781215) ^ [] : [c_Int_Oiszero(_1094963, hAPP(c_Int_Onumber__class_Onumber__of(_1094963), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094965), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1094963), _1094965) = c_Groups_Ozero__class_Ozero(_1094963))], (17539 ^ _781215) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1094963), _1094965) = c_Groups_Ozero__class_Ozero(_1094963), -(c_Int_Oiszero(_1094963, hAPP(c_Int_Onumber__class_Onumber__of(_1094963), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094965), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (10624 ^ _781215) ^ [_963023, _963025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963023), _963025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963023)), _963025)))], (33344 ^ _781215) ^ [_1401613, _1401615, _1401617] : [class_Orderings_Oorder(_1401613), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401613, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1401613), _1401615)), c_SetInterval_Oord__class_OatLeastAtMost(_1401613, _1401615, _1401617)) = c_Orderings_Obot__class_Obot(tc_fun(_1401613, tc_HOL_Obool)))], (49351 ^ _781215) ^ [_1779019, _1779021, _1779023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1779019, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1779019, _1779019, _1779021), _1779023)), _1779023)), -(hAPP(c_Relation_OImage(_1779019, _1779019, c_Transitive__Closure_Ortrancl(_1779019, _1779021)), _1779023) = _1779023)], (11900 ^ _781215) ^ [_988154] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _988154) = _988154)], (20391 ^ _781215) ^ [_1147143] : [20392 ^ _781215 : [(20393 ^ _781215) ^ [_1147200] : [hBOOL(hAPP(_1147143, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147200)))]], 20395 ^ _781215 : [(20398 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1147143, 20394 ^ [_1147143])))], (20396 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20394 ^ [_1147143])))]]], (17887 ^ _781215) ^ [_1100589, _1100591] : [17888 ^ _781215 : [(17891 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100591))], (17889 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100589))]], 17892 ^ _781215 : [(17899 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100589), _1100591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1100589)), hAPP(c_Int_Onat, _1100591))))], (17893 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1100589)), hAPP(c_Int_Onat, _1100591))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1100589), _1100591)))]]], (33014 ^ _781215) ^ [_1393731, _1393733, _1393735] : [class_Lattices_Osemilattice__inf(_1393731), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393731), _1393733), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393731), _1393733), _1393735)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1393731), _1393733), _1393735))], (10702 ^ _781215) ^ [_964503, _964505, _964507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964503), _964505)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964507), _964505)), _964503) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964507), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964505), _964503)))], (8748 ^ _781215) ^ [_929608, _929610, _929612, _929614] : [class_Orderings_Oorder(_929608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929608), _929610), _929612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929608), _929614), _929610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929608), _929614), _929612)))], (41551 ^ _781215) ^ [_1598578, _1598580, _1598582, _1598584, _1598586, _1598588, _1598590] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1598578, _1598580, _1598582), hAPP(c_Fun_Ocomp(_1598584, tc_fun(_1598580, _1598582), _1598578, _1598586), _1598588)), _1598590) = hAPP(hAPP(_1598586, hAPP(_1598588, hAPP(c_Product__Type_Ofst(_1598578, _1598580), _1598590))), hAPP(c_Product__Type_Osnd(_1598578, _1598580), _1598590)))], (38258 ^ _781215) ^ [_1510150, _1510152, _1510154, _1510156, _1510158] : [-(hAPP(c_Set_Ovimage(_1510150, _1510152, _1510154), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1510152, tc_HOL_Obool)), _1510156), _1510158)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1510150, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1510150, _1510152, _1510154), _1510156)), hAPP(c_Set_Ovimage(_1510150, _1510152, _1510154), _1510158)))], (1098 ^ _781215) ^ [_797910, _797912] : [-(class_Rings_Oring__1__no__zero__divisors(_797910)), _797912 = _797910, class_Rings_Oring__1__no__zero__divisors(_797912)], (24622 ^ _781215) ^ [_1225654, _1225656, _1225658, _1225660] : [class_Rings_Olinordered__semidom(_1225654), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225654), c_Groups_Oone__class_Oone(_1225654)), _1225656)), 24629 ^ _781215 : [(24636 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1225658), _1225660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225654), hAPP(hAPP(c_Power_Opower__class_Opower(_1225654), _1225656), _1225658)), hAPP(hAPP(c_Power_Opower__class_Opower(_1225654), _1225656), _1225660))))], (24630 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225654), hAPP(hAPP(c_Power_Opower__class_Opower(_1225654), _1225656), _1225658)), hAPP(hAPP(c_Power_Opower__class_Opower(_1225654), _1225656), _1225660))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1225658), _1225660)))]]], (51268 ^ _781215) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (43740 ^ _781215) ^ [_1654762, _1654764, _1654766, _1654768] : [hAPP(hAPP(c_List_Olist__update(_1654762, _1654764), _1654766), _1654768) = c_List_Olist_ONil(_1654762), -(_1654764 = c_List_Olist_ONil(_1654762))], (49050 ^ _781215) ^ [_1770983, _1770985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770983), _1770985)), -(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), _1770983), _1770985)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (43470 ^ _781215) ^ [_1648857, _1648859] : [-(c_Hilbert__Choice_OEps(_1648857, hAPP(c_fequal, _1648859)) = _1648859)], (49403 ^ _781215) ^ [_1780261] : [-(hAPP(c_Relation_ODomain(_1780261, _1780261), c_Relation_OId(_1780261)) = c_Orderings_Otop__class_Otop(tc_fun(_1780261, tc_HOL_Obool)))], (31447 ^ _781215) ^ [_1357732, _1357734, _1357736, _1357738] : [-(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), _1357732), _1357734)), 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), _1357736), _1357738)), 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), _1357732), _1357736)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1357734), _1357738))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1357732), _1357738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1357734), _1357736)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (9515 ^ _781215) ^ [_943111, _943113, _943115] : [class_Orderings_Olinorder(_943111), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943111), _943113), _943115))), 9522 ^ _781215 : [(9529 ^ _781215) ^ [] : [_943113 = _943115, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943111), _943113), _943115)))], (9523 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943111), _943113), _943115)), -(_943113 = _943115)]]], (43984 ^ _781215) ^ [_1660203, _1660205, _1660207, _1660209, _1660211, _1660213] : [-(hAPP(c_List_Olist_Olist__case(_1660203, _1660205, _1660207, _1660209), hAPP(hAPP(c_List_Olist_OCons(_1660205), _1660211), _1660213)) = hAPP(hAPP(_1660209, _1660211), _1660213))], (38518 ^ _781215) ^ [_1516954, _1516956, _1516958] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1516954, _1516956), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1516954, _1516956), c_Orderings_Otop__class_Otop(tc_fun(_1516954, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1516956, tc_HOL_Obool), _1516954), _1516958))) = hAPP(hAPP(c_Product__Type_OSigma(_1516954, _1516956), c_Orderings_Otop__class_Otop(tc_fun(_1516954, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1516956, tc_HOL_Obool), _1516954), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1516956, tc_HOL_Obool)), _1516958))))], (14371 ^ _781215) ^ [_1032609] : [class_Rings_Oring__1(_1032609), -(hBOOL(hAPP(hAPP(c_member(_1032609), c_Groups_Oone__class_Oone(_1032609)), c_Int_Oring__1__class_OInts(_1032609))))], (47214 ^ _781215) ^ [_1731244, _1731246] : [class_Enum_Oenum(_1731244), 47217 ^ _781215 : [(47226 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1731244)), _1731246))), hBOOL(hAPP(_1731246, c_Option_Ooption_ONone(_1731244))), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1731244), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1731244), tc_HOL_Obool, _1731244), _1731246), c_Option_Ooption_OSome(_1731244))))], (47218 ^ _781215) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1731244)), _1731246)), 47221 ^ _781215 : [(47224 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1731244), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1731244), tc_HOL_Obool, _1731244), _1731246), c_Option_Ooption_OSome(_1731244)))))], (47222 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1731246, c_Option_Ooption_ONone(_1731244))))]]]]], (21398 ^ _781215) ^ [_1165253, _1165255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1165253), _1165255)), -(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)), _1165253)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1165255))))], (4202 ^ _781215) ^ [_844986, _844988, _844990, _844992] : [-(c_List_Omap(_844992, _844988) = c_List_Omap(_844990, _844986)), _844992 = _844990, _844988 = _844986], (18403 ^ _781215) ^ [_1110649] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1110649) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5639 ^ _781215) ^ [_870099] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _870099))), -(hAPP(c_Com_Obody, _870099) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 5642 ^ [_870099]))], (11569 ^ _781215) ^ [_983124, _983126, _983128, _983130, _983132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983124, tc_HOL_Obool)), _983126), hAPP(c_Set_Oimage(_983128, _983124, _983130), _983132))), 11573 ^ _781215 : [(11576 ^ _781215) ^ [] : [-(_983126 = hAPP(c_Set_Oimage(_983128, _983124, _983130), 11572 ^ [_983124, _983126, _983128, _983130, _983132]))], (11574 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983128, tc_HOL_Obool)), 11572 ^ [_983124, _983126, _983128, _983130, _983132]), _983132)))]]], (36932 ^ _781215) ^ [_1477467, _1477469, _1477471, _1477473] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477467, tc_fun(_1477469, tc_HOL_Obool)), _1477471), _1477473) = c_Orderings_Otop__class_Otop(tc_fun(_1477469, tc_HOL_Obool)), 36935 ^ _781215 : [(36936 ^ _781215) ^ [_1477583] : [hBOOL(hAPP(hAPP(c_member(_1477467), _1477583), _1477471)), -(hAPP(_1477473, _1477583) = c_Orderings_Otop__class_Otop(tc_fun(_1477469, tc_HOL_Obool)))]]], (44890 ^ _781215) ^ [_1681498, _1681500, _1681502] : [-(hAPP(c_List_Orotate(_1681498, hAPP(c_Nat_OSuc, _1681500)), _1681502) = hAPP(c_List_Orotate1(_1681498), hAPP(c_List_Orotate(_1681498, _1681500), _1681502)))], (30796 ^ _781215) ^ [_1345022, _1345024, _1345026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1345022)), 30799 ^ _781215 : [(30800 ^ _781215) ^ [_1345156] : [30802 ^ _781215 : [(30808 ^ _781215) ^ [] : [-(_1345156 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30804 ^ [_1345022, _1345024, _1345026, _1345156]), 30801 ^ [_1345022, _1345024, _1345026, _1345156]))], (30806 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30804 ^ [_1345022, _1345024, _1345026, _1345156]), _1345024)))], (30803 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30801 ^ [_1345022, _1345024, _1345026, _1345156]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1345022))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1345026), _1345156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1345026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1345156), _1345022))))]]], (11158 ^ _781215) ^ [_974633, _974635, _974637] : [class_Rings_Ocomm__semiring__1(_974633), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974633), _974635), _974637) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974633), _974637), _974635))], (50886 ^ _781215) ^ [_1815198] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1815198)))], (37223 ^ _781215) ^ [_1486306, _1486308, _1486310, _1486312, _1486314] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486306, tc_HOL_Obool)), _1486308), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486310, tc_fun(_1486306, tc_HOL_Obool)), _1486312), _1486314)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486310, tc_fun(_1486306, tc_HOL_Obool)), _1486312), hAPP(hAPP(c_COMBB(tc_fun(_1486306, tc_HOL_Obool), tc_fun(_1486306, tc_HOL_Obool), _1486310), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486306, tc_HOL_Obool)), _1486308)), _1486314)))], (34696 ^ _781215) ^ [_1431379, _1431381, _1431383, _1431385, _1431387] : [c_Fun_Oinj__on(_1431379, _1431381, _1431383, _1431385), -(c_Fun_Oinj__on(_1431379, _1431381, _1431383, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1431379, tc_HOL_Obool)), _1431385), _1431387)))], (23306 ^ _781215) ^ [_1201116, _1201118, _1201120, _1201122] : [_1201116 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201118), _1201120)), _1201122), -(_1201118 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1201116), _1201118) = _1201120), 23313 ^ _781215 : [(23316 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201122), _1201118))], (23314 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201118)))]], 23321 ^ _781215 : [(23324 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201118), _1201122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1201122), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23322 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201118))]]], (6776 ^ _781215) ^ [_892474, _892476, _892478, _892480] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_892474), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892474, tc_HOL_Obool)), _892476), hAPP(hAPP(c_Set_Oinsert(_892474), _892478), _892480)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_892474), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892474, tc_HOL_Obool)), _892476), _892480))))], (45762 ^ _781215) ^ [_1699023, _1699025] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1699023, _1699025)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1699025), _1699023))], (32604 ^ _781215) ^ [_1385081, _1385083, _1385085] : [class_Lattices_Olattice(_1385081), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385081), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1385081), _1385083), _1385085)), _1385083)))], (6407 ^ _781215) ^ [_885450, _885452, _885454] : [hBOOL(hAPP(hAPP(c_member(_885450), _885452), _885454)), -(hBOOL(hAPP(_885454, _885452)))], (34756 ^ _781215) ^ [_1432516, _1432518, _1432520, _1432522, _1432524, _1432526, _1432528] : [c_Finite__Set_Ofolding__image__simple(_1432516, _1432518, _1432520, _1432522, _1432524, _1432526), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432518), _1432528)), -(hAPP(_1432526, _1432528) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1432516, _1432518, _1432520), _1432524), _1432522), _1432528))], (31958 ^ _781215) ^ [_1370253, _1370255, _1370257, _1370259] : [class_Groups_Ocomm__monoid__add(_1370253), 31961 ^ _781215 : [(31968 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1370255)), _1370257))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370253), _1370259), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1370257, hAPP(c_Nat_OSuc, _1370255))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1370253), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370253), _1370259), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1370257, _1370255))), hAPP(_1370259, hAPP(c_Nat_OSuc, _1370255))))], (31962 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1370255)), _1370257)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370253), _1370259), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1370257, hAPP(c_Nat_OSuc, _1370255))) = c_Groups_Ozero__class_Ozero(_1370253))]]], (5754 ^ _781215) ^ [_872242, _872244, _872246, _872248] : [5755 ^ _781215 : [(5758 ^ _781215) ^ [] : [hBOOL(hAPP(_872246, _872248))], (5756 ^ _781215) ^ [] : [_872244 = _872248]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_872242), _872244), _872246), _872248)))], (1618 ^ _781215) ^ [_804410, _804412] : [-(class_Groups_Oab__semigroup__add(_804410)), _804412 = _804410, class_Groups_Oab__semigroup__add(_804412)], (8442 ^ _781215) ^ [_924288, _924290, _924292, _924294, _924296] : [class_Groups_Oab__semigroup__mult(_924288), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_924288, _924288, c_Groups_Otimes__class_Otimes(_924288), _924290, _924292), _924294)), hBOOL(hAPP(hAPP(c_member(_924288), _924296), _924292)), -(hBOOL(hAPP(hAPP(c_member(_924288), _924290), _924292))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_924288, _924288, c_Groups_Otimes__class_Otimes(_924288), _924296, hAPP(hAPP(c_Set_Oinsert(_924288), _924290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924288, tc_HOL_Obool)), _924292), hAPP(hAPP(c_Set_Oinsert(_924288), _924296), c_Orderings_Obot__class_Obot(tc_fun(_924288, tc_HOL_Obool)))))), _924294)))], (46231 ^ _781215) ^ [_1709038, _1709040, _1709042] : [-(c_List_Oconcat(_1709038, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1709038)), _1709040), _1709042)) = hAPP(hAPP(c_List_Oappend(_1709038), _1709040), c_List_Oconcat(_1709038, _1709042)))], (26155 ^ _781215) ^ [_1255570] : [class_Rings_Oring__1(_1255570), -(hAPP(c_Int_Oring__1__class_Oof__int(_1255570), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1255570))], (38699 ^ _781215) ^ [_1522259, _1522261, _1522263, _1522265] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522261, _1522259), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1522259, tc_prod(_1522261, _1522259), 38695 ^ [_1522259, _1522261, _1522263, _1522265]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1522261, tc_fun(_1522259, tc_HOL_Obool)), _1522263), _1522265))), hAPP(hAPP(c_Product__Type_OSigma(_1522261, _1522259), _1522263), _1522265))))], (18697 ^ _781215) ^ [_1116280, _1116282] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1116280)), hAPP(c_Nat_OSuc, _1116282)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1116280))), 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, _1116282))), 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)), _1116282)))))], (46596 ^ _781215) ^ [_1718237, _1718239] : [-(hAPP(c_List_Oset(_1718237), c_List_Oremdups(_1718237, _1718239)) = hAPP(c_List_Oset(_1718237), _1718239))], (25592 ^ _781215) ^ [_1241804, _1241806, _1241808] : [class_Orderings_Oorder(_1241804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241804), _1241806), _1241808)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1241804, _1241808, _1241806) = c_Orderings_Obot__class_Obot(tc_fun(_1241804, tc_HOL_Obool)))], (8327 ^ _781215) ^ [_921661, _921663] : [class_Groups_Oone(_921661), 8330 ^ _781215 : [(8337 ^ _781215) ^ [] : [_921663 = c_Groups_Oone__class_Oone(_921661), -(c_Groups_Oone__class_Oone(_921661) = _921663)], (8331 ^ _781215) ^ [] : [c_Groups_Oone__class_Oone(_921661) = _921663, -(_921663 = c_Groups_Oone__class_Oone(_921661))]]], (41929 ^ _781215) ^ [_1607706, _1607708, _1607710, _1607712, _1607714, _1607716] : [-(hAPP(hAPP(c_List_Ozip(_1607706, _1607708), hAPP(hAPP(c_List_Omap(_1607710, _1607706), _1607712), _1607714)), _1607716) = hAPP(hAPP(c_List_Omap(tc_prod(_1607710, _1607708), tc_prod(_1607706, _1607708)), hAPP(c_Product__Type_Oprod_Oprod__case(_1607710, _1607708, tc_prod(_1607706, _1607708)), hAPP(hAPP(c_COMBB(_1607706, tc_fun(_1607708, tc_prod(_1607706, _1607708)), _1607710), c_Product__Type_OPair(_1607706, _1607708)), _1607712))), hAPP(hAPP(c_List_Ozip(_1607710, _1607708), _1607714), _1607716)))], (51274 ^ _781215) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (20378 ^ _781215) ^ [_1146933] : [-(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), _1146933))))], (31236 ^ _781215) ^ [_1353188, _1353190, _1353192] : [class_Orderings_Olinorder(_1353188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1353188), _1353190), _1353192)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353188, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1353188), _1353190)), c_SetInterval_Oord__class_OatLeastAtMost(_1353188, _1353190, _1353192)) = hAPP(c_SetInterval_Oord__class_OatMost(_1353188), _1353192))], (42843 ^ _781215) ^ [_1632783, _1632785, _1632787, _1632789] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632783), tc_List_Olist(_1632783))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632783), tc_List_Olist(_1632783)), _1632785), _1632787)), c_List_Olistrel(_1632783, _1632789)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632783)), _1632785) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632783)), _1632787), 42849 ^ _781215 : [(42852 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632783, _1632783)), hAPP(hAPP(c_Product__Type_OPair(_1632783, _1632783), hAPP(hAPP(c_List_Onth(_1632783), _1632785), 42848 ^ [_1632783, _1632785, _1632787, _1632789])), hAPP(hAPP(c_List_Onth(_1632783), _1632787), 42848 ^ [_1632783, _1632785, _1632787, _1632789]))), _1632789))], (42850 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42848 ^ [_1632783, _1632785, _1632787, _1632789]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632783)), _1632785))))]]], (746 ^ _781215) ^ [_792748, _792750, _792752, _792754] : [-(c_List_Olinorder__class_Osorted(_792752, _792748)), c_List_Olinorder__class_Osorted(_792754, _792750), _792754 = _792752, _792750 = _792748], (3614 ^ _781215) ^ [_835948, _835950, _835952, _835954] : [-(c_Enum_Osublists(_835954, _835950) = c_Enum_Osublists(_835952, _835948)), _835954 = _835952, _835950 = _835948], (46894 ^ _781215) ^ [_1724631, _1724633] : [-(c_Enum_Oenum__the(_1724631, _1724633) = c_HOL_OThe(_1724631, _1724633))], (40159 ^ _781215) ^ [_1565445, _1565447] : [40161 ^ _781215 : [(40162 ^ _781215) ^ [_1565470] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565445, _1565445)), hAPP(hAPP(c_Product__Type_OPair(_1565445, _1565445), hAPP(40160 ^ [_1565445, _1565447], hAPP(c_Nat_OSuc, _1565470))), hAPP(40160 ^ [_1565445, _1565447], _1565470))), _1565447)))]], -(c_Wellfounded_Owf(_1565445, _1565447))], (51232 ^ _781215) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (7418 ^ _781215) ^ [_906061, _906063, _906065] : [class_Orderings_Opreorder(_906061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906061), _906063), _906065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906061), _906065), _906063))], (13498 ^ _781215) ^ [_1015874, _1015876, _1015878] : [class_Groups_Oordered__comm__monoid__add(_1015874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015874), c_Groups_Ozero__class_Ozero(_1015874)), _1015876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015874), c_Groups_Ozero__class_Ozero(_1015874)), _1015878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015874), c_Groups_Ozero__class_Ozero(_1015874)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015874), _1015876), _1015878))))], (13568 ^ _781215) ^ [_1017191, _1017193, _1017195, _1017197] : [class_Rings_Olinordered__semiring(_1017191), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017191), _1017193), _1017195)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017191), _1017193), _1017197))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017191), c_Groups_Ozero__class_Ozero(_1017191)), _1017193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017191), _1017195), _1017197)))], (25564 ^ _781215) ^ [_1241249, _1241251] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1241249), _1241251) = c_Smallcheck_Osmall_H(_1241249, hAPP(c_Code__Numeral_Oint__of, _1241251), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1241251))))], (22154 ^ _781215) ^ [_1180534, _1180536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180534)), -(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)))), _1180536)), 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)))), _1180534)) = 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, _1180536, _1180534))))], (11146 ^ _781215) ^ [_974347, _974349, _974351, _974353] : [class_Rings_Ocomm__semiring__1(_974347), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974347), _974349), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974347), _974351), _974353)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974347), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974347), _974349), _974351)), _974353))], (46367 ^ _781215) ^ [_1712843, _1712845, _1712847, _1712849] : [-(c_List_Oconcat(_1712843, hAPP(hAPP(c_List_Omap(_1712845, tc_List_Olist(_1712843)), hAPP(hAPP(c_COMBC(_1712845, tc_List_Olist(_1712843), tc_List_Olist(_1712843)), hAPP(hAPP(c_COMBB(_1712843, tc_fun(tc_List_Olist(_1712843), tc_List_Olist(_1712843)), _1712845), c_List_Olist_OCons(_1712843)), _1712847)), c_List_Olist_ONil(_1712843))), _1712849)) = hAPP(hAPP(c_List_Omap(_1712845, _1712843), _1712847), _1712849))], (15100 ^ _781215) ^ [_1046329, _1046331] : [class_Int_Onumber__ring(_1046329), -(hAPP(c_Int_Onumber__class_Onumber__of(_1046329), c_Int_Opred(_1046331)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046329), hAPP(c_Groups_Ouminus__class_Ouminus(_1046329), c_Groups_Oone__class_Oone(_1046329))), hAPP(c_Int_Onumber__class_Onumber__of(_1046329), _1046331)))], (30014 ^ _781215) ^ [_1329269, _1329271] : [-(c_FunDef_Orp__inv__image(_1329269, _1329271) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool), tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool), tc_fun(tc_fun(_1329271, _1329269), tc_prod(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool), tc_fun(tc_fun(_1329271, _1329269), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool), tc_fun(tc_fun(_1329271, _1329269), tc_prod(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1329271, _1329269), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)), tc_fun(tc_fun(_1329271, _1329269), tc_prod(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool), tc_fun(tc_fun(_1329271, _1329269), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool), tc_fun(tc_fun(_1329271, _1329269), tc_prod(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool))))), tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1329271, _1329269), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)), tc_fun(tc_fun(_1329271, _1329269), tc_prod(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool))), tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1329271, _1329269), tc_fun(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1329271, _1329269), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)), tc_fun(tc_fun(_1329271, _1329269), tc_prod(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)))), tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool)), c_COMBS(tc_fun(_1329271, _1329269), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1329271, _1329269), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)), tc_fun(tc_fun(_1329271, _1329269), tc_fun(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)))), tc_fun(tc_prod(_1329269, _1329269), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool))), tc_fun(_1329271, _1329269)), c_Product__Type_OPair(tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool), tc_fun(tc_prod(_1329271, _1329271), tc_HOL_Obool)))), c_Relation_Oinv__image(_1329269, _1329271))))), c_Relation_Oinv__image(_1329269, _1329271))))], (32118 ^ _781215) ^ [_1374101, _1374103, _1374105, _1374107, _1374109] : [class_Groups_Oordered__ab__semigroup__add(_1374101), class_Rings_Osemiring__1(_1374101), 32128 ^ _781215 : [(32131 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374101), hAPP(_1374107, 32127 ^ [_1374101, _1374103, _1374105, _1374107, _1374109])), _1374109))], (32129 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1374103), 32127 ^ [_1374101, _1374103, _1374105, _1374107, _1374109]), _1374105)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374101), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1374103, _1374101), _1374107), _1374105)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374101), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1374101), hAPP(c_Finite__Set_Ocard(_1374103), _1374105))), _1374109))))], (21788 ^ _781215) ^ [_1172073, _1172075] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1172073)), c_Int_OBit1(_1172075)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1172073)), _1172075)))], (8123 ^ _781215) ^ [_918103, _918105, _918107] : [class_Groups_Ogroup__add(_918103), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918103), _918105), _918107)), _918107) = _918105)], (16085 ^ _781215) ^ [_1065500, _1065502, _1065504] : [class_Lattices_Osemilattice__sup(_1065500), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065500), _1065502), _1065504) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065500), _1065504), _1065502))], (20497 ^ _781215) ^ [_1149132, _1149134] : [20498 ^ _781215 : [(20499 ^ _781215) ^ [_1149185] : [_1149134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149132), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149185))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1149132), _1149134)))], (25498 ^ _781215) ^ [_1240268, _1240270] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240268), _1240270) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 25499 ^ _781215 : [(25506 ^ _781215) ^ [] : [_1240268 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1240270 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (25500 ^ _781215) ^ [] : [_1240268 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1240270 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (45446 ^ _781215) ^ [_1693728, _1693730, _1693732] : [-(c_List_Osublist(_1693728, _1693730, _1693732) = hAPP(hAPP(c_List_Omap(tc_prod(_1693728, tc_Nat_Onat), _1693728), c_Product__Type_Ofst(_1693728, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1693728, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1693728, 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(_1693728, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1693728, tc_Nat_Onat))), _1693732)), hAPP(hAPP(c_List_Ozip(_1693728, tc_Nat_Onat), _1693730), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693728)), _1693730))))))], (23692 ^ _781215) ^ [_1208377] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1208377), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1208377)], (31800 ^ _781215) ^ [_1366673, _1366675, _1366677, _1366679, _1366681] : [class_Groups_Ocomm__monoid__add(_1366673), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366675), _1366677)), 31807 ^ _781215 : [(31814 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366675), _1366679), _1366677))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1366675, _1366673), hAPP(hAPP(c_COMBC(_1366675, _1366673, _1366673), hAPP(hAPP(c_COMBS(_1366675, _1366673, tc_fun(_1366673, _1366673)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1366673, tc_fun(_1366673, _1366673)), _1366675), c_If(_1366673)), hAPP(c_fequal, _1366679))), _1366681)), c_Groups_Ozero__class_Ozero(_1366673))), _1366677) = c_Groups_Ozero__class_Ozero(_1366673))], (31808 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1366675), _1366679), _1366677)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1366675, _1366673), hAPP(hAPP(c_COMBC(_1366675, _1366673, _1366673), hAPP(hAPP(c_COMBS(_1366675, _1366673, tc_fun(_1366673, _1366673)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1366673, tc_fun(_1366673, _1366673)), _1366675), c_If(_1366673)), hAPP(c_fequal, _1366679))), _1366681)), c_Groups_Ozero__class_Ozero(_1366673))), _1366677) = hAPP(_1366681, _1366679))]]], (48932 ^ _781215) ^ [_1768947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1768947)), _1768947 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51594 ^ _781215) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (21906 ^ _781215) ^ [_1175082, _1175084, _1175086, _1175088, _1175090] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175082, tc_fun(_1175084, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1175082, tc_HOL_Obool)), _1175086), _1175088)), _1175090) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1175084, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175082, tc_fun(_1175084, tc_HOL_Obool)), _1175086), _1175090)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1175082, tc_fun(_1175084, tc_HOL_Obool)), _1175088), _1175090)))], (41992 ^ _781215) ^ [_1609495, _1609497, _1609499, _1609501, _1609503] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609495), tc_List_Olist(_1609495))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609495), tc_List_Olist(_1609495)), _1609497), _1609499)), hAPP(c_List_Olexn(_1609495, _1609501), _1609503))), 41995 ^ _781215 : [(41998 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609495)), _1609499) = _1609503)], (41996 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609495)), _1609497) = _1609503)]]], (14926 ^ _781215) ^ [_1042976] : [class_Groups_Osgn__if(_1042976), -(c_Groups_Osgn__class_Osgn(_1042976, c_Groups_Ozero__class_Ozero(_1042976)) = c_Groups_Ozero__class_Ozero(_1042976))], (19038 ^ _781215) ^ [_1122534] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1122534) = c_Orderings_Oord__class_Omax(_1122534)), class_Lattices_Osemilattice__sup(_1122534), class_Orderings_Olinorder(_1122534)], (30437 ^ _781215) ^ [_1337976, _1337978, _1337980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337976)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1337978), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1337980)), 30444 ^ _781215 : [(30445 ^ _781215) ^ [_1338184] : [30447 ^ _781215 : [(30453 ^ _781215) ^ [] : [-(_1338184 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30449 ^ [_1337976, _1337978, _1337980, _1338184]), 30446 ^ [_1337976, _1337978, _1337980, _1338184]))], (30451 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30449 ^ [_1337976, _1337978, _1337980, _1338184]), _1337980)))], (30448 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30446 ^ [_1337976, _1337978, _1337980, _1338184]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1337976))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1338184), _1337978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1338184), _1337976)), _1337978)))]]], (34830 ^ _781215) ^ [_1433941, _1433943, _1433945, _1433947, _1433949, _1433951] : [c_Fun_Oinj__on(_1433941, _1433943, _1433945, _1433947), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1433941, tc_HOL_Obool)), _1433949), _1433947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1433941, tc_HOL_Obool)), _1433951), _1433947)), -(hAPP(c_Set_Oimage(_1433941, _1433943, _1433945), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1433941, tc_HOL_Obool)), _1433949), _1433951)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1433943, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1433941, _1433943, _1433945), _1433949)), hAPP(c_Set_Oimage(_1433941, _1433943, _1433945), _1433951)))], (41369 ^ _781215) ^ [_1594087, _1594089, _1594091, _1594093, _1594095] : [hAPP(c_Set_Oimage(_1594087, _1594089, _1594091), c_Orderings_Otop__class_Otop(tc_fun(_1594087, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1594089, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1594089, _1594093, _1594095), c_Orderings_Otop__class_Otop(tc_fun(_1594089, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1594093, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1594087, _1594093, hAPP(c_Fun_Ocomp(_1594089, _1594093, _1594087, _1594095), _1594091)), c_Orderings_Otop__class_Otop(tc_fun(_1594087, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1594093, tc_HOL_Obool)))], (14204 ^ _781215) ^ [_1029400, _1029402, _1029404, _1029406, _1029408, _1029410, _1029412] : [-(c_Nitpick_Ofold__graph_H(_1029400, _1029402, _1029404, _1029406, _1029408, hAPP(hAPP(_1029404, _1029410), _1029412))), 14205 ^ _781215 : [(14212 ^ _781215) ^ [_1029629, _1029631] : [hAPP(hAPP(_1029404, _1029410), _1029412) = hAPP(hAPP(_1029404, _1029631), _1029629), hBOOL(hAPP(hAPP(c_member(_1029400), _1029631), _1029408)), c_Nitpick_Ofold__graph_H(_1029400, _1029402, _1029404, _1029406, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1029400, tc_HOL_Obool)), _1029408), hAPP(hAPP(c_Set_Oinsert(_1029400), _1029631), c_Orderings_Obot__class_Obot(tc_fun(_1029400, tc_HOL_Obool)))), _1029629)], (14206 ^ _781215) ^ [] : [_1029408 = c_Orderings_Obot__class_Obot(tc_fun(_1029400, tc_HOL_Obool)), hAPP(hAPP(_1029404, _1029410), _1029412) = _1029406]]], (37129 ^ _781215) ^ [_1483897, _1483899, _1483901, _1483903, _1483905] : [hBOOL(hAPP(hAPP(c_member(_1483897), _1483899), _1483901)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483903, tc_HOL_Obool)), hAPP(_1483905, _1483899)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483897, tc_fun(_1483903, tc_HOL_Obool)), _1483901), _1483905)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483897, tc_fun(_1483903, tc_HOL_Obool)), _1483901), _1483905))], (15530 ^ _781215) ^ [_1053580, _1053582, _1053584, _1053586] : [class_Groups_Ouminus(_1053580), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1053582, _1053580)), _1053584), _1053586) = hAPP(c_Groups_Ouminus__class_Ouminus(_1053580), hAPP(_1053584, _1053586)))], (14451 ^ _781215) ^ [_1033870, _1033872] : [class_Rings_Olinordered__idom(_1033870), 14454 ^ _781215 : [(14461 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033870), _1033872), c_Groups_Ozero__class_Ozero(_1033870))), -(c_Groups_Osgn__class_Osgn(_1033870, _1033872) = hAPP(c_Groups_Ouminus__class_Ouminus(_1033870), c_Groups_Oone__class_Oone(_1033870)))], (14455 ^ _781215) ^ [] : [c_Groups_Osgn__class_Osgn(_1033870, _1033872) = hAPP(c_Groups_Ouminus__class_Ouminus(_1033870), c_Groups_Oone__class_Oone(_1033870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033870), _1033872), c_Groups_Ozero__class_Ozero(_1033870))))]]], (20466 ^ _781215) ^ [_1148510, _1148512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1148510), _1148512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148510)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148512))))], (44584 ^ _781215) ^ [_1674873, _1674875] : [hBOOL(hAPP(c_List_Odistinct(_1674873), hAPP(c_List_Orotate1(_1674873), _1674875))), -(hBOOL(hAPP(c_List_Odistinct(_1674873), _1674875)))], (25875 ^ _781215) ^ [_1250433, _1250435, _1250437, _1250439] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1250433), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250435, tc_Int_Oint), _1250437), _1250439)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1250435, _1250433), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1250433, _1250435), c_Int_Oring__1__class_Oof__int(_1250433)), _1250437)), _1250439)), class_Groups_Ocomm__monoid__mult(_1250433), class_Rings_Oring__1(_1250433)], (15847 ^ _781215) ^ [_1060063, _1060065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1060063)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1060065)), -(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), _1060063), _1060065))))], (46948 ^ _781215) ^ [_1725731] : [class_Enum_Oenum(_1725731), -(hBOOL(hAPP(c_List_Odistinct(_1725731), c_Enum_Oenum__class_Oenum(_1725731))))], (2820 ^ _781215) ^ [_823343, _823345, _823347, _823349] : [-(c_Predicate_OPowp(_823349, _823345) = c_Predicate_OPowp(_823347, _823343)), _823349 = _823347, _823345 = _823343], (15032 ^ _781215) ^ [_1045204, _1045206] : [class_Int_Onumber__ring(_1045204), -(hBOOL(hAPP(hAPP(c_member(_1045204), hAPP(c_Int_Onumber__class_Onumber__of(_1045204), _1045206)), c_Int_Oring__1__class_OInts(_1045204))))], (49672 ^ _781215) ^ [_1787415, _1787417, _1787419] : [-(hAPP(c_Relation_Oconverse(_1787415, _1787417), hAPP(c_Relation_Oconverse(_1787417, _1787415), _1787419)) = _1787419)], (5490 ^ _781215) ^ [_865018, _865020, _865022, _865024, _865026, _865028] : [-(c_COMBB(_865028, _865024, _865020) = c_COMBB(_865026, _865022, _865018)), _865028 = _865026, _865024 = _865022, _865020 = _865018], (17851 ^ _781215) ^ [_1100015, _1100017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100015)), 17854 ^ _781215 : [(17861 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100015), _1100017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1100015)), hAPP(c_Int_Onat, _1100017))))], (17855 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1100015)), hAPP(c_Int_Onat, _1100017))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1100015), _1100017)))]]], (46626 ^ _781215) ^ [_1718733, _1718735] : [c_List_Olist_ONil(_1718733) = c_List_Oremdups(_1718733, _1718735), -(_1718735 = c_List_Olist_ONil(_1718733))], (22580 ^ _781215) ^ [_1188955, _1188957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188957)), -(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, _1188955, _1188957))))], (27396 ^ _781215) ^ [_1279675, _1279677, _1279679, _1279681, _1279683] : [hAPP(c_Product__Type_Ofst(_1279675, _1279677), hAPP(hAPP(c_Product__Type_OPair(_1279675, _1279677), _1279679), _1279681)) = _1279683, -(_1279679 = _1279683)], (21159 ^ _781215) ^ [_1159933, _1159935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1159933)), 21162 ^ _781215 : [(21169 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159933), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1159935))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1159933)), _1159935)))], (21163 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1159933)), _1159935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159933), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1159935))))]]], (31974 ^ _781215) ^ [_1370589, _1370591, _1370593, _1370595] : [class_Groups_Ocomm__monoid__add(_1370589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1370591), _1370593)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370589), _1370595), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1370591, _1370593)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1370589), hAPP(_1370595, _1370591)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370589), _1370595), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1370591, _1370593))))], (48952 ^ _781215) ^ [_1769317] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1769317)) = _1769317)], (42152 ^ _781215) ^ [_1613404, _1613406] : [-(c_List_Olenlex(_1613404, _1613406) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1613404)), tc_List_Olist(_1613404)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1613404), c_Wellfounded_Oless__than, c_List_Olex(_1613404, _1613406))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1613404), tc_List_Olist(_1613404), tc_prod(tc_Nat_Onat, tc_List_Olist(_1613404))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1613404), tc_prod(tc_Nat_Onat, tc_List_Olist(_1613404))), tc_List_Olist(_1613404)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1613404))), c_Nat_Osize__class_Osize(tc_List_Olist(_1613404)))), c_COMBI(tc_List_Olist(_1613404)))))], (27544 ^ _781215) ^ [_1282519, _1282521, _1282523, _1282525, _1282527] : [-(c_Product__Type_Oprod_Oprod__size(_1282519, _1282521, _1282523, _1282525, _1282527) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1282523, hAPP(c_Product__Type_Ofst(_1282519, _1282521), _1282527))), hAPP(_1282525, hAPP(c_Product__Type_Osnd(_1282519, _1282521), _1282527)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6060 ^ _781215) ^ [_878506, _878508, _878510, _878512, _878514, _878516] : [-(c_Map_Omap__comp(_878506, _878508, _878510, _878512, _878514, _878516) = c_Option_Ooption_ONone(_878508)), 6061 ^ _781215 : [(6064 ^ _781215) ^ [_878618] : [hAPP(_878514, _878516) = hAPP(c_Option_Ooption_OSome(_878506), _878618), hAPP(_878512, _878618) = c_Option_Ooption_ONone(_878508)], (6062 ^ _781215) ^ [] : [hAPP(_878514, _878516) = c_Option_Ooption_ONone(_878506)]]], (44676 ^ _781215) ^ [_1676950, _1676952, _1676954, _1676956, _1676958] : [hAPP(hAPP(c_List_Oappend(_1676950), _1676952), _1676954) = hAPP(hAPP(c_List_Oappend(_1676950), _1676956), _1676958), 44679 ^ _781215 : [(44688 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676950)), _1676952)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676950)), _1676956)))), 44691 ^ _781215 : [(44694 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1676950), hAPP(hAPP(c_List_Odrop(_1676950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676950)), _1676956)), _1676952)), _1676954) = _1676958)], (44692 ^ _781215) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1676950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676950)), _1676956)), _1676952) = _1676956)]]], (44680 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676950)), _1676952)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676950)), _1676956))), 44683 ^ _781215 : [(44686 ^ _781215) ^ [] : [-(_1676954 = hAPP(hAPP(c_List_Oappend(_1676950), hAPP(hAPP(c_List_Odrop(_1676950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676950)), _1676952)), _1676956)), _1676958))], (44684 ^ _781215) ^ [] : [-(_1676952 = hAPP(hAPP(c_List_Otake(_1676950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676950)), _1676952)), _1676956))]]]]], (24438 ^ _781215) ^ [_1221847, _1221849, _1221851] : [class_Rings_Olinordered__idom(_1221847), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221847), c_Groups_Ozero__class_Ozero(_1221847)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221847), hAPP(hAPP(c_Power_Opower__class_Opower(_1221847), _1221849), 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(_1221847), _1221851), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (51188 ^ _781215) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (21548 ^ _781215) ^ [_1167824, _1167826] : [c_Int_OBit1(_1167824) = c_Int_OBit0(_1167826)], (19320 ^ _781215) ^ [_1127846, _1127848, _1127850] : [class_Orderings_Olinorder(_1127846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1127846, tc_HOL_Obool)), _1127848), _1127850)), -(_1127848 = c_Orderings_Obot__class_Obot(tc_fun(_1127846, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127846), _1127850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127846), c_Big__Operators_Olinorder__class_OMin(_1127846, _1127850)), c_Big__Operators_Olinorder__class_OMin(_1127846, _1127848))))], (31493 ^ _781215) ^ [_1359167, _1359169, _1359171] : [-(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), _1359167)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1359169))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1359171))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1359171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1359167), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1359167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1359171), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1359169)))))], (18313 ^ _781215) ^ [_1109001, _1109003, _1109005] : [class_Orderings_Olinorder(_1109001), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109001), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1109001), _1109003), _1109005)), _1109005)))], (2992 ^ _781215) ^ [_826053, _826055] : [_826055 = _826053, -(c_Hoare__Mirabelle_Otriple_Otriple(_826055) = c_Hoare__Mirabelle_Otriple_Otriple(_826053))], (51606 ^ _781215) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (39024 ^ _781215) ^ [_1530395] : [-(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)), _1530395)))))], (15272 ^ _781215) ^ [_1049085, _1049087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049085), _1049087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1049085), _1049087)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51216 ^ _781215) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (31310 ^ _781215) ^ [_1354743] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1354743)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1354743))], (11872 ^ _781215) ^ [_987849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987849), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51080 ^ _781215) ^ [_1819539, _1819541] : [class_Lattices_Odistrib__lattice(_1819539), -(class_Lattices_Odistrib__lattice(tc_fun(_1819541, _1819539)))], (48164 ^ _781215) ^ [_1752595, _1752597] : [class_Orderings_Olinorder(_1752595), hBOOL(hAPP(c_Finite__Set_Ofinite(_1752595), _1752597)), 48172 ^ _781215 : [(48175 ^ _781215) ^ [] : [-(c_List_Olinorder__class_Osorted(_1752595, 48171 ^ [_1752595, _1752597]))], (48177 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1752595), 48171 ^ [_1752595, _1752597])))], (48179 ^ _781215) ^ [_1752921] : [-(_1752921 = 48171 ^ [_1752595, _1752597]), hAPP(c_List_Oset(_1752595), _1752921) = _1752597, c_List_Olinorder__class_Osorted(_1752595, _1752921), hBOOL(hAPP(c_List_Odistinct(_1752595), _1752921))], (48173 ^ _781215) ^ [] : [-(hAPP(c_List_Oset(_1752595), 48171 ^ [_1752595, _1752597]) = _1752597)]]], (17771 ^ _781215) ^ [_1098711, _1098713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1098711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1098713)), 17778 ^ _781215 : [(17785 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098711), _1098713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1098711)), hAPP(c_Int_Onat, _1098713))))], (17779 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1098711)), hAPP(c_Int_Onat, _1098713))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098711), _1098713)))]]], (800 ^ _781215) ^ [_793563, _793565, _793567, _793569, _793571, _793573, _793575, _793577, _793579, _793581] : [-(c_Typedef_Otype__definition(_793579, _793575, _793571, _793567, _793563)), c_Typedef_Otype__definition(_793581, _793577, _793573, _793569, _793565), _793581 = _793579, _793577 = _793575, _793573 = _793571, _793569 = _793567, _793565 = _793563], (42240 ^ _781215) ^ [_1615595, _1615597, _1615599] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1615595), _1615597)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1615595)), hAPP(c_Set_OCollect(tc_List_Olist(_1615595)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1615595), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1615595)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1615595), tc_fun(_1615595, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1615595, tc_HOL_Obool), tc_fun(tc_fun(_1615595, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1615595)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1615595, tc_HOL_Obool))), c_List_Oset(_1615595))), _1615597))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1615595), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1615595)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1615595)))), _1615599))))))], (8870 ^ _781215) ^ [_931573, _931575, _931577] : [class_Orderings_Oorder(_931573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931573), _931575), _931577)), 8877 ^ _781215 : [(8884 ^ _781215) ^ [] : [_931577 = _931575, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931573), _931577), _931575)))], (8878 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931573), _931577), _931575)), -(_931577 = _931575)]]], (15632 ^ _781215) ^ [_1055869, _1055871, _1055873, _1055875, _1055877] : [c_Com_Ocom_OLocal(_1055869, _1055871, _1055873) = c_Com_Ocom_OSemi(_1055875, _1055877)], (32274 ^ _781215) ^ [_1377635, _1377637, _1377639, _1377641] : [_1377635 = _1377637, hBOOL(hAPP(hAPP(c_member(_1377639), _1377635), _1377641)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1377639, _1377639)), hAPP(hAPP(c_Product__Type_OPair(_1377639, _1377639), _1377635), _1377637)), c_Relation_OId__on(_1377639, _1377641))))], (46878 ^ _781215) ^ [_1724134, _1724136] : [-(_1724134 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1724136, _1724134, c_List_Olist_ONil(_1724136)) = c_List_Olist_ONil(tc_List_Olist(_1724136)))], (10974 ^ _781215) ^ [_970223, _970225, _970227] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_970223), _970225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970223, tc_HOL_Obool)), _970225), _970227)), -(hAPP(c_Finite__Set_Ocard(_970223), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970223, tc_HOL_Obool)), _970227), _970225)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_970223), _970227)), hAPP(c_Finite__Set_Ocard(_970223), _970225)))], (25474 ^ _781215) ^ [_1239967, _1239969] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1239967), _1239969) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1239967 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1239967 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (43555 ^ _781215) ^ [_1650799, _1650801, _1650803] : [-(c_Hilbert__Choice_OEps(tc_prod(_1650799, _1650801), hAPP(c_Product__Type_Oprod_Oprod__case(_1650799, _1650801, tc_HOL_Obool), _1650803)) = c_Hilbert__Choice_OEps(tc_prod(_1650799, _1650801), hAPP(hAPP(c_COMBS(tc_prod(_1650799, _1650801), _1650801, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1650799, tc_fun(_1650801, tc_HOL_Obool), tc_prod(_1650799, _1650801)), _1650803), c_Product__Type_Ofst(_1650799, _1650801))), c_Product__Type_Osnd(_1650799, _1650801))))], (1228 ^ _781215) ^ [_799535, _799537] : [-(class_Int_Oring__char__0(_799535)), _799537 = _799535, class_Int_Oring__char__0(_799537)], (16191 ^ _781215) ^ [_1067412, _1067414, _1067416] : [class_Lattices_Osemilattice__sup(_1067412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067412), _1067414), _1067416)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067412), _1067414), _1067416) = _1067416)], (23861 ^ _781215) ^ [_1211294, _1211296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211294)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211294), _1211296)), _1211294) = _1211296)], (19026 ^ _781215) ^ [_1122274] : [class_Orderings_Olinorder(_1122274), -(c_Orderings_Oord_Omin(_1122274, hAPP(c_COMBC(_1122274, _1122274, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1122274))) = c_Orderings_Oord__class_Omax(_1122274))], (1608 ^ _781215) ^ [_804285, _804287] : [-(class_Groups_Ocomm__monoid__mult(_804285)), _804287 = _804285, class_Groups_Ocomm__monoid__mult(_804287)], (29282 ^ _781215) ^ [_1314746, _1314748, _1314750] : [class_Fields_Olinordered__field(_1314746), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314746), _1314748), c_Groups_Ozero__class_Ozero(_1314746))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314746), c_Groups_Ozero__class_Ozero(_1314746)), _1314750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314746), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1314746), _1314748), _1314750)), c_Groups_Ozero__class_Ozero(_1314746))))], (20860 ^ _781215) ^ [_1155160, _1155162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1155160), _1155162)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155162)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155160)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1155162), _1155160)))], (30293 ^ _781215) ^ [_1335266, _1335268] : [class_Orderings_Oorder(_1335266), -(c_SetInterval_Oord__class_OatLeastAtMost(_1335266, _1335268, _1335268) = hAPP(hAPP(c_Set_Oinsert(_1335266), _1335268), c_Orderings_Obot__class_Obot(tc_fun(_1335266, tc_HOL_Obool))))], (35903 ^ _781215) ^ [_1456287, _1456289] : [class_Groups_Oordered__ab__group__add__abs(_1456287), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456287), hAPP(c_Groups_Ouminus__class_Ouminus(_1456287), _1456289)), hAPP(c_Groups_Oabs__class_Oabs(_1456287), _1456289))))], (34844 ^ _781215) ^ [_1434276, _1434278, _1434280, _1434282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1434276), hAPP(c_Set_Oimage(_1434278, _1434276, _1434280), _1434282))), hAPP(c_Finite__Set_Ocard(_1434278), _1434282))), c_Fun_Oinj__on(_1434278, _1434276, _1434280, _1434282)], (8201 ^ _781215) ^ [_919571, _919573, _919575, _919577, _919579] : [class_Groups_Oordered__cancel__ab__semigroup__add(_919571), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919571), _919573), _919575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919571), _919577), _919579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919571), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919571), _919573), _919577)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919571), _919575), _919579))))], (22826 ^ _781215) ^ [_1193078, _1193080] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1193078), _1193080) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22827 ^ _781215 : [(22836 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193078), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193080), _1193078))], (22830 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193078), _1193080))], (22828 ^ _781215) ^ [] : [_1193080 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (31760 ^ _781215) ^ [_1365689, _1365691, _1365693, _1365695, _1365697] : [class_Groups_Oab__group__add(_1365689), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1365691), _1365693)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1365693), _1365695)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1365689), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1365689), _1365697), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1365691), _1365695))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1365689), _1365697), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1365691), _1365693))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1365689), _1365697), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1365693), _1365695)))], (42034 ^ _781215) ^ [_1610380, _1610382, _1610384, _1610386] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610380)), hAPP(hAPP(c_List_Omap(_1610382, _1610380), _1610384), _1610386)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610382)), _1610386))], (42501 ^ _781215) ^ [_1624091, _1624093, _1624095, _1624097, _1624099] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1624091), tc_List_Olist(_1624091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1624091), tc_List_Olist(_1624091)), _1624093), hAPP(hAPP(c_List_Olist_OCons(_1624091), _1624095), _1624097))), c_List_Olistrel(_1624091, _1624099))), 42506 ^ _781215 : [(42511 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1624091), tc_List_Olist(_1624091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1624091), tc_List_Olist(_1624091)), 42505 ^ [_1624091, _1624093, _1624095, _1624097, _1624099]), _1624097)), c_List_Olistrel(_1624091, _1624099))))], (42509 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624091, _1624091)), hAPP(hAPP(c_Product__Type_OPair(_1624091, _1624091), 42504 ^ [_1624091, _1624093, _1624095, _1624097, _1624099]), _1624095)), _1624099)))], (42507 ^ _781215) ^ [] : [-(_1624093 = hAPP(hAPP(c_List_Olist_OCons(_1624091), 42504 ^ [_1624091, _1624093, _1624095, _1624097, _1624099]), 42505 ^ [_1624091, _1624093, _1624095, _1624097, _1624099]))]]], (28600 ^ _781215) ^ [_1302397, _1302399, _1302401, _1302403] : [class_Fields_Olinordered__field__inverse__zero(_1302397), class_Int_Onumber(_1302397), 28607 ^ _781215 : [(28608 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302397), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302397), _1302399), _1302401)), hAPP(c_Int_Onumber__class_Onumber__of(_1302397), _1302403))), 28611 ^ _781215 : [(28618 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302397), c_Groups_Ozero__class_Ozero(_1302397)), _1302401))), 28621 ^ _781215 : [(28628 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302397), _1302401), c_Groups_Ozero__class_Ozero(_1302397)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302397), c_Groups_Ozero__class_Ozero(_1302397)), hAPP(c_Int_Onumber__class_Onumber__of(_1302397), _1302403))))], (28622 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302397), _1302401), c_Groups_Ozero__class_Ozero(_1302397))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302397), hAPP(c_Int_Onumber__class_Onumber__of(_1302397), _1302403)), _1302401)), _1302399)))]]], (28612 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302397), c_Groups_Ozero__class_Ozero(_1302397)), _1302401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302397), _1302399), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302397), hAPP(c_Int_Onumber__class_Onumber__of(_1302397), _1302403)), _1302401))))]]], (28634 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302397), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302397), _1302399), _1302401)), hAPP(c_Int_Onumber__class_Onumber__of(_1302397), _1302403)))), 28637 ^ _781215 : [(28640 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302397), _1302399), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302397), hAPP(c_Int_Onumber__class_Onumber__of(_1302397), _1302403)), _1302401)))], (28638 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302397), c_Groups_Ozero__class_Ozero(_1302397)), _1302401)))]], 28641 ^ _781215 : [(28644 ^ _781215) ^ [] : [28645 ^ _781215 : [(28648 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302397), hAPP(c_Int_Onumber__class_Onumber__of(_1302397), _1302403)), _1302401)), _1302399))], (28646 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302397), _1302401), c_Groups_Ozero__class_Ozero(_1302397))))]], 28649 ^ _781215 : [(28652 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302397), c_Groups_Ozero__class_Ozero(_1302397)), hAPP(c_Int_Onumber__class_Onumber__of(_1302397), _1302403)))], (28650 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302397), _1302401), c_Groups_Ozero__class_Ozero(_1302397)))]]], (28642 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302397), c_Groups_Ozero__class_Ozero(_1302397)), _1302401))]]]]], (39679 ^ _781215) ^ [_1552299] : [-(hAPP(c_Set_Oimage(_1552299, _1552299, c_Fun_Oid(_1552299)), c_Orderings_Otop__class_Otop(tc_fun(_1552299, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1552299, tc_HOL_Obool)))], (47787 ^ _781215) ^ [_1743266, _1743268, _1743270, _1743272, _1743274] : [c_List_Olist__all2(_1743266, _1743268, _1743270, _1743272, _1743274), 47790 ^ _781215 : [(47793 ^ _781215) ^ [_1743429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743429), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743266)), _1743272))), -(hBOOL(hAPP(hAPP(_1743270, hAPP(hAPP(c_List_Onth(_1743266), _1743272), _1743429)), hAPP(hAPP(c_List_Onth(_1743268), _1743274), _1743429))))], (47791 ^ _781215) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743266)), _1743272) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743268)), _1743274))]]], (40190 ^ _781215) ^ [_1566005, _1566007, _1566009, _1566011] : [hBOOL(hAPP(hAPP(c_member(_1566005), _1566007), hAPP(c_Relation_ODomain(_1566005, _1566009), _1566011))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566005, _1566009)), hAPP(hAPP(c_Product__Type_OPair(_1566005, _1566009), _1566007), 40193 ^ [_1566005, _1566007, _1566009, _1566011])), _1566011)))], (6838 ^ _781215) ^ [_893763, _893765, _893767] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _893763))), _893765), _893767)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _893763)), _893765), _893767)))], (38916 ^ _781215) ^ [_1528019, _1528021, _1528023, _1528025, _1528027] : [c_Relation_Orefl__on(_1528019, _1528021, _1528023), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528019, _1528019)), hAPP(hAPP(c_Product__Type_OPair(_1528019, _1528019), _1528025), _1528027)), _1528023)), -(hBOOL(hAPP(hAPP(c_member(_1528019), _1528025), _1528021)))], (15650 ^ _781215) ^ [_1056337] : [-(hAPP(c_Hoare__Mirabelle_OMGT, _1056337) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _1056337), c_Natural_Oevalc(_1056337)))], (6146 ^ _781215) ^ [_880026, _880028, _880030] : [c_Com_Ocom_OCall(_880026, _880028, _880030) = c_Com_Ocom_OSKIP], (18439 ^ _781215) ^ [_1111378, _1111380, _1111382, _1111384] : [-(c_Nat_Onat_Onat__case(_1111378, _1111380, _1111382, hAPP(c_Nat_OSuc, _1111384)) = hAPP(_1111382, _1111384))], (10648 ^ _781215) ^ [_963461, _963463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963461)), _963463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963461), _963463)))], (42535 ^ _781215) ^ [_1625068, _1625070, _1625072, _1625074, _1625076, _1625078] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625068), tc_List_Olist(_1625068))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625068), tc_List_Olist(_1625068)), hAPP(hAPP(c_List_Olist_OCons(_1625068), _1625070), _1625072)), hAPP(hAPP(c_List_Olist_OCons(_1625068), _1625074), _1625076))), c_List_Olexord(_1625068, _1625078))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625068, _1625068)), hAPP(hAPP(c_Product__Type_OPair(_1625068, _1625068), _1625070), _1625074)), _1625078))), 42542 ^ _781215 : [(42545 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625068), tc_List_Olist(_1625068))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625068), tc_List_Olist(_1625068)), _1625072), _1625076)), c_List_Olexord(_1625068, _1625078))))], (42543 ^ _781215) ^ [] : [-(_1625070 = _1625074)]]], (44840 ^ _781215) ^ [_1680495, _1680497, _1680499] : [_1680499 = c_List_Olist_ONil(_1680495), -(hAPP(c_List_Orotate(_1680495, _1680497), _1680499) = c_List_Olist_ONil(_1680495))], (39116 ^ _781215) ^ [_1532333, _1532335, _1532337, _1532339, _1532341] : [c_Finite__Set_Ofun__left__comm__idem(_1532333, _1532335, _1532337), -(c_Finite__Set_Ofun__left__comm__idem(_1532339, _1532335, hAPP(hAPP(c_COMBB(_1532333, tc_fun(_1532335, _1532335), _1532339), _1532337), _1532341)))], (18734 ^ _781215) ^ [_1117030, _1117032, _1117034] : [class_Orderings_Olinorder(_1117030), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117030), _1117032), _1117034) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117030), _1117034), _1117032))], (16709 ^ _781215) ^ [_1080299, _1080301, _1080303, _1080305] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1080299, tc_HOL_Obool)), _1080301), _1080303), _1080305)), -(hBOOL(hAPP(_1080301, _1080305))), -(hBOOL(hAPP(_1080303, _1080305)))], (43071 ^ _781215) ^ [_1638672] : [-(c_List_Olists(_1638672, c_Orderings_Otop__class_Otop(tc_fun(_1638672, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1638672), tc_HOL_Obool)))], (48244 ^ _781215) ^ [_1754305, _1754307, _1754309, _1754311, _1754313] : [hAPP(c_List_Ofilter(_1754305, _1754307), _1754309) = hAPP(hAPP(c_List_Olist_OCons(_1754305), _1754311), _1754313), 48249 ^ _781215 : [(48258 ^ _781215) ^ [] : [-(hBOOL(hAPP(_1754307, _1754311)))], (48260 ^ _781215) ^ [] : [-(_1754313 = hAPP(c_List_Ofilter(_1754305, _1754307), 48248 ^ [_1754305, _1754307, _1754309, _1754311, _1754313]))], (48252 ^ _781215) ^ [_1754619] : [hBOOL(hAPP(hAPP(c_member(_1754305), _1754619), hAPP(c_List_Oset(_1754305), 48247 ^ [_1754305, _1754307, _1754309, _1754311, _1754313]))), hBOOL(hAPP(_1754307, _1754619))], (48250 ^ _781215) ^ [] : [-(_1754309 = hAPP(hAPP(c_List_Oappend(_1754305), 48247 ^ [_1754305, _1754307, _1754309, _1754311, _1754313]), hAPP(hAPP(c_List_Olist_OCons(_1754305), _1754311), 48248 ^ [_1754305, _1754307, _1754309, _1754311, _1754313])))]]], (14920 ^ _781215) ^ [_1042846, _1042848, _1042850, _1042852, _1042854] : [c_Com_Ocom_OCond(_1042846, _1042848, _1042850) = c_Com_Ocom_OSemi(_1042852, _1042854)], (43634 ^ _781215) ^ [_1652730, _1652732, _1652734, _1652736] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652730) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1652732), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652730)), hAPP(hAPP(c_List_Olist_OCons(_1652732), _1652734), _1652736)) = hAPP(hAPP(c_List_Olist_OCons(_1652732), _1652734), hAPP(hAPP(c_List_Otake(_1652732), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652730)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1652736)))], (51004 ^ _781215) ^ [_1818307, _1818309] : [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), _1818307), _1818309))), 51007 ^ _781215 : [(51014 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1818307), _1818309))), -(c_Lazy__Sequence_Osmall__lazy_H(_1818307, _1818309) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1818309), c_Lazy__Sequence_Osmall__lazy_H(_1818307, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1818309), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (51008 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1818307), _1818309)), -(c_Lazy__Sequence_Osmall__lazy_H(_1818307, _1818309) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (19638 ^ _781215) ^ [_1133814, _1133816] : [class_Orderings_Olinorder(_1133814), -(c_Big__Operators_Olinorder__class_OMax(_1133814, hAPP(hAPP(c_Set_Oinsert(_1133814), _1133816), c_Orderings_Obot__class_Obot(tc_fun(_1133814, tc_HOL_Obool)))) = _1133816)], (42931 ^ _781215) ^ [_1635210, _1635212, _1635214, _1635216, _1635218, _1635220] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1635210, _1635212), hAPP(hAPP(c_List_Ozip(_1635210, _1635212), _1635214), _1635216)), _1635218), _1635220) = hAPP(hAPP(c_List_Ozip(_1635210, _1635212), hAPP(hAPP(c_List_Olist__update(_1635210, _1635214), _1635218), hAPP(c_Product__Type_Ofst(_1635210, _1635212), _1635220))), hAPP(hAPP(c_List_Olist__update(_1635212, _1635216), _1635218), hAPP(c_Product__Type_Osnd(_1635210, _1635212), _1635220))))], (42353 ^ _781215) ^ [_1620008, _1620010, _1620012, _1620014, _1620016] : [-(hAPP(hAPP(c_List_Olist_OCons(_1620008), _1620010), _1620012) = hAPP(hAPP(c_List_Olist_OCons(_1620008), _1620014), _1620016)), _1620010 = _1620014, _1620012 = _1620016], (7842 ^ _781215) ^ [_913657, _913659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913657), _913659)), -(_913659 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _913657), 7845 ^ [_913657, _913659])))], (48444 ^ _781215) ^ [_1759423, _1759425, _1759427, _1759429] : [class_Orderings_Olinorder(_1759423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1759423), _1759425)), 48454 ^ _781215 : [(48457 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759423), _1759427), 48453 ^ [_1759423, _1759425, _1759427, _1759429]))], (48455 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759423), 48453 ^ [_1759423, _1759425, _1759427, _1759429]), _1759425)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759423), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1759423), _1759427), _1759429)), hAPP(hAPP(c_Finite__Set_Ofold(_1759423, _1759423, c_Orderings_Oord__class_Omin(_1759423)), _1759429), _1759425))))], (16465 ^ _781215) ^ [_1072555, _1072557, _1072559] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072555, tc_HOL_Obool)), _1072557), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072555, tc_HOL_Obool)), _1072559), _1072557))))], (33038 ^ _781215) ^ [_1394215, _1394217, _1394219] : [class_Lattices_Olattice(_1394215), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1394215), _1394217), _1394219) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1394215), _1394219), _1394217))], (20265 ^ _781215) ^ [_1144965, _1144967, _1144969] : [class_Nat_Osemiring__char__0(_1144965), 20268 ^ _781215 : [(20275 ^ _781215) ^ [] : [_1144967 = _1144969, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1144965), _1144967) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1144965), _1144969))], (20269 ^ _781215) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1144965), _1144967) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1144965), _1144969), -(_1144967 = _1144969)]]], (36883 ^ _781215) ^ [_1476288, _1476290, _1476292, _1476294, _1476296, _1476298, _1476300, _1476302] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1476288, tc_fun(_1476290, tc_fun(_1476292, tc_HOL_Obool))), _1476294), _1476296), _1476298), _1476300)), -(hBOOL(hAPP(hAPP(hAPP(_1476296, _1476302), _1476298), _1476300))), hBOOL(hAPP(hAPP(c_member(_1476288), _1476302), _1476294))], (10746 ^ _781215) ^ [_965299, _965301, _965303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965299), _965301)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965303), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965301), _965299)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965303), _965301)), _965299))], (39663 ^ _781215) ^ [_1552024, _1552026] : [-(c_Product__Type_Oapsnd(_1552024, _1552024, _1552026, c_Fun_Oid(_1552024)) = c_Fun_Oid(tc_prod(_1552026, _1552024)))], (37063 ^ _781215) ^ [_1482293, _1482295, _1482297, _1482299, _1482301, _1482303] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482293, tc_fun(_1482295, tc_HOL_Obool)), _1482297), hAPP(hAPP(c_COMBC(_1482293, tc_fun(_1482299, tc_fun(_1482295, tc_HOL_Obool)), tc_fun(_1482295, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1482299, tc_HOL_Obool), tc_fun(tc_fun(_1482299, tc_fun(_1482295, tc_HOL_Obool)), tc_fun(_1482295, tc_HOL_Obool)), _1482293), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482299, tc_fun(_1482295, tc_HOL_Obool))), _1482301)), _1482303)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482299, tc_fun(_1482295, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482293, tc_fun(_1482299, tc_HOL_Obool)), _1482297), _1482301)), _1482303))], (826 ^ _781215) ^ [_794008, _794010, _794012, _794014] : [-(c_Relation_Oirrefl(_794012, _794008)), c_Relation_Oirrefl(_794014, _794010), _794014 = _794012, _794010 = _794008], (15644 ^ _781215) ^ [_1056188, _1056190, _1056192, _1056194, _1056196] : [hBOOL(hAPP(hAPP(c_member(_1056188), _1056190), _1056192)), -(hAPP(c_Set_Oimage(_1056188, _1056194, hAPP(c_COMBK(_1056194, _1056188), _1056196)), _1056192) = hAPP(hAPP(c_Set_Oinsert(_1056194), _1056196), c_Orderings_Obot__class_Obot(tc_fun(_1056194, tc_HOL_Obool))))], (4548 ^ _781215) ^ [_850187, _850189, _850191, _850193] : [-(c_HOL_OLet(_850193, _850189) = c_HOL_OLet(_850191, _850187)), _850193 = _850191, _850189 = _850187], (3668 ^ _781215) ^ [_836781, _836783, _836785, _836787] : [-(c_List_Olinorder__class_Osorted__list__of__set(_836787, _836783) = c_List_Olinorder__class_Osorted__list__of__set(_836785, _836781)), _836787 = _836785, _836783 = _836781], (36281 ^ _781215) ^ [_1463411, _1463413, _1463415, _1463417, _1463419] : [-(hAPP(c_Product__Type_Osnd(_1463411, _1463413), hAPP(c_Product__Type_Oapfst(_1463415, _1463411, _1463413, _1463417), _1463419)) = hAPP(c_Product__Type_Osnd(_1463415, _1463413), _1463419))], (40669 ^ _781215) ^ [_1578148, _1578150, _1578152, _1578154, _1578156] : [c_Com_Ocom_OWhile(_1578148, _1578150) = c_Com_Ocom_OCond(_1578152, _1578154, _1578156)], (51436 ^ _781215) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (49812 ^ _781215) ^ [_1790722, _1790724, _1790726, _1790728, _1790730] : [c_Relation_Osingle__valued(_1790722, _1790724, _1790726), c_Relation_Osingle__valued(_1790724, _1790728, _1790730), -(c_Relation_Osingle__valued(_1790722, _1790728, hAPP(hAPP(c_Relation_Orel__comp(_1790722, _1790724, _1790728), _1790726), _1790730)))], (44503 ^ _781215) ^ [_1672665, _1672667, _1672669, _1672671] : [-(c_List_Osublist(_1672665, hAPP(hAPP(c_List_Olist_OCons(_1672665), _1672667), _1672669), _1672671) = hAPP(hAPP(c_List_Oappend(_1672665), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1672665)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1672671)), hAPP(hAPP(c_List_Olist_OCons(_1672665), _1672667), c_List_Olist_ONil(_1672665))), c_List_Olist_ONil(_1672665))), c_List_Osublist(_1672665, _1672669, 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)), _1672671)))))], (51220 ^ _781215) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (21197 ^ _781215) ^ [_1160622, _1160624, _1160626] : [-(hBOOL(hAPP(_1160622, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160624), _1160626))))), 21200 ^ _781215 : [(21203 ^ _781215) ^ [] : [hBOOL(hAPP(_1160622, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1160624)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1160626))))], (21201 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1160626), _1160624)))]], 21204 ^ _781215 : [(21207 ^ _781215) ^ [] : [hBOOL(hAPP(_1160622, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21205 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160624), _1160626)))]]], (33543 ^ _781215) ^ [_1406015, _1406017, _1406019] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1406015), _1406017)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406015), _1406019)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1406015), _1406017)), hAPP(c_Finite__Set_Ocard(_1406015), _1406019)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1406015), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406015, tc_HOL_Obool)), _1406017), _1406019))), hAPP(c_Finite__Set_Ocard(_1406015), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406015, tc_HOL_Obool)), _1406017), _1406019))))], (38462 ^ _781215) ^ [_1515312, _1515314, _1515316, _1515318] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1515312, _1515314), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1515312, tc_HOL_Obool), _1515316)), _1515318) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1515312, tc_HOL_Obool), tc_fun(tc_prod(_1515312, _1515314), tc_HOL_Obool)), _1515316), hAPP(hAPP(c_COMBC(tc_fun(_1515312, tc_HOL_Obool), tc_fun(_1515312, tc_fun(_1515314, tc_HOL_Obool)), tc_fun(tc_prod(_1515312, _1515314), tc_HOL_Obool)), c_Product__Type_OSigma(_1515312, _1515314)), _1515318)))], (22166 ^ _781215) ^ [_1180802, _1180804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180802)), -(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)))), _1180804))), 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)))), _1180802)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180804), _1180802))], (46209 ^ _781215) ^ [_1708562, _1708564, _1708566] : [_1708564 = _1708566, -(hAPP(c_List_Orev(_1708562), _1708564) = hAPP(c_List_Orev(_1708562), _1708566))], (21566 ^ _781215) ^ [_1168151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1168151), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1168151)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7951 ^ _781215) ^ [_915288, _915290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915288), _915290)), _915288 = _915290], (23012 ^ _781215) ^ [_1196105, _1196107, _1196109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196105)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1196107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1196109), _1196105)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1196107), _1196109)), _1196105))], (25388 ^ _781215) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (44339 ^ _781215) ^ [_1668143, _1668145, _1668147, _1668149] : [-(hAPP(hAPP(c_List_Onth(_1668143), hAPP(hAPP(c_List_Oappend(_1668143), _1668145), hAPP(hAPP(c_List_Olist_OCons(_1668143), _1668147), _1668149))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668143)), _1668145)) = _1668147)], (11934 ^ _781215) ^ [_988660] : [_988660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988660), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4508 ^ _781215) ^ [_849583, _849585] : [_849585 = _849583, -(c_Lattices_Osemilattice__inf__class_Oinf(_849585) = c_Lattices_Osemilattice__inf__class_Oinf(_849583))], (38322 ^ _781215) ^ [_1511794, _1511796, _1511798, _1511800, _1511802] : [hBOOL(hAPP(hAPP(c_member(_1511794), _1511796), hAPP(c_Set_Ovimage(_1511794, _1511798, _1511800), hAPP(hAPP(c_Set_Oinsert(_1511798), _1511802), c_Orderings_Obot__class_Obot(tc_fun(_1511798, tc_HOL_Obool)))))), -(hAPP(_1511800, _1511796) = _1511802)], (36798 ^ _781215) ^ [_1473964, _1473966, _1473968, _1473970, _1473972, _1473974] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1473966, _1473968)), hAPP(hAPP(c_Product__Type_OPair(_1473966, _1473968), _1473972), _1473974)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473964, tc_fun(tc_prod(_1473966, _1473968), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1473964, tc_HOL_Obool))), _1473970))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473964, tc_fun(_1473966, tc_fun(_1473968, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1473964, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1473966, _1473968), tc_HOL_Obool), tc_fun(_1473966, tc_fun(_1473968, tc_HOL_Obool)), _1473964), hAPP(c_COMBC(_1473966, tc_fun(tc_prod(_1473966, _1473968), tc_HOL_Obool), tc_fun(_1473968, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473968, tc_fun(tc_fun(tc_prod(_1473966, _1473968), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1473966, _1473968), tc_HOL_Obool), tc_fun(_1473968, tc_HOL_Obool)), _1473966), c_COMBC(_1473968, tc_fun(tc_prod(_1473966, _1473968), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473968, tc_prod(_1473966, _1473968)), tc_fun(_1473968, tc_fun(tc_fun(tc_prod(_1473966, _1473968), tc_HOL_Obool), tc_HOL_Obool)), _1473966), hAPP(c_COMBB(tc_prod(_1473966, _1473968), tc_fun(tc_fun(tc_prod(_1473966, _1473968), tc_HOL_Obool), tc_HOL_Obool), _1473968), c_member(tc_prod(_1473966, _1473968)))), c_Product__Type_OPair(_1473966, _1473968))))), _1473970)), _1473972), _1473974)))], (32888 ^ _781215) ^ [_1390909, _1390911, _1390913] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1390909, tc_HOL_Obool)), _1390911), _1390913) = c_Orderings_Obot__class_Obot(tc_fun(_1390909, tc_HOL_Obool)), 32891 ^ _781215 : [(32892 ^ _781215) ^ [_1391033] : [hBOOL(hAPP(hAPP(c_member(_1390909), _1391033), _1390911)), 32895 ^ _781215 : [(32896 ^ _781215) ^ [_1391123] : [hBOOL(hAPP(hAPP(c_member(_1390909), _1391123), _1390913)), _1391033 = _1391123]]]]], (50872 ^ _781215) ^ [_1814934, _1814936] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1814934)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1814936))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1814934), _1814936)))], (7062 ^ _781215) ^ [_898694, _898696, _898698, _898700, _898702] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_898694, _898696)), _898698), _898700), _898702))), 7063 ^ _781215 : [(7064 ^ _781215) ^ [_898776] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _898694), _898698), _898700), _898776)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _898696), _898776), _898700), _898702))]]], (10590 ^ _781215) ^ [_962462, _962464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962462), _962464)), 10593 ^ _781215 : [(10600 ^ _781215) ^ [] : [_962464 = _962462, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962464), hAPP(c_Nat_OSuc, _962462))))], (10594 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962464), hAPP(c_Nat_OSuc, _962462))), -(_962464 = _962462)]]], (10838 ^ _781215) ^ [_967089, _967091, _967093, _967095, _967097, _967099, _967101, _967103] : [c_Finite__Set_Ofolding__image__simple__idem(_967089, _967091, _967093, _967095, _967097, _967099), hBOOL(hAPP(c_Finite__Set_Ofinite(_967091), _967101)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_967091, tc_HOL_Obool)), _967103), _967101)), -(hAPP(hAPP(_967093, hAPP(_967099, _967103)), hAPP(_967099, _967101)) = hAPP(_967099, _967101))], (32188 ^ _781215) ^ [_1375751, _1375753, _1375755, _1375757, _1375759, _1375761] : [class_Groups_Oordered__ab__group__add(_1375751), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375753), _1375755)), 32198 ^ _781215 : [(32201 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375751), c_Groups_Ozero__class_Ozero(_1375751)), hAPP(_1375757, 32197 ^ [_1375751, _1375753, _1375755, _1375757, _1375759, _1375761])))], (32199 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1375753), 32197 ^ [_1375751, _1375753, _1375755, _1375757, _1375759, _1375761]), _1375755)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1375753, _1375751), _1375757), _1375755) = _1375759, hBOOL(hAPP(hAPP(c_member(_1375753), _1375761), _1375755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375751), hAPP(_1375757, _1375761)), _1375759)))], (9993 ^ _781215) ^ [_951106, _951108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _951106), _951108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951106), _951108)))], (6223 ^ _781215) ^ [_881546, _881548, _881550, _881552] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_881546, _881548, hAPP(hAPP(c_Set_Oinsert(_881546), _881550), c_Orderings_Obot__class_Obot(tc_fun(_881546, tc_HOL_Obool)))), _881552)), -(_881550 = _881552)], (19048 ^ _781215) ^ [_1122663] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122663) = _1122663)], (37003 ^ _781215) ^ [_1480095, _1480097, _1480099, _1480101, _1480103] : [37005 ^ _781215 : [(37008 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480095, tc_HOL_Obool)), _1480097), hAPP(_1480103, 37004 ^ [_1480095, _1480097, _1480099, _1480101, _1480103])))], (37006 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480099), 37004 ^ [_1480095, _1480097, _1480099, _1480101, _1480103]), _1480101)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480095, tc_HOL_Obool)), _1480097), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1480099, tc_fun(_1480095, tc_HOL_Obool)), _1480101), _1480103))))], (38532 ^ _781215) ^ [_1517599, _1517601, _1517603, _1517605] : [-(hAPP(c_Set_Oimage(tc_prod(_1517599, _1517601), tc_prod(_1517601, _1517599), hAPP(c_Product__Type_Oprod_Oprod__case(_1517599, _1517601, tc_prod(_1517601, _1517599)), hAPP(c_COMBC(_1517601, _1517599, tc_prod(_1517601, _1517599)), c_Product__Type_OPair(_1517601, _1517599)))), hAPP(hAPP(c_Product__Type_OSigma(_1517599, _1517601), _1517603), hAPP(c_COMBK(tc_fun(_1517601, tc_HOL_Obool), _1517599), _1517605))) = hAPP(hAPP(c_Product__Type_OSigma(_1517601, _1517599), _1517605), hAPP(c_COMBK(tc_fun(_1517599, tc_HOL_Obool), _1517601), _1517603)))], (44168 ^ _781215) ^ [_1664263, _1664265, _1664267] : [_1664267 = c_List_Olist_ONil(_1664263), -(hAPP(hAPP(c_List_Oappend(_1664263), _1664265), _1664267) = _1664265)], (30389 ^ _781215) ^ [_1337084, _1337086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337084), _1337086)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1337086, _1337084) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (43842 ^ _781215) ^ [_1656566, _1656568, _1656570] : [-(_1656566 = c_List_Olist_ONil(_1656568)), -(c_List_Obutlast(_1656568, hAPP(hAPP(c_List_Olist_OCons(_1656568), _1656570), _1656566)) = hAPP(hAPP(c_List_Olist_OCons(_1656568), _1656570), c_List_Obutlast(_1656568, _1656566)))], (3484 ^ _781215) ^ [_833915, _833917] : [_833917 = _833915, -(c_List_Otranspose__rel(_833917) = c_List_Otranspose__rel(_833915))], (51204 ^ _781215) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (39803 ^ _781215) ^ [_1555902, _1555904, _1555906, _1555908, _1555910, _1555912, _1555914, _1555916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555902, _1555904), tc_HOL_Obool)), _1555906), hAPP(hAPP(c_Product__Type_OSigma(_1555902, _1555904), _1555908), hAPP(c_COMBK(tc_fun(_1555904, tc_HOL_Obool), _1555902), _1555910)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555904, _1555912), tc_HOL_Obool)), _1555914), hAPP(hAPP(c_Product__Type_OSigma(_1555904, _1555912), _1555910), hAPP(c_COMBK(tc_fun(_1555912, tc_HOL_Obool), _1555904), _1555916)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555902, _1555912), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1555902, _1555904, _1555912), _1555906), _1555914)), hAPP(hAPP(c_Product__Type_OSigma(_1555902, _1555912), _1555908), hAPP(c_COMBK(tc_fun(_1555912, tc_HOL_Obool), _1555902), _1555916)))))], (16812 ^ _781215) ^ [_1083018, _1083020, _1083022, _1083024] : [hBOOL(hAPP(_1083018, _1083020)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1083022, tc_HOL_Obool)), _1083018), _1083024), _1083020)))], (50025 ^ _781215) ^ [_1796134, _1796136] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1796134, _1796134), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1796136) = c_Relation_OId(_1796134))], (38778 ^ _781215) ^ [_1524480, _1524482, _1524484, _1524486, _1524488] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524480, _1524482)), _1524484), hAPP(hAPP(c_Product__Type_OSigma(_1524480, _1524482), _1524486), _1524488))), 38782 ^ _781215 : [(38788 ^ _781215) ^ [] : [-(_1524484 = hAPP(hAPP(c_Product__Type_OPair(_1524480, _1524482), 38781 ^ [_1524480, _1524482, _1524484, _1524486, _1524488]), 38784 ^ [_1524480, _1524482, _1524484, _1524486, _1524488]))], (38786 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524482), 38784 ^ [_1524480, _1524482, _1524484, _1524486, _1524488]), hAPP(_1524488, 38781 ^ [_1524480, _1524482, _1524484, _1524486, _1524488]))))], (38783 ^ _781215) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524480), 38781 ^ [_1524480, _1524482, _1524484, _1524486, _1524488]), _1524486)))]]], (29318 ^ _781215) ^ [_1315424, _1315426, _1315428, _1315430, _1315432] : [class_Fields_Olinordered__field(_1315424), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315424), c_Groups_Ozero__class_Ozero(_1315424)), _1315426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315424), _1315426), _1315428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315424), c_Groups_Ozero__class_Ozero(_1315424)), _1315430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315424), _1315430), _1315432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315424), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315424), _1315426), _1315432)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1315424), _1315428), _1315430))))], (41293 ^ _781215) ^ [_1592318, _1592320, _1592322, _1592324, _1592326, _1592328, _1592330] : [hAPP(c_Fun_Ocomp(_1592318, _1592320, _1592322, _1592324), _1592326) = _1592328, -(hAPP(_1592324, hAPP(_1592326, _1592330)) = hAPP(_1592328, _1592330))], (39697 ^ _781215) ^ [_1552663, _1552665, _1552667, _1552669] : [class_Groups_Ocomm__monoid__mult(_1552663), c_Fun_Oinj__on(_1552665, _1552663, _1552667, _1552669), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1552665, _1552663), _1552667), _1552669) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1552663, _1552663), c_Fun_Oid(_1552663)), hAPP(c_Set_Oimage(_1552665, _1552663, _1552667), _1552669)))], (6471 ^ _781215) ^ [_886626, _886628, _886630, _886632] : [_886626 = _886628, hBOOL(hAPP(hAPP(c_member(_886630), _886628), _886632)), -(hBOOL(hAPP(hAPP(c_member(_886630), _886626), _886632)))], (17725 ^ _781215) ^ [_1097951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097951), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1097951) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8149 ^ _781215) ^ [_918567, _918569, _918571, _918573] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_918567), 8152 ^ _781215 : [(8159 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918567), _918569), _918573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918567), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918567), _918569), _918571)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918567), _918573), _918571))))], (8153 ^ _781215) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918567), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918567), _918569), _918571)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918567), _918573), _918571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918567), _918569), _918573)))]]]], input).
% 47.31/45.96 ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, v_pn))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))],start(51776 ^ 0)).
% 47.31/45.96 ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, v_pn))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))), c_Hoare__Mirabelle_Ostate__not__singleton, c_Com_OWT__bodies, hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, v_pn)))],extension(5587 ^ 1,bind([[_869254], [hAPP(c_Com_Ocom_OBODY, v_pn)]]))).
% 47.31/45.96 ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ostate__not__singleton)],extension(51768 ^ 2)).
% 47.31/45.96 ncf('1.1.2',plain,[-(c_Com_OWT__bodies)],extension(51770 ^ 2)).
% 47.31/45.96 ncf('1.1.3',plain,[-(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, v_pn)))), 5648 : hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y)],extension(5646 ^ 2,bind([[_870202, _870250], [v_pn, v_y]]))).
% 47.31/45.96 ncf('1.1.3.1',plain,[-(hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))],extension(51774 ^ 5)).
% 47.31/45.96 %-----------------------------------------------------
% 47.31/45.96 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------